close

Вход

Забыли?

вход по аккаунту

?

Investigation of low cost techniques for realising microwave and millimeter-wave network analysers

код для вставкиСкачать
7384901
UNIVERSITY OF SURREY LIBRARY
Investigation of Low Cost Techniques for
Realising Microwave and Millimeter-Wave
Network Analysers
Bilal Altrabsheh
Submitted for the Degree of
Doctor of Philosophy
from the
University of Surrey
UniS
Microwave Systems Research Group
Advanced Technology Institute
School of Electronics and Physical Sciences
University of Suney
Guildford, Surrey GU2 7XH, UK
June 2003
© B .M Altrabsheh 2003
ProQ uest Number: 10131174
All rights reserved
INFORMATION TO ALL U SE R S
The quality of this reproduction is d ep endent upon the quality of the copy submitted.
In the unlikely event that the author did not sen d a com plete manuscript
and there are m issing p a g es, th e se will be noted. Also, if material had to be removed,
a note will indicate the deletion.
uest.
ProQ uest 10131174
Published by ProQ uest LLC(2016). Copyright of the Dissertation is held by the Author.
All rights reserved.
This work is protected against unauthorized copying under Title 17, United States C ode.
Microform Edition © ProQ uest LLC.
ProQ uest LLC
789 East Eisenhow er Parkway
P.O. Box 1346
Ann Arbor, Ml 48106-1346
Abstract
The work presented in this thesis is on the developm ent o f reliable low cost measurement
system s for measuring m icrowave and m illim etre-w ave devices. The puipose o f this work
is to find techniques which use m ultiple power detectors and can measure magnitude and
phase without the need for expensive superheterodyne receivers. T w o novel m icrowave
measurement system s have been designed with the intention o f providing a measurement
facility which enables the characterisation o f both active and passive devices in terms o f
their scattering parameters.
The first method is based on using a multistate reflectometer, which uses dielectric
w aveguide in the frequency range o f llO G H z up to 170G Hz. The dielectric multistate
reflectom eter is a four-port reflectometer, which uses a programmable phase shifter to
give a flat relative phase shift over the entire frequency range o f the dielectric waveguides
used in the multistate reflectometer. The phase shifter has an eccentric rotating cylinder
with an offset axis to allow a number o f different phase shifts to the w ave travelling in the
dielectric w aveguides in the multistate reflectometer. This system has been developed as
an equivalent to a one-port network analyser.
The second method is based on using the multi-probe reflectom eter in which the standing
wave in a line is measured using a number o f fixed detector probes. A microstrip line
prototype in the frequency range o f IG H z to 5.5G H z has been demonstrated and the
design o f a m onolithic m icrowave integrated circuit (M MIC) version for the frequency
range o f 40G H z to 325G H z has been earned out. Improved m ethods o f calibration o f the
system have been derived as w ell as different methods for eiTor con ection . The
realisation o f a full two-port network analyser using the technique has been demonstrated.
K ey words: dielectric multistate reflectom eter, programmable phase shifter, multi-probe
reflectometer,
detection,
m icrowave
calibration, error conections.
measurement,
m illim etre-w ave
measurement,
I ll
Acknowledgments
I w ould like to thank m y parents, m y brother and the rest o f the fam ily for their support
and encouragem ent and for looldng after m y w ife and children throughout this research.
Special thanks com bined with love and deep appreciation to m y w ife for bearing the load
o f looking after the fam ily. Thanks goes also to m y children w ho have been patient with
m e when m issing out on their D ad during this research
I w ish to convey m y thanks to m y supervisor, Prof. I D . Robertson, for his guidance,
support, encouragements and his lovely since o f humour throughout this research. M y
thanks also go to Dr. R.J. Collier for his support and advice.
I w ould like to thanks Prof. M. Underhill and Dr. C. Free for their valuable com ments
during the transfer examination.
I w ould like to thank Mr. I. Jalaly for his support and valuable advice.
I w ould like to thank friends and fam ily for their supports.
I w ould like to acknow ledge the financial support o f the Engineering and Physical
Scien ce Research Council (BPSRC).
Contents
Contents
A bstract............................................................................................................................................................ ii
A cknow ledgm ents
iv
C on ten ts........................................................................................................................................................... v
List o f F igu res............................................................................................................................................ viii
List o f T a b le s................................................................................................................................................ xi
Chapter 1 .......................................................................................................................................................... 1
1 Introduction..................................................................................................................................................1
1.1
Background........................................................................................................................................ 1
1.2
Structure of the Thesis......................................................................................................................3
1.3
Contributions of this T hesis............................................................................................................4
Chapter 2 .......................................................................................................................................................... 5
2 D ielectric W aveguide M easurement S y stem ..................................................................................5
2.1
Introduction........................................................................................................................................5
2.2
Principles of microwave measurements....................................................................................... 6
2.2.1
Reflectometers........................................................................................................................... 7
2.2.2
Network analysers......................................................................................................................8
2.3
Measurement system ...................................................................................................................... 11
2.4
Dielectric Multistate Reflectometer (DMR)...............................................................................13
2.4.1
Dielectric Waveguide and Dielectric Waveguide Couplers............................................15
2.4.2
Phase shifter.............................................................................................................................. 17
2.5
System Control................................................................................................................................ 22
2.6
System Characterisation.................................................................. ,............................................. 24
2.7
Conclusion........................................................................................................................................28
Chapter 3 .........................................................................................................................................
29
3 D ielectric M ultistate R eflectom eter (DM R) Calibration............................................................ 29
3.1
Introduction..................................................................................................................................... 29
3.2
Calibration Consideration of the D M R ...................................................................................... 30
3.3
System configuration and measurements................................................................................... 31
V
1
_____________________________________________________________________________________ Contents
3.4 Measurement Consistency Over Frequency................................................................................36
3.5 Repeatability......................................................................................................................................38
3.6 Dielectric Multistate Reflectometer Calibration........................................................................39
3.6.1
Calibration Constants............................................................................................................. 39
3.6.2
Practical Measurements.........................................................................................................43
3.7 Conclusion......................................................................................................................................... 46
Chapter 4 ....................................................................................................................................................... 47
4 M ulti-Probe R eflectom eter System ...................................................................................................47
4.1
Introduction.......................................................................................................................................47
4.2 Transmission Line Theory.............................................................................................................. 48
4.2.1
Lossless L in e...........................................................................................................................51
4.2.2
Termination of Lossless and Lossy Transmission Lines.................................................52
4.2.3
Standing Wave on a Transmission L in e.............................................................................54
4.2.4
Line Match and Mismatch.................................................................................................... 57
4.3
One-Port Microstrip Measurement System.................................................................................59
4.3.1
Multi-probe Reflectometer................................................................................................... 60
4.3.2
Microstrip Lines...................................................................................................................... 61
4.3.3
Probe Spacing..........................................................................................................................63
4.3.4
Coupling and M atching.........................................................................................................64
4.3.5
Diode Detector Circuit........................................................................................................... 67
4.4 Conclusion......................................................................................................................................... 74
Chapter 5 ....................................................................................................................................................... 75
5 One-Port M easurement Set-up and Calibration............................................................................75
5.1
Measurement Set-up........................................................................................................................ 75
5.2 System Calibration...........................................................................................................................76
5.2.1
Ideal Microstrip Line Reflectometer....................................................................................77
5.2.1.1
5.2.2
Solving with Reference to the Middle Probe............................................................. 82
Non- Ideal Microstrip Line Reflectometer......................................................................... 85
5.3 Practical Measurements and Results............................................................................................ 91
5.4 System Error and Error Corrections............................................................................................. 94
5.5 Conclusion....................................................................................................................................... 103
Chapter 6 ..................................................................................................................................................... 104
6 Two-Port M ulti-Probe M easurem ent S y s te m ............................................................................. 104
______________________________________________________________________________________Contents
6.1
Introduction.................................................................................................................................... 104
6.2
System Description.......................................................................................................................104
6.2.1
6.3
6.3.1
6.4
Two-Port Multi-Probe Reflectometer................................................................................ 105
Two-Port Network S-Parameters............................................................................................... 107
Shifting Reference Plane......................................................................................................110
Principle of Operation of the Two-Port Multi-Probe Reflectometer................................... I l l
6.4.1
Multi-Probe Scalar Network Analyser............................................................................... 112
6.4.2
Multi-Probe Vector Network Analyser.............................................................................. 112
6.4.3
Reflection Coefficient Measurements................................................................................ 114
6.4.4
Attenuation Measurements.................................................................................................. 116
6.5
Attenuation Error Measurement................................................................................................. 118
6.5.1
Mismatch Error.......................................................................................................................119
6.5.2
Leakage Error......................................................................................................................... 119
6.6
Calibration Procedure and Error Corrections...........................................................................120
6.7
Scalar Network Analyser Results............................................................................................... 128
6.8
Vector Network Analyser Results.............................................................................................. 135
6.9
Measurement Uncertainty............................................................................................................138
6.10 Conclusion...................................................................................................................................... 140
C h a p ter? ..................................................................................................................................................... 141
7 C onclusions and Future W o r k ......................................................................................................... 141
7.1
Achievements.................................................................................................................................141
7.1.1
Dielectric Multistate Reflectometer....................................................................................141
7.1.2
Multi-Probe Reflectometer System..................................................................................... 142
7.2
Possible Future Work................................................................................................................... 143
R eferences................................................................................................................................................... 145
Appendix A .................................................................................................................................................152
Appendix B .................................................................................................................................................162
Appendix C .................................................................................................................................................172
Appendix D .................................................................................................................................................184
List o f Figures
List of Figures
Figure 2-1: Simple 4-Port Reflectometer.................................................................................................... 7
Figure 2-2: Block diagram o f Vector network analyser........................................................................... 9
Figure 2-3: Directional coupler................................................................................................................... 10
Figure 2-4: Dielectric Waveguide Measurement System....................................................................... 12
Figure 2-5: Dielectric Multistate Reflectometer....................................................................................... 14
Figure 2-6: Dielectric waveguide................................................................................................................ 16
Figure 2-7: Dielectric Waveguide Coupler............................................................................................... 17
Figure 2-8: Dominant electric field transverse to the metal w all.......................................................... 18
Figure 2-9: Measurement of the waveguide short circuit device with 0mm offset at 140 GHz
21
Figure 2-10: Metal cylinder distance from the dielectric waveguide against phase at 140 G H z... 21
Figure 2-11: DMR Front Panel Measurement Programme....................................................................23
Figure 2-12: 4-Port Device Incident and reflected signals.....................................................................24
Figure 3-1: Measurement of the waveguide short at offset of 0*Xg at 140 G H z...............................32
Figure 3-2: Measurements of a variable short at 140 GHz over a full wavelength........................... 34
Figure 3-3: Measurements o f a Short circuit device at 140 GHz repeatable every
................... 35
Figure 3-4: Measurement at 140 GHz with Àg/4 offset (Open & Short)............................................ 35
Figure 3-5: Measurements at 140 GHz for a Short Circuit & a Matched L oad.................................36
Figure 3-6: Measurements of a short circuit device over the frequency band of (110-170) GHz.. 37
Figure 3-7: Measurements of a match load at (110,140 & 170) G H z..................................................37
Figure 3-8: The repeatability of measurements at 140 G H z................................................................. 38
Figure 3-9: Measurements of a short circuit with zero offset at 140 G H z..........................................40
Figure 3-10: Measurement data analysed at 140GHz.............................................................................46
Figure 4-1: Equivalent circuit of a lossy line........................................................................................... 48
Figure 4-2: Transmission line terminated by load impedance Z l..........................................................52
Figure 4-3: Standing wave on Transmission line..................................................................................... 55
Figure 4-4: Standing-wave pattern for complete reflection on a lossless line.................................... 56
Figure 4-5: Transmission line load and generator connected................................................................ 57
Figure 4-6: One-port measurement system ...............................................................................................59
Figure 4-7: Microstrip multi-probe reflectometer block diagram.........................................................60
Figure 4-8: Actual one-port reflectometer........................................................................................................60
Figure 4-9: One port reflectometer circuit diagram................................................................................. 61
Figure 4-10: Microstrip lin e.........................................................................................................................61
viii
L ist o f Figures
Figure 4-11: Attenuation vs Coupling Resistance....................................................................................65
Figure 4-12; Coupling Coefficients of 3 Probes with 2kQ connected............................................................66
Figure 4-13: Microstrip Reflectometer Insertion L oss............................................................................66
Figure 4-14: Return loss, simulated and measured................................................................................. 67
Figure 4-15: Diode Detector Circuit........................................................................................................... 68
Figure 4-16: Zero-Bias Diode 1/V Characteristic.....................................................................................68
Figure 4-17: Schottky diode chip cross section and its equivalent circuit..........................................69
Figure 4-18: Input Level vs Shunt Resistance.......................................................................................... 72
Figure 5-1: Measurement Set-Up................................................................................................................76
Figure 5-2: Probes location on a standing wave.......................................................................................77
Figure 5-3: General Multi-Probe Reflectometer......................................................................................78
Figure 5-4: Simulated results of an offset short.......................................................................................91
Figure 5-5: Simulated results of 3dB attenuator.......................................................................................91
Figure 5-6: Offset Short measured with Multi-Probe Reflectometer...................................................92
Figure 5-7: Offset Short measured with Agilent 8753E Analyser....................................................... 92
Figure 5-8: Offset Open measured with Multi-Probe Reflectometer...................................................93
Figure 5-9: Offset Open measured with Agilent 8753E Analyser....................................................... 93
Figure 5-10: 50 Ohm load measured with Multi-Probe reflectometer.................................................93
Figure 5-11: 50 Ohm Load measured with Agilent 8753E Analyser...................................................93
Figure 5-12: Different attenuators measured with the Multi-Probe Reflectometer........................... 94
Figure 5-13: One-Port measurement system with error corrections..................................................... 96
Figure 5-14: Decomposition of the error flow graph..............................................................................97
Figure 5-15: Relationship of deriving the directivity term.....................................................................98
Figure 5-16: Sliding Load and resultant vectors......................................................................................98
Figure 5-17: Simulated results before error corrections applied.........................................................102
Figure 5-18: Simulated results after error corrections applied............................................................ 102
Figure 5-19: 3dB Attenuator before and after corrections................................................................... 103
Figure 6-1: Two-Port measurement system ............................................................................................105
Figure 6-2: Full-Port multi-probe reflectometer.....................................................................................106
Figure 6-3: Actual two-port multi-probe reflectometer.........................................................................106
Figure 6-4: Non-reflective sw itch.............................................................................................................107
Figure 6-5: Definition of incident and reflected wave of a two-port network.................................. 108
Figure 6-6: Two-port network flow graph............................................................................................... 108
Figure 6-7: Shifting reference plane........................................................................................................110
Figure 6-8: Two-port multi-probe vector network analyser.................................................................113
Figure 6-9: Simplified two-port multi-probe vector network analyser..............................................114
Figure 6-10: Flow graph of two-port device connected through reflectometer................................ 115
ix
L ist o f Figures
Figure 6-11; Transmission coefficients....................................................................................................121
Figure 6-12: Load match error flow graph.............................................................................................. 122
Figure 6-13: Isolation eiTor flow graph ....................................................................................................123
Figure 6-14: Two-port flow graph with 12 error terms.........................................................................124
Figure 6-15: Attenuation calculation of various simulated attenuators..............................................128
Figure 6-16: Gain calculation of various simulated amplifiers ......................................................... 129
Figure 6-17: Simulation data of a Band-Pass Filter with IdB insertion loss.....................................129
Figure 6-18: Stop-Band filter with IdB insertion lo s s ..........................................................................130
Figure 6-19: Low-Pass filter with IdB insertion loss............................................................................ 130
Figure 6-20: High-Pass filter with IdB insertion lo ss...........................................................................131
Figure 6-21: Simulated S 21 magnitude of various devices using the 2-port system of Fig. 6-9... 135
Figure 6-22: Simulated S 21 phase o f 5.1mm and 20.4mm delay using vectornetwork analyser. 136
Figure 6-23: Simulated S 21 phase o f amplifiers with phase delay of (45 and 90 ).........................136
Figure 6-24: S 21 phase measurements of a delay line measured with the.......................................... 137
Figure 6-25: S 21 phase measurements of various attenuators measuredwith the.............................. 137
Figure 6-26: S21 magnitude measurements of various attenuators measured with the....................138
Figure 7-1: Two-Port Dielectric Multistate Reflectometer.................................................................. 144
Figure 7-2: On-Wafer Multi-Probe Reflectometer.................................................................................144
L ist o f Tables
List of Tables
Table 3-1: Average output ratio power over whole frequency band.................................................... 36
Table 3-2: Calibration constants of the DMR calculated at 140GHz...................................................44
Table 3-3: Measurement data measured with DMR at 140GHz...........................................................45
Table 5-1: Simulated results for an Ideal Multi-Probe reflectometer................................................... 84
Table 5-2: Simulated data calculated by using the non-ideal line method..........................................90
Table 5-3: Reflection coefficient and error correction parameters from simulated data of the
Multi-Probe Reflectometer................................................................................................................ 101
Table 6-1: 12 error terms o f a two-port system...................................................................................... 124
Table 6-2: Calculated results o f lOdB attenuator using simulated probe voltages (withand without
error correction)................................................................................................................................... 132
Table 6-3: Calculated forward error terms o f the practical two-port multi-probe scalar analyser 133
Table 6-4: Calculated reverse error terms o f the practical two-port multi-probe scalar analyser 133
Table 6-5: Measured attenuators and amplifier with the practical two-port multi-probe scalar
analyser..................................................................................................................................................134
Table 6-6: Reflection measurement uncertainties..................................................................................139
Chapter 1. Introduction
Chapter 1
1 Introduction
1.1 Background
M icrow ave measurement techniques have been investigated and thoroughly developed for
the past few decades. The need for device characterisation in the frequency and time
dom ains has always been the focus for many industrial users. The electrical properties o f
a com ponent, such as loss, phase-shift and m atching at m icrow ave frequencies are usually
described in terms o f scattering parameters.
D ifferent methods have been developed for this puipose such as the slotted line
reflectom eter
[1],
six-port
reflectom eter
[2,5]
and,
of
course,
conventional
superheterodyne-type network analysers, which have becom e one o f the m ost important
measurement tools for characterising high-frequency com ponents and devices. Network
analysers differ in forni and function from the other tools com m only used to characterised
com munication system and components: the spectrum analyser, for exam ple, measures
unknown external signals. In contrast, modern network analysers utilize frequencysynthesised sources to provide a known test stimulus that can be sw ept across a range o f
frequencies or pow er levels. Network analysers can also perform ratio measurements
including phase, which cannot be performed with a spectrum analyser.
Network analysers have improved greatly nowadays from earlier versions, where they
only provided raw m easurements o f an unknown device in terms o f phase and magnitude.
Vector network analysers (V N A s) can nowadays measure enor-corrected magnitude,
phase, and group delay, show port im pedances on a Smith chart, and, with time-domain
capability, show the distance from a test port to an im pedance m ism atch or circuit fault.
They can also be extended to perform on-w afer m easurements.
Chapter 1. Introduction
H ow ever, conventional V N A s using superheterodyne techniques are com plicated and
expensive due to the number o f couplers, m ixers, sources and receivers...etc. One can see
the need for finding an alternative and a rival to these expensive and com plicated
measurement system s has drawn the attention o f many researchers for many years. It has
always been a challenge to provide a low cost, reliable and fully automated user-friendly
m icrowave m easurement system to be a viable alternative to these conventional network
analysers. In this T hesis, two different techniques are described, which have been
developed for this puipose.
The first measurement system is a dielectric w aveguide multistate reflectometer, which
operates in the frequency band o f 110 GHz up to 170 GHz. This work was carried out at
the U niversity o f Kent, Canterbury, and supervised by Dr R.J. Collier. The second system
is a fixed multiprobe reflectom eter which was designed at the U niversity o f Surrey under
the supervision o f Professor I.D. Robertson. It has been demonstrated practically in the
frequency band from I G Hz up to 5.5 GHz, and a higher frequency system operating up
to 325 GHz has also been investigated.
B efore going into detail in the follow in g chapters it might be useful to point out a few
points. Even though a considerable work and research has been done so far to find
alternative measurement system s, which are rival to the com m ercial network analysers,
there is still plenty o f scope for novel work in this field. For exam ple, the two system s
w hich are described here: one was built by using a dielectric w aveguide and the other by
using a microstrip line with low cost conventional com ponents. Problems such as
mism atch, coupling effects, stability, repeatability and noise are dealt with by using
different methods o f calibration and eiTor correction, and w hile developing and
im plem enting user-friendly fully-autom ated m easurement system is another challenge.
A ll these w ill be review ed and discussed in detail throughout the Thesis.
C hapter 1. Introduction
1.2 Structure of the Thesis
Chapter 2 describes the D ielectric M ultistate Reflectom eter (D M R ) measurem ent system.
It provides an overview o f the configuration and the operation o f the system. It also
describes the key equipment and com ponents o f the system , such as the source, DM R
with its associated com ponents; Phaseshifter, dielectric
w aveguide
and dielectric
couplers. The properties and the advantage o f using dielectric w aveguide especially at
high frequency are explained. The system ’s parameters have been derived.
Chapter 3 introduees the dielectric multistate reflectom eter system
eonfiguration,
calibration and measurement routines, which have been used during the implementation
and automation o f the system . It describes the basic theory o f the D M R and a way to
derive the calibration constants. The stability and repeatability o f the phase shifter have
been measured. Practical measurement results have been num erically analysed and
compared with the theory.
Chapter 4 describes the principle o f the multi-probe reflectom eter realised in microstrip.
The standing w ave on the line and the effects o f uniforai loads and arbitrary loads on the
standing w ave on the microstrip line are investigated. The design o f a one-port microstrip
multi-probe reflectom eter is presented and the principle o f operation o f the diode
detectors as w ell as their input matching and sensitivity are described.
Chapter 5 describes the measurement setup o f the one-port m ulti-probe reflectom eter
system . The algorithms used to calibrate the system as w ell as to find the measurement
errors for one-port eiTor con ection are described. Various sim ulation data as w ell as
practical measurements for several m icrowave com ponents are presented, as well as a
com parison o f these results with ones taken with a com m ercial analyser.
Chapter 6 describes the design o f a two-port multi-probe reflectom eter measurement
system . The ealibration m ethod and algorithms have been derived and the two-port tw elve
error-term m odel is described. Sim ulation data and practical results are presented. The
m easurement uncertainty has been derived and calculated.
C hapter 1. Introduction
Chapter 7 summarises the work and the results achieved in this research and makes som e
suggestions for future work.
1.3 Contributions of this Thesis
The novel work carried out during this research is about im plem enting reliable and low
cost m icrowave and m illim etre-w ave measurement system s. A thorough investigation o f a
programmable phase shifter used in dielectric multistate reflectom eter has been carried
out. Practical measurements using the dielectric multi state reflectom eter have been
earned out, and the principles for calculation o f the system parameters are described
The multi-probe reflectometer, in which the standing w ave in a line is measured by using
a number o f fixed detector probes, has been realised using low cost surface mount
com ponents. Improved algorithms o f calibrating and coiTccting the measurement enors o f
the multi-probe reflectom eter have been developed. The proof-of-concept design o f a full
two-port measurement system based on the multi-probe techniques has been described.
C hapter 2 D ielectric W aveguide M easurem ent System
Chapter 2
2 Dielectric Waveguide Measurement System
2.1 Introduction
A m easurement system was developed at the Electronics Laboratory at the U niversity o f
Kent at Canterbury with the intention o f providing measurement facilities. This enabled
the user to measure passive devices and their scattering parameters within the w aveguide
band 110 GHz up to 170 GHz. In order to carry out these measurem ents, a Dielectric
Multi state R eflectom eter (DM R) [6], was used in conjunction with other test equipment,
as w ill be discussed later. The system had to be developed, as no com m ercial measuring
equipment was available, which covered the sam e w aveguide band at the tim e [7].
D ue to a number o f advantages o f the dielectric w aveguide [8,9], such as low loss
transmission [10], a higher usable bandwidth, easy fabrication with low cost and its
flexibility unlike a metallic waveguide, a dielectric w aveguide w as used in the
reflectometer.
The idea was to establish a reliable measurement system to enable one to measure and
calculate the scattering parameters at the required m illim etre-w ave frequencies. A reliable
system with minim um human, measurement and system atic errors w ould necessitate the
system automation and computer control. This w ill be discussed later.
B efore any measurem ents can be carried out, the system must be calibrated. B y
calibrating the system , it can be norm alized in order to offset system atic errors, which
w ould effect the real measurements o f an unknown device. The system was calibrated by
using conventional w aveguide standards such as a sliding short circuit and a calibrated
C hapter 2 D ielectric W aveguide M easurem ent System
m atched load termination. The calibration procedure w ill be discussed later in the next
chapter.
O nce confidence is gained in the m easurement system , a measurement o f the reflection
coefficients and the impedance o f an unknown device can be carried out at fixed or swept
frequencies in the w aveguide band 110 G Hz up to 170 GHz.
2.2 Principles of microwave measurements
M icrow ave measurements such as im pedance measurement, attenuation measurement,
phase measurement or delay measurements have so far played an important and an
essential support service for many high frequency users such as m obile radio, astronomy,
satellite, m obile p h on es...etc. A s the frequency goes higher the w avelength gets shorter
and hence, methods o f circuit representation and analysis need to be m odified.
M icrow ave system s differ from low frequency system s in many w ays, especially in the
analysis o f the signals conveyed by the waveguides. M ost com m on w aveguides are
coaxial lines and rectangular ones, where the width is tw ice its height. One major
difference between coaxial line and rectangular w aveguide is that rectangular w aveguide
does not sustain propagation below a certain frequency, i.e. the cu t-off frequency, w hile
coaxial line can be used in the TEM m ode from dc to the frequency at which propagation
becom es possible in another unwanted m ode.
W hen a m icrowave source is conneeted to a load by means o f a transmission line,
reflections o f the signal w ill in general occur at the conneeting points and also within the
com ponents (D U T ) them selves. In practice this m eans that the pow er delivered by a
source to a load w ill depend on the reflection coefficients o f the source and the load. This
w ill be analysed in detail in chapter 4.
There are many different methods and different algorithms, w hich have been developed
for m icrowave measurements where the m icrowave circuits or m icrow ave com ponents
are analysed in terms o f electric and m agnetic fields associated with them. A very
6
Chapter 2 Dielectric Waveguide Measurement System
com m only used method o f microwave measurements is based on the study o f a standing
wave pattern formed along the transmission line because o f the interference o f the
incident and reflected waves. It is from the ratio o f the amplitude and the phase
relationship between
the
incident
and the
reflected
waves
that the
impedance
characterisation o f the component causing the reflection can be carried out, or from the
ratio o f the absorbed power to the incident power the attenuation can be calculated.
Nowadays there are different measurements methods, and various types o f equipment
available to the m icrowave engineer, such as network analysers, scalar or vector, and
various types o f reflectometers, as will be discussed briefly in the next two sections.
2.2.1 Reflectometers
A reflectometer is a passive device, which measures the magnitude and the phase o f the
reflection coefficient o f a DUT by using a number of power detectors to monitor the
power at different ports. There are different types o f reflectometers, which have been
investigated and developed such as the six-port reflectometer, four-port reflectometer and
the multistate reflectometer in both normal metallic waveguides and dielectric wave­
guides [2,3,12-21]. In all o f these types the principle of reflectometers stays the same
from a hardware point o f view; it mainly consists o f directional couplers and power
detectors. Figure 2-1 shows one o f the simplest forms o f reflectometers capable of
measuring the amplitude o f the reflection coefficient o f a DUT.
04
03
4
AA/V
X
3
AAA
X
Figure 2-1: Simple 4-Port Reflectometer
DUT
Chapter 2 D ielectric W aveguide M easurem ent System
A source is connected to one port known as the input port, the D U T is connected to
another port known as the test port and the detectors are connected to the remaining ports.
One detector monitors primarily the energy incident on the D U X where are the remaining
detectors monitoring a com bination o f the incident and the reflected energies, normally
separated by different path lengths. The voltage ratio o f the incident w ave detector to each
o f the remaining detectors are used when calibrated to determine the reflectom eter
characteristics and hence the reflection coefficient o f the DU T.
It can be quite numerically involved to calculate the reflection coefficien t from the
various detector readings. Therefore a computer is norm ally used to generate and apply
the correction factors to simulate peifect performance from im perfect circuit components.
M ore details about the reflectom eter parameters and the numerical calculation will be
introduced later in Chapter 3.
2.2.2 Network analysers
It w as clear from the previous section that the reflectom eter w as described as a one-port
measuring instrument, which determines the com plex reflection coefficien t o f unknown
loads. Network analysers are described as a two-port measuring instrument that can
determine all four scattering coefficients for a two-port device. It is clear from this that
two com patible reflectometers can be used in conjunction with each other to constitute a
network analyser; similarly, a network analyser measuring one-port D U T is equivalent to
a reflectometer.
Network analysers have becom e one o f the m ost important measurement tools for
characterising the performance o f high frequency com ponents and devices. A m odem
vector network analyser is capable o f measuring magnitude, phase and group delay, they
show the port im pedances on a smith chart, and, with tim e-domain capability, show the
distance from a test port to an im pedance mismatch. Understanding a network analyser
can help the operator derive optimum perfom iance from the instrument.
Chapter 2 Dielectric Waveguide Measurement System
The principle operation o f network analysers is based on the use o f power detection,
power splitting and power coupling as well as frequency conversion. There is also a
mathematical process, which is done nowadays by powerful computational methods.
Figure 2-2 below illustrates a sim plified diagram of a vector network analyser with Sparameter test set.
"Network
Analyser"
A to D
COMPUTER -►
display
IF signals
LO Signal
Frequency Converter
Generator
TEST SET
DUT
Dual directional couplers
PORT I
PORT2
Dual directional couplers
RF Signal
Generator
Figure 2-2: Block diagram of Vector network analyser
Signal separation hardware such as power dividers and directional couplers allow
measurements o f a portion o f the incident signal to provide a reference for the ratio
measurements, and separate the incident and the reflected signals present at the input o f
the DUT.
Chapter 2 Dielectric Waveguide Measurement System
The network analyser’s radio frequency (RF) source is the stimulus signal for the DUT.
The two splitters and couplers take samples o f the incident and reflected signals. The
receiver converts the RF signals into intermediate frequency (IF) signals where amplitude
and phase differences can be measured directly and presented on a display.
Power dividers are resistive and broadband, but have high insertion loss. Directional
couplers have low insertion loss but are usually limited in bandwidth. Directional
couplers are useful for measuring both the incident and reflected signals present at the
input o f the device under test (DUT). Directional couplers consist o f a through path and a
coupled path, which diverts a small amount o f the power travelling along the through path
as shown in Figure 2-3.
Isolated
Port
Input Reverse
Port
Test
Port
Figure 2-3: Directional coupler
The amount o f coupled power is determined by the coupling factor:
rp
Coupling Factor (dB) = - 1 0 Log
\
couplingjorw ard
incident
For example, in a 20-dB coupler, the coupled power level is 20 dB less than the incident
power level at the input port. In addition to the coupling factor, a directional coupler has
other parameters, such as frequency response and directivity that contribute to the overall
power level seen at both the main output port and the coupled port. Ideally, if a signal is
travelling in reverse though a coupler, it should not appear at the coupled port. In reality.
10
C hapter 2 D ielectric W aveguide M easurem ent System
som e energy always appears at the coupled port due to the coupler’s finite port-to-port
isolation. Isolation can be m easured by sending pow er through the coupler in the reverse
direction, and can be defined as the leakage pow er at the coupled port relative to the
incident pow er as below:
f P
Isolation(dB ) - -lO L o g
reverse coupled
\
|
-
O ne o f the m ost important measured parameters for the couplers is their directivity.
D irectivity is a measure o f a coupler’s ability to separate signals flow ing in opposite
directions along the through path o f the coupler. It can be defined som etim es as the
dynamic range available for reflection measurements and can be represented as:
D irectivity {dB )
=
Isolation {dB ) - Coupling F actor {dB ) -
{dB)
Errors due to finite directivity are often responsible for ripple patterns in many
m easurements o f return loss. At the peaks o f the ripple, directivity adds in-phase with
reflections from the D U T ’s reflection; at other tim es it is out-of-phase, resulting in a sharp
dip in the retum -loss response.
Directional bridges are also useful for measuring reflected signals over a broad bandwidth
but have significant loss.
2.3 Measurement system
The dielectric w aveguide measurement system was designed to use a dielectric multistate
reflectometer. The system operates in the frequency band o f 1 10 G Hz up to 170 GHz. The
basic configuration o f the system is illustrated in Figure 2-4.
11
Chapter 2 Dielectric Waveguide Measurement System
PC
Serial Port
Connector
GPIB
Backward
Oscillator
(BWO)
RF Inport
DMM
Phase
Shifter
Stepper
Motor
Measurement
y Port
DMR
Mon Itor
Port
Test
Port
DUT
Figure 2-4: Dielectric Waveguide Measurement System
The system consists o f a dielectric multistate reflectometer (DM R), backward wave
oscillator, digital multimeter and a standard PC. The PC contains all the software
routines, which are required to control the system and process the measurement data. An
IEEE card with a GPIB parallel connection controls the source oscillator and the digital
multimeter. The phase shifter in the DMR is driven and controlled directly by a stepper
motor, which is controlled by the PC through the parallel port output.
12
Chapter 2 D ielectric W aveguide M easurem ent System
The calibration routine involves the deteiTnination o f the system parameters for the DM R,
based on the measured pow er ratio at the D M R monitor port (port 3) and measurement
port (port 4) for different calibration devices. The calibration process w ill be described in
detail in the next chapter.
The source oscillator used in the system is a Backward W ave O scillator (BW O ). This
device offers a relatively high output pow er and also a w ide tuning range to cover the
w hole bandwidth from 118 GHz to 178 GHz [10]. It can also perform a frequency sw eep
over the w hole bandwidth. The BW O produces an output pow er between 20 m W to 30
mW and can be controlled by the PC through the GPIB port.
The digital multimeter is the H P 34401A , which has uncertainty better than ±0.0015% on
D C voltage measurements. It is capable o f measuring D C voltage ratios and can be
controlled by the PC through the GPIB. The ratio o f the m onitor port voltage to the
measuring port voltage o f the D M R represents the pow er seen out o f the diode detectors
at these ports.
2.4 Dielectric Multistate Reflectometer (DMR)
The dielectric multistate reflectom eter (DM R) is equivalent to a one-port network
analyser and can be used to measure the reflection coefficient m agnitude and phase. As
shown in Figure 2-5, it is basically a four port device, where port 1 is connected to the
source oscillator, port 2 connected to the D ev ice Under Test (D U T ), port 3 and port 4 are
each connected to a pow er detector [1,5,22,23,24].
The w aveguide com ponents used for the dielectric multi state reflectom eter include:
a) T w o broadband dielectric couplers
b) D ielectric w aveguide phase shifter
c) T w o power detectors
d) A short circuit and a matched load or absorber
13
Chapter 2 Dielectric Waveguide Measurement System
Port 4
Measurement
Port
Absortwr
Porti
Port 2
DUT
HP Input
Phase
Shifter
Short
Stepper
Metpr
Port 3
Mon tor
Figure 2-5: Dielectric Multistate Reflectometer
Part o f the incident signal at port 1, which com es out o f the backward wave oscillator
(BW O), will pass through coupler I and is reflected at coupler II, so that it is finally
detected by the power monitor detector at port 3. Part o f that signal will propagate
through coupler II to the device under test (DUT) at port 2.
Monitoring the source power level o f the BWO and using the power ratios for the actual
measurements can make the operation o f the reflectometer independent from any
variation in the output power of the BWO [22]. While part o f the power is used for
monitoring the input power, the other part propagates through coupler I and through
coupler II to the D U T connected at port 2. The wave which is reflected by the D U T will
propagate back through coupler II and will be partially reflected at coupler I, so that it can
be coupled into the measurement port 4. At this stage it superposes with the wave
propagated along the phaseshifter up to the short and back again, which experienced a
defined and repeatable phaseshift at a full circle 360° with 48 steps.
14
Chapter 2 D ielectric W aveguide M easurem ent System
Exam ining the pow er ratio measurements, three different states o f the phaseshifter w ill be
chosen, nonnally 120 apart to calculate the magnitude and the phase o f the reflection
coefficient o f the DU T.
2.4.1 Dielectric Waveguide and Dielectric Waveguide Couplers
Operating at high frequencies using a m etallic w aveguide can be a problem due to the
increase in losses due to the Skin effect, which increases with the frequency. These losses
are proportional to ^ [f and are very significant above 35G H z [25]. The surface or edge
roughness increases the losses particularly above 100 GHz, as w ell the reduction in size
contributing to the increase in loss. Therefore, in order to avoid additional losses in
m etallic
w aveguides, non-m etallic w aveguides
such
as dielectric w aveguides are
prefeiTed.
A s mentioned earlier, dielectric w aveguides have advantages over the m etallic ones such
as they have low transmission loss, they are easy to fabricate at low cost and they have
higher useable bandwidth. The basic principle o f operation o f all dielectric w aveguides is
based on total internal reflection, and the surface o f the guide has to be sm ooth to avoid
radiation losses. Furthermore, the m edium suiTounding the guide has also to be free o f
losses and be uniform in the near field region where relatively high field strengths exist.
A s the frequency is inversely proportional to the dim ensions o f the w aveguide, it w ill be
relatively easy to suiTound the w aveguide with another dielectric m edium , which will
control the field.
A cross section o f a dielectric w aveguide is illustrated in Figure 2-6. The wave in the
dielectric cannot propagate faster than the velocity o f a plane w ave in the surrounding
medium. Therefore the phase velocity V^can be expressed as;
15
Chapter 2 D ielectric W aveguide M easurem ent System
W here c is the speed o f light - 3 x 1 0 ^ ms"' and
is the effective dielectric permittivity.
Then in more general way Vp can be expressed relative to the suiTounding medium as in
Equation 2-1.
c
c
> --y::-'-":'
>
c
(2 1)
Where: g, is the relative dielectric constant o f the w aveguide and 62 is that o f the
surrounding medium . Therefore:
T
Figure 2-6: Dielectric waveguide
D ielectric w aveguides suiTounded by air have the low est losses; hence it is the practice to
use air as the surrounding medium. H ow ever it is som etim es convenient to have a ground
plane, which elim inates som e o f the higher order m odes [ 1 ].
The dielectric w aveguides used inside the dielectric multi state reflectom eter are
Pol y tetraPl uoroEth ylene (PTFE) rectangular w aveguide with a cross section o f 1.651m m
by 0.8255m m and a relative peiTnittivity o f 6 ^ = 2 . 1 .
The operational frequency
bandwidth is 110 GHz to 170 GHz [22]. The principal design o f the dielectric couplers
being used inside the dielectric multistate reflectometer is show n in Figure 2-7 and is
described in greater detail in [26].
16
Chapter 2 Dielectric Waveguide Measurement System
Isolated Port
Dilectric
Sheet
Input
Output
Port
Port
a
Coupled Port
Figure 2-7: Dielectric Waveguide Coupler
The coupler is a four port device, which consist o f a symmetric dielectric waveguide cross
junction and contains a thin piece o f dielectric sheet material with a higher dielectric
constant in the middle o f this junction. The dielectric sheet material is positioned at an
angle o f 45°, where the travelling wave no longer has a perpendicular incident component
[ 2 2 ].
The incident wave at the input port will be partially reflected to the coupled port, and
partially
transmitted
through
the
dielectric
sheet
material,
which
has
different
permittivity. The thin material is a piece o f alumina with a relative dielectric permittivity
o f 9.6, which is higher than that o f the dielectric waveguide (2.1).
2.4.2 Phase shifter
A programmable phase shifter has been designed and used in the dielectric multistate
reflectometer (DM R), which gives a flat relative phase shift over the entire frequency
range from 110 GHz up to 170 GHz [22,27]. It consists o f an eccentric rotating cylinder,
adjacent to a dielectric guide, which is driven by a stepping motor. Although the dielectric
phase shifter has been designed and described in greater detail in [22,27], it was
investigated further in greater detail from a practical point o f view [28].
17
Chapter 2 Dielectric Waveguide Measurement System
The phase shifter is a metallic cylinder, which has been arranged eccentrically to allow a
number o f different values for the gap between the dielectric waveguide and the metal
cylinder. The number o f offsets between the metal wall o f the phaseshifter cylinder and
the dielectric waveguide depends on the number o f steps o f the controlled stepper motor.
This number is half o f the maximum number o f steps o f the stepper motor, which controls
the rotation o f the cylinder o f the phase shifter. This particular stepper motor has a
movement o f 48 steps for a complete cycle, with 7.5° each step.
With this number o f
steps, a sufficient range of phase shift is available over the entire frequency range. This
device is the key component o f the DM R [22,29].
The conducting wall o f the cylinder causes a perturbation o f the m icrowave field just
outside the dielectric waveguide.
When the wall is nearer to the waveguide, the
maximum of the field inside the waveguide is shifted away from the centre in a direction
away from the wall, so that more o f the field propagates in the air outside the guide than
in the dielectric. This will reduce the wave number and as a consequence the phase shift
per unit length along the guide in comparison to an unperturbed wave. Figure 2-8 below
illustrates the dominant electric field transverse to the metal wall.
Electrical
Wal
Figure 2-8: Dominant electric field transverse to the metal wall
18
Chapter 2 D ielectric W aveguide M easurem ent System
Since the properties o f the dielectric guides are known, the effect o f the metal plate can
also be evaluated. The relationship between the field propagating in the regions 1,2,3 as
shown in Figure 2-8 and for the boundary condition is illustrated in equations (2.2 and
2.3) [27]:
E; sinh a { d
= E 2 cos(k^ -^ + D)
(2 .2 )
and
■a E i cosh a ( d ~
= ~ ^ x ^ 2 sin(A:^ -^ + D )
(2.3)
and
k^ E 2 &va{-k^ — + D ) = aE ^ e
^
Therefore from equation 2.2 and 2.3 the relationship between the distance d o f the metal
plate from the dielectric wall and the perturbation D can be obtained and expressed in
equation 2.4. This is by assum ing the dielectric guide is approxim ately a slab guide and
calculated for the boundary conditions [22,27];
,
a
1
.
u
d = — + — tanh
2
6 %,
ta n (A :^ --D )
(2.4)
tan(A:^^ + D )
oCx is the transverse decay constant, kx is the longitudinal propagation constant, and are
related as follow s: -
tan (A :^ --D )
For a dielectric w aveguide with relative permittivity
(2.5)
kx can be expressed as:
19
C hapter 2 D ielectric W aveguide M easurem ent System
(2 .6)
and hence the transverse constant a can be elim inated, giving:-
1 + tan^
^ - D )j - ^
B y assum ing a value o f D , the values o f k% and
(g;. - 1 ) = 0
(2.7)
can be determined and hence from
equation (2.4) a value o f d can be found [11]. A s mentioned earlier the phase shifter is
arranged eccentrically so the rotating metal cylinder o f the phase shifter w ill cause
different changes to the phase o f the w aves propagating in the dielectric guide. W hen the
metal cylinder is nearest to the dielectric guide, the perturbation D is largest and hence the
phase change is also largest. This happens at the beginning and at the end o f the cycle.
Gradually, as the cylinder m oves round and m oves away from the dielectric w all, the
perturbation D w ill decrease and hence the change in phase w ill be m inimal, until it
reaches a point in the m iddle o f the cycle, where at that distance it is no longer effective.
This is illustrated in Figure 2-9, which is a practical measurem ent carried out by
connecting the sliding short circuit at the measurement port o f the dielectric multi state
reflectometer. This w ill be discussed later in greater details in Chapter 3.
The size o f the phase shifter w ill affect the size and the w eight o f the dielectric multistate
reflectometer. It was designed to make it possible to give enough phase shift o f the signal;
an undersized phase shifter m ight not produce enough phase shifts and could cause loss in
the measurement accuracy. A 35m m long cylinder was used [22].
20
Chapter 2 Dielectric Waveguide Measurement System
S h o r t c i r c u i t d e v i c e at 1 4 0 G H z , Z e r o w a v e i e n g t h o f fs e t
1.6
-
1.4 -
I
u
1.0
»
0.8 -
k
-
-
0.6 -
&
a
0.4 -
O
0.2
-
-
0.2
0
10
20
30
40
50
N u m b e r of p h a s e shifts for a c o m p le te cycle
Figure 2-9: Measurement of the waveguide short circuit device with 0mm offset at 140 GHz
The relationship between the distance o f the metal cylinder from the dielectric guide and
the phase shift was measured as illustrated in Figure 2-10. This agrees with the simulated
results carried out in earlier studies [22].
200
50
-50
-200
Figure 2-10: Metal cylinder distance from the dielectric waveguide against phase at 140 GHz
21
C hapter 2 D ielectric W aveguide M easurem ent System
The broadband response o f the phase shifter is due to the follow in g two factors, which
they alm ost cancel each other over the entire bandwidth:
1. The extent o f the fields outside the guide, which decreases with frequency
2. The propagation phase constant, which increases with frequency.
2.5 System Control
The m easurement system can be manual or use automatic control through a conventional
PC. The automated measurements have a number o f advantages over the manual
measurements such as:
a) M inim ise system atic enors.
b) M inim ise human errors.
c) Faster m easurements
d) Faster in com puting the measured data
e) Processing and storage o f calibration data.
f)
Calculation and display o f the measured characteristics
Lab V iew software was selected to control the measurement system due to its features
and advantages over the conventional software such as C programming, Pascal or Visual
Basic. LabV iew is a revolutionary graphical programming environment; it gives the
flexibility o f a powerful programming language without the associated difficulty and
com plexity. It is a faster way to program and drive an instrumentation system without
sacrificing performance. Figure 2-11 show s a front panel control o f the programme. Refer
to Appendix A for full programme listings.
22
Chapter 2 Dielectric Waveguide Measurement System
F r e q u e n c y ( GHz)
40.00000
Device Connected
Short circuit lb connected
^^Npower Ratio
Power Ratio
PbtO
Wêvetorm Chart
f / v
S S E iz f
îlïW
g
210
2
^ “
jiô sr
lâ â r
2)0.159
ig ïïr
2iÔÏÎ5~
Nimbei o( messutements
100
Figure 2-11: DMR Front Panel Measurement Programme
One o f the biggest advantages o f LabView is the productivity gain that it offers. In
traditional languages, software developers often spend substantial time specifying a
system before they begin actual development. With LabView, w e have the ability to
rapidly prototype, design, and m odify system s in a short amount o f time.
LabView provides a powerful analysis library, which is capable o f computing the real
results and displaying them in graphical form or tabulating them in real time. It has the
flexibility to write data into Excel files, and carry out further analysis on the data if
required. LabView is the only graphical programming system with a compiler that
generates optim ised code with execution speeds comparable to com piled C programs.
Finally, instrument control using LabView software can be preformed by using either a
GPIB interface, or through the serial ports.
23
Chapter 2 Dielectric Waveguide Measurement System
2.6
System Characterisation
The electrical properties o f a component such as, loss, phase shift and impedance at
m icrowave frequencies, where component dimensions are comparable to the wavelength
o f the electrical radiation in vacuum are usually described in terms o f the scattering
coefficients. The impedance measurement is basically the detection o f the RF voltages
under specific conditions and can be expressed as a com plex ratio using scattering
parameters.
The reflectometer is basically a linear and time invariant four-port device and can be
com pletely described using the scattering parameters o f the devices it contains. Once
these parameters are found by applying a direct normal calibration routine, the linear
network is com pletely characterised and the measurements can be carried out, and then
the characteristic equation o f the system can be derived. The incident waves a and the
reflected waves b at the ports o f the DMR can be described in terms o f its scattering
parameters as illustrated in Figure 2-12 and represented in equation (2.8).
Dielectric Multlstate
Reflectom eter
[S]
Figure 2-12: 4-Port Device Incident and reflected signals
24
C hapter 2 D ielectric W aveguide M easurem ent System
The index i stands for the different states applied to the internal phase shifter, which can
have an influence on all parameters. O nly three states are needed to calculate the system
parameters, as this w ill be discussed later.
(2 .8)
The full representation o f the scattering parameters can be represented as in equation
(2.9):
b ,'
111
^13
^14
E2
^21
^22
^23
^24
0.2
h
^31
^32
^33
^34
«3
_i^41
^42
^43
i^44. i .«4_
b4. i
= 1 ,2 ,3
(2.9)
The incident w aves a; at ports 3 and 4, which are connected to the pow er diode detectors
can be elim inated in terms o f the their reflection coefficients,
w ave at port
2
£ 3
and £ 4 . The incident
can be expressed in terms o f T, which is actually the reflection coefficient
o f the device under test (D U T). Therefore, the expression in equation (2.9) becom es
equation ( 2 . 1 0 ):
bi
Sn
^12
^13
i^l4
«1
E2
1^21
^22
^23
:^24
r ^2
b3
1^31
^32
^33
^34
E363
b4. i
_:^41
^42
^43
^44. i E 4 6 4
If = 1 ,2 ,3
(2 .10)
B y solving the equation (2.10) and re-arranging it, the results is equation (2.11):
-4,
^3,
+
c,r+i
;/ = 1,2,3
(2 . 11)
25
C hapter 2 D ielectric W aveguide M easurem ent System
This equation is a version o f the characteristic equation in terms o f the com plex system
parameters o f the DM R, which are a*',
and ^ ,where:
a I - ( A I + F j • A 2 )j-
Al; = (5^2)542 - ^ 22^41 )f
A2 ,. = (A 3 + A4 + A5 ),.
A3,- =
5 4 1 ( ^ 3 3 5 2 2
A 41= -
;f = 1,2,3
~ ^ 23 ^ 22)1
-
5 4 2 ( 5 3 3 5 2 1
5 2 3 5 3 1
).
A5,- =543(521532 -5 2 2 5 3 1 ).
- (541+ E 3 • (531543
533541)).
- 1,2,3
and
where
Ç 1 , = ( Ç 3 + F 3 .Ç 4 ) .
Ç-^i —{^21^32 ~ ^ 2 2 ^ 3 l) i
Ç 4 ,. = ( Ç 5 + Ç 6 + Ç 7 ),.
C5,. =
Ç
6 ,.
=
ÇJ i =
5 4 1 ( 5 2 4 5 3 2
-
-5 4 2 (5 2 4 5 3 1
5 4 4 ( 5 2 2 5 3 1
5 2 2 5 3 4
-5215
-5 2 1 5 3
2
).
3 4 )f
)/
and
C 2 ,. —(5 3 1 + £ 4 • (534541
531544)).
—1,2,3
Therefore, the characteristic equation (2.11) w ill help to measure the com plex voltages
occu n in g at ports 3 and 4 o f the dielectric multi state reflectometer. H ow ever, diode
detectors w ill measure the pow er em erging at these ports, therefore the expression in
26
C hapter 2 D ielectric W aveguide M easurem ent System
equation (2.11) needs to be m odified. B y taking the square value o f the magnitude o f the
com plex values for b3 and b4, the characteristic equation o f the D M R can be represented
in terms o f voltage squared as in equation (2.12) below . This is a well known
characteristic equation for a four port reflectometer, which contains the voltage squared
ratio on one side o f the equation and the unknown reflection coefficients o f the D U T on
the other side. This expression is important when the system needs to be calibrated before
the real measurements begin as it w ill discuss in the next chapter and it takes into account
all possible com plex parameters with their state dependency.
2
2
a F + b
h
i
;%=1,2,3
(2.12)
cF + l
The denominator can be considered to be com pletely state independent. The reason for
this, is that the path from ports 1 and 3, the return loss parameters at any port, and the
isolation o f the couplers should provide a non-dependency for all parameters in the
denominator. It is necessary to explain when these sim plifications m ight not be applicable
and what are their influences. W hen the denominator diverges from unity, which is due to
the insufficient coupler isolation or a high return loss at the D M R port, this means the
reflectom eter becom es unstable and temperamental in terms o f its calibration and
measurement performance. Therefore, the assumptions being made on the basis that the
denominator is nearly one, which means that it has little effects on the actual
measurements, i.e. it is considered as a correction factor.
The characteristic equation (2.12) is used in m ost calibration m ethods. It assum es that the
com plex coefficient in the denominator is not dependent on the different states set by the
phase shifter. That is based on the assumption that the variation is not large for the
different states applied. If the variation is large for the different states applied then the
characteristic equation for the system w ill not be valid any more. D epending on how large
the variation o f the pow er level is and how sensitive the calibration routine is for
numerical perturbation, this can cause problems in carrying out the calibration o f the
system . It can also lead to a failure o f the calibration, as finding the system parameters
w ill be difficult.
27
C hapter 2 D ielectric Waveguide M easurem ent System
2.7 Conclusion
This chapter has described the configuration o f the dielectric w aveguide measurement
system and its basic requirements. The advantages o f using a dielectric waveguide
particularly at high frequency, and the individual main and sub com ponents o f the system
have been described.
D etails o f the operation o f the dielectric phase shifter have been described and the
analytie equations for the relationship between phase shift and o f the distanee o f the phase
shifter from the dielectric w aveguide have been given. Practieal measurement show ing
the phase change characteristic with respect to the distance from the dielectric w aveguide
has been illustrated.
The characteristic equations o f the multistate reflectometer have been derived.
28
C hapter 3 D ielectric M ultistate R eflectom eter (DM R)
Chapter 3
3 Dielectric Multistate Reflectometer (DMR)
Calibration
3.1 Introduction
B efore any measurements can be earned out using the dielectric multistate reflectom eter
or any other m easurement system , it has to be characterised or calibrated. A ny system in
general w ill have som e errors; these errors prevent the measured data from being an
accurate representation o f the true value o f the device under test (D U T). These system
errors can be rem oved by calibrating the dielectric multi state reflectom eter with known
im pedance standards.
A set o f m icrowave standards that are defined physically and electrically are used to
provide a reference for the physical interface between the D U T and the DM R. After the
system has been calibrated using the im pedance standards and the developed software o f
the DM R , measurements o f the D U T can be made. Under ideal conditions, with perfectly
known standards, all system eiTors w ould be com pletely characterised and rem oved. After
finding the system parameters, which are known as the calibration constants, the
measurements o f the D U T can be carried out.
The accuracy to which these standards are known establishes how w ell the system enors
can be characterised and removed. L ess than perfect m odelling o f the calibration
standards w ill result in unconected system atic enors, which are known as residual errors.
The magnitude o f the residual errors after calibration w ill prevent measured data being a
true representation o f the D U T.
29
C hapter 3 D ielectric M ultistate Reflectom eter (DM R)
3.2 Calibration Consideration of the DMR
In recent years, considerable effort has been devoted to develop a suitable calibration
routine for the reflectometer, or to calculate the calibration constants using different
algorithms [30-50]. These calibration routines have to fulfil certain requirements to be
useful in real measurements. The hardware o f the DM R is relatively sim ple as was
explained earlier, but it is quite involved to get the reflection coefficien t determined from
several scalar pow er measurements. D espite the numerical com plexity, the calibration and
measurement routines have to be fast in order to com e up with the final data. This is even
more important when a user cannot tolerate any delay in getting measurement results, as
in the case o f com mercial test equipment. For fast measurements with the D M R , not only
should the calibration routine needs be efficient, but also the computational unit has to
have hardware to cope with these requirements. Generally, com m ercial products, which
perform real time measurements, contain sophisticated com putational units to speed up
the numerical process. In the D M R calibration and measurements all the numerical
computation w ill be earned out through mathematical routines built in to the controlling
software.
Another requirement o f the calibration routines is to use as few standards as possible. A
larger number o f calibration standards m eans more operator involvem ent in the
calibration and more connections w ill be carried out. Therefore, the system atic enors
o ccu n in g during the connection o f the calibration standards can lead to greater enors in
later measurements.
The calibration standards required to calibrate the DM R are sim ple. Calibration can be
carried out either by using a w aveguide variable short only where a m inimum o f four
different offsets are required or by using a sliding short circuit with a calibrated matched
load. In this case only three short offsets are required as a m inimum . B y m oving the
variable short, the phase o f the reflected w ave w ill be altered. This means that when the
sliding short is m oved by a quarter wavelength ~
, the short circuit w ould be acting like
an open circuit, where the phase is shifted by 180 . And by m oving the short by a distance
30
C hapter 3 D ielectric M ultistate Reflectom eter (DM R)
of
, the phase o f the reflected w ave w ill be altered by 90 , which represents +j on the
Smith chart. Clearly for a m ovem ent o f —
, the phase o f the reflected w ave w ill be
altered by 270 or (-90 ).
3.3 System configuration and measurements
A com pletely new software programme using the LabV iew programming language has
been developed to control the w hole o f the measurement system and to enable one to
caiTy out the calibration o f the DM R and measure unknown im pedance in terms o f
magnitude and phase. The system is connected as illustrated earlier in Figure 2-4. Refer to
Appendix A for full listing o f the programmes,
The software provides a user-friendly environment, where the user can see clearly on the
front panel control w indow the progress o f the measurement. The phase shifter w ill go
through a com plete cycle at each standard setting, achieving 48 steps with 7.5 for each
step. W hile the digital multimeter (DM M ) continuously takes data at each step o f the
phase shifter, the measured data is being displayed on a continuous basis in a graphical
way and tabulated as w ell as shown earlier in Figure 2-11. The data is analysed instantly
as w ell as being written to a spreadsheet file for further analysis if required. Appendix A
provides further details o f the programs that have been developed and their graphical
representations.
B y setting the backward oscillator (BW O ) to give a 140 G Hz continuous w ave signal and
by connecting directly a w aveguide variable short at the D M R port 2 (the D U T port) and
by running the program, the phase shift w ill run a com plete cycle.
Figure 3-1 below
illustrates these results.
31
Chapter 3 Dielectric Multistate Reflectometer (DMR)
S h o r t c i r c u i t d ev ice at 140 G H z , Z e r o w a v e i e n g t h offset
1 80
1.6
-
1 . 4 ---------
0.8
0 .6
Q.
0 . 4 ----0.2
-
0.0
-
0. 2
10
20
30
40
50
N u m b e r of p h a s e shifts for a c o m p l e t e cycle
Figure 3-1: Measurement of the waveguide short at offset o f 0*A,g at 140 GHz
The output power ratio o f the detectors is directly proportional to the voltage reflection
coefficient o f the device under test and the spacer phase combination. This relation can be
derived from the principle equation (2.13) as mentioned earlier in section (2.5).
Therefore, equation (2.13) can be rearranged as in equation (3.1) below.
2
- r
2
A4
A3 i
+
;/= 1 ,2 ,3
f
(3.1)
g r + i
br+i
y.2,
1
/
& E
+
; (= 1,2,3
(3.2)
1
N ow if:
b=
, r = r e ‘^'' and g=ge'^^
then equation (3.2) becom es
32
C hapter 3 D ielectric M ultistate Reflectom eter (DM R)
2
= fl;
h
;i = 1,2,3
(3.3)
i
and hence
—Cli
\ + ( b T f + 2bT co& {e^+e^)
l + (gP)^ + 2gT cos(6> + Oy )
; i = 1,2,3
(3.4)
//
The numerator is dominant because the denominator represents interactions between the
device under test and the residual voltage reflection coefficient at the measurement port.
From previous analysis [1], the denominator can be approximated to unity; therefore
equation (3.4) can be written as:
= a,- (l + ( b V Ÿ + 21>Tco&{Ofy +
))/
(3.5)
î ^~ 1,2,3
Therefore, one can see that the pow er ratio is directly proportional to the cosine o f the
phase 6 ^ k , where the phase varies between - 1 8 0 to 180 as illustrated in Figure 3-1.
From a theoretical point view , by varying the sliding short’s position it w ill act as an
offset short. This means that the measurement should be repeatable every half a
w avelength, com pletely out o f phase every quarter wavelength and 90
every
phase shifted
. A com plete set o f results were taken over a w hole o f w avelength. Figure 3-2
illustrate these results.
33
Chapter 3 Dielectric Multistate Reflectometer (DMR)
S h o r t c i r c u i t d e v i c e at 1 40 G H z , D i f f e r e n t w a v e i e n g t h o f f s e t s
O xxo
Xg/8
Xg/2
Q.
0.8
0 .6
0.4
0.2
Xg
0.0
D
100
200
300
400
N u m b e r of p h a s e shifts for a c o m p l e t e c y c l e and c o m p l e t e Xg
Figure 3-2: Measurements of a variable short at 140 GHz over a full wavelength
It is clear from the results in Figure 3-2 that, the measurement system is behaving as
predicted by the theory. The measurements results are repeated every
À
com pletely opposite in phase every
o
and 90 phase shifted every
and
À„
. Figures (3-3 to
3-4) also confirm this.
34
Chapter 3 Dielectric Multistate Reflectometer (DMR)
S h o r t ci rcui t d e v i c e at 140 G H z r epeat ed ever y Xg/2
—
Ox Xg
—• —Xg/2
0.4
0.2
0.0
-
0.2
10
20
30
40
50
N u m b e r o f p h a s e s h i f t s for a c o m p l e t e c y c l e
Figure 3-3: Measurements o f a Short circuit device at 140 GHz repeatable every —
It is com pletely out o f phase every - ^ a s illustrated below:-
S h o r t c i r c u i t d e v i c e at 1 4 0 G H z r e p e a t e d w ith A.g/4
0 .2
0.0
0
10
20
30
40
50
N u m b e r of p h a s e shi f t s for a c o m p l e t e c y c l e
Figure 3-4: Measurement at 140 GHz with Xg/4 offset (Open & Short)
When the waveguide matched load was connected to the D U T port, the reflection
coefficient would be expected to be zero and the power ratio magnitude would be
35
Chapter 3 Dielectric Multistate Reflectometer (DMR)
constant over the whole o f a phase shift cycle. The practical measurement at 140 GHz
shows that the average matched load power ratio magnitude is 0.3037 and fairly constant
over the whole cycle o f phase shift. Figure 3-5 illustrates the results o f a matched load
and compares it with a short circuit. This data was used to calculate the system calibration
constants as will be demonstrated in section 3.6.
S h o r t c i r c u i t d e vic e at 14 0 G H z a n d m ate h L o a d
o
—* — S hort C r c u l
*
M a t c h Load
B 0 .6
°0.4
-r»
0 .2
0 .0
0
10
20
30
SO
40
N u m b e r of p h a s e shi f t s for a c o m p l e t e c y c l e
Figure 3-5: Measurements at 140 GHz for a Short Circuit & a Matched Load
3.4
M easurem ent Consistency O ver Frequency
The system stability over the whole o f the waveguide band 110 GHz up to 170 GHz was
tested and analysed. The stability o f the system is tested by taking number o f readings at
different frequencies for the same setting o f the device under test, which is in this case a
waveguide short. The measurements were carried out between llO G H z to 170 GHz with
10 GHz steps at a position o f OxA,g, i.e. zero short offset. Table 3-1 summaries the
average output power ratio for these measurements and Figure 3-6 illustrates the results
for these measurements.
Frequency
(G H Z)
P ow er R atio
110
120
130
140
150
160
170
0.366
0.369
0.367
0.371
0.377
0.382
0.380
Table 3-1: Average output ratio power over whole frequency band
36
Chapter 3 Dielectric Multistate Reflectometer (DMR)
S h o r t c i r c u i t devi ce r e p e a t e d o v e r the m e a s u r e d o v e r t he whoi e f r e q u e n c y b a n d
2 .0
1— 1 1 0
OHl
e
n
Pt
DOOM:
»
s,
3
a
3
o
0.8
ISO O H :
0.6
0. 4
0 .2
0.0
10
0
20
30
40
50
N u m b e r of p h a s e shifts for a c o m p l e t e cycle
Figure 3-6: Measurements of a short circuit device over the frequency band of (110-170) GHz
The matched load was connected as the D U T and the detectors’ pow er ratio outputs were
recorded at the bottom, middle and top end o f the frequency band i.e. 110 GHz, 140 GHz
and 170 GHz. Figure 3-7 illustrates these results.
M a tch L oa d me a s ured a t (110, 140 and 1 7 0 ) G H z
0.8
o
QC
110 O H l
I
140 QH s
O
a
3
*
0.0
0
*
10
' ^^44 a a s a a a #s s
20
&a I
30
170 O H l
40
50
N u m b e r of p h a s e shifts for a c o m p l e t e cycle
Figure 3-7: Measurements of a match load at (110,140 & 170) GHz
37
Chapter 3 Dielectric Multistate Reflectometer (DMR)
It is clear that changing the frequency has little effect on the phase shifter in both aspects
o f the output power ratio and the phase. The average standard deviation (Stedev) output
power ratio is calculated using:
(3 .6 )
Stedev(x) =
n ( n - l)
Where x is the average power output and n is the number o f measurement.
The Stedev(x) is calculated to be 0.64% and the maximum phase standard deviation is
±10.8°' These calculations will be taken into consideration when the system error and
measurement uncertainty are calculated, and hence will be taken into account in any
measurements.
3.5
Repeatability
The repeatability o f the DM R including the phase shifter was tested at the middle o f the
operating waveguide band, 140 GHz. By repeating the same measurement many times
while both the system settings and the frequency remained unchanged. Figure 3-8
illustrates the repeatability for 10 measurement results.
Re a pea ta billy m e a u r e m e n t s for a s h o r t devi ce a t 140 G H z
—
1 ft
—
2nd
3r d
o
ai
s
£.
- 6t h
1 0
7t h
I
O
0. 5
.-6th
10th
0.0
10
20
30
40
SO
N u m b e r o f p h a s e s h i f t s f o r a c o m p le t e c y c l e
Figure 3-8: The repeatability of measurements at 140 GHz
38
Chapter 3 D ielectric M ultistate R eflectom eter (DM R)
The standard deviation
o f the average output power ratio for the repeatability
measurements was calculated to be 3.46% and the m axim um phase standard deviation
w as calculated to be +14.1 . This w ill contribute to, and be used later in the calculations
of, the overall system uncertainty. It w ill be used to correct the actual measurements.
There are other factors, which affect both the stability and repeatability o f the phase
shifter, such as the stepper motor itself and the m echanical vibrations o f the w aveguide
inside the DM R.
The stepper motor positional accuracy is typically 5-10% [54]. The
standard deviation in both stability and repeatability both fall within this specification.
3.6
Dielectric Multistate Reflectometer Calibration
A ny test equipment w ill have measurements e n o r as only perfect ones w ill have no error,
even though im perfections exist in the finest test equipment and w ill cause less than ideal
measurement results or errors. T hese errors can be rem oved or characterised by
performing a measurem ent calibration step before the actual unknown device can be
measured.
The main requirements o f the calibration procedure o f the dielectric multi state
reflectom eter are the sim plicity, stability, repeatability and efficien cy. The last one can
experienced during the calibration that the routines fails to give a reasonable system
parameters as it might happened when the dominator in equation (2.13) differs very much
from unity. This can happen due to a large or fatal en o r during the calibration
3.6.1 Calibration Constants
Different calibration algorithms can be different in their numerical stability with regard to
perturbation o f the pow er ratios used for calibration. The main criterion for the calibration
routine is numerical robustness, which has been tested extensively. In addition, the use o f
a m inim um number o f standards, as few er calibration standards can result in less eiTors.
During calibration, with the algorithms applied as in the follow in g sections, the system
calibration constants can be determined which will enable the user to carry out the
measurements o f the D U T .
39
Chapter 3 Dielectric Multistate Reflectometer (DMR)
The dielectric multistate reflectometer has physically four ports, and it requires three
different states o f phase shifting or three different settings to calculate the magnitude and
the phase o f the device under test. For each setting o f the phase shifter the network inside
the reflectometer changes its characteristics. For greater accuracy o f finding the
calibration constants o f the system, it is recommended to chose three points which are
o
o
o
o
120 apart i.e. 0 , 120 , 240 , or any other three points can be chosen with reasonable
phase shift between them as shown in Figure 3-9.
S e l e c t i n g c a li b r a t i o n p o in ts from s h o r t c i r c u i t d e v ic e
m e a s u r e m e n t at 1 4 0 G H z
2nd Point
3rd Point
O
•a
eg
o
a.
BO
0 .2
0
20
10
30
40
50
N u m b e r o f p h a s e shifts for a c o m p l e t e c y cle
Figure 3-9: Measurements of a short circuit with zero offset at 140 GHz
M ost methods presented so far have considered the six-port reflectometer calibration and
the method o f six-port to four-port reduction. It has been stated earlier that the voltage
ratio in the multistate reflectometer can be represented as:
2
A4
aT + b
A3 i
cT + l
; /= 1,2,3
(3.7)
where, a, b and C are the characteristic parameters o f the multistate reflectometer.
40
C hapter 3 D ielectric M ultistate R eflectom eter (DM R)
A number o f analyses have proved that finding the full terms o f the characteristic
parameters w ill require a m inimum o f seven calibration standards [22,39,41,44]. This will
make the calibration process lengthy and vulnerable to operator and connection errors.
It has also been shown that for a stable reflectom eter the dominator in equation (3.7) w ill
not differ much from unity and the characteristic parameter C is considered as a correction
factor and it is very small. Therefore, it w ill have very little effect on the overall
behaviour o f the multi state reflectom eter and hence can be neglected. B y doing that, it
w ill m ake the calibration process o f the multistate reflectom eter a lot simpler as the
number o f calibration standards can be reduced to four as w ill be show n in the follow in g
analysis.
/
B y considering neglecting c, equation (3.7) can be written as:
2
\aT + ^ ]
1,2,3
(3.8)
B y taking a,- out, equation (3.8) can be arranged as follow s:-
y-A
;f=1,2,3
= e , | / r + l|"
(3.9)
;i = 1,2,3
Where
€; = \a;
and
41
Chapter 3 D ielectric M ultistate Reflectom eter (DM R)
In this method two calibration standards are required, a matched load and a sliding short
circuit, where the sliding short circuit can be used as an offset short as w ell. The offset ^
nÀ„
- ; n = integer
W hen the matched load connected at the D U T port 2, the reflection coefficien t T = 0, and
equation (3.10) w ill becom e
—1,2,3
(3 11)
W hen the short circuit device is connected to the D U T port 2, the reflection coefficient F
= -1, therefore (3.10) w ill becom e:-
y-A
- Pl^
(1
/ke,. ) + i/lm ,
- PSi
’^
and then
(^5 ,- - -^L,.
+ /k e
+ /lm
^ /k e ));
- 1,2,3
(3.13)
And when the offset o f the variable short is set by - j - it presents an open circuit device
where the reflection coefficient F = 1, therefore equation (3.10) can be written as:
-
Pti
(1
/k e, ) +
jflmi
-
Pqi
’ *-
CF14)
and then
k
= n , (‘ + A / + f M
+ 2 /R e
I
= 1.2.3
(3.15)
B y solving (3.10), (3.13) and (3.15), the system calibration constants can be found:
42
C hapter 3 D ielectric M ultistate Reflectom eter (DM R)
6 : = P,
Re,
^ l6 P ^ P o ,- ( 4 P L ,+ P o r P s ,Ÿ
/im ,
4Pr
where,
Pq.
The pow er ratio when a short circuit offset by Àg/4 is connected at the D U T port.
g.
A,.
The pow er ratio when a short circuit with no offset i.e. (k g = 0) is connected at the
D U T port.
P[^
The power ratio when a matched load is connected at the D U T port
There are two possible solutions for
, the c o n e ct one can be found by taking one
more m easurement by connecting the variable short circuit at the D U T port with a known
/I ,
value o f offset such as —
where the reflection coefficient F = +j. B y substituting the
measured pow er ratio, e,-, /^ g ., and both values o f
into equation (3.9), one answer
w ill fulfil the measurement results and the other value will be rejected.
3.6.2
Practical Measurements
B y taking three different states as m entioned earlier from each m easurements, where there
is enough phase shift between these points, such as states number 2, 5 and
8
o f the phase
shifter as illustrated earlier if Figure 3-9. The three different phase shift is ideal separated
by
1 2 0
°.
43
Chapter 3 D ielectric M ultistate R eflectom eter (DM R)
B y taking the calibration results from the middle o f the operating frequency band,
140G Hz, the voltage ratios and the calibration constants are tabulated in Table 3-2:
Position
e
Ae
/im
0.549
0.370
0.931
0.026
0.325
1.330
0.325
-0.861
0.587
0.334
0.290
0.3334
-0.932
0.840
Ps
Po
Pl
P^j
1
0 . 0 0 2
1.380
0.370
2
1.442
0.231
3
1.271
0 . 1 2 1
Table 3-2: Calibration constants of the DMR calculated at 140GHz
Therefore, the three com plex constant vectors basically are;
la tO °
= 0 .9 3 1 + 0 .0 2 6 ;
/ a f 120" = - 0 . 8 6 1 + 0 .5 8 7 ;
/ o f 2 40" = - 0 .9 3 2 - 0 . 8 4 0 ;
A s mentioned earlier, the principle o f solving the multi state reflectom eter characteristic
equation depends on using three different calibration standards. O nce the calibration
constants are found, then it w ill be easy to m easure the impedance o f the DU T.
The reflection coefficient F =
where F is the magnitude and ^ is the phase o f the
reflection coefficient. This can be represented as F = x + y ; , by substituting this in
equation (3.10), then
2
|2
Pd, =
|(/R e + if\m )(^ + j y ) + 1|;
; ( = 1,2,3
Where P^, is the measured voltage squared ration when an unknown device connected at
the D U T port. Therefore, equation (3.17) can be solved as:
44
Chapter 3 D ielectric M ultistate Reflectom eter (DM R)
—
( /R e ,. + / i m ,
-
But | / |
=
,
+ y ^ ( /r c ,. + /im , f
- 2yf^ ^, + l)
and so equat i on (3.18) can be written as
p
/|.
+ 7^) + 2,xfRe. - +
1
C3 19)
H ence, as there are three different positions, then equation (3.19) can be written for the
three different states.
-1
Id;
2 / r0,
2 / i^^
Id
2 /R e , - 2 / i m ,
V
1
f d k
/
>
(3.20)
-1
,« 2
Id ;
\
2 /R e ,
-1
k«3
Therefore, from equation (3.20) the reflection coefficient T in terms o f both magnitude
and phase can be calculated. This principle has been applied to different measurement
data and the results are tabulated in Table 3-3 and illustrated in Figure 3-lO.(Smith chart
plots)
DVT
Offset
( F ) Complex
Notation
( r ) Magnitnde
& Phase
Ideal
Vaine
Magnitude.
%Error
Phase Error
(Degrees)
Short
0 \
-1+Oj
-1<180"
-1<180"
0
0
-0.0883+0.9878)
0.9917 Z 95. r
+)<90"
0^ 3
5.6
1 + Oj
1<0"
1<0"
0
0
0.1646-0.9794)
0.9932<-80.5"
-)<-90"
0.68
10.6
Short
Short
V4
Short
Short
Xg/2
-0.9947+0.0444)
0.9957<177.5"
-1<180"
0.43
1.4
Short
5Àg/8
-0.0999+0.9894)
0.9944<95.8"
+)<90"
0.56
6 .4
Short
3V 4
0.9936+0.0019)
0 .9 9 3 6 < 0 .ir
1<0^
0.64
0.06
Short
7Àg/8
0.0459-0.989)
0.9901<-87.3"
-)<-90"
1.0
3.0
Short
À,
-0.9949-0.007)
0.9949<-179.6”
-1<180”
0.51
0.20
Matched
Load
N/A
0 + 0)
0<0"
0<0^
0
0
Table 3-3: Measurement data measured with DMR at 140GHz
45
Chapter S Dielectric Multistate Reflectometer (DMR)
Figure 3-10: Measurement data analysed at 140GHz
Therefore, from these results it can be seen that the calculated measured results agree with
the expected values. The difference can be due to the follow ing reasons:
•
The accuracy o f the sliding short micrometer vernier, as it is manually adjusted.
•
The mechanical tolerance o f the phase shifter.
•
The accuracy o f the voltage ratio measurements o f the digital multimeter.
•
The approximation o f assuming the dominator to be unity.
One can see that with this approximation method reasonable measurement results can be
achieved, while the calibration process has been made easier and the computation o f the
results is faster, as fewer calibration standards are used to characterise the multi state
reflectometer system.
3.7
C onclusion
The chapter described the dielectric multistate reflectometer calibration process, which
enable the calculation o f the system parameters. The stability and repeatability o f the
phase shifter has been measured. Practical results have been measured and the
measurements errors have been calculated for various loads.
46
C hapter 4 M ulti-Probe R eflectom eter System
Chapter 4
4 Multi-Probe Reflectometer System
4.1 Introduction
A similar approach to that described in chapters 2 and 3 has been used at the University o f
Surrey as a continuation o f the previous work earned out at the University o f Kent, but
with the aim o f realising a simpler low cost design. A sim ple low cost automated
m icrowave m easurement system has been developed. The system is a microstrip m ulti­
probe reflectom eter constructed using normal surface mount discrete com ponents. The
im pedance o f an unknown load can be measured fully automated in terms o f magnitude
and phase by reading the output o f the pow er detectors. The prototype system is designed
to operate in the frequency range o f 1 G Hz up to 6 GHz, w hile the possibility o f a higher
frequency system has been investigated.
The multi-probe reflectom eter has been investigated and used by a number o f researchers
for som e years [55-71]. M ost o f the researchers approached the slotted line method and
the multi port reflectom eter as a replacement to the conventional network analysers.
These methods have their own disadvantages such as the need to use pow er meters and
directional couplers, which are rather expensive, bulky and com plicated. H owever, the
idea o f designing and developing a reliable, low
cost and practical impedance
characterisation device is still quite a challenge.
The microstrip multi-probe reflectom eter described in this thesis offers som e solutions to
these problems. It is sim ply a microstrip line with a few surface mount com ponents in a
space o f not more than 40m m by 20m m .
t
47
C hapter 4 M ulti-Probe Reflectom eter System
The sim plicity o f the hardware m akes it easy to deploy it and perform im pedance
m easurement in tight spaces, which offers a solution for many desirable measurements.
The system has been fully automated and is presented in a user friendly way just as it is in
a com mercial network analyser. It enables the user to specify the test frequencies and
pow er levels in a very convenient way. Lab V iew programmes have been developed to
operate and control the measurement system in a W indow s-based environment. Full
programme listings are given in Appendix B,
4.2 Transmission Line Theory
The principle o f the multi-probe reflectom eter is based on transmission line theory, where
the line is considered as a distributed parameter network, where voltages and currents can
vary in magnitude and phase over the transmission line length. Before going into detail
describing the design o f the multi-probe reflectometer, it is useful to review briefly the
properties o f a w ave propagating on a transmission line and the cases o f the transmission
line being matched, mismatched, lossless and lossy.
The transmission line in general is often represented by an equivalent circuit containing
distributed im pedance [1,72-75]. B y considering a length o f uniform two-conductor line
connected between a source and a load, it can be seen for any short length o f the line that
there w ill be energy storage, as m agnetic and electrostatic energy, and energy dissipation
occurs both in conductors and in the dielectric. A transmission line can be m odelled as a
lum ped elem ent circuit as shown in Figure 4-1.
I + ÔZ
I Z. t)
r m
V(z, I
Figure 4-1: Equivalent circuit of a lossy line.
48
C hapter 4 M ulti-Probe Reflectom eter System
where
R = Series resistance per unit length, Q /m .
L = Series inductance per unit length, H/m.
G = Shunt conductance per unit length. S/m.
C = Shunt capacitance per unit length, F/m.
B y assum ing that ôz —> 0, the symm etry automatically appears so that the voltage and
cunent can be described in terms o f z and t. Expressing the changes in voltage and cuiTcnt
can be done by applying K irchhoff’s voltage and cunent law s resulting in:
V -\V +
=
/ —I i + â z
\Sz
(4.1)
+ C — \5z
(4.2)
Therefore, by arranging (4.1) and (4.2):
!
= -(« ,>
l
| |
(4.3)
|
=-(
gv4 c
| |
(4.4)
T hese equations are the tim e-domain form o f a transmission line and often known as the
Telegrapher’s equations. For a sinusoidal steady-state condition, with cosine-based
phasors, equations (4.3) and (4.4) can be sim plified to:
^ ^ = -(/;4.;A;Z,)/(z)
(4.5)
az
^ ^ = -(G + ;VüC)y(z)
(4.6)
az
Differentiating equation (4.5) and substituting (4.6) results in:
=
(4 . 7 )
49
C hapter 4 M ulti-Probe Reflectom eter System
where y is the com plex propagation constant and can be expressed as:
y = ^ { r + jcoL ){G + jc o C ) = a + j p
a is
(4.8)
the attenuation constant and P is the phase constant. A s there are tw o w aves
travelling
on the transmission line, the incident and the reflected w ave, which are opposite
in direction, equation (4.7) can be solved as:
y(z) = y+e-)^+y-e>"
(4.9)
and in a sim ilar manner
=
Where
(4.10)
represents w ave propagation in the +z direction, and
represents wave
propagation in the - z direction. Therefore, substituting (4.5) into (4.9) gives:-
K -r JCOL
If, ---------R + jcoL
= — , then Zn
Zq
, which is the characteristic im pedance on the
+ jœ C
transm ission line, in O.
yTherefore,
—^
.
A w ave travelling from a source down a transmission line w ill have a phase velocity Vp,
where the phase velocity is the velocity o f a point o f constant phase on the waveform.
Since the w ave takes a finite time to an ive, it is delayed in phase as it travels along the
transmission line. The amount o f phase delay can be represented as 2n radians per
w avelength, Àg.
Therefore, the phase delay per meter is known as the phase constant P and can be
represented as:
P Zg
and the phase velocity Vp = ^ = A ^ f .
p
50
C hapter 4 M ulti-Probe Reflectom eter System
4.2.1 Lossless Line
The above solution is a general one for the transmission line as the loss effects are
included, and the propagation constant as w ell as the characteristic im pedance are
com plex. In many practical cases, the loss o f the transmission line is very small and can
be neglected. This results in a sim plification o f the previous terms. If the line is lossless
then R = G = Q . Then, the propagation constant y can be expressed in terms o f the
attenuation constant a and the phase constant P:
Y = a + j P = jc o 4 L C
/3 =
co4 l C
(4.12)
a =Q
when a is the attenuation constant = 0. Then the characteristic im pedance Zo w ill be a real
number and represented as:
^ 0 = -^
(4.13)
The general solution for the voltages and currents on a lossless transmission line can be
expressed as:
y(z) = y
(4.i4)
/(z)
(4.15)
The w avelength is:
and the phase velocity is
V = ~ =- ^
”
p
4
(4.17)
l c
51
C hapter 4 M ulti-Probe R eflectom eter System
4.2.2 Termination of Lossless and Lossy Transmission Lines
If a transmission line is terminated by an arbitrary load o f im pedance Z l, as illustrated in
Figure 4-2, where the line characteristic im pedance is not equal to the load impedance,
part o f the w ave travelling a long the transmission line gets reflected back along the
transmission line.
V(z). I(z)
Figure 4-2: Transm ission line term inated by load im pedance Z l.
By
taking the first case where the transmission line is lo ssless, where the attenuation
constant, a = 0, the incident w ave generated from the source at z < 0 w ill be
the reflected w ave from the terminated load w ill be
and
. A s the line is terminated by
an arbitrary load Zl, then Z^ ^ Z q and the ratio o f the voltage to the current at the load
must be Zl. The reflected w ave must be excited with appropriate amplitude and phase to
satisfy this condition.
Therefore, the total voltage and cu n en t on the transmission line as expressed earlier in
equations (4.14) and (4.15), which is the sum o f the incident and reflected w aves and the
total voltage and current at the load can be related by the load im pedance, so at z = 0, it
results in:
(4.18)
Then,
52
C hapter 4 M ulti-Probe R eflectom eter System
v: =
y;
(4.19)
\^ L + Z o y
The voltage reflection coefficient, F, is the amplitude o f the reflected voltage wave
noiTnalised to the amplitude o f the incident voltage wave and can be expressed as:
^Z ^ - Z
q
(4.20)
Therefore, the total voltage and current w aves on the transm ission line expressed earlier
in (4.14) and (4.15) can be written as:
1^(Z) =
]
(4.21)
/(z ) =
- F e ]
(4.22)
Zq
N ow in the second case where the transmission line is lossy, the attenuation constant a
0, i.e.
there is som e energy losses occur to the w ave travelling
a long the transmission
line. In this case equations (4.21) and (4.22) can be re-written as:
F (z) = + Fe-/)^ ]
Z(z) = ^
k'^'^ -
(4.23)
]
(4.24)
Zq
A s / = -z , therefore equation (4.23) can be expressed in more general form as:
I^(z)| = k 1 k | | l + rc-2^'^|
(4.25)
where:
Vg
F - |F|g^^
the incident voltage from a source on the line .
Unknown load reflection coefficient.
Y
Propagation co n sta n t.
f= -z
P ositive distance measured from the load at z= 0
6
phase o f the reflection coefficient
53
C hapter 4 M ulti-Probe Reflectom eter System
Therefore, in more general form, equation (4.25) can be re-written as:
|y ( z ) | =
(4.26)
or it can be expressed for the special case o f a lossless line where, a = 0, as:
y(z) =
|l +
j
(4.27)
4.2.3 Standing Wave on a Transmission Line
From (4.26), it has been shown that the w ave on a transmission line consists o f a
superposition o f an incident and reflected w aves. When both o f these w aves are present
on the line, it w ill result in a standing wave. Since the incident and the reflected w aves
travel in the opposite direction there w ill be a change in phase in the opposite direction, so
there w ill be som e points where the w aves are in phase and at som e other points on the
transmission line they w ill be out o f phase. Since all w aves change phase by 2 ti radians
per wavelength then the m axim a are separated by half a w avelength., i.e. the forward
w ave delayed by 180 w hilst the reverse w ave is advanced by 180 .
W hen the incident and the reflected w aves are in phase their voltages w ill add, and this
results in a m axim um amplitude. W hen the opposite happens, i.e. when the two w aves are
out o f phase, there w ill be a minimum amplitude. Figure 4-3 illustrates this for a reflected
signal on a lossless transm ission line terminated by a mism atched load.
54
Chapter 4 Multi-Probe Reflectometer System
V
X/2
Figure 4-3: Standing wave on Transmission line.
It is clear that the maximum value o f the standing wave on a transmission line occurs
when the phase term in equation (4.27) above,
= 1 , and is given by:
V'm ax=V';(l + |r |)
The minimum value occurs when the phase term
V'min = C ( l - | r | )
Therefore, as the magnitude o f the reflection coefficient
(4.28)
= - 1 , and is given by:
(4.29)
|r| increases, the ratio o f Vmax to
Kmin increases, so that when T is present, the line is said to be mismatched and the
measure o f this mismatch is known as the Voltage Standing W ave Ratio (V SW R ), which
can be defined as:
VSWR =
max _ 1 + r
(4.30)
Chapter 4 Multi-Probe Reflectometer System
or
(4 .31 )
VSW R +1
The VSW R is real number such that 1 < VSW R < o ° . In the case o f VSW R = 1 it implies
that the transmission line is matched, i.e. there is no reflected w ave from the termination.
If a short circuit device is connected at the end o f the transmission line there will be total
reflection o f the incident wave, i.e. the reflection coefficient |r| = 1. This means that the
voltage falls to zero at the minima as shown in Figure 4-4 for a standing wave on a
lossless transmission line.
x/2
5
g
I
>
I
Distance from
load
Figure 4-4: Standing-wave pattern for complete reflection on a lossless line.
These standing-wave patterns will change and becom e more complicated if the
transmission line is lossy. If the attenuation constant a is not small enough, the reflection
coefficient T will decay away, where the reflections will be attenuated to a negligible
level by the time the source has been reached. Therefore, the standing-wave patterns
shown in Figures 4.3 and 4.4 are valid only for a lossless transmission line or if the
attenuation in one wavelength is negligible.
56
Chapter 4 M ulti-Probe Reflectom eter System
4.2.4 Line Match and Mismatch
It has been considered so far that the line m atching and m ism atching occuiTcd only from
the load connected as the D U T at the end o f the transmission line. The generator signal
source has been assum ed matched to the line. But, in general, both the generator and the
load m ay present a mism atched im pedance to the transmission line.
If one end o f a transm ission line is connected to a source generator with im pedance Zg
and the other end is connected to a load im pedance Z^, and the transmission line is
assum ed to be lo ssless for the time being with length
I and characteristic im pedance Zq,
then, as the generator and the load are m ism atched to the transmission line, multiple
reflections can occur to the w ave on the transmission line as shown in Figure 4-5.
Vl
o
F igure 4-5: Transm ission line load and generator connected
Z,„ is the input im pedance looking into the terminated transm ission line from the
generator end. The reflection coefficient at a point I on the line can be expressed as;
r(Z) =
r e fle c te d v o lta g e
(4.32)
in c id e n t v o lta g e
57
C hapter 4 M ulti-Probe Reflectom eter System
The input im pedance Z„, is :
(4.33)
But, as r , = — — — , then, Z,„ can be derived as:
+ 7 Z 0 tany@ "
(4.34)
Z q + J Z i tanjSl^
The voltage on the transmission line can be written as
Z;„
Z;„ + Z ,
(4.35)
Therefore,
Z ,,
(4.36)
Z...+Z, A
But as the reflection coefficient seen looking into the generator T is:
r„ =
'8
^0
Zg+Zo
(4.37)
Then, the incident voltage can be written as:
I'
Zo
1
(4.38)
L Z o+zJ
This is valid in the case when the generator is not matched to the load im pedance Z/,.
W hen the generator is m atched to the load im pedance Z l, then the input impedance
Z,„ - Zg . Therefore the overall reflection, T is:
Z ., - Z .
In the case where the generator is matched to the line w hile the load im pedance is
mism atched to the line, the cases discussed earlier in section 4.2 .2 above w ill apply.
58
C hapter 4 M ulti-Probe Reflectom eter System
4.3 One-Port Microstrip Measurement System
The one-port measurement system is multi-probe reflectom eter system capable o f
measuring the unknown im pedance o f a D U T in terms o f magnitude and phase. The
multi-probe reflectom eter system has been designed to be low cost and sim ple to operate.
It consists o f nothing more than a microstrip line with a number o f square law detectors
mounted onto it, to measure the standing w ave voltages at certain places, a signal source,
an A nalogue to D igital Converter (A D C ) unit and a normal PC. Figure 4-6 show s the
block diagram o f the measurement system .
PC
Signal
G e n e ra to r
Da ta A cq u Istio n
U n it
MIcrostrip
M u I tl -p r o b e
Refleotom eter
De t e c t o r s O u t p u t
F igure 4-6: O ne-port m easurem ent system
The signal generator can be any standard signal generator, w hich covers the required
frequency range, (A gilent 83623B or E 4433B is used here). The data acquisition unit is
capable o f converting a low amplitude analogue voltage into a digital readout, (A gilent
34970A with H P 34901A was used in this system ).
59
Chapter 4 Multi-Probe Reflectometer System
4.3.1 Multi-probe Reflectometer
As mentioned earlier the multi-probe reflectometer consists o f a microstrip line with a
few low cost surface mount components. The standing-wave voltages are sampled along
the transmission line at certain positions with known intervals. Figure 4-7 shows the
block diagram o f the multi-probe reflectometer and Figure 4-8 is a photograph o f the
actual one-port multi-probe reflectometer. Figure 4-9 shows the circuit diagram.
Voltage
Detection
Probe
Voltage
Detection
Probe
Voltage
Detection
Probe
MIcrostrIp Line
DUT
Signal
Generator
Figure 4-7: Microstrip multi-probe reflectometer block diagram
Figure 4-8: Actual one-port reflectometer
60
Chapter 4 Multi-Probe Reflectometer System
Figure 4-9: One port reflectometer circuit diagram
4.3.2 Microstrip Lines
The microstrip transmission line is one o f the most popular types used to propagate
m icrowave frequencies due to the relatively easy fabrication by photolithographic
processing and the easy integration with active and passive m icrowave devices. A typical
geometry o f a microstrip line is shown in Figure 4-10:
Top Conductor
/ Dielectric
^ Substrate
G round plane
Figure 4-10: M icrostrip line
61
Chapter 4 M ulti-Probe Reflectom eter System
W is the width o f the conductor printed on top o f the grounded dielectric substrate with
thickness h and relative permittivity constant
.
Since the w aves travelling down the microstrip line m ove partly in the dielectric substrate
and partly in the air above the substrate, the w ave velocity is in the range:
C
0*39)
<Vp<C
W here C is the speed o f light in vacuum. Thus, the w aves travel faster than a plane w ave
in the dielectric substrate but slow er than a plane w ave in air. This is usually described by
an effective dielectric constant,
, which is given by:
C
0L4O)
Therefore,
can be given approximately by [72]:
-I
01.41)
1+
\2h
W
The characteristic im pedance a microstrip line can be calculated [72]:
fo rW l h < l
01.42)
120;r
w
fw
A
LA
forW/h>\
— +1.393 + 0.667 In — +1.444
The attenuation in the microstrip line can be taken care o f by perfonning basic
calibration, as w ill be explained later. The microstrip line used in the multi-probe
reflectom eter was carefully m odelled to take care o f the periodic loading and to maintain
a characteristic im pedance o f 5 0 0 .
62
C hapter 4 M ulti-Probe Reflectom eter System
The substrate material used in the system is FR4 with substrate thickness h = 1.6mm and
dielectric permittivity constant
= 4 .5 5 . The line width W w as calculated and rounded
to be 3m m and the wavelength
calculated by to be 162m m at IG H z by using equation
(4.43)
below:
(4.43)
4.3.3 Probe Spacing
The electrical spacing o f the detection probes needs to be known for the calibration
calculations. If the spacing betw een each pair o f adjacent detection probes is m ade equal
the process o f calibration w ill be easier as few er calibration standards w ill be required.
This w ill be explained later.
As the maxim a and minima o f the standing w ave are repeatable every
probes should not be separated by
, the detection
over the w hole operating frequency bandwidth,
where n is an integer. The signal propagating on the transmission line w ill have phase
delay in both forward and backward direction, so it is important for the detection probes
spacing I which is the electrical delay for the round trip o f a propagating w ave on the
microstrip line, to satisfy the condition of:
0 < l < ^
4
On this basis, the spacing o f the detection probes was calculated to be 5.1m m . The phase
constant P has been expressed as:
Therefore, as the signal propagates in a round trip, there w ill be a phase delay constant o f
2/? and, hence, the m aximum phase change that can take place betw een two adjacent
probes w ill be:
63
C h apter 4 M ulti-Probe R eflectom eter System
A O ; = 2J31 =
for i = l,2
(4.44)
where I is the distance betw een tw o adjacent probes with m inim um value zero and
m axim um value
Then, from (4.44), the phase change betw een two adjacent probes
w ill satisfy the condition:
0<A O <;r
for i = l,2
(4.45)
Therefore, working within these guides the operating bandwidth o f the one port
microstrip reflectom eter im plem ented w ill be in the frequency range from IG H z up to 5.5
GHz.
4.3.4 Coupling and Matching
The detection probes detect the standing-wave voltages on the microstrip line. These
probes should be ananged in a way such that they should not disturb, or to have as little
effect as possible, on the im pedance o f the microstrip line, which in turn should be
carefully kept as close as possible to 50Q . Different m ethods have been used to couple
the probes to the main transmission line, such as coupled line, loosely coupled or coupled
by using som e external com ponents, depending on the operating frequency.
The coupled line and loosely coupled detectors can be used for high operating frequency
system s. But as the operating frequency o f the system is between IG H z and 5.5G H z, it
was found that the best way to couple the detectors to the main line w as through a series
combination o f resistor and capacitor.
The resistance o f the resistor w ill be relatively
high compared to the impedance o f the main line, w hile the reactance o f the capacitor will
be small and is used to block any D C com ponent going into the diodes.
Figure 4-11 illustrates the attenuation with respect to the coupling resistance at the centre
frequency o f 2.75 GHz for the m iddle probe.
64
Chapter 4 Multi-Probe Reflectometer System
A t l e n u a l i o n vs C o u p l i n g R e s i s t a n c e
m
I
-2 0
I:::
•3 5
-4 0
0
2000
4000
6000
8000
1 0000
R e si s t a n c e (fi )
Figure 4-11: Attenuation vs Coupling Resistance
The amount o f coupling needs to be a trade o ff between m inim ising the periodic loading
o f the main line whilst maintaining a sufficient signal into the detector diodes. One can
see that for a 2k£2 resistor the amount o f attenuation is approximately 18dB, which
corresponds to 1.5% o f the power propagating on the microstrip line being presented at
each o f the diode detectors.
In a perfect well matched and lossless transmission line, the three coupling coefficients
should be the same, but in practice as the microstrip line has som e attenuation and the
detector probes mounted onto it have a loading effect, the three couplings will be
different. Figure 4-12 show s the coupling coefficients for the three probes with 2kS2
resistor connected in series with a 22pF capacitor and a shunt resistor o f 4 7 0 0 .
65
Chapter 4 Multi-Probe Reflectometer System
Coupling coefficient of the 3 probes
0
•2
•4
-6
-8
2. -10
^
CD
O
CD
*
V3
-12
* - V I C oupled
14
ë
-16
^
-18
ly.l-Doup ■d.V2 Couplad
a re behin J V3 Coupled]
*
V2 C oupled
*
V3 C oulped
-20
-22
-24
3
4
F r e q u e n c y (GHz)
Figure 4-12: Coupling Coefficients of 3 Probes with 2kS2 connected
One can see that the coupling is nearly the same for all probes, which shows that the
losses in the line are small, and that the microstrip reflectometer is reciprocal. 0.5% to
2.8% o f the signal goes through to the diode detectors.
A s m entioned earlier, the microstrip line is not lossless and hence there is som e
attenuation o f the signal propagating along the line. The attenuation o f the microstrip
reflectometer was simulated and practically measured. Figure 4-13 show s these results.
M u U i - P r o b e R e f l e c t o m e t e r In s e rt io n L os s
-0.3
F r e q u e n c y (G Hz)
Figure 4-13: M icrostrip Reflectometer Insertion Loss
66
Chapter 4 Multi-Probe Reflectometer System
The multi-probe microstrip line was designed to be reciprocal and matched. The line
return loss was simulated over the w hole frequency bandwidth and later measured by
using the HP8510C network analyser. Figure 4-14 shows these measurements.
R e t u r n l o s s S i m u l a t e d vs M e a s u r e d
-2 0
•
3
M e a su re d
-30
—
0) -35
S i mu l a i e d
a:
-4 0
-4 5
1
2
3
4
5
6
F r e q u e n c y (G H z)
Figure 4-14: Return loss, simulated and measured
4.3.5 Diode Detector Circuit
It has been shown previously that a signal propagating along the microstrip transmission
line can be described in terms o f its amplitude and phase. The phase o f the travelling
wave can only be defined relative to another at the same frequency while the amplitude
can be measured sim ply by detection using microwave detectors, which com m only make
use o f a semiconductor diode. The detectors basically convert the RF voltage into a DC
level [1,72,76-78]. A com m only-used diode detector circuit is shown in Figure 4-15.
67
Chapter 4 Multi-Probe Reflectometer System
DC B l o c k i n g
V = V , c o s wt
Termination
Resistor
Shottky Diode
Smoothing
Capacitor
Load
Realator
V Id 80
ou t pu t
Figure 4-15: Diode Detector Circuit
M ost o f the incom ing signal is terminated with the termination resistor, but som e o f this
signal gets converted to a DC current by the diode, which causes an output voltage Vo to
be developed across the load resistor. At a high power level such as lOdBm, the circuit is
sim ply half-wave rectifying the RF signal, and so the output voltage is proportional to the
peak RF voltage. However, at low levels such as below -2 0 d B m , the output voltage is
proportional to the square o f the RF voltage, or directly proportional to the RF power.
This phenomenon requires that the diode be operated at the knee o f its I/V characteristic
as shown in Figure 4-16. Special Schottky diodes are w idely available for this purpose.
► V
Figure 4-16: Zero-Bias Diode I / V C haracteristic
68
Chapter 4 Multi-Probe Reflectometer System
Therefore, as the signal coupled into the diode is small in amplitude, an Agilent H SM S285A /B zero bias Schottky diode has been used for detection in the multi-probe
reflectometer. These low cost diodes are capable o f small signal detection o f less than 20dBm. A s they are zero bias, no DC bias is required which makes the design simpler.
A Schottky diode consists o f a metal-semiconductor barrier formed by deposition o f a
metal layer on a semiconductor. The most com m on o f several types is the passivated
diode as shown in Figure 4-17 along with its equivalent circuit.
Metal
Passivation
Passivation
N-Type or P-Type EPI Layer
Schottky Junction
N-Type or P-Type Silicon Substrate
Figure 4-17: Schottky diode chip cross section and its equivalent circuit
In the model, Rs is the parasitic series resistance o f the diode, which is the sum o f the
bond wire and the leadframe resistance as well as the resistance o f the bulk layer o f the
silicon. The RF energy, which gets coupled into Rs, is considered as lost heat, which does
not contribute to the rectified output o f the diode. Cj is the parasitic junction capacitance
o f the diode, which is controlled by the thickness o f the epitaxial layer and the diameter o f
the Schottky contact. Rj is the junction resistance o f the diode, which is a function o f the
total current flow ing though the diode and can be expressed as [79-82]:
8 .3 3 x 1 0 ^ n T
0 .0 2 6
a f2 5 0 (:
(4.46)
69
Chapter 4 M ulti-Probe Reflectom eter System
where
Is is the saturation current
h is the external applied bias current
T is the temperature in degrees K elvin
n is the ideality factor o f the diode, 1.05 to 1.2
Is is a function o f the diode barrier height, and can be in the range o f a few Pico Am ps for
high barrier diodes to 5 juA for very low barrier height diodes. The characteristics o f a
Schottky diode can be determined through the choice o f p-type or n-type silicon and the
selection o f the metal being used, this w ill affect barrier height and then Cj and Rs w ill be
changed. The current-voltage characteristic can be expressed as:
;==/, ext) - 4 - - --1
tL47)
where
i is the forward cunent due to voltage v
-19
q is the charge on an electron, 1.602 x 10
Coulomb
-23
k is B oltzm ann’s constant, 1.3804 x 10
J/K
In general, very low barrier height diodes with high values o f Is are suitable for zero bias
applications, which are realised on p-type silicon. Such diodes suffer from higher values
o f R s than their counterpart n-type ones. But, generally, p-type diodes are reserved for
small signal detector applications.
Since there is no internal energy source, the cuiTent through a sem iconductor diode is zero
when zero voltage is applied. W ith reverse bias voltage less than that needed for
avalanche breakdown, the reverse current is asymptotic to a constant saturation current Is.
W ith forward voltage bias, the diode conducts and the current-voltage characteristics can
be approximated as in (4.47).
70
C hapter 4 M ulti-Probe Reflectom eter System
From Figure 4-15, the voltage developed across the diode is given by:
(4.48)
V = (1/ COS,cot)-Vg
by substituting (4.48) into (4.47) it results in [1]:
(4.49)
But since the D C output is the load resistor (R) tim es the mean cu n en t i over one RF
cycle and by substituting 0 = m t, then w e have:
dû
qV,
COS0
de
04 51)
B y series expansion using Taylor’s m ethod on the right hand side and integration o f each
term over 1 RF cycle, it can be shown that for sm all signals:
V = L R -----------------------
+ higher even pow ers o f — -
(4.52)
The odd powers vanish, because the odd cosq terms integrated to zero over 1 cycle. The
fourth and higher even powers o f
can be neglected. Therefore, it can be concluded
nkT
that the diode detector provides an output approximately proportional to the square o f the
signal amplitude for small RF voltages, i.e V^a
.
The matching input impedance o f the diode is the m ost difficult part o f the design o f a
detector circuit as there is a trade-off between a good diode match and the detection
sensitivity. For broadband detectors, a termination resistor between (50-60) Ç1 will give a
good input match, but at the expense o f detection sensitivity. W hen m axim um sensitivity
is required over a naiTow band o f frequencies, a reactive m atching network is optimum.
71
Chapter 4 Multi-Probe Reflectometer System
Such networks can be realised with either lumped or distributed elem ents, depending
upon frequency, size constraints and cost limitations.
As the multi-probe reflectometer is intended to operate over a wide frequency range, it
has been found that the best way to match the diode detectors is by a shunt resistor, where
the sensitivity o f the diodes will depend on the value o f the shunt resistor. As it was stated
earlier, due to the coupling between the microstrip line and the detectors, only a small
fraction o f the standing wave voltage will go through to the detectors, which means it will
be small voltage. Therefore, the value o f the shunt resistor has to set a balance between
the diode sensitivity and the DC return to ground. Simulation data o f the effects o f the
shunt resistor on the sensitivity o f the detector diodes are shown in Figure 4-18.
I n p u tL e v e l vs S h u n t R e sistan c e
-10
-12
-14
-16
â
c
-18
a
8
-20
"
-22
-24
-26
-28
0
200
40 0
600
800
1000
1200
1400
1600
S h u n t R e s i s t a n c e (Si)
Figure 4-18; Input Level vs Shunt Resistance
There are som e disadvantages o f using zero bias detectors, such as they are sensitive to
temperature changes. Any variation o f the detectors output will affect the measurements
o f the DUT. As well as the temperature changes there are several noise mechanisms
effecting broadband detectors [1,82]. The most widely known noise is the thermal noise.
72
C hapter 4 M ulti-Probe Reflectom eter System
where a noise pow er is equal to k T B , where B is the bandwidth in H z, and this is
generated by the random thermal m ovem ent o f electrons. This m echanism , which causes
a noise voltage to be developed across the diode, lim its the sm allest pow er that may be
detected. The pow er spectrum o f the noise is uniform over all frequencies. Therefore,
kTB is known as the white noise floor and is w idely quoted with the standard figure o f 174dBm /H z at 273k.
In addition, there are other noise types present in the sem iconductor junctions, such as
flicker noise, known as 1/f noise, where the noise power varies inversely with frequency.
Shot noise or current noise, also affects the Schottky diode operation which is known as
the spectrum o f white noise and can be represented as an equivalent current source:
where,
B = Bandwidth
R = Load resistance
The value o f the load resistor affects the range o f the square law operation o f the
detectors, where the small signal sensitivity depends on the value o f the load resistor. This
load resistor is normally in parallel with a capacitor, where this com bination is used for
D C detection and discharge to ground. For best operation the ratio o f the diode resistance
to the load resistance should be sm all, with the load resistance kept below 100kS2 in order
to keep the response time small to handle fast pulses. H ow ever, all the associated
com ponents attached to the main microstrip transmission line will introduce a small
disturbance to the line impedance, and this needs to be c o n e cte d by performing
calibration.
73
C hapter 4 M u lti-Probe Reflectom eter System
4.4 Conclusion
This chapter has summarised the principles o f transmission lines. The basic equation for
the w ave propagating on the transmission line was derived. The types o f transm ission line
such as lossless and lossy ones were compared. The effect o f m atched and m ism atched
terminations connected at the end o f the transmission line was described as w ell as the
effect o f the generator. The standing-wave on the line was explained as w ell.
The design o f the one port microstrip multi-port reflectom eter has been discussed. The
effects o f coupling and the mismatch on the line have been simulated. The principle o f
operation o f the diode detectors, their input matching and sensitivity have been described.
74
C hapter 5 O ne-Port M easurem ent Set-up an d C alibration
Chapter 5
5 One-Port
Measurement
Set-up
and
Calibration
5.1 Measurement Set-up
The one port multi-probe reflectom eter measurement system is easy to use as shown
earlier in chapter 4. A stable source is connected to one port o f the microstrip circuit, and
the device under test (D U T ) is connected to the other port, w hile the data acquisition unit
is connected to the output ports o f the diodes to measure the output voltage level o f these
detectors. The prototype device has been built to operate in the m icrow ave frequency
band o f 1.0 GHz to 5.5 GHz, which is the operating frequency o f the Schottky diodes.
D u e to the advantages mentioned earlier in Chapter 3, LabV iew software has been used
again in this project to control the multi-probe measurement system and to com pute the
measurement results. The software has been developed to be user-friendly and enables the
user to specify the test frequencies in terms o f start, stop and step frequency and has the
option o f varying the output pow er o f the source. The operating system gives the choice
o f performing a measurement with or without calibration.
Graphical and numerical results o f the reflection coefficient o f the measured device are
available in terms o f magnitude and phase, as w ell as the im pedance and the return loss
values. Figure 5-1 show s the front control panel o f the programme.
75
Chapter 5 One-Port Measurement Set-up and Calibration
i-rjT x i
£ie £(ft Qpwat* look gromo W^dow tldp
[ÏT II 13ptAppicationFont
] - ||^ - »
SIdp Calibration
Mods (CW mode: 2)
W
Mode (TMad/«ingle output bvai:2)
«nÿrtmÿïnôi
(nôïlScïf J
|pSS
Steit Fiequonqp
3
îâ»oii|xjliwS
inotllact)
Slotting Power
IIOOE+ 9
I
Stop Fioquoncj^
3 B M .7
I
Slip Power
Slop Ftoquoncy
I
I
Channoj L
ie*(em
pty)
101:10
{
•31 2-
O 31.3-
1.1
1.2
1.3
1.4
Frequency (GHz)
w
1
________________ :______________
I ÜJE»pl<inn8-Sl.iplJn«.Ptog..| LWMCW
a i5 H rt|
I QColectingMeamementi..-[[j^ C o ie c tin g MowMieoi.T QShor|_So#\_CharLP1ot$
|
0&53
Figure 5-1; Measurement Set-Up
5.2
System Calibration
Before any measurements to be can be trusted, the system has to be characterised. To
characterise the system , a set o f known impedance standards, known as calibration
standards, is measured. The calibration standards can be a matched load, perfect short
circuit and an open circuit. For the reasons mentioned earlier in Chapter 3 it is advisable
that the minimum number o f calibration standards be used to characterise the system.
There are various methods o f calibration which can be used to calibrate the multi-probe
reflectometer.
In
these
methods
there
are
different
cases
of
assumptions
and
approximation. This chapter describes som e o f these methods.
76
Chapter 5 One-Port Measurement Set-up and Calibration
5.2.1 Ideal Microstrip Line Reflectometer
The first case o f characterising the multi-probe reflectometer is to assume that:
1. The microstrip line is lossless
2. The coupling o f all probes to the line are equal.
3. The probes lie at an exactly known distance from the load.
4. The line is not disturbed by the probe coupling and is well matched.
There are forward and reverse w ave on the microstrip line, which com bine together to
give a standing wave. Three detectors spaced by a known distance are placed on the line
to read the voltage level o f the standing wave on the microstrip line. A s the probes have
been placed away from the load by a certain distance, there will be a certain phase delay
to the signal between each o f these probes and the load. Figure 5-2 show s the standing
w ave and the probes.
V
Probe2
Ptobel
Figure 5-2: Probes location on a standing wave
where
is the magnitude o f the incident voltage and F is the magnitude o f the
reflection coefficient.
77
Chapter 5 One-Port Measurement Set-up and Calibration
There are three outputs from the detectors, and from these outputs the system constants
will be found. A sim plified illustration o f the multi-probe reflectometer is shown in
Figure 5-3.
L oad
P ro b e s
P ro b e2
P ro b e l
Figure 5-3: General Multi-Probe Reflectometer
In this situation the test frequency is known but the incident power and the com plex
reflection coefficient o f the unknown load are not known.
Let V = F / be the incident voltage and V (z) = V, be the standing w ave voltage on the
microstrip transmission line at the location o f the i
Ih
probe. Assum ing the attenuation
constant, a = 0, then equation (4.26) will become:
V; = V
(5.1)
where.
r and ^are the magnitude and the phase o f the reflection coefficient o f the D U T
load.
i p i = <j)^is the phase shift corresponding to the distance from the probe to the load
and back, which is accurately known.
78
C hapter 5 O ne-Port M easurem ent Set-up and C alibration
Therefore, Equation (5.1) can be expressed as:
y = y | i + r g ^ ( ^ - < ^ ) j ; f = i,2,3
( 5 .2 )
Then, as
e
= c o s ( 0 - (^) + j sin (^ - (p)
equation (5.2) can be written as;
V. = V [l + T c o s ( g -<Pi) + j T s i n i d - (p^)]
;/ - 1 ,2 ,3
(5.3)
Therefore, taking the square o f both sides o f (5.3) and taking the absolute value w ill result
in:
\Vi\^ = \V \^ [l + r ^ + 2 r c o s ( 0 - < p i ) ] ;; = 1,2,3
A s, cos(^ - (Z)) - cos ^ cos
+ sin <9sin ^ , (5.4) can be re-written as:
= |V p [ l + r ^ - l - 2 r ( c o s 6 ’cos(Zi,-H-sin(9sin(Z);)] ; / = 1,2,3
A s m entioned earlier, the Schottky diodes used are square-1 aw detectors,
output from the
(5.4)
(5.5)
and so the
probe w ill be proportional to |V", p , or can be assum ed as Pj =|V, |^ , and
by assum ing that:
2 |y p r c o s ^ = L
(5.6)
2 |V |V s i n ^ = M
' (5.7)
79
C hapter 5 O ne-Port M easurem ent Set-up an d C alibration
(5.8)
Then, from (5.6) and (5.7) the phase o f the reflection coefficient can be found as:
(M
9 = arctani —
(5.9)
and by taking,
+ M ^ = 4r^ |y I"*(cos^ « + sin ^
(5.10)
Then,
[Û+M^]
(5.11)
A \V \‘
B y substituting (5.11) into (5.8) results in:
f t2 , , , 2 \
U+M=
\
0
(5.12)
y
and then.
|y p = Û
n
± [ n '^
(5.13)
Then, from (5.5):
+ Lcos
+ M sin (Z); ;i = 1,2,3
(5.14)
For the three probes (5.14) can be expressed as:
P ^ = N + Lcos
+ M sin
(5.15)
P2 = N + L c o s ^ 2
P3 = N + Z,cos(Z>3 + M sin<p2
Therefore, solving the three cases in (5.15) results in finding the calibration constants as:
L=-
P, (sin (Z>3 - sin < ^ 2 ) +
^ 2
(sin A - sin
(^3
) + P3 (sin
sin(<z>3 - (Z>2 ) + sin(<z>, - <z>3 ) + sin ( < ^ 2 “
- sin (Z), )
( 5 . 16)
)
80
C hapter 5 O ne-Port M easurem ent Set-up an d C alibration
M
P, (cos ^ 3 - COS (Z>2 ) + P2 (cos
TV-
-cos<
- COS <p^)+ Pj (cOS
sin ( ^ 3 —^ 2 ) + sin(^i —^3 ) + sin ( ^ 2 ~
^1
(5.17)
)
P, sin (^ 3 - ^ 2 ) + ^ sin(<^, -<^3) + P3 sin (^ 2 “ <^i)
(5.18)
sin(^3 - (Z>2) + sin((Z)i - (Z>3) + sin(^2 “ A )
This is the general case o f a lossless multi-probe reflectometer, but in the case o f equally
spaced probes, as used in this work, the result can be further sim plified using:
(5.19)
and.
(5.20)
A “ ^3 = - %
Then, Equations (5.16-5.18) can be re-written as:
P\ (sin <z>3 - sin ^ 2 )+ 7^ (sin
- sin ^ 3 ) + P3 (sin
^ 2
~ s in ,
2sin(Z), -sin2<z>,.
M =
Pi (cos ^ 3 - COS <Z>2 ) +
7 2
2
N-2
(cos
- COS (Z>3 ) + P3 (cOS ^2 ” COS (Z), )
sin^^ - sin 2 <^,
sin ^ - s i n Itp^
(5.21)
(5.22)
(5.23)
This w ill be one method used to find the reflection coefficient in terms o f amplitude and
phase for an unknown device by using the multi-probe reflectom eter with three probe
detectors. A s the line is ideal and by considering the assum ptions made earlier, no
calibration w ill be needed in this situation. But in practice there w ill be som e eiTors,
which need to be con ected for, as w ill be explained later.
81
C hapter 5 O ne-Port M easurem ent Set-up and C alibration
5.2.1.1 Solving with Reference to the Middle Probe
The ideal multi-probe reflectom eter can be solved with a different m ethod with respect to
the m iddle
probe. B y considering the same assumptions as in section 5.2.1, the pow er at
probe 2 can be expressed as [69]:
P 2 = \v f\l + l f
Where, F =
(5.24)
. Then (5.24) can be re-written as:
; ^ = | y | ^ ^ + r ^ + 2rcos<z)^}
(5.25)
For probe 1, the pow er can be expressed as:
Pi = | y p | l + re^'^^p
(5.26)
or
Pi = |F p {l +
-t- 2 F c o s (p2 cos 0^ - 2 F sin ^ sin 0^}
(5.27)
The power at probe 3 is:
(5.28)
l + Fg
P3 = |F p
{1
+ F^ + 2 F c o s ^2 cos 0^ + 2 F sin ^
sin 0^}
(5.29)
Therefore, by letting :
F cos^ = w
(5.30)
Fsin(Z>2 = v
(5.31)
and,
then, subtracting (5.27) from (5.29) gives:
82
C hapter 5 O ne-Port M easurem ent Set-up and C alibration
(5.32)
4|y| sin^.
In a similar manner by adding (5.27) and (5.29):
P1 + P 3 = 2 | y p { l + r 2 + 2 A c o s 0 , }
(5.33)
H ence, by substituting (5.25) into (5.33), results in:
f, + R -
2
A
(5.34)
4 |y [ ( l- c o s ^ J
Therefore, as F =
, then:
T
= ' ^
=
« + > ------COS ^ 2 + ./ s i n
^2
The measurement results calculated by this m ethod agree with the results calculated by
using equation (5.11) derived earlier in section 5.2.1.
To produce a set o f sim ulated data for an ideal multi-probe reflectom eter is very difficult
due to the periodic loading introduced by the probes. A sim ulation has been can ied out
where the loading o f the probes on the main microstrip line has been made as low as
possible for the detectors to pick up a signal (the m inim um level o f detections for the
detectors is -50d B m ).
In this simulation the coupling resistor was 100ki2, and the source signal level was OdBm.
The signal from the main microstrip line to the detectors input was attenuated by
approximately 49dB. This means that only a very small fraction o f the signal (less than
0.001% ) w ill go through to the detectors. Table 5-1 contains data for three different
calibration standards: a matched load with reflection coefficient F =
0
Z
0
, a perfect
83
C hapter 5 O ne-Port M easurem ent Set-up and C alibration
short circuit device with reflection coefficient F =
1
Z 180 and a perfect open circuit
device with reflection coefficient F = 1 Z 0°. The calculation o f the reflection coefficient
has been carried out using the technique described above.
F re q . (G H z)
M atch ed L o ad
O p en L o ad
S h o rt L o ad
1 .0 0
0.00318 Z 44.35°
0.99779 Z -0.52°
0.99924 Z 179.8°
1.05
0.00328 Z 46.84°
0.99785 Z -6.41°
0.99917 Z 173.9°
1 .1 0
0.00337 Z 49.39°
0.99792 Z -12.3°
0.99911 Z 168.0°
0.00345 Z 52.00°
0.99799 Z -18.2°
0.99904 Z 162.1°
1 .2 0
0.00351 Z 54.66°
0.99806 Z -24.1°
0.99897 Z 156.2°
1.25
0.00357 Z 57.36°
0.99813 Z -25.0°
0.99889 Z 150.2°
1.30
0.00361 Z 60.11°
0.99820 Z -35.9°
0.99882 Z 144.3°
1.35
0.00364 Z 62.71°
0.99827 Z ^1.8°
0.99875 Z 138.4°
1.40
0.00366 Z 65.71°
0.99834 Z -47.7°
0.99868 Z 132.4°
1.45
0.00367 Z 68.56°
0.99841 Z -53.6°
0.99861 Z 126.5°
1.5
0.00366 Z 71.46°
0.99848 Z -59.5°
0.99854 Z 120.5°
1.15
Table 5-1: Sim ulated results for an Ideal M ulti-Probe reflectom eter
It can be seen from the calculated results that it is not even possible in simulatiott^to have
a completely ideal, lossless multi-probe reflectometer with no periodic loading effect
from the probe detectors. The eiTor is simply due to the effects of the probes’ periodic
loading on the main microstrip line. These eiTors can be corrected by performing basic
eiTor coiTcction as will be discussed later.
84
C hapter 5 O ne-Port M easurem ent Set-up an d C alibration
5.2.2 Non- Ideal Microstrip Line Reflectometer
The case o f an ideal microstrip line reflectom eter has been described, but in a practical
realisation the assumptions stated earlier are no longer valid. There w ill be losses along
the line and there w ill be a m ism atch due to the probes’ loading on the line. A lso, the
probes’ distance from the D U T m ight not be exactly known. Calculation algorithms need
to be found which consider all o f these parameters affecting the m easurement system .
Let
be the incident voltage and V( z ) = Vj be the standing w ave voltage on the
microstrip transmission line at the location o f the i‘'‘ probe, as w ell as the attenuation
constant, a?!:0. Then, equation (4.27) given earlier w ill become:
y. =
where, y = a +
] ;; = 1,2,3
. B y considering
(5.36)
=Vç,.and a phase error
for each probe,
equation (5.36) w ill become:
=y
;i = 1,2,3
9,
(5.37)
W here, Q// - 2/31) , conespon ds to the detection probe distance from the load with som e
phase enor, i//.. Therefore, let
d,
This m odification factor C,- can account for the microstrip line losses, effects o f the
connectors, discontinuities and the accuracy o f positioning o f the probes. Vq. accounts
for the unequal coupling coefficients between the probes and the main line as w ell as the
mism atch o f the detectors.
85
C hapter 5 O ne-Port M easurem ent Set-up an d C alibration
In this case, unlike the lossless line, calibration is required to find out the system ’s
parameters. Three calibration standards are required to determine these constants: a
matched load, a short circuit and an open circuit. After m easuring these calibration
standards, the im pedance o f the unknown load can be determined by measuring the
detectors output.
B y considering the diodes to be square-law detectors where the pow er ,i^- oc
then
(5.37) can be re-written as:
* |l + (a,- + j b i )T e
I
; / = 1,2,3
(5.39)
W hen a perfectly matched load is connected at the D U T port, it is assum ed that the
reflection coefficient F =
0
, therefore w e have:
= /%
Where
;/ = 1,2,3
(5.40)
is the measured detector pow er level when a m atched load is connected.
Therefore, the calibration factor Vq^ is determined by sim ply measuring the power
detectors output level when a matched load is connected at the D U T port.
T o deteiTnine the other calibration constants, a, and
6
, , additional calibration standards
are required. W hen a short circuit device is connected at the D U T port, there w ill be total
reflection with phase 180°, i.e. the reflection coefficient, F = -1. Then, equation (5.39)
becom es:
W here P^, is the m easured detector pow er level when a short circuit device is connected.
H ence, by substituting the results o f equation (5.40) into (5.41):
86
Chapter 5 O ne-Port M easurem ent Set-up an d C alibration
f;
a, r +(,,?} ;,- = l,2 ,3
(5.42)
or
Ps,
= f i , . W + 6 , ? - 2 a , + 1} ;i = l,2,3
(5.43)
W hen the open circuit standard is connected at the D U T port, there w ill be total reflection
with 0° phase, i.e. the reflection coefficient F = 1. This is only by assum ing that the open
circuit is a perfect precision standard and by ignoring its fringing capacitance, which is a
function o f its physical geom etry and the frequency o f the signal. Therefore, in a similar
manner, when the short device is connected, equation (5.39) can be written as:
^
W +
+ 2 o , + i j ; ; = 1,2,3
(5.44)
Where Pq, is the measured detector pow er level when a short circuit device is connected.
Therefore, taking (5.44) - (5.43) results in:
=
(5 /K )
Then, by substituting (5.45) into (5.44):
-A ,.
x = 1,2,3
(5.46)
Where,
A , = 1 6 / > ^ ^ + / > 4 + P |- 2 / > o / s , + 8 P i . P o , - 8 P ^ / > j ,
;i = l,2,3
(5.47)
Then, (5.46) can be re-arranged as:
J l6 P ,P ,_ ( 4 P ,+ P ,_ ^
(5.4S)
4P,
87
C hapter 5 O ne-Port M easurem ent Set-up an d C alibration
There are tw o possible solutions for
6
, ; the correct one can be chosen by performing one
more calibration measurement when the short circuit device is connected w hile being
offset by a known length and measuring the detectors output level again.
H aving found the calibration constants, V q .,
and
, the reflection coefficient o f an
unknown load can be measured by connecting it at the D U T port and measuring the three
detectors’ output voltage levels. N ow , by assuming:
re -^ ^ = u + j v
(5.49)
M= r cos 6*
(5.50)
v = rsin<9
(5.51)
where:
and
Substituting (5.40) and (5.49) into (5.39) results in:
I
f
where
|2
|l + (a , + j b ,)*(M + » !
;i = 1,2,3
(5.52)
is the detector’s pow er measured when the unknown device is connected at the
D U T port. Therefore, for the three probes (5.52) can give three equations:
- 1 = |Q p * ( m H
P
^
P
) + 2a^u - 2 b iv
(5.53)
- 1 = |C 2 p *
\
)+
(5.54)
/
- 1 = |C 3 p * ( m H
\
) + 243% -
/
2 ü 2U - 2b2V
2 6 3
V
(5.55)
C hapter 5 O ne-Port M easurem ent Set-up and C alibration
Solving (5.53-5.55) yields the real and imaginary parts o f the reflection coefficient as
follow s:
_ ^ 2 -^ 0
^0
^2^1 “ A
^ 2
(5.56)
^ 2
(5.57)
^ 2
A ~ A A
Where,
- c
A = C
I
A, =
2
A, =
2
| a, c l
Z?|C.
|2
I
P
(5.58)
|2
-a ,
(5.59)
—bo\C
(5.60)
and
_A L _i
A = C
(5.62)
A —2 l
A =
The return loss or the
2
|
(5.61)
6
,|c l'-
6
Jcl'
(5.63)
J can be expressed in dB as:
(5.64)
To demonstrate the validity o f the theory derived above, sim ulation for the non-ideal
multi-probe reflectometer, with parameters as illustrated earlier in Chapter 4, Figure 4-9,
89
C hapter 5 O ne-Port M easurem ent Set-up and C alibration
has been earned out at different frequencies. The calibration standards used to calibrate
the multi-probe reflectom eter are a perfect matched load, a perfect short circuit and a
perfect open circuit. Table 5-2 illustrates the results for a
6
dB attenuator terminated by a
short circuit. The return loss is calculated by using the non-ideal microstrip line
reflectom eter method as mentioned above.
An offset short has been simulated as w ell as a 3dB attenuator teiTninated by a short
circuit. The reflection coefficient was calculated and coiTected to the sam e calibration
standard in the sam e m ethod described above.
Figure 5-4 illustrates the results o f the
offset short w hile Figure 5-5 illustrates the results o f the 3dB attenuator terminated by a
short circuit.
Calculated reflection coefflcient or retu rn loss
Freq.
(GHz)
1.00
1.25
1.50
1.75
2.00
2.50
2.75
3.00
3.25
3.50
3.75
4.00
4.25
4.50
4.75
5.00
5.25
5.50
M atched Load
Open Load
Short Load
(E)
(E)
(E)
0Z0°
1 zo°
1 Z 180°
1 zo°
1 Z 180°
zo°
1 zo°
ozo"
ozo"
ozo"
ozo"
ozo"
ozo"
ozo"
ozo"
ozo"
o z o °
1
1 zo°
1Z0°
6dB A ttenuator
A 5 1 1| (dB)
% |51l|
11.99
0.00083
0.083
11.99
0.00083
0.083
1 Z 180°
11.99
0.00083
0.083
1 Z 180°
12.01
0.00083
0.083
Ï Z 180°
12.00
0
0
1 Z 180°
12.00
0
0
5 1 1| (dB)
1 zo°
1 Z 180°
11.99
0.00083
0.083
1 z o “
1 Z 180°
11.99
0.00083
0.083
1 z o ”
1 Z 180°
12.00
0
0
1zo°
1 Z 180°
11.99
0.00083
0.083
1Z0°
1 Z 180°
12.01
0.00083
0.083
1 zo°
1 Z 180°
11.99
0.00083
0.083
1Z0°
1 Z 180°
12.00
0
0
1 zo°
1 Z 180°
12.01
0.00083
0.083
1 zo°
1 Z 180°
12.00
0
0
1 Z 180°
11.99
0.00083
0.083
1 Z 180°
11.99
0.00083
0.083
1 Z 180°
12.00
0
0
ozo"
ozo"
ozo"
ozo"
ozo"
ozo"
1
o z o °
1 zo°
1 zo°
zo°
Table 5-2: Sim ulated data calculated by using the non-ideai line m ethod
90
Chapter 5 One-Port Measurement Set-up and Calibration
CorrBCted Offset Short Circuit Device Data
Figure 5-4: Simulated results o f an offset short
Corrected Data of 3dB Attenuator
Figure 5-5: Simulated results of 3dB attenuator
One can see even from these calculated results of simulation data that there is a very big
improvement compared with the performed using the previous method in section 5.2.1. In
this improved method the probe is not ideal just as it is in practical environments, where
there are losses in the microstrip line, there is mismatch and coupling effects from the
probes. The very small errors are due to the numerical accuracy read out during
simulation o f the detectors used in the calculations o f the reflection coefficient and this
can be ignored.
5.3
Practical M easurem ents and Results
The practical measurement procedure using the multi-probe reflectometer was designed
to be sim ple, fully automated and user-friendly Just as it is in m ost m odem commercial
analysers. Before performing measurements for an unknown load, calibration needs to be
carried out to characterise the measurement system. The system allow s the user to specify
the test frequency, (a choice o f fixed or swept is available), the generator power output
and if measurements needs to be done with calibration or without calibration in the
situation where a recent calibration had been performed.
91
Chapter 5 One-Port Measurement Set-up and Calibration
Normal calibration standards, i.e. matched load, short circuit, open circuit and an offset
short are used to perform the calibration. All data are stored in the PC where a
com prehensive mathematical analysis is carried out to calculate the system constants and
then the reflection coefficients in terms o f magnitude and phase.
To demonstrate the operation and the accuracy o f the design, measurements have been
carried out for various loads. These measurements were repeated for comparison by using
the Agilent 8753E analyser and the H P8510 Network Analyser. Since the maximum
recommended frequency o f operation o f the diode detectors is
1.5GHz [79], the
measurements were kept within this frequency range. Figures 5.6-5.11, illustrate som e o f
these measurements.
Offset Short Multi-Probe
Figure 5-6: Offset Short measured with MultiProbe Reflectometer
Offset Short 8753 AnatveefI
Figure 5-7: Offset Short measured with Agilent
8753E Analyser
92
Chapter 5 One-Port Measurement Set-up and Calibration
Offset Open Multi-Probe Reflectomaterl
Offset Open 8753 Anslvserl
Figure 5-8: Offset Open measured with MultiProbe Reflectometer
Figure 5-9: Offset Open measured with Agilent
8753E Analyser
M atched Load Termination M easu red
with Multi-probe R eflectom eter
-30.5
Matched Load Termination M easu red
with Agilent 8753E
-30.6-
■n -30.6cn
Ü1
P -30.7-
30.7-
2 -30.8-
-30.9-
Frequency (GHz)
Figure 5-10: 50 Ohm load measured with MultiProbe reflectometer
Frequency (GHz)
Figure 5-11: 50 Ohm Load measured with Agilent
8753E Analyser
More measurements were carried out by using the one-port multi-probe measurement
system and the Agilent 8753 analyser for different attenuators terminated by a short
circuit device. Illustrations o f the results o f these measurements are shown in Figure 5-12.
93
Chapter 5 One-Port Measurement Set-up and Calibration
M e a s u r e d R e t u r n L o s s o f A t t e n u a t o r s T e r m i na t e d b y S h o r t C i r c u i t D e v i c e
u s i n g O n e - P o r t M e a s u r e m e n t s S y s t e m a n d the 8 7 5 3 A g i l e n t A n a l y s e r
22
21
20
19
18
CO
■o
§
17
16
15
14
13
—*
3dB O ne-Port
3dB A nalyser
6dB O ne-Port
6dB A nalyser
12
§
1 1
<
10
9
8
7
*
1 OdB O n e - P o r t
1 OdB A n a l y s e r
•-------
6
5
1 .0
1 .2
1.1
1 .4
1 .3
1 .5
F r e q u e n c y ( GHz )
Figure 5-12: Different attenuators measured with the Multi-Probe Reflectometer
and the Agilent 8753E Analyser
It is clear that all measurements taken by the multi-probe system agree with the ones
taken by the H P8510 and the Agilent 8753E. The small difference will be discussed in
follow ing section.
5.4
System E rror and E rror Corrections
When measuring the reflection coefficient in terms o f magnitude and phase o f an
unknown device, the measured data will differ from the actual one, no matter how
carefully the measurement is made. This is due to the measurement system errors. These
errors can be separated into two categories; random and system atic errors. Both random
and systematic errors are vector quantities, which means there are magnitude and phase
errors.
Random
errors
are
non-repeatable
measurement
variations
and
usually
unpredictable. These random errors in the multi-probe measurement system can be due to
the change in detectors characteristics, which is drift over temperature and time, noise
pick-up, repeatability o f the connections and operator error.
94
C hapter 5 O ne-Port M easurem ent Set-up an d C alibration
The system atic en ors are repeatable measurement variations in the test setup, which can
be due to the mismatch, coupling effects, the periodic loading o f the detectors, leakage
signals from the source and the system frequency response. System atic errors are the m ost
significant source o f the measurement uncertainty and can be c o n e cte d by means o f the
so-called system error coirection or calibrations. In general, for any m icrow ave one-port
measurement system , the system atic eiTors can be grouped into three terms as shown in
Figure 5-13:-
1. Directivity
2.
Source Match
3. Frequency Tracking
The directivity e n o r term Ex,p, is due to the cross talk between the incident signal and the
reflected signal, this happens when the measurements system is using a coupler to
separate these signals. But, in the multi-probe reflectometer m easurement system , no
couplers have been used to separate the incident signal from the reflected one. In fact, the
measurements are done on the standing w ave on the line, which is combination o f the
incident signal and the reflected signal. Therefore, in theory this e n o r term should not
exist, but in practice it can be still there but does not correspond to the cross talk or the
leakage o f the signal. Instead it relates to the un-equal coupling o f the probes to the main
transm ission line, but to avoid confusion w e w ill stick to the sam e eiTor term inology, Ex,p.
The source match en o r term,
is caused by the test port being mism atched to the
system impedance. This phenom enon causes som e o f the reflected signal to bounce off
the test port, or other im pedance transitions further down the line, and back to the DU T,
and then adds to the original incident signal. This effect causes the magnitude and phase
o f the incident signal to vary as a function o f the reflection coefficient and the frequency.
This eiTor can be reduced by levelling the source to produce a constant incident signal,
but since this cannot be done exactly, there w ill be alw ays pow er variations which will
cause re-reflection effects and the resultant o f these variations is called the source match
error, E^p.
95
Chapter 5 One-Port Measurement Set-up and Calibration
The frequency tracking error, also known as the frequency response error,
is caused
by variations in magnitude and phase flatness versus frequency between the test and
reference signal paths. But since there is no reference signal channel in the multi-probe
reflectometer measurement system , this error can be defined as the transmission losses in
the signal path from the source port to the D U T port.
These errors are illustrated as a flow graph in Figure 5-13.
Ideal
Reflectometer
« 0
Error Model
DUT
h.
Test
Port
Figure 5-13: One-Port measurement system with error corrections
F a is the actual D U T reflection coefficient and F m is the measured reflection
coefficient. U sing the flow graph reduction techniques as shown in Figure 5-14 gives
the value o f F m as shown in equation (5.65).
96
Chapter 5 One-Port Measurement Set-up and Calibration
(b)
H
a/
RF
A
(C)
(d)
Figure 5-14: Decomposition of the error flow graph
(5.65)
All the parameters used in (5.65) are com plex quantities having both real and com plex
parts. Therefore, if the value o f these three errors
E d f. E r f
and
E s f
are known, together
with the measured reflection coefficient Tm for each frequency, equation (5.65) can be
solved for the actual reflection coefficient Fa to obtain the actual D U T response. Because
each o f these errors changes with frequency, it is necessary to know their value at each
test frequency. These values can be found by measuring the system with three
independent standards w hose reflection coefficients are known at all frequencies.
The first standard used to find the errors in (5.65) is a perfect load with reflection
coefficient F = 0, where all the incident power will be absorbed and no power will be
reflected. Applying that to (5.65) will results in:
L
m
= K
d f
=1^l
( 5 .6 6 )
In practice the perfect load is difficult to achieve, and since the measured value for
directivity is the vector sum o f the actual directivity plus the non-zero reflection
97
Chapter 5 One-Port Measurement Set-up and Calibration
coefficient o f the practical load termination, any reflection from the termination
represents an error as illustrated in Figure 5-15. In general, any termination having a
return loss better than the uncorrected system direetivity will be sufficient to reduce the
reflection measurement uncertainty.
C oeffic le n t of th
L oad
A c tu a I
Effective
Di r e c t i vi t y
Me a s u r e d
E ff a c t i v e
Di r e ct i v i t y
►
Figure 5-15: Relationship o f deriving the directivity term
A s it is difficult to obtain a load which has an excellent match to the 50Q impedance o f
the system over a broad frequency range, an alternative which can be used to characterise
directivity over a broad frequency range is the sliding load or offset load with known
length o f an air line. The directivity vector at a given frequency is determined by sliding
the load inside its airline to create a circle o f data points as shown in Figure 5-16.
Load
Element
►
Figure 5-16: Sliding Load and resultant vectors
98
C hapter 5 O ne-Port M easurem ent Set-up an d C alibration
The centre o f the circle is the direetivity vector, w hilst the radius o f the circle is the load
vector. W hen using this m ethod the airline section o f the sliding load defines the 50Ê2
im pedance standard.
O nce the directivity term Enr has been determined, the other error tenns, the frequency
tracking error E rf and the source match error
still need to be determined. This can be
determined by using a short circuit with reflection coefficient F = -1 and an open circuit
with reflection coefficient F = +1. In reality the open circuit is a non-perfect precision
standard due to the fringing capacitance, which is a function o f its physical geom etry and
the frequency o f the signal. But, all calibration kits standards now adays use a shielded
open to reduce the variation in capacitance and when this open capacitance is accounted
for the open can be considered as a perfect open with reflection coefficient F = 1.
A pplying these two calibration standards, to equation (5.65) results in:
Hm
E5 - ^DF
; when the short is connected
(5.67)
^
; when the open is connected
l - E SF
(5.68)
1 + E SF
and,
Em = E o - K d f +
Therefore, solving the three equations (5.66-5.68) results in:
2F , - F , - F.
EsF = " ~ t
Fc - Fi-o
.
(5.69)
and,
2
K sf=
f c - r
5
)(r,.-ro)
( 5 .70 )
99
Chapter 5 O ne-Port M easurem ent Set-up an d C alibration
N ow , since all the eixor terms and the m easure reflection coefficient F m are known for
each test frequency, then F a can be com puted as follow s:
r .=
(5,71)
Sim ulated m easurements for a matched load, short circuit, open circuit and a 3dB
attenuator terminated by short circuit have been earned out using a non-ideal multi-probe
reflectometer. The calculation o f the reflection coefficient before error corrections is
earned out on the basis o f the method discussed in section 5.2.1 earlier.
The system enors or parameters have been calculated and the measurements o f the 3dB
attenuator teim inated by a short circuit have been con ected using the m ethod o f one-port
e n o r con ection s as mentioned above. Table 5-3 tabulates these results.
100
C hapter 5 One-Port M easurem ent Set-up and Calibration
C alculated R eflection C oefficient
I
1
Frequency
(GHz)
M atched
Load
S hort circuit
Open
circuit
System E rro rs
DUX Before
DUT A fter
correction
correction
Edf
E sf
E rf
1.00
0.0295Z-110.6°
0.968Z-179.8°
0.911Z-0.64°
0.486Z178.0°
0.5011Z157.4°
0.0295Z-110.6°
0.030Z131.6°
0.940Z-0.16°
1.05
0.0295Z-113.2“
0.960Z174.3°
0.913Z-6.5°
0.484Z176.2°
0.5011Z156.2°
0.0295Z-113.2°
0.029Z129.0°
0.939Z-6.1°
1.10
0.0294Z-115.9°
0.963Z168.4°
0.916Z-12.4°
0.482Z170.3°
0.501 lZ 155.r
0.0294Z-115.9°
0.029Z126.4°
0.939Z-12.0°
1.15
0.0293Z-118.9
0.960Z162.4
0.918Z-18.3°
0.481Z164.4°
0.5011Z154.0“
0.0293Z-118.9°
0.029Z123.7°
0.939Z-17.9°
1.20
0.0293Z-121.2°
0.956Z156.5°
0 .9 2 1 Z -2 4 y
0.478Z158.5°
0.5010Z152.8°
0.0293Z-121.2°
0.029Z121.0°
0.939Z-23.8°
1.25
0.0292Z-124.0°
0.953Z150.5°
0.923Z-30.1°
0.476Z152.6°
0.5010Z151.7°
0.0292Z-124.0°
0.029<118.3°
0.939Z-29.7°
1.30
0.0291Z-126.7
0.951Z144.6°
0.923Z-36.0“
0.474Z146.6°
0.5010Z150.6°
0.0291Z-126.7°
0.029Z115.5°
0.939Z-35.6°
1.35
0.0290Z-129.5
0.947Z138.6
0.923Z-41.9°
0.472Z140.7°
0.5010Z149.4°
0.0290Z-129.5°
0.029Z112.7°
0.938Z-41.6°
1.40
0.0288Z-132.3
0.944Z132.7
0.931Z-47.7°
0.470Z134.8°
0.5010Z148.3°
0.0288Z-132.3°
0.029Z109.9°
0.938Z-47.5°
1.45
0.0287Z-135.1
0.941Z126.7
0.933Z-53.6°
0.468Z128.8°
0.5010Z147.2°
0.0287Z-135.1°
0.029Z107.1°
0.938Z-53.4°
1.50
0.0285Z-138.0
0.938Z120.7
0.936Z-59.5°
0.467Z122.8°
0.5010Z146.1°
0.0285Z-138.0°
0.029Z104.2°
0.938Z-59.4°
Table 5-3: Reflection coefficient and e rro r correction param eters from sim ulated data of the M ulti-Probe Reflectometer
101
Chapter 5 One-Port Measurement Set-up and Calibration
The length o f the attenuator was 5.1m m , which is equivalent to an electrical length of
= — . This means that there will be a phase delay o f =1.13
16
O
for every 0.05 GHz, the
maximum phase delay in the frequency band o f IGHz to 1.5GHz is 11.3°, which agrees
with the calculation from Table 5.3 above.
The data has been plotted in Smith chart representation before system error correction
being applied as shown in Figure 5-17 and after system error being implemented as
shown in Figure 5-18.
3dB Attenuator Before Error Correction!
3dB Attenuator After Error Correction
Figure 5-17: Simulated results before error
corrections applied
Figure 5-18: Simulated results after error
corrections applied
Figure 5-19 shows the magnitude simulated results o f the return loss for the a 3dB
attenuator terminated by a short circuit before and after error corrections.
102
Chapter 5 One-Port Measurement Set-up and Calibration
3 d B A t t e n u a t o r t e r m i n a t e d by s h o r t c i r c u i t d e v i c e
8.0
7.5
CO
xy
I
E
2
0)
cc
5.0
4 5
4.0
1.0
1 ,1
1. 2
1.3
14
1.5
F r e q u e n c y (GHz)
Figure 5-19: 3dB Attenuator before and after corrections
5.5
C onclusion
This chapter described the techniques for calibration o f a practical one-port multi-probe
reflectometer. Tw o algorithms for calibrating the multi-probe reflectometer have been
derived. Simulation data and practical results have been calculated using the new
algorithms. One-port error corrections have been discussed and applied to the multi-probe
reflectometer.
103
Chapter 6 T w o-Port M u lti-Probe M easurem ent System
Chapter 6
6 Two-Port
Multi-Probe
Measurement
System
6.1 Introduction
M icrow ave devices can be classified as one-port, two-port, or N-port networks. The
majority o f circuits under analysis are two-port networks. H aving discussed a one-port
measurement system in the previous chapter, this chapter w ill focus primarily on two-port
network characterisation and the possibility o f designing a low cost, reliable two-port
measurement system
based on
the sam e principles as the one-port multi-probe
measurement system . This system is investigated as a prospective reliable and econom ical
rival to current com m ercial network analysers.
A two-port measurement system based on using six-port or multi-probe reflectom eters
has been discussed by a number o f researchers [3,83-85]. The system discussed in this
chapter is based on using the microstrip multi-probe technique. The system is capable o f
performing the full two-port measurement; forward return loss S n , reverse return loss S.2 2 ,
forward transmission S 2 1 and reverse transmission S 1 2 .
6.2 System Description
A s has been discussed in Chapter 4, the multi-probe reflectom eter can consist o f a
microstrip line with surface mount diode detectors and passive com ponents. The
standing-wave voltages are sam pled along the transmission line at certain positions with
known intervals by voltage detectors. From these voltages the required measurements o f
an unknown load can be found. The two-port multi-probe system basically consists o f two
one-port reflectom eters where the RF pow er input is connected through a m icrowave
switch. Figure 6-1 show s the block diagram o f the two-port m easurem ent system .
104
C hapter 6 T w o-Port M ulti-Probe M easurem ent System
PC
G PI B
Signal
G enerator
R F O utput
Data A c q u i s t io n
Uni t
Two-Port
Multl-probe
Reflectometer
Figure 6-1: Tw o-Port m easurem ent system
As m entioned earlier in Chapter 4, the signal generator can be any standard signal
generator, which covers the required frequency range, (A gilent 83623B or E 4433B is
used here). The data acquisition unit is capable o f converting a low amplitude analogue
voltage into a digital readout, (A gilent 34970A with H P 34901A was used in this system ).
6.2.1 Two-Port Multi-Probe Reflectometer
The two-port multi-probe reflectom eter is basically a pair one-port microstrip multi-probe
reflectometers. The values o f the surface mounts com ponents used in the one-port
reflectom eter are kept the same. Figure 6-2 show s the block diagram o f the two-port
multi-probe reflectom eter and Figure 6-3
show s the actual two-port multi-probe
reflectometer.
105
Chapter 6 Two-Port Multi-Probe Measurement System
Voltage
Detection
Probe
voltage
Detection
Probe
Voltage
Detection
Probe
Micro#trip Line
S ig n a l
G e n e ra to r
Microwave
Switch
D lJT
1
L
Mlcroatrlp Line
eqojd
uogoeiea
eOetiOA
eqoJd
uouoeiea
eSstioA
eqoJd
uojioeiea
eSeiiOA
Figure 6-2; Full-Port multi-probe reflectometer
Figure 6-3: Actual two-port multi-probe reflectometer
The m icrowave switch is chosen to be a non-reflective single pole double throw (SPDT)
switch. Hittite model number H M C270M S8G. The frequency o f operation o f the switch
is between DC to 8GHz, the switch isolation can vary from 33dB up to 48dB depending
on the frequency and it has a return loss between OdB and 14dB [86].
The switch needs to be a non-reflective one so that the other unused port o f the m ulti­
probe reflectometer is terminated by a load o f 50^2. i.e. when the S ,,
and
measurements being performed, the internal matched load o f the switch will terminate the
106
Chapter 6 Two-Port Multi-Probe Measurement System
S 22 port and when S 22 and S 12 measurements are being carried out the S ,, port will be
terminated by the internal matched load o f the switch. Figure 6-4 show s the internal
connections o f the switch.
The insertion loss o f the switch varies between 1.2dB to 2.4dB depending on the
operating frequency. The insertion loss is defined as the maximum loss measured in a
50S2 system when only a single port o f the switch is in the ON state.
The isolation o f the switch can be defined as the ratio o f the power level when the switch
port is ON to the power level measured when the switch port is OFF. The switch can be
controlled by +5V and - 5 V DC voltages.
+5V DC
I -5V DC
RF Comm on
Figure 6-4: Non-reflective switch
The system was designed to be fully automated using the same principle o f the one-port
measurement system. Lab view software was used to control the instruments while
calculations was carried out by using MatLab software. Refer to Appendix C for full
programmes.
6.3
Tw o-Port N etw ork S-Param eters
The two-port m icrowave network can be characterised in terms o f its S-parameters, where
they are based on the concept o f travelling waves. The scattered w aves, which are known
as the reflected and the transmitted wave amplitudes, are linearly related to the incident
wave amplitude. The matrix describing this linear relationship is called the scattering
matrix or [S].
107
Chapter 6 Two-Port Multi-Probe Measurement System
To characterise a two-port network that has an identical characteristic impedance Zo at
both the input and output ports, consider the incident and reflected voltage waves at each
port as shown in Figure 6-5 below:
v;
P or t 1
Zg
Tw o-Port
Network
[S]
— W lA ;
Zg
P or t 2
AAAAv— ^ ^ 2Figure 6-5: Definition of incident and reflected wave of a two-port network
These incident and reflected waves on the and from the two-port network can be
represented as a signal flow graph as shown in Figure 6-6.
22
Figure 6-6: Two-port network flow graph
Each port o f the m icrowave network has two nodes, a-node and 6-node, where
, is
defined as the wave entering port i and V,” is defined as the w ave reflected from port i.
Each node will have branches, where every branch has an associated S parameter or
reflection coefficient.
When a wave with amplitude y / incident at port 1, it will be split into parts, one part
travels through S |, and other part com bined with a reflected signal travel through
to
node b 2, where it will goes out o f b 2 as V2 . If a load with nonzero reflection coefficient
108
C hapter 6 Tw o-Port M ulti-Probe M easurem ent System
is connected at port
2
, the w ave w ill be partially reflected and re-enter the two-port
network at node a2 , where part o f this w ave can be reflected back out o f port
the other part can be transmitted out o f port
2
via S 2 2 and
through S 2 1 .
1
N ow the scattering matrix [S] can be derived from the incident and reflected w aves at
each port. At node b, and node b 2 , the total voltages can be represented as:
(6 . 1)
^ 2"
=
+
^
22
^ 2"
(6 .2 )
or, in matrix form,
■^11 ‘^12 V
.*^21 ^ _ X.
(6.3)
22
Each elem ent o f the [S] matrix can be defined as:
.V
;Input reflection coefficient when output port is terminated by a matched load
( 6 .4 )
; Forward transmission when output port is terminated by a matched load
( 6 .5 )
; Reverse transmission when input port is terminated by a matched load
( 6 .6 )
; Output reflection coefficient when input port is terminated by a matched load
( 6 .7 )
Vf=0
■^22
“
5 :
^ 2"
V f= 0
109
Chapter 6 Two-Port Multi-Probe Measurement System
6.3.1 Shifting Reference Plane
The S-parameters relate the magnitude and phase o f travelling w aves that are incident on,
reflected from and transmitted through a network port. Therefore, the location o f the
reference plane must be precisely known in order to measure the exact phase o f the Sparameters.
Consider a two-port network in which the reference plane at port 1 has m oved a distance
l\ to port T. Similarly, the reference plane at port 2 has m oved a distance h to port 2' as
shown in Figure 6-7.
,
/,
2
i
Two-Port
Network
[S]
Port 1 '
Port 1
Port 2
Port 2'
Figure 6-7: Shifting reference plane
Then, the terms o f the incident and reflected port voltages can be expressed as:
( 6 .8 )
V 'J = v r e ~ -'^ ‘ ;i = l,2
Where, Oi =
(6.9)
, is the electrical length corresponding to the reference plane shift at
each port.
The shifted S'-parameters can be represented as:
110
C hapter 6 T w o-Port M ulti-Probe M easurem ent System
V 't
(6 .10)
7 2 .
Therefore, in general:
(6 .11)
(6 .12)
Equation (6.11) show s that the phase o f Su is shifted tw ice the electrical length o f the shift
in terminal plane; this is due to the w ave travel tw ice over this length upon incidence and
reflection.
6.4 Principle of Operation of the Two-Port Multi-Probe Reflectometer
A two-port multi-probe reflectom eter needs to measure the full S-parameters o f a twoport network; input port reflection coefficient, forward transmission coefficient, reverse
transmission coefficient and output port reflection coefficient. The principle o f the
m easurement o f these S-parameters is basically to measure the probe output voltages on
both sides o f the D U T and to sw itch the stimulus signal from port 1 to port 2.
The full S-parameters need to be measured in terms o f both magnitude and phase. To
calculate the phase o f the device, a standing w ave has to be present for the microstrip
multi-probe reflectom eter to measure. The standing w ave can only be created if part o f
the incident signal gets reflected where it w ill meet up with the original incident signal
and they get added or subtracted according to the phase o f both o f them.
If no standing w ave is present on the microstrip line, attenuation measurem ents can still
be performed in terms o f magnitude only. In this case the multi-probe reflectom eter is
known as a scalar network analyser.
Ill
C hapter 6 T w o-Port M ulti-Probe M easurem ent System
6.4.1 Multi-Probe Scalar Network Analyser
The multi-probe scalar network analyser is capable o f performing transmission coefficient
magnitude only without the phase. W hen the source signal is passing through multi-probe
reflectom eter number one to a two-port device, which is connected between the two
multi-probe reflectom eters, as shown earlier in Figure 6-2, the forward transmission
coefficient S 2 1 can be measured. H ow ever, the other end o f multi-probe reflectom eter
number tw o w ill be matched by the internal 50Q load o f the switch.
Therefore, there w ill be no standing w ave present in the microstrip line o f multi-probe 2
as the incident signal w ill be absorbed by the termination load, and only a magnitude
measurement o f S 2 1 can be performed. The sam e thing w ill happened in the case o f
measuring the reverse transmission coefficient S 1 2 . This is probably w hy little appears to
have been published so far on a two-port multi-probe system . Therefore, the airangement
presented in Figure 6-2 can be seen as a scalar network analyser in terms o f measuring the
forward and reverse transmissions.
6.4.2 Multi-Probe Vector Network Analyser
A multi-probe vector network analyser w ould be capable o f performing the full
measurement terms in both magnitude and phase. There are tw o m ethods to overcom e the
measurement phase o f the transmission coefficients problem discussed in section 6.4.1. If
either o f these m ethods can be made to work then the two-port multi-probe reflectom eter
can be used as a proper two-port vector network analyser.
Firstly, a standing w ave could be created by deliberately m ism atching the output multi­
probe reflectometer. This m ethod w ill make the process o f finding the system parameters
more com plicated as there w ill be more unknowns, which need to be found in order to
characterise the system . H ence, more calibration standards w ill be needed which makes
the calibration process lengthy and vulnerable to errors.
Secondly, a new method presented here for the first time, is to split the incident signal
through a pow er splitter and inject part o f the incident signal to the other end o f the output
112
Chapter 6 Two-Port Multi-Probe Measurement System
multi-probe reflectometer through a non-reflective single pole single throw switch (SPST)
and a circulator. Figure 6-8 illustrates this technique.
VolUs>
Switchi
(SPST)
Non RefkcUve
Vonaoi
Mlcrostrlp Line
v f\
signal /
DUT
G e n e ra to r^
Swltch2
(SPST)
Non-Reflective
C iio u la to r
Microstrip Line
Figure 6-8: Two-port multi-probe vector network analyser
W hen S || measurement is performed, sw itchi will be closed which allow s part A o f the
incident signal to travel to multi-probe 1 and sw itch ! will be open and switched to the
termination position which will block part B o f the incident signal to travel to multi­
probe!. The versa-visa operation happened when
measurement is performed.
When S 21 measurement is performed both switches are closed where part A o f the
incident signal will travel through the D U T and the emerging signal from port ! o f the
D U T will be acting as the incident signal on the second multi-probe reflectometer. Part B
o f the incident signal goes to the circulator input, where it will be passed through a one­
way system to the other end o f the second multi-probe reflectometer. This signal will be
seen by the second multi-probe reflectometer as a reflected signal where it will meets up
with part A o f the signal to form a standing wave on the microstrip line o f the second
multi-probe reflectometer. This “reflection coefficient” is actually ^ / a ,, yielding
113
Chapter 6 Two-Port Multi-Probe Measurement System
magnitude and phase. The versa-visa operation happened when S 12 measurement is
performed.
In a special case, when the forward transmission coefficient
or the reverse
transmission coefficient S 12 can be measured by physically reversing the two-port
network D U T, a much simpler technique can be used as illustrated in Figure 6-9.
Power
Signal
Generator
Voltage
Detection
Probe
Voltage ^
Detection ^
Probe ^
Voltage
Detection
Probe
M lcrostrlp Line
Figure 6-9: Simplified two-port multi-probe vector network analyser
The measurements carried out using the vector network analysers can be classified into
two main measurement groups; reflection coefficients measurements and attenuation
measurements.
6.4.3 Reflection Coefficient Measurements
The input port reflection coefficient o f a two-port network can be defined as Tin, while
the output port reflection coefficient can be defined as Tout- Figure 6-10 illustrates a flow
graph o f a two-port device connected by the multi-probe reflectometer. The principle
measurements using the one-port multi-probe reflectometer as have been discussed earlier
in Chapter 5 can be used to measure the input port reflection coefficient and the output
port reflection coefficient, using the one-port error correction method to eliminate the
measurement errors.
114
Chapter 6 Two-Port Multi-Probe Measurement System
22
12
out
Figure 6-10: Flow graph of two-port device connected through reflectometer
In Figure 6-10 Fs represents the source reflection coefficient (or in other word the
reflection coefficient o f the multi-probe reflectometer connecting to the input port o f the
DU T), while F l
represents the output reflection coefficient o f the multi-probe
reflectometer connected to the output port o f the DU T, which is acting as a termination
load to the two-port DUT.
After using the signal flow graph reduction techniques, the flow graph in Figure 6-10 can
be sim plified to give the follow ing results:
(6 J 3 )
^ l2 ^
2
lC s
(6.14)
Therefore, it can be seen that if the multi-probe reflectometer is matched at both ends o f
the input and output ports, Fs = E l = 0. The input and output reflection coefficients will
be:
—
— >i l ri . =o
r
— Ç
Lout
ii2 2 |r j = o
(6.15)
(6.16)
115
C hapter 6 T w o-Port M ulti-Probe M easurem ent System
6.4.4 Attenuation Measurements
Attenuation can be defined as the amount o f reduction in the pow er transmitted from one
port o f the device to the other port o f the device when both ports are com pletely matched.
W hen a source generator with reflection coefficient, Fs, is connected directly to a load
with reflection coefficient, F l, let the pow er dissipated by the load to be P i. N ow , when a
two-port network device is connected between the source generator and the load, let the
pow er dissipated in the load to be ? 2 . Therefore, the insertion loss or the attenuation o f
this two-port network can be expressed as:
a = lQ ^ L o g
dB
(6.15)
k Pi j
B y using again the flow graph reduction rules [1, 72,75], the flow graph in Figure 6-10
can be reduced to get the expression:
A ssum ing the characteristic im pedance o f the load to be Z q, then the power incident on
the load and the pow er reflected from the load are:
k i'
Pl,^ = - — —
;Power incident
(6.17)
; Power reflected
(6.18)
^ 0
I
|2
=
^ 0
Therefore, the pow er dissipated in the load, P 2 , will be:
|2
(619)
0
Then, substituting (6.19) into (6.16) gives:
116
C hapter 6 T w o-Port M ulti-Probe M easurem ent System
Po =
(6.20)
Zq
+r^5'22 + r 5 5'2 ir^ 5 'i2 |
N ow , when the source generator is connected directly to the load, the pow er dissipated in
the load is P i, and by assum ing the S-parameters to be S u = S 2 2 = 0 and S 2 1 = S 1 2 = 1,
then by using the terms in (6 .2 0 ), ? i w ill be:
05.21)
P =
z „ * |i- r c r j '
Therefore, inserting (6.20) and (6.21) into (6.15) results in:
a = 10* Log
|i + r ^ 5 ' i i r ^ 5 ' 2 2
+ r ^ > s '2 2 + r ^ * s '2 ir ^ L *^i2)|
dB
(6.22)
A ll o f these variables are com plex quantities. In the special case when the two-port D U T
is perfectly matched by the source generator and the load. Es = F l =
0
, the attenuation
w ill be:
c
a,n = 1 0 * L o g ^
\
J_
dB
(6.23)
>2l|
In a more general form, the attenuation can be separated into tw o com ponents, reflected
power and dissipation power:
a — (x^ T
(6.24)
Where,
oCr is the reflected com ponent o f the power
Od is the dissipated com ponent o f the power
117
C h apter 6 T w o-Port M ulti-Probe M easurem ent System
B y letting:
Pi = Incident pow er upon two-port device.
P r = reflected pow er by from two-port device.
P l = D issipation pow er in the m atched load.
Then, the attenuation com ponents are given by:
=
1 0
*L o^
% =
1 0
* lo g ,
05.25)
(6.26)
V
Pl
or, in the case when source generator and load are matched:
(6.27)
D -P s il
0^28)
Then, (6.25) and (6.26) can be expressed as:
or,. = 1 0 * L o g
05.29)
= 1 0 * L og
Then, by adding (6.29) and (6.30) w ill prove the results shown earlier in (6.23)
6.5
Attenuation Error Measurement
Practical attenuation measurement can involve some eiTors. These eiTors can be classified
into two main enors, a mismatch enor and a leakage eiTor.
118
C hapter 6 T w o-Port M ulti-Probe M easurem ent System
6.5.1 Mismatch Error
If the attenuation measurement is earned out when the source generator and the load are
not perfectly matched there w ill be a measurement enor, this e n o r is known as a
mismatch error and can be represented as:
M = a-a„^
(6.31)
or, in other representation from (6.22) and (6.23) [1]:
M = 1 0 * L og
|i+ r ^ 5 ;ir ^ 5 '2 2
/T-.n
. r,
r. m
+F£^5'22+T5;5'2ir^5'i2)|
2
L\
The uncertainty in the attenuation measurements can lie within the lim its of:
1 ± |r^
^
ir^5'221 i
Limit - 2 0 * L o g
>Si 11± |r^»s'221 ±
‘^2iFz,5' 1 2
0133)
6.5.2 Leakage Error
The other type o f error is leakage enor, where part o f the signal w ill not travel through
the proper channel o f the attenuator path, but instead w ill travel though a leakage path
shunting the attenuator. If
is the amount o f the attenuation in dB through an attenuator
under test and «L is the leakage attenuation in dB through an external path, then the actual
measured attenuation w ill be:
a = a ^ -a i^
(6.34)
The attenuation measurement error « l due to leakage w ill be within the lim its given in
equation (6.33) and normally very sm all compared to amount o f attenuation
and can
be normally 0.00125% o f the actual measured attenuation [1], hence it might be
negligible.
119
C hapter 6 T w o-Port M u lti-Probe M easurem ent System
6.6 Calibration Procedure and Error Corrections
A calibration procedure for the two-port multi-probe reflectom eter needs to be performed
before any real measurements can be earned out in order to rem ove the system enors by
finding the system parameters. Calibration can be earned out using the same principle
used in the commercial network analysers [33,87-92]. It can be performed by using Line,
R eflection, Match, (LRM ) techniques, or it can be performed by using short circuit, open
circuit, matched load, and through connections (SOLT).
In the special case o f the sim plified multi-probe vector network analyser illustrated in
Figure 6-9 earlier, the calibration can be done as follow s:
1. Calibrating port D by using open circuit, short circuit and matched load as for the
one-port m easurement system , w hile port C is terminated by a matched load all
the time.
2. Performing a thru response calibration by connecting port B directly to port D
through a short cable. This cable w ill be used in the D U T measurement.
The error m odel o f the two-port network measurement system can be divided into two
eiTor m odels, a forward en o r m odel and a reverse error m odel. T hese eiTor m odels are
more com plicated than the one-port measurement system as the two-port measurement
system provides more measurement functions such as the transmission coefficients in
terms o f m agnitude and phase. H ow ever, these additional e n o r terms can be derived in a
similar manner to that described in the one-port en or con ection in the previous chapter.
The major sources o f en o r can be classified as:
•
Frequency response (tracking)
•
Source match
•
Load match
•
Isolation
120
Chapter 6 Tw o-Port M u lti-Probe M easurem ent System
These enors can be effectively rem oved by perfonning a full two-port calibration and
hence the two-port error model terms can be determined.
The transmission coefficient is measured by taking the ratio o f the transmitted signal V t
to the incident signal Vi, where ideally V, consists only o f the pow er delivered by the
source at the input port o f the D U T and V t consists only o f the pow er em erging at the
D U T output port as illustrated in Figure 6-11. This m eans in the ideal situation when the
two-port D U T is perfectly matched at both ports, the transmission coefficients can be
represented as:
12\A
Forward Transm ission
(6 3 5 )
Reverse Transm ission
06 3 5 )
'-TF
'- \2 M
-12A
‘-TR
Where;
S21A
Actual forward transmission
S i2 A
Actual reverse transmission
S21M
M easured forward transmission
S i2 M
M easured reverse transmission
E tf
Forward transm ission tracking
E tr
R everse transmission tracking
V,
Vt
^TF
F or war d
Reverse
S12
Vt
^TR
V|
Figure 6-11: T ransm ission coefficients
121
Chapter 6 Two-Port Multi-Probe Measurement System
The transmission tracking terms
E
tf
and
E
tr,
can be measured when a through
connection is made between the S | , and S 22 ports, but to determine the actual transmission
coefficients other terms have to be included from the source match and the isolation
measurements.
The source match can cause the incident signal to vary as a function o f the D U T input
reflection coefficient Sha- As the transmission return port is never perfectly matched to
the characteristic impedance o f the multi-probe reflectometers, som e o f the transmitted
signal will be reflected at port 2. This reflection will effect the measurement o f S 21M or
part o f the signal will be transmitted through the device in the reverse direction to appear
at port 1, which affects the measurement value o f Sum- This means that a new error term
can be introduced, which causes the transmitted signal to vary as a function o f S 22A and
this term is called load match
(E
l f ).
Figure 6-12 shows a flow graph o f this error.
Porti
Ror12
DUT
Figure 6-12: Load match error flow graph
It can be seen from the flow graph that the measured forward transmission coefficient,
&IM, consists o f signal components that vary as a function o f the relationship between the
source match error, Esf, and the actual measured S,iA o f the DU T. The input and output
reflection coefficients o f the two-port D U T must be measured and stored, as it will be
used in the S21A error corrections.
The directivity error term, Edf, and the source match error, Esf, together with the
reflection frequency response error.
E
rf,
can be found using the same principle described
122
Chapter 6 Two-Port Multi-Probe Measurement System
previously in the one-port measurement system error correction, using a matched load,
short circuit and an open circuit.
After calibrating the measurement system ports for reflection measurements, the through
measurement can be made and the load match. E lf, will be determined by measuring the
reflection coefficients o f the through connection. Then, the transmission signal path
frequency response,
E
tf,
is measured and corrected for the source and the load match
effects.
The last step o f the calibration is the isolation measurements in order to find the cross talk
or the leakage from port 1 to port 2 o f the DUT, where part o f the incident signal at port 1
o f the DU T may be presented at port 2 o f the D U T without actually passing through the
DUT. Isolation is done by placing a matched load at the test port o f each o f the multi­
probe reflectometer and these terms can be represented as E xf and E xr for forward and
reverse isolation respectively. Figure 6-13 shows a flow graph o f this situation.
— 11
— 12
DUT
Porti
Porta
Figure 6-13: Isolation error flow graph
As m entioned earlier, there are two sets o f errors, forward and reverse, and each set
consists o f six error terms. These errors are tabulated in Table 6-1.
123
Chapter 6 Two-Port Multi-Probe Measurement System
Error
Forward
Reverse
Directivity
E df
E dr
Isolation
E xf
E xr
Source Match
E sf
E sr
Load Match
E lf
E lr
Transmission Tracking
E tf
E tr
Reflection Tracking
E rf
E rr
Table 6-1: 12 error terms of a two-port system
In a conventional network analyser, an S-parameter test set can measure the forward and
the reverse characteristics o f the two-port D U T without the need for the D U T to be
manually removed and physically reversed. With these test sets, the full two-port error
model effectively removes both forward and reverse error terms for both transmission and
reflection measurements. These errors are illustrated in the flow graph in Figure 6-14.
RF in
—TF
— 11M
— 11A
F orward
Error
Model
CM
DUT
Reverse
Error
Model
—TR
RF in
Figure 6-14: Two-port flow graph with 12 erro r terms
124
C hapter 6 T w o-Port M ulti-Probe M easurem ent System
B y using flow graph reduction techniques [89,93], the forward flow graph yields
measurements o f the measured input reflection coefficient. Sum, and the measured
forward transmission eoefficient S 2 1 M as follow s:
§-\\M ~
^21M -
K l F^§-
^ —{ K d f ’^ E . r f Y
Ho
^ ~ { K xF
K tf)’
(6.37)
1 K sf^ w
K l f ^ i i '^ ^ S f S-LF^^.
These tw o equations contain all four actual S-parameters o f the two-port D U T and the six
forward error terms.
B y using the sam e techniques on the reverse flow graph, the m easured output reflection
coefficient, S 2 2 M, and the measured reverse transmission coefficient, S 1 2 M, can be found to
be:
^22M ~
§-\2M -
b'
^ —{ K d r ' ^ K r r )'
H3
b\
^ ~ { K xR ^ K
^22A
K lR ^ ^
K sR^\[
K lR^22'^ ^ S r E-LR^^J
K sR ^n
K lR ^ 2 2 ^ ^ S R ^ L R ^ ^ J
'-\2A
trY
(6.38)
(6.39)
These two equations contain all four actual S-parameters o f the two-port D U T and the six
reverse error terms. Therefore, the forward and reverse equations com bine to give four
125
C h apter 6 T w o-Port M ulti-Probe M easurem ent System
equations containing the actual S-parameters o f the two-port D U T and the 12 error terms.
If the 12 error terms are known, these four equations can be solved for the actual Sparameters o f the two-port D U T as follow s [88,92]:
Ü 11M
!= L D F
1+
122M
^2\M ^XF
i=2DR
Ç
_ /T
^ \2 M
& -X R
^
E .L F
(6.40)
D
'-22M
i^DR
1
+1
'-2 1 M
IE,
K L xX f
i=
F
^\2M
K
Kx
y
tr
(6.41)
D
§ -2 lM
^ X F
1+
___
{ K sr
K rr
K tf
K
l f
)
y
(6.42)
D
(6.43)
S t-}A —
D
where.
D
1+
LllM
Knr
i^DF
\
1+
§-22M
^DR
1
-
K sr
y
^21M
^XF
'-12M
i^XR
E,„E,
J
One can see that for each o f the actual S-parameters calculated, it requires measuring all
four S-parameters as w ell as know ing the
1 2
en o r terms.
126
C hapter 6 T w o-Port M ulti-Probe M easurem ent System
The determination o f the 12 eiTor terms can be sim plified in three steps, having solved for
the
6
6
error terms in the forward direction, the sam e procedure can be used to solve for the
error terms in the reverse direction. Solving for the forward direction is achieved as
follow s:
1. A one-port calibration is perfonned using a m atched load, a short circuit and an
open circuit. This w ill determine the directivity,
E
d f,
source match,
E
sf,
and
reflection tracking E rf e n o r terms.
2. The leakage or crosstalk is measured by placing matched loads on each o f the test
ports. This w ill determine the leakage error,
E
x f-
3. Test port 1 and test port 2 are connected together, which is known as the through
connection. This w ill deteim ine the remaining tw o error terms, load match, E, p.
and the transmission tracking,
The load match error ,
E
lf,
E
tf-
and the leakage eiTor,
E
xf,
can be found by sim plifying the
flow graph in Figure 6-14, in the case when the two ports are com pletely matched, where
S ii = S 2 2 =0 and
8 2 1
= S 1 2 =1. This results in:
= P
, f f
A.RF
_
EldF^—SF
(6-44)
(6.45)
1
£lsF^LF
In addition to the eiTors removed by accuracy enhancement, other systematic eiTors exist
due to limitations of dynamic accuracy, microwave switch repeatability, eiTors in the
definition of the short and open circuits, test cable stability. These errors are combined
together with random errors to give the total system measurement uncertainty.
127
Chapter 6 Two-Port Multi-Probe Measurement System
6.7 Scalar Network Analyser Results
The design configuration illustrated in Figure 6-2 earlier is a two-port multi-probe scalar
analyser. It is capable o f measuring the input and output reflection coefficients in terms of
magnitude and phase, but for the reasons mentioned earlier, it is capable of performing
forward and reverse transmission measurements only in terms o f magnitude.
If the two-port D U T is com pletely reciprocal, such as an attenuator, the transmission
coefficients,
and S 12, can be measured by using the one-port multi-probe reflectometer
with the DUT is terminated with a short circuit [85]. Simulation and practical results have
been shown in the previous chapter. However, such a system is o f limited interest.
Simulations have been carried out o f measuring various devices by using the two-port
multi-probe scalar analyser. The calibration method described previously in section 6.6
has been used to correct the system. Figures (6.15 -6 .2 0 ) show the calculated results. For
all these results, the multi-probe system is m odelled on A D S, and simulated detector
voltages are manually entered into the MatLab and Lab V iew programmes. Note that ADS
simulation does not include noise.
S im u la tio n
o f v a rio u s a tte n u a to rs b e fo re a n d a fte r c a lib ra tio n
24
27
30
33
F re q u e n c y (GHz)
Figure 6-15: Attenuation calculation of various simulated attenuators
128
Chapter 6 Two-Port Multi-Probe Measurement System
Simulation gain of various amplifiers before and after calibration
35
30
25
m 20
*o
c
(0
O
•
•
1
2
3
4
5
3 0 d B U n c a lib
3 0 d B C a lib r a
6
F r e q u e n c y (GH z)
Figure 6-16: Gain calculation of various simulated amplifiers
Band-Pass filter before and after calibration
U ncaH txated trac >is u n d e rn e a th
C a litx a te d tr a c e
-50
■O
-1 0 0
3
-150
-200
-250
F re q u e n cy (GHz)
Figure 6-17: Simulation data of a Band-Pass Filter with IdB insertion loss
129
Chapter 6 Two-Port Multi-Probe Measurement System
Stop-Band Filter before and after calibration
-50
U ncalibrated tract is u n d e rn ea th
C a litra te d tra c e
-100
-150
-200
-250
-300
Frequency (GHz)
Figure 6-18; Stop-Band filter with IdB insertion loss
L o w -P a ss F ile te r b e fo re and a fte r ca lib ra tio n
-20
-40
-60
-80
-100
F r e q u e n c y (GHz)
Figure 6-19: Low-Pass filter with IdB insertion loss
130
Chapter 6 Two-Port Multi-Probe Measurement System
H ig h _ p a s s filter b e fo re an d after ca lib ra tio n
-50
S
-100
-2 0 0
-250
F r e q u e n c y (GHz)
Figure 6-20: High-Pass filter with IdB insertion loss
Table 6-2 shows the forward error terms for the simulation data o f the lOdB attenuator
taken using the two-port multi-probe scalar analyser. The reverse error terms are identical
to the forward ones as the device is reciprocal and the two one-port multi-probe
reflectometers are identical.
131
Chapter 6 Two-Port M ulti-Probe M easurement System
Freq.
EuF
E sf
E rf
E lF
SllM
Iv
1
|^2 m | |H2m1
(dB)
(GHz)
0.0295Z-110.6
0.030Z131.5
0.940Z-0.16
1.25
0.0291Z-123.9
0.030Z117.9
1.50
0.0285Z-138.0
0.029Z103.9
1.00
ttM
«A
(dB)
10.54
10.00
0.316
10.54
10.00
0.316
10.55
10.00
0.0295Z131.6
0.0283Z-115.6
0.939
0.297
0.316
0.939Z-29.71
0.0292Z118.3
0.0269Z-127.1
0.938
0.297
0.938Z-59.33
0.0285Z104.2
0.0258Z-138.3
0.937
0.297
1.75
0.0275Z-152.7
0.027Z89.5
0.938Z-89.96
0.0275Z89.5
0.0253Z-150.1
0.936
0.296
0.316
10.56
10.00
2.00
0.0263Z-168.2
0.026Z74.0
0.936Z-118.8
0.0263Z74.1
0.0250Z-163.4
0.935
0.296
0.316
10.57
10.00
2.25
0.0248Z175.9
0.025Z57.7
0.935Z-148.6
0.0248Z58.1
0.0247Z-178.8
0.935
0.296
0.316
10.57
10.00
2.50
0.0231Z159.4
0.023Z41.2
0.935Z-178.4
0.0231Z41.6
0.0241Z164.0
0.935
0.296
0.316
10.57
10.00
2.75
0.0212Z142.9
0.021Z24.2
0.934Z151.7
0.0212Z25.1
0.0229Z145.6
0.934
0.295
0.316
10.58
10.00
3.00
0.0192Z126.5
0.019Z6.36
0.934Z121.68"
0.0193Z8.6
0.0210Z126.8“
0.934
0.295
0.316
10.59
10.00
3.25
0.0172Z110.7
0.017Z-4.8
0.933Z91.5
0.0172Z-7.1
0.0187Z108.5
0.933
0.295
0.316
10.59
10.00
3.50
0.0151Z96.11
0.015Z-20.0
0.932Z61.40
0.0151Z-21.6
0.0159Z91.9
0.933
0.295
0.316
10.60
10.00
3.75
0.0130Z83.47
0.013Z-33.8
0.932Z31.22
0.0130Z-34.3
0.0131Z78.2
0.932
0.295
0.316
10.60
10.00
0.0110Z73.7
O.OllZ-42.8
0.932Z0.94
0.0109Z-44.1
0.0105Z68.7
0.932
0.295
0.316
10.61
10.00
4.25
0.0090Z67.8
0.009Z-48.1
0.931Z-29.4
0.0090Z-49.9
0.0083Z64.7
0.931
0.294
0.316
10.61
10.00
4.50
0.0075Z66.8
o.oosz^o.g"
0.931Z-59.9
0.0075Z-51.0
0.0068Z66.5“
0.931
0.294
0.316
10.59
10.00
4.75
0.0066Z70.0
0.007Z-52.51
0.931Z-90.4
0.0066Z-47.7
0.0060Z72.7
0.931
0.294
0.316
10.62
10.00
5.00
0.0061Z75.2
0.007Z-47.9
0.930Z-121.1
0.0061Z-42.6
0.0058Z79.9
0.930
0.294
0.316
10.62
10.00
4.00
5.25
0.0058Z81.0
0.006Z-37.6
0.930Z-151.7
0.0058Z-36.9
0.0058Z86.3
0.930
0.294
0.316
10.63
10.00
5 J0
0.0056Z89.0
0.006Z-30.3
0.930Z177.6
0.0055Z-28.7
0.0058Z93.4
0.930
0.294
0.316
10.63
10.00
Table 6-2: Calculated results o f lOdB attenuator using sim ulated probe voltages (with and w ithout e rro r correction)
132
Chapter 6 T w o-Port M ulti-Probe M easurem ent System
The two-port measurement system described in Figure 6-2 earlier has been characterised
by performing full calibration. The calibration standards used as m entioned earlier are,
m atched load, open circuit, short circuit and a through connection. Tables 6.3 and 6.4
contain the system error terms for m ulti-probel
and m ulti-probe 2
reflectom eters
respectively. The leakage error terms have been neglected and set to zero.
Freq.
E df
E sf
ERF
E lf
S um
1.00
0.063Z99.4
0.084Z-171.1
0.94Z12.10
0.033Z0.75
0.072Z73.9
1.05
0.065Z97.0
0.086Z-167.5
0.93Z 5.51
0.043Z3.21
0.077Z65.9
0.836
1.10
0.066Z94.6
0.083Z-164.3
0.95Z 0.23
0.035Z6.43
0.075Z68.3
0.856
1.15
0 .0 6 8 Z 9 2 .r
0.85Z-161.5
0.96Z-4.62
0.039Z9.54
0.079Z64.0
0.835
(G H z )
0.843
1.20
0.066Z89.7
0.088Z-157.1
0.95Z-10.0
0.036Z12.3
0.076Z62.9
0.820
1.25
0.067Z87.1
0.087Z-153.2
0.94Z-14.8
0.029Z15.2
0.074Z65.5
0.832
1.30
0.070Z84.8
0.086Z-150.3
0.94Z-17.1
0.031Z17.9
0.079Z63.2
0.834
1.35
0.072Z82.2
0.085Z-147.5
0.93Z-23.3
0.034Z20.0
0.081Z59.3
0.855
1.40
0.074Z79.9
0.091Z-143.6
0.92Z-27.4
0.037Z22.7
0.084Z56.2
0.842
1.45
0.072Z76.4
0.092Z-140.0
0.95Z-31.2
0.035Z25.1
0.083Z53.0
0.812
1.50
0.075Z73.9
0.093Z-137.2
0.94Z-36.5
0.038Z27.8
0.087Z49.9
0.827
Table 6-3: Calculated forward error terms of the practical two-port multi-probe scalar analyser
Freq.
E
dr
E
sr
E
rr
E
lr
S 22M
K l
(G H z )
1.00
0.059Z75.2
0.081Z-155.3
1.05
0.061Z73.1
1.10
0.063Z70.3
1.15
0.066Z47.7
0.862
0.96Z0.50
0.032Z-15.6
0.083Z -152.4
0.95Z -3.2
0.035Z-12.3
0.070Z44.9
0.853
0.082Z -147.5
0.95Z -6.4
0.031Z-9.42
0.071Z46.0
0.846
0.061Z68.2
0.084Z-144.5
0.96Z-9.5
0.034Z-6.28
0.072Z41.5
0.858
1.20
0.058Z65.7
0.086Z-142.1
0.97Z-14.0
0.035Z-3.82
0.070Z37.1
0.848
1.25
0.062Z63.5
0.083Z -139.2
0.95Z-17.6
0.03 IZ -1.42
0.072Z39.6"
0.847
1.30
0.065Z60.9
0.085Z-136.0
0.94Z-20.1
0.031Z2.64
0.076Z39.0
0.842
1.35
0.069Z58.2
0.084Z -133.6
0.95Z-24.7
0.034Z5.12
0.082Z35.6
0.859
1.40
0.072Z55.7
0.090Z-130.1
0.94Z-29.8
0.036Z8.49
0.086Z33.2
0.852
1.45
0.068Z52.2
0.089Z -127.4
0.95Z-34.5
0.033Z11.7
0.082Z30.5
0.832
1.50
0.071Z49.6
0.09 IZ -124.6
0.94Z-39.7
0.034Z14.1
0.085Z28.3
0.847
Table 6-4: Calculated reverse error terms of the practical two-port multi-probe scalar analyser
Practical measurements have been carried out on various devices. The results are
tabulated in Table 6-5.
133
Chapter 6 Two-Port M ulti-Probe M easurem ent System
3dB A tte n u ato r (dB)
1
6dB A tten u ato r
28dB A m plifier
Freq.
Before
After
Before
After
Before
After
(GHz)
Correction
Correction
Correction
Correction
Correction
Correction
1.00
-3.86
-2.98
-6.89
-6.02
27.50
1.05
-4.01
-3.00
-7.07
-6.06
27.38
28.39
1.10
-3.88
-2.99
-6.97
-6.07
27.53
28.43
1.15
-4.11
-3.01
-7.25
-6.09
27.12
28.26
1.20
^ .1 8
-2.96
-7.21
-5.98
27.23
28.47
1.25
-4.15
-2.99
-7.19
-6.03
27.46
28.62
1.30
-4.01
-2.97
-7.03
-5.99
27.64
28.68
1.35
-3.85
-3.04
-6.87
-6.08
27.35
28.15
28.37
1.40
-4.05
-3.02
-6.99
-5.95
27.35
28.38
1.45
-4.26
-2.98
-7.31
-6.03
27.12
28.45
1.5
-4.26
-3.04
-7.29
-6.07
27.20
28.42
Table 6-5: M easured attenuators and am plifier with the practical two-port m ulti-prohe scalar analyser
134
Chapter 6 Two-Port Measurement System
6.8
V ector Netw ork A nalyser Results
The design configuration illustrated earlier in Figure 6-9 earlier is a two-port multi-probe
vector network analyser. The configuration allows a standing wave to be presented on the
microstrip line o f the multi-probe reflectometer, which it will make it possible for the
magnitude and the phase o f the transmission coefficient to be measured.
Simulations have been carried out o f measuring various devices using the sim plified twoport multi-probe network analyser. Figures (6.21-6.23) show the simulated results.
S im u la tio n o f v a r io u s d e v ic e s
10
8
m
6
.5
4
(0
■ - 3 d B A tte n u
O)
2
- «
c
O
c5
3
S
*
lO d B A m p lif
2
c
<
6 d B A tte n u
0
* —
1
4
6
1
2
3
4
5
6
Frequency (GHz)
Figure 6-21: Simulated S 21 magnitude of various devices using the 2-port system of Fig. 6-9
135
Chapter 6 Two-Port Measurement System
Si mul a t e d phase o f 5 . 1 m m del ay and 2 0 . 4 m m delay
200
160
100
—
50
S’
"O
5 . 1m m C a lc u
5.1 m m I d e a l
0
<d
SI
Û.
2 0 .4 m m C alcu
■5 0
20.4
deal
100
-150
-200
1
2
3
4
5
6
F r e q u e n o y ( GH z )
Figure 6-22: Simulated S 21 phase of 5.1mm and 20.4mm delay using vector network analyser
S im u la ted P ha s e o f ampl i fiers with ( 45 & 9 0 ) d e g r e e phase
1
100
90
80
O)
«
0)
(0
CO
—*"— 9 0 D e g r e e
70
60
50
30
20
1
3
2
4
6
6
Fr e qu e n c y (G H z)
Figure 6-23: Simulated S 21 phase of amplifiers with phase delay of (45 and 90 )
The magnitude and phase o f different devices were practically measured using the multi­
probe vector network analyser. These measurements were repeated by using the Agilent
8753E
network
analyser.
Figures
(6.24-6.26)
show
the results o f the practical
measurements o f a delay line and various attenuators measured with the multi-probe
vector analyser and compared with the measurement by using the Agilent 8753E analyser.
136
Chapter 6 Two-Port Measurement System
P h a s e m e a s u r e m e n t s o f a d e l a y line b y u s i n g
Multi-probe vector analyser and HP8753E analyser
200
150
100
50
•5 0
H P 8 7 53E
•100
•150
•200
Frequency
(GHz)
Figure 6-24: S 21 phase measurements of a delay line measured with the
multi-probe vector analyser and the Agilent 8753E analyser
P h a s e m e a s u r e m e n t s o f v a r i o u s atte n uat or s
•2 0
-3 0
■A0
•5 0
•6 0
- 3 0 8 Ag 6 h i V S3
o>
T5
•7 0
3 0 8 M ul# P r o b e
-8 0
-9 0
£L
9 0 8 A gi lent 87 S3
9 0 8 M ulII P r o b e
- 1 0 0
- 1 1 0
-120
-130
1 .0
1 .1
1 .2
1 .3
1 .4
1 .5
F r e q u e n c y ( GH z )
Figure 6-25: S 21 phase measurements of various attenuators measured with the
multi-probe vector analyser and the Agilent 8753E analyser
137
Chapter 6 Two-Port Measurement System
M e a s u r e m e n t s of various attenuators
u s i n g t he m u l t i - p r o b e v e c t o r a n a l y s e r
2
4
6
8
1 0
1 2
1 .0
1 .2
1 ,1
1 .3
1 .4
1 .5
Frequen cy (GHz)
Figure 6-26: S 21 magnitude measurements of various attenuators measured with the
multi-probe vector analyser and the Agilent 8753E analyser
6.9
M easurem ent U ncertainty
Any m icrowave measurements regardless o f the accuracy o f the measurement system will
have some kind o f uncertainty or what is known as the measurement confidence.
Uncertainty can be defined as the assigned allowance for error. There are many possible
sources o f uncertainty such:
•
Instrument resolution o f reading out the detectors output voltages.
•
Changes in the characteristics or performance o f the measuring instruments or
reference standard since the last calibration.
•
Approximation and assumptions incorporated in the measurement method and
procedure.
•
Variation in repeated observations made under similar but not identical conditions,
such as, random effects caused by noise, temperature variation, humidity and air
pressure.
Measurement uncertainties in the two-port measurements system can be classified
into two types: 1. Reflection uncertainty
2. Transmission uncertainty
138
C hapter 6 Tw o-Port M easurem ent System
The reflection uncertainty assigned to the allow ance in eiTors when either input reflection
or output reflection measurement is carried out. The transmission uncertainty assigned to
the allow ance in errors when either forward or reverse transm ission earned out. The
forward measurement uncertainties can be defined as in equations (6.46-6.47) [ 8 8 ].
(6.46)
E,
(6.47)
^2IM ~ ^ 2 1 A —^21A
,^2lA ~^§-\Ia K sF
^21A^12A^SF E ip + ^ 22/l^i,F "f
K_Tf \
The reverse measurement uncertainties can be defined in a sim ilar manner.
For the 3dB attenuator measurements tabulated in Tables (6.2-6.3) the m easurement
uncertainties have been calculated. Table
Frequency
Is
6 - 6
illustrates these results:-
1
Is
1^1 i m |
(GHz)
Uncertainty
1
|H 2 2 M 1
Uncertainty
Uncertainty
<|>22M
Uncertainty
1.00
±0.0017
±3.58°
±0.0023
±2.99°
1.05
±0.0019
±3.80°
±0.0026
±3.29°
1.10
±0.0013
±4.00°
±0.0026
±3.57°
1.15
±0.0013
±4.33°
±0.0027
±3.62°
1.20
±0.0010
±4.51°
±0.0026
±3.70°
1.25
±0.0006
±4.78°
±0.0027
±4.14°
1.30
±0.0008
±5.18°
±0.0032
±4.51°
1.35
±0.0009
±5.79°
±0.0039
±5.07°
1.40
±0.0013
±6.35°
±0.0047
±5.65
1.45
±0.0014
±6.44°
±0.0046
±5.62°
1.50
±0.0020
±7.19°
±0.0055
±6.12°
Table 6-6: Reflection measurement uncertainties
139
C hapter 6 T w o-Port M easurem ent System
T hese individual uncertainties need to be com bined with the uncertainties o f the
calibration standards and the test equipment to calculated the overall system uncertainty.
The com bined uncertainty can be expressed as:
Combined Uncertainty =
+ U2
+ ....... + [/«
(6.48)
Where, U ^ , is the individual uncertainty, and n is an integer. The calculation o f the
com bined uncertainty can be a com plicated task. Therefore, as the system is not for
com mercial use at this stage the overall uncertainty has not been investigated in this work.
6.10 Conclusion
This chapter has described the design o f the two-port multi-probe measurement system .
D ifferent techniques o f m easuring the transmissions coefficient in both magnitude and
phase have been described. The multi-probe scalar and vector analyser have been
described and compared. The calibration m ethods have been discussed and calibration
algorithm has been derived as w ell as the two-port twelve-error terni model. Simulation
data and practical results haven been presented. The measurement uncertainty has been
derived and calculated.
140
C hapter 7 Conclusions and Future Work
Chapter 7
7 Conclusions and Future Work
7.1 Achievements
The aim o f this research was to find a reliable and a low cost m icrow ave measurement
system to rival the very expensive com mercial network analysers. T w o different m ethods
have been investigated during the research at tw o different U niversities. The details o f the
design and the measurement results are described and presented in this thesis.
The main achievem ents o f this research can be summarised as follow s:
7.1.1 Dielectric Multistate Reflectometer
•
The phase shifter in a dielectric multistate reflectom eter has been investigated in
the frequency band o f 1 lOGHz to 170GHz.
•
A new m ethod o f controlling the phase shifter by using LabV iew software has
been presented.
•
Calibration routines to calibrate the dielectric multi state reflectom eter have been
investigated and comparisons between these routines have been presented.
•
Various measurements o f m icrowave com ponents have been carried out in the
frequency band o f llO G H z up to 170GHz. The results have been calculated,
w hile comparisons o f these have been shown before and after calibrating the
system in order to validate the proper operation o f the measurement system.
•
The stability o f the dielectric multistate reflectom eter and the measurement
reliability have been measured.
•
Paper published in the European M icrow ave conference [28].
141
C hapter 7 Conclusions and Future Work
7.1.2 Multi-Probe Reflectometer System
•
The design o f a microstrip multi-probe reflectometer using low cost surface mount
com ponents has been carried out.
•
The assum ptions made by previous researchers (lossless, perfectly matched and
without coupling effects) have been discussed and proved need to be considered in
practice.
•
T w o different algorithms have been introduced to calculate the calibration
constants o f the one-port multi-probe reflectom eter and the measurement data o f
an unknown device. B y taking into account line losses, mismatch, coupling
effects, and the loading introduced by detectors, greatly im proved results have
been achieved. N o reported work has fully taken all these into account before.
•
Error correction has been analysed and applied to the raw device measurements.
•
The system characteristic parameters have been calculated and presented.
•
Various m icrowave com ponents have been
measured with the multi-probe
reflectometer. Results have been achieved with good accuracies after being
compared with data taken by existing com mercial analysers.
•
M easuring the reflection coefficient in terms o f its m agnitude and phase as w ell as
the transm ission measurements o f reciprocal m icrowave devices have been shown
by using the one-port measurement system .
•
The two-port multi-probe reflectom eter has been investigated, which is capable o f
performing the full S-parameter m easurement in principle.
• EiTor model
correction
has
been
derived
for the
two-port multi-probe
reflectometer. These enor coiTections have been applied to coiTect various
measured microwave devices.
•
The problem o f the transmission phase measurements using the two-port m ulti­
probe reflectom eter has been presented and the solutions for that were proposed.
•
Paper has been published in the AR M M S conference [93].
142
C hapter 7 Conclusions and Future Work
7.2
Possible Future Work
There are a number o f interesting research areas which can be pursued further:
•
The dielectric m ultistate m easurements system can be extended to be two-port
measurement system in order to perform the full two-port measurements o f a
network or device. Figure 7-1 show s the suggested design o f the two-port system .
•
The m etallic w aveguide horns used in the dielectric multi state reflectom eter ports
can be replaced by dielectric w aveguide transitions.
•
The pow er detectors used to detect the signal from the
dielectric multistate
reflectom eter could be connected directly to the dielectric w aveguides inside the
reflectometer. Other types o f detectors with higher frequency operation such as
thermistor detectors, which are extrem ely broadband and can operate up to optical
frequency range, can be used instead o f the expensive w aveguide detectors.
•
The high frequency M M IC multi-probe reflectom eter can be fabricated and tested
(Refer to Appendix D for the design and layout).
•
The principle o f measuring the magnitude and the phase o f the transmission
coefficients o f a two-port network device using the multi-probe reflectom eter
technique needs to be developed further.
•
The implementation o f the multi-probe reflectom eter for on-w afer m easurement
can be investigated. Figure 7-2 illustrates a suggested design.
•
The feasibility o f designing a handheld analyser using the multi-probe technique is
worthy o f further investigation.
143
Chapter 7 Conclusions and Future Work
NonReflective
S w i tc h
DMR 1
DUT
DMR 2
Figure 7-1: Two-Port Dielectric Multistate Reflectometer
NonRef lectlve
S w i tc h
Figure 7-2: On-W afer M ulti-Probe Reflectometer
144
References
References
[1] Bailey, A. E., : “Microwave Measurements”, Peter Peregrinus Ltd 2" Edition 1989, ISBN 0
[2] Hoer, C.A., : “The six-port coupler: A new approach to measuring voltage, current, power,
impedance, and phase”, IEEE Trans, IM-2I, 1972, pp. 446-470.
[3] Hoer, C.A., : “A network analyser incorporating two six-port reflectometer”, IEEE Trans.,
MTT-25, 1977, pp. I070-I074.
[4] Bertil Hansson, E.R., and Riblet, G.P., : “An ideal six-port reflectometer consisting o f a
matched reciprocal lossless five-port and a perfect directional coupler”, IEEE Trans., MTTJ A 79% pp. 2 8 4 -2% .
[5] Engen, G.E., : “The six-port reflectometer: An alternative network analyser”, IEEE Trans.,
MTT-25, 1977, pp. I075-I080.
[6 ] Boese, I.M., and Collier, R.J.: “Novel measurement system within 110 -
170 GHz”,
Proceeding o f 26’’' European Microwave conference, Prague, 1996, pp. 806-810.
[7] Boese, I.M., and Collier, R.J.: “M^IC Measurements at 140 GHz”, 8th International
Conference on Electromagnetic Measurement. Conference Digest. NPL. 1997, pp.9-I-5.
Teddington, UK.
[8 ] Yeh, C., Shimabukuro, F.I., and Chu, J.: “Dielectric ribbon waveguide: An optimum
configuration for ultra-low-loss millimeter/submillimeter dielectric waveguide”, IEEE Trans.
Microw. Theory Tech. 1990, 38, (6), pp. 691-702.
[9] Collier, R.J., and D'Souza, M.F.: “Comparison of junctions in both dielectric guides and
metallic guides above 75 GHz”, lEEproc. A, 1992, Vol. 139, (5), pp. 226-228.
[10]
Engel, A. G., and Katechi, L. P. B.: “Low-Loss Monolithic Transmission Lines for
Submillimeter and Terahertz Frequency Application”, IEEE Trans. On Microwave Theory
and Techniques, Vol 39, No II, Nov. 7997, pp. I847-I854.
[11]
Oldfield, L. C., Ide, J. P, and Griffin, E.J “A Multi-State reflectometer”, IEEE Trans.
Instrum. Meas., Vol. IM-34, pp. 198-201, Jun 1985.
[12]
Hoer, C.A.: “Performance of a dual six-port network analyser”, IEEE Trans., MTT-27,
1979, pp. 993-998.
145
______________________________________________________________________________ References
[13]
Groll, P.H and Kohl, W.: “Six-port consisting of two directional couplers and two voltage
probes for impedance measurement in millimetre wave range”, 1&' European Microwave
conference, 1980, pp. 295-298.
[14]
Bertil Hansson, E.R and Riblet, G.P.: “An ideal six-port reflectometer consisting of a
matched reciprocal lossless five-port and a perfect directional coupler”, IEEE Trans., MTT^ 7, 798^, pp. 2 84-2 8 8 .
[15]
Engen, G.F and Beatty, R.W.: “Microwave reflectometer techniques”, IRE Trans., MTT7. 79J 9, PP.8 5 7 -8J J .
[16]
Dobrowolski, J.A.: “Improved six-port circuit for complex reflection coefficient
measurements”. Electron. Lett., August 1980, Vol. 18, pp. 748-750.
[17]
Riblet, G.P.: “A compact waveguide ‘resolver’ for accurate measurement of complex
reflection and transmission coefficients using the 6 -port measurement concept”, IEEE Trans.,
Feb 1981, MTT-29, pp. 155-162.
[18]
Engen, G. P.: “An improved circuit for implementing the sis-port technique of microwave
measurements”, IEEE Trans., Dec. 1977, MTT-25, pp. 1080-1083.
[19]
Hoer, C.A.: “The six-port coupler: A new approach to measuring voltage current, power
impedance and phase”, IEEE Trans. Instrument Meas., Nov. 1972, lM-21, pp. 466-470.
[20]
Engen, G. P.: “A (Historical) Review of the Six-Port Measurement Technique”, IEEE
Trans., Dec. 1997, MTT-45, No 12, pp. 2414-2417.
[21]
Hjipieris, G., Collier, R. J., and Griffin, E.
J.: “A Millimeter-Wave Six-Port
Reflectometer using Dielectric Waveguide”, IEEE Trans. Microw. Theory Tech. 1990, Vol,
38, pp.54-61
[22]
Boese, I.M.: “Millimeter wave measurements and device characterisation at 140 GHz”,
Ph.D. Thesis at the University o f Kent at Canterbury, 1997.
[23]Collier, R.J., and D ’Souza, M.P.: “A
multistate reflectometer in dielectric guide for the
frequency range 75-140 GHz”,IEEE MTT(S) Proce.,
o f Intern., Symposium, Boston, Jun
1991, Vol. 3, pp. 1027-1030.
[24]
Hjipieris, G., Collier, R. J., and Griffin, E.
J.: “A Millimeter-Wave Six-Port
Reflectometer using Dielectric Waveguide”, IEEE Trans. Microw. Theory Tech. 1990, Vol,
38, pp. 54-61.
[25]
Tischer, P.J.,: “Excess Condition losses at Millimetre Wavelengths”, IEEE Trans, MTT24, N o.77, 7976, pp. 858-8J 8 .
146
_____________________________________________________________________________ References
[26]
Collier, R.J., : “A Broad-Band Directional Coupler for
Both Dielectric and Image
Guides”, IEEE Transaction on Microwave Theory and techniques, Vol. MTT-33, No. 2, Feb
[27]
Collier, R.J., and D ’Souza, M.F.: “Phase shifters for dielectric guides”, lEE proceeding-
77, 7992, Vol. 7 % (2), pp. 202-204.
[28]
Altrabsheh, B.M., and Collier, R.J., “ A programmable Phase Shifter for a Dielectric
Waveguide Multistate Reflectometer”, 31st European Microwave
Conference 2001.
Conference Proceedings. Microwave Eng. Europe. Part vol.3, 2001, pp. 189-92 vol.3.
[29]
Engen, G. P., ‘Calibrating the six-port reflectometer by means o f sliding terminations’,
IEEE Trans. Microwave. Theory Tech. 1978, Vol MTT-26, pp. 951-957.
[30]
Engen, G. P., An Improved Technique for calibrating the dual six-port automatic network
analyser’, IEEE Trans. Microw. Theory Tech. 1979, Vol MTT-26, pp. 987-993.
[31]
Herman, J. E., and Burkhard. S.: A Generalized Theory and New calibration procedures
for Network analyser self-calibration’, IEEE Trans. Microw. Theory Tech. 1991, MTT-39, Vol
4, pp. 724-7.37.
[32]
Wiedmann, P., et al, “A New Robust Method for Six-Port Reflectometer Calibration”,
IEEE Transactions on Instrumentation & Measurement, vol.48, no.5, Oct. 1999, pp.927-31.
Publisher: USA.
[33]
Engen, G. P., and Hoer, C.A., “Thru-Reflection-Line : An Improved Technique for
Calibrating the Dual Aix-Port Automatic Network Analyzer”, IEEE Trans. MTT, Vol. 27,
pp.987-993, Dec. 7979.
[34]
Engen, G. P., and Hoer, C.A.: “Application of arbitrary
6
-port junctions to power-
measurement problems”, IEEE Trans. Instrum. Meas., vol. lM-21, Nov. 1972, pp. 470-474.
[35]
Neumeyer, B., “A new Analytical method for Complete Six-Port reflectometer
Calibration”, IEEE Trans. Instrumentation Measurement, Vol. 39, pp. 376-379, April 1990.
[36]
Potter, C. M., and Hjipieris, G., “A Robust Six-to-Pour Port Reduction Algorithm”, IEEE
MTT-S Int. Micr. Symp. Dig., pp. 1263-1266.
[37]
Judish, R. M., and Engen, G. P., “On-Line Accuracy Assessment for the Dual Six-Port
ANA: Statical Methods for Random Errors”, IEEE Trans. Instrum. Meas. Vol. 36, pp. 507513, June 1987.
[38]
Kaliouby, L and Bosisio, R.G.: “A new method for six-port swept frequency automatic
network analysis”, IEEE Trans. Microwave Theory Tech., vol. MTT-32, Dec. 1984, pp. 1678-
7682.
147
______________________________________________________________________________ References
[39]
Hoer, C. A., “Calibrating Two Six-Port Reflectometers with only one Impedance
Standard”, NBS tech. Note 1004, 1978.
[40]
Engen, G. P., “Calibration o f an arbitrary Six-Port Junction for Measurement o f Active
and Passive Circuit Parameters”, IEEE Trans. Instrum. Meas., Vol. IM-22, pp. 295-299, Dec.
[41]
Li, S. and Bosisio, R., “ Calibrating of Multiport Reflectometer by Means of Four
Open/Short Circuits”, IEEE Trans., Vol. MTT-30, No. 7, pp. 1085-1089, July 1982.
[42]
Woods, D.,”Analysis and Calibration Theory of the general
6
-Port reflectometer
Employing Four Amplitude detectors”, in Proc. Int. Elec. Eng., Vol. 126, No. 2, pp. 221-228,
7979.
[43]
Judah S. K.:
Calibration o f multiport reflectometers”, lEE Proceedings-H Microwaves
Antennas & Propagation, vol. 132, no.7, Dec. 1985, pp.468-70. UK.
[44]
Engen, G. F.: “Calibrating the six-port reflectometer by means of sliding terminations”,
IEEE Trans. Microw. Theory Tech. 1978, Vol MTT-26, pp. 951-957.
[45]
Woods, D.: “Analysis and calibration theory of the general
6
-port reflectometer
employing four amplitude detectors”, lEE Proce., Feb. 1979, Vol. 126, No. 2, pp. 221-228.
[46]
Neumeyer, B.: “A new analytical method for complete six-port reflectometer calibration”,
IEEE Trans. On Instrum. And Meas., April 1990, Vol. 39, No.2.
[47]
De Silva, E.F and McPhun, M.K.: “Calibration of an automatic network analyser using
transmission lines of unknown impedance, loss and dispersion”. The Radio Electronic
Engineer, Vol. 48, No. 5, pp. 227-234.
[48]
Collier, R.J and Boese, I.M.: “Impedance measurements using a multistate reflectometer
from 110-170GHz”, Proce., o f British Electo., Meas. Conf, Malvern Nov. 1996, pp. 3-1/3-4.
[49]
Engen, G.E.: “Calibration theory for the six-port reflectometer”, NBS Tech. Note 1006.
[50]
Kasa, L: “Closed-form mathematical solutions
to some network analyser calibration
equations”, IEEE Trans., Instrum., Meas., Dec. 1974, Vol. lM-23, pp. 399-402.
[51]
Abou Chahine, S, Huyart, B., Bergeault, E. and
calibration using Schottky diodes operationg in AC
Jallet, L.: “A six
port reflectometer
detection mode”,
IEEE Instru., and
Meas., Special issue on the CPEM 92, April 1993.
[52]
Bergeault, E, Huyart, B, Geneves, G. and Jallet, L.: “Charactrization of diode detectors
used in six-port reflectometers”, IEEE Micro. Trans. Instrum. And Meas., lM-40, No. 6, Dec.
1991.
148
______
[53]
References
Hunter, J and Somlo, P.: “Simple derivation of six-port reflectometer equations”, Electro.
Lett., vol. 21 Apr. 1985, pp. 370-371.
[54]
RS data sheet number B 17058, March 1994.
[55]
Chang, K, Ming-Yili, and Sauter, T. H.: “Low-Cost Microwave / Millimeter-Wave
Impedance Measuring Scheme Using a Three-Probe Microstrip Circuit”, IEEE Transactiotts
on Microwave Theory and Techniques, Vol. 38, 10, October 1990, pp. 1455-1460.
[56]
Duffin, W.J.: “Three-probe methode o f impedance measurements”. Wireless Engineer,
Dec. 1952, pp. 317-320.
[57]
Chang, K, Li, M ND Sauter, T.: “A three-port microstrip impedance measurements
system”. Microwave and Opt. Technol. Lett., vol. 1, May 1988, pp. 90-93.
[58]
King, D . D.: “M easurements at Centimeter W avelength”, N ew
York:
Van
N ostrand, 1952, pp. 197-199.
[59]
Martin, E., M argineda, J and ZamaiTo, J.: “ An automatic network analyser using
a slotted line reflectom eter”, IEEE Trans. M icrow ave Theroy Tech., vol. M TT-30, No.
5, M ay 1982, pp. 667-669.
[60]
Engen, G. F.: “Determ ination o f m icrowave phase and amplitude from power
measurements”, IEEE Trans. Instrum. M eas., vol. IM -25, D ec. 1976, pp. 414-418.
[61]
Hu, C.J.: “An improved design of the swept-frequency, automatic impedance measuring
schemes using multi-probes”, in Proce. 1981 Int. Micro. Sys., Los Angeles, CA, May 28,
1981.
[62]
Hu, C.J.: “Design of signal processors for automatic impedance measurering schemes
using fixed probes”, in Proc. 19"' Automatic RF Tech. Group Meeting, Dallas, TX, June 19,
7982.
[63]
Hu, C.J.: “Experiments on X-band automatic impedance measuring schemes using three
fixed probes”, in Proc. 20"' Automatic RF Tech. Group Meeting, Boulder Co, Nov. 5, 1982.
[64]
Caldecott, R.: ‘The Generalized Multi-probe Reflectometer and its Application to
Automated Transmission Line Measurements’. IEEE Transactions on Antennas and
Propagation, Vol. AP-21, No 4, July 1973, pp. 550-554.
[65]
Samuel, A. L.: “An oscillographic method of presenting impedances on the reflectioncoefficient plane”, Proc. IRE, vol. 35, Nov. 1974, pp. 1279-1283.
149
______________________________________________________________________________ References
[6 6 ]
Probert, P and Carroll, J.: “Design features of multi-port reflectometers”, Proc. Inst.
Elect. Eng., vol. 129, Oct. 1982, pp. 245-252.
[67]
Ulker, S and Weikle, R. M.: “A miilimeter-wave six-port reflectometer based on
sampled-transmission line architecture”, IEEE Micro. And Wireless Componenets Lett, vol. 11
No. 8, August 2001, pp. 340-342.
[6 8 ]
L ’vov, A. A and Semenov, K. V.: “A method of calibrating an automatic multi-probe
measurement line” Measurement Tech. USA, vol. 42 No. 4, 1999, pp. 357-365.
[69]
Hu, C.J.: “Microwave Automatic Impedance Measuring Schemes Using Three Fixed
Probes”, IEEE Transactions on Microwave Theory and Techniques, Vol. MTT-31, No. 9,1983,
pp. 756-461.
[70]
Hu, C.J.: “A Novel Approach to the Design of Multi-Probe High-Power Microwave
Automated Impedance Measuring Schemes”, IEEE Trans. Microw. Theory Tech. Vol. MTT28, 7987, No. 72, pp. 7'722-7'/2 8 .
[71]
Madonna, G, Fenero, A, and Pirola, M.: “Design of a Broad Multi-probe Reflectometer”,
IEEE Transactions on Instrumentation and Measurement, Vol. 48, No. 2 April 1999, pp. 622625.
[72]
Pozar, D.M. : “Microwave Engineering”, John Wiley & Sons Inc. 2"'* Edition, 1998, ISBN
77096 8 .
[73]
Radmanesh, M.M.: “Radio Frequency and Microwave Electronics”, Prentice Hall PTR
2001, ISBN 0 1 3 027958 7.
[74]
Sander, K.F and Reed, G.A.L.: “Transmission and Propagation of Electromagnetic
Waves”, Cambridge University Press. 2"'^ Edition, 1986, ISBN 0 521 31192 6.
[75]
[76]
Gupta, K.C.: “Microwaves”, Wiley Eastern Ltd., 1979, ISBN 0 85226 346 5.
Horowitz, P. and Hill, W.: “The Art of Electronics”, Cambridge University Press., 1980,
ISBN 0 521 23151 5.
[77]
Bogart, T. F.: “Electronics Device and Circuits”, Merrill Publishing Company., 1986,
ISBN 0 675 20317 1.
[78]
King, R. I.: “Microwave Homodyne Systems”, Peter Peregrinus Ltd., 1978, ISBN 0
907228 52 2
[79]
A gilent T echnologies.: “ Technical data sheet for H S M S -2850 se r ie s ” 1999.
[80]
A gilent
T echnologies.:
“A ll
Schottky
D iodes
are
Zero
B ias
D etectors”,
A pplication N ote 988, 1999.
150
______________________________________________________________________________ References
[81]
A gilent T echnologies.: “The Zero B ias Schottky D etectors D iod e”, Application
N ote 9 6 9 , 1999.
[82]
Alpha Industries. : “Mixer and Detector Diode”, Application Note 80800, 1992.
[83]
Kerkels, H. and Schiek, B.: “A Closed form theory for calibrating a dual six-port Network
analyzer”, IEEE Transactions on Instrumentation and Measurement, Vol 46, No. 5, October
1997, pp. 1115-1119.
[84]
Szczypka, Z.: “Scattering parameters analyzer of microwave two ports based on multi­
probe standing wave pattern investigation”. Electronics and telecommunications Letter,
Poland, Vol. 3, No. 5-6, 1988.
[85]
Szczypka, Z.: “Estimation of complex reflection coefficient based on a few discrete
values of squared voltage standing wave pattern”. Electronics and telecommunications Letter,
Poland, Vol. 1, No. 1-2, 1986..
[8 6 ]
Hittite M icrow ave Corporation.: “ Technical data sheet for H M C 270M S 8G ”.
[87]
Renmark, S. :”On the calibration process o f automatic network analyser system s”,
IEEE Transaction on Microwave Theory and Techniques, April 1974, pp 457-458.
[8 8 ]
A gilent
T echnologies.:
“A pplying
eiTor
con ection
to
network
analyser
mGSLmtQmQXiis”, A pplication N ote A gilen t PtN 1287-3, 1997.
[89]
A gilent T echnologies.: “Specifying calibration standards for the A gilent 8510
network analyzer”. A pplication N ote 8510-5B, 2001.
[90]
Rohde and Schwarz.: “Calibration techniques and m easurement accuracy”. Vector
Network Analyzer Family ZVR, Application note.
[91]
Rohde and Schwarz.: “M easurement uncertainties for vector network analysis”.
Application note 1EZ29_1E, 1996.
[92]
Rytting, D.: “Network analyser e n o r m odels and calibration m ethods”, Agilent
Technologies.
[93]
Altrabsheh, B .M and Robertson, I.D.: “Low cost m icrow ave automatic im pedance
measuring system ”, ARMMS RF and Microwave Society Conference, November 2001.
151
Appendix A
Appendix A
Dielectric
Multistate
Reflectometer
Programmes
152
Appendix A
This
programme
controls
the
D ielectric
M ultistate
R eflectom eter
(DM R)
measurements system test equipments and calculate the results. The programme
performs the follow ings:
1. Initialises all test equipment at the start o f each test.
2.
Controls and derives the stepper motor which controls the D M R phaseshifter.
3.
Controls and derive the D M M H P34401A .
4. Record the voltage ratio o f each m easurement for each
step o f the
phaseshifter. The measured results recorded into two ways:
•
Recorded into aiTays. This is for instance results display.
•
Recorded into E xcel file. This is for later results analyses to calculate
the system constants and then the reflection coefficien t o f unknown
device.
5. D isplay and record error if any during the test.
153
Appendix A
Address/Port(22)
Port Address
register address 21
Timeout (10000 ms)
Interface (F;GPIB)
"P78
Bit #(0-7)1
value I
Range/Resolution (TiAuto)
Function (0;V DC)
a
On Time (mS)
gP0~
Off Time (mS)
S 1ÏÔÔÔ'
Read Byte
Steps Number!
M Z
OFF
Manual Res. (1 ; 5.5 Digits)
Source (Oilnternal)
r ^|5,5 Digits
|0 ~ ^kntemal
Manual Range (1.00) Samples (1)
Manual Delay (0)
«I 1.00
2
il
error in (no error)
Position in Degrees 2
Auto J
P ^ IVDCiVDC Ratio
Zero Position Limit
status
)0 . 0 0 0 0 0
error out
code
status
code
1360.00
DVMReading Time
Interval (mS)
source
KXice
Hkioo
_l
_l
ym|pôwërRâtîô~
DC Voltage
Ratio
^
I5.93E-1
Zero Indication |
„
$.79E-1
$.54E-1
^.70E-1
I6.41E-1
I6.11E-1
$.79E-1
I5.64E-1
I5.82E-1
I6.32E-1
7.0-|
6.0-^
5.0^
4.03.0^
2.01.00.0-,
0
I
100
16.08E-1
_ iU
Front panel of the DMR measurement system programme
154
Appendix A
DMR programme Hierarchy window
155
Appendix A
5teps Number I
— E
l^cift Address!
-----M t# (0-7)1
This programme w i do the fblowings:
1. Initialise the DMM and the Stepper motor.
2 . Takes a reading of voltage ratio for each
step by using a FOR Loop.
3. Write th e results into an array.
4. Close up the application._______________
ILÜ^I
%
eqister address 2|
1 Off Time (mS)| luw Jl-------- Ip
ruwlj
Port
1 -n s-
kerolndkat^
ED
tead Byte I
kero Position Limit 11!
Ik
□ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ D C
0
fawer Ratiol
Position in Degrees 2l
Interface (FiGPIB)l
-I [ o b l I
'C BC IrimeoutdOOOOmslI
ISamoles
(1)1 iLIliJf
!
Write To Spreadsheet File.vi
i
hlavefarm O w tf
k o u rce (0 :ln tern al)l li "re
lftdckess/Port(22)ll
t:IN5TR|-
lerror in (no error
)VM Reading Time
Interval (mS)
Kjnction (0;V DÔ1 [fuull
ttanqe/Resolution(T:Autô)] jl
t f
!
||
M anual Res. (1; 5.5 Digits)!
M anual Range (1.00)1
M anual Delay (0)1 i
156
Appendix A
This provides an example of how to use the HP34401A subVIs programmatically.
Configure
Trigger
M easure
Timeout (10000 ms) |l uM
Function (0:V DC) || U16 1--------Manual Res. (1: 5.5 Digits) jl U16 i|---------
Source (Oilnternal) |l uis l|-------
VISA session |l I/o l|------ 9
F
error in (no error)
[d b l]
Measurements
I I/o l|
dup VISA session
error out
Range/Resolution (TiAuto) t u x J l
Manual Range (1.00)
r
\ . m 2 --------
Manual Delay (0)
DBl
Samples (1)
512
157
Appendix A
This will configures the range, resolution, and other settings for the multimeter measurement
Manual Range (0.00) [
— I
Manual Ranging & Resolution
VISA session irfTo'
I/o
error in (no error) invT
l|dup VISA session
ror out
|% ,;% 3.2E ,
Function (0;V DC) [r5ÜïV
Range/Resolution (T :Auto) II r r j[
Manual Res. (1 :5 .5 Digits)
H
DC Current
a
|DET:BAND 3;
:DET;BAND 20;
|DET:BAND 200;
AC Filter ( 1: Medium)
jl ui6 IIZERO:AUTO ON;
ZERO:AUTO OFf U
Autozero (F: Off)
|l r r !|
INP:IMP;AUTO OFF;
Fixed DC Input Res. (T: On)
jl r r || -
158
Appendix A
This takes a given value and determines if that value is one of a specified array of discrete numbers
r
Fnl
nm
“
B
H
r ”B Ü E $ r
&—
t~0-9Ee-+.T+| —
-
1?
rB ê n l Ranged Number
M
It r r || Range Found
I
0
Numeric Data (Empty) |l >bc it— E
| i db I I I
Index
(§1
EF
error In (no error) |l
it-
VISA session |l i/o ik-
Number to Range (0.00)
— Il -°*i l| error out
I I.") l| dup VISA session
159
Appendix A
This configures the triggefing system for the multimeter,
|:TRIG;50UR
Source (0; Internal)
Delay (F; Auto) I H ^ I
Manual Delay (0)
;TRIG:DEL:
AUTO ON;
|:TRIG:COUN
Auto Del
Trigger Count (1)
|
ll
|:SAMP;COUN %d;
Samples (1)
|i
—
VISA session
error in (no error)
W
dup VISA session
I -“- i l| error out
160
Appendix A
TNs reads the error queue from the instrument
Q-j
Loop Until Queue
Empty or I/O
I/O
dup VISA session
VISA session
I
error in (no error)
Update Error Cluster
With Instrument Error
OR If Zero, Then
Any Warinigs.
1 error out
BFFC08FF
HP34401A Error Query;
nstrument reports;
Error Message
[i32] Error
161
Appendix B
Appendix B
One-Port
Multi-Probe
Reflectometer
Programmes
162
Appendix B
This programme controls the One-port reflectom eter measurem ent system test
equipments and calculates the results. The programme performs the follow ings:
1.
Initialises all test equipment at the start of each test.
2.
Controls and derives the frequency source either Agilent 83623B or E4433B. This
will control the:
3.
4.
•
Start and stop frequency.
•
Step frequency.
•
Power output
Controls and derive data acquisition unit H P34970A . This w ill control:
•
Channel activated.
•
M easurements mode.
•
M easurement resolutions.
Record the voltage o f each m easurement for each probe. The measured results
recorded into tw o ways:
5.
Recorded into an ays. This is for instance results display, which incorporates
M ate Lab for the calculations.
6
. Recorded into E xcel file. This is for later results analyses to calculate the
system constants and then the reflection coefficient o f unknown device.
7.
A
choice
o f performing
calibration
m easurements
o f the
multi-probe
reflectom eter in order to calculate the system constants or skipping the
calibration if calibration has recently been performed.
8
. D isplay the results o f the reflection coefficient o f the unknown D U T in terms
o f magnitude and phase as w ell as in Smith chart display.
9. D isplay and record eiTor if any during the test.
163
Appendix B
Skip Calibration
O utput P ow er (dBm)
s t a r t Frequency (GHz)
S top Frequency (GHz)
j|l.00E+9
3|1.50E+9
B efore Calibration D ata
2fe.50E+7
A l l e r ( ; , ililv . . d io n f ) n !n
error In (no error)
status
a
s te p Frequency (GHz)
code
error out
status
code
w
source
Front panel of the one-port reflectometer measurement system programme
164
Appendix B
jxk H
E>°
Plot
Stglo
G«
Grids
One-port reflectometer programme Hierarchy window
165
Appendix B
irxj
Cüc
S eg
S ect
r*
Continuation o f one-port reflectometer programme Hierarchy window
166
Appendix B
lode (Fixed/siriQle output level :2il
This programme wJI do the folowings;
1. Initialise the te st equipments.
2. Specify the te st frequency.
3. Specify the te st power.
4. Oioice of running with or
without calibration.
nstrument descriptor!
jutput Power
(c w liiddeT l )!
D
0
o o a o o y p q (r tr q - 1 3 - p q m i r o „ 7 i ^ . p q a a n . o a . o j a p ^ P ..a jQ -a .ü .flj.Æ
_ar^requency (GHz)
rnsnl
Measurlnq Frequency I
[s ig i
_
Step Frequency (GHz)l
rpBTii
r 83623
Zhamel List(empty)|
ruiriT
intry Mode(Numeric:T^
Tt t i I
' ............... "■■■■■
_____
ISA session
|ftl chan Output I ■'[dblÏ
RSê*l'’~^
3peration(Fixed;0)
(no error)
!^ l
p to o
Frequency (GHz)
Output Power (dBm)l
jkip Calbrationj^
□ □ □ □ a bZbü g n p
0
0
0
0
o o _ o o c o o c i o o o o o o o o o o o o o o û O O O O PTTtr
167
Appendix B
This programme wl do the folowings:
1. Switch the output power off.
2. CalaJate the system parameters,
3. Cakxialte the reflection coefficient,
4. Display the results on Smith chart.
n H H H a H B H B H f l [TH
P
instrum ent descriptor
lO'jTpui: Powetr
□ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ d o n n n D D D o ac
before Cafcr ation Datai
— jrs in i
_______
Idup VISA session
[F re q u e ric y
Reflection Pd Corrected I
- 0
p.
Return loss (dB)l
ter Cagyation Data
□ □ □ □ o a a o n a n n n o Q
l o o o p o D o o D o o p D a n a o D g o o o o o a a o b b o D n o a o a o
168
Appendix B
This calculates the calbratlon constants and the reflection coefficient of the DUT
gygHBaBBgHHMoro..3i^paBPHHggBBBB
□ □ □ □ □ □ □ □ □ □ □ □ a d~H
i,g .0 g .0 D .0. H 0 ro. .3i KP Q
b
m
r c
eflectionPdl
[tp<»]i
(efkcüon Pd Corrected
Unes ' h - p
[<»»]|
jMITh JUhcorrected Data
Chat
^Corrected Magi
[DPI] I
rror in (no error)
P-f l D Q J D û Q a O D Q O OTTc a ^ ^ o o o o o o o o a o o o o o o c
169
Appendix B
True M
Prepare Scales -->
ll.OO+O.OOII
[«PB]
1. 00 !
M II
'.i<l 0
lodl
This calculates;
1. The caSbration constants of the measurements system.
2. The reflection coefficient of the DUT.
3. Plots the measured resdts in Smith chart format
4. Give the results in numerical format.
lolof 4|
170
Appendix B
ir ™
™
" ^ W
lA8 ScMpt|
This calculates the calibration constants of
he measurements system by using MATLAB
software language:
1, al, a2, a3,
al=(pol-psl)j(4*pll);
j2=(po2-ps2)il(4*pt2);
fequency
L
bl=(sq[t(lt>rplH 4*plltpol-psl)"2))ji:4*pll);
b2=(sqrt(lt*po2*pl2-(4»(il2+po2-pi)"2M4*pl2)i
b3=(sqit(16*po3*pl3-(4*pl3+poHs3)*2M4*pl3);
bl=ibsD)l);
b2=Bbs^);
b 3 = # 3 );
cl=abs(al+bl’''i)'2;
2.bl,b2,b3
3,V(î=Pü
,,|C2=abs(a2+b2*ir2;
% " '(3 = # 3 + b 3 Y 2 ;
I R=0)
* - iMsk=0 ;
tmpblsbl;
I Inipb2=b2;
I tfflpb3^3]
M fo r m is k ïO i,
■
blstm pbl;
I b2=tmpb2;
I
b3=ttnpb3;
*
ifm ask==l
bl=-bl)
nI
fm aik==2
b2=-b2)
end
ifm aik==3
b3=-b3)
end
...-J ifmask==4
r
bl=-bl
r
IDBI
Reflection Coef Mag
Ml
r
iw l'ifm ask = = 5
H
b2=-b2
I
b3=-b3;
a
end
ifmask==6
b ls-b l
b3=-b3)
end
A0=cl*((pd2/pl2>l>(c2*((p(ll)pll>l));
r
Al=2*(a2*cl-al*c2)i
A2=2*0)l*c2-b2*cl);
M =tl*(|pd3ipl3>lM c3*((pdl/^l>l)))
r
& l=2*(a3*(|.al*(3);
B2=2*D)1^3-b3*cl);
Ri=(A2*B0-A0*62]j(A2*Bl-Al*B2];
Ry=(A0*BWl*B0)j(A2*Bl-Al*B2);
Gama=R>+i*Ry
R=abs(Gama)
v:f(R > 0 2 )& (R < l,2 )
break;
end
end
n=(mask);bl;b2;b3
Rk)H=-2(l*lo(ilO(l?l
RCorrdex
I
1
[DBTi
iDBt
I
Return Loss
Ë
[M]
îfrorout
171
Appendix C
Appendix C
Two-Port
Multi-Probe
Reflectometer
Programmes
172
Appendix C
This programme controls the Two-port reflectom eter measurement system test
equipments and calculates the results. The programme performs the follow ings:
1.
2.
Initialises all test equipment at the start of each test.
Controls and derives the frequency source either Agilent 83623B or E4433B. This
will control the:
3.
4.
•
Start and stop frequency.
•
Step frequency.
•
Pow er output
Controls and derive data acquisition unit H P34970A . This w ill control:
•
Channel activated.
•
M easurements mode.
•
M easurement resolutions.
Record the voltage o f each measurement for each probe. The measured results
recorded into tw o ways:
5. Recorded into arrays. This is for instance results display, which incorporates
M ate Lab for the calculations.
6
. Recorded into E xcel file. This is for later results analyses to calculate the
system constants and then the reflection coefficient o f unknown device.
7.
A
choice
o f performing calibration
measurements
o f the
multi-probe
reflectom eter in order to calculate the system constants or skipping the
calibration if calibration has recently been performed.
8
. A choice o f selecting the desired test.
9. D isplay the results o f the reflection coefficient o f the unknown D U T in terms
o f magnitude and phase as w ell as in Smith chart display.
Display and record erro r if any during the test.
173
Appendix C
O utput Pow er (dBm)
j|o.oo
s t a rt Frequency (GHz)
s to p Frequency (GHz)
j|l.00E+9
1.50E+9
B efore Calibration D ata
S tep Frequency (GFt)
jg.50E+7
\ f t ' j r C a lib iV itU n D.:it:i
Skip Calibration
rF u l2 -P o rt
F? 511 Port
r 522 Port
r S21 Through
r 512 Trou*
CONTINUE
PtotO
S21 Un-Corrected Data
521 Corrected Data
0.0
-5.0
«
i
-
10.0
-15.0
-15.0
- 20.0
-26.01.1
1.3
Frequency (GHz)
1.2
1.5
1.2
1.3
Frequency (GHz)
F ro n t panel o f the T w o-port reflectom eter m easurem ent system program m e
174
Appendix C
a
Iftterti
Load
fchait
PW
StgW
Two-port reflectometer programme Hierarchy window
175
Appendix C
Get
Grids
trxj
+ -•
<t t a
Draw
S ag s
Circ
Seg
S ect
Arcs
C ontinuation o f T w o-port reflectom eter program m e H ierarchy window
176
Appendix C
abcO
TV
Draw
C irc
Seg
Segs
\W
TV
Sect
A rc s
C»BL
TV^
L in e
TV
C o n tinuation of Tw o p o rt reflectom eter program m e H ierarchy window
177
Appendix C
OOOOOQOOOODOQOOOOOOOOOOQOOObOOOaOOOaQOOOObaOOOOdOOoaOOOOOOOOOO
=ul2-Port|
This selects which m easurem ent
is carried out, S11,S22,S21,S12.
■valijt-
►
V-alfj-T
ISelect Port Measurements and hit Continue!
H a w
grror In (no error)!
Zononue
□ □ □ □ □ □ □ □ □ □ □ a □□□□□□□
p p p a p~o f l a a a P B H P B O P a f l a B B P a B H B a n a o p a n n a o P B B H B a p o B P a o B f l a B a o f l f l 'g B'm n n
178
Appendix C
[Dquwyl nstrument descriptor! Xjtput Power 1
1 i.bc il
: t e ]|
lZE]|
*
/ISA sessiônl
S l l M e a su r e m e n ts
k a r t Frequency (GHzM
- J ___________
e œ
□ tf □ d D O □ □ o □ g □ □ □ n 1^11 ro ^g-i
□ p fl
]
Ùa ÜÜa
aaaflaaoaaaacrB
k e p Frequency
True K
asurinq Frequency I
This will do the followings;
I . Initialise all test equipments.
Configure the power supply.
3. Configure the frequency
xxirce.
t. Configure the data
acquisition unit.
5. Record measurements for
aach frequency step.
rLoads 51
instrument descriptor
IobliT
jutput Po'/;er •
l.OOE+6
M Chan Outcn
Istop Frequency (GHz) |
[“»'•] I
3 -
h
putput Power (dBm)l
j
lioool- 0
Skip CaibrationI
□ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ b aa D b p aaD n D D D
O D O oooo ooo d o □
n B o o o a g P D D P P O o n a a D B D P o a D P D O B o o a a o p p o o' o n a p p o o o b p o a n p a p p p p p p o ‘b '6 a a o o i
179
Appendix C
This perform the calculations of the
refiectbn and transmission coefficients:
S l l , S22, 521, 512.
□□□□□□□□□
OOOOOOOQOaOOOOOOOOOOOOQOOOHzKUl HW^ aOOOOOOOOOOOOOOOOOOOOOQOO
^pWWWWBBWOWWOPWWWWW
521 Caicuiations
su
I
7=001
II
F req _ 5 2 l |
521
521 Corrected Datai
|P C .y r e ':te d Mag ;[
21 Un-Corrected Data]
Insertion i
1 Corrected With 511
DUT-:_521i
Corrected)!
[obÜ
k21 Uncorrected I
[0 8 i;
krroroutl
•H i ■°‘ * il
OODOOOOOQ
0000000000000000000000000000000000000000000000000000000000:
180
Appendix C
This perform the calculations of the system calbratlon constants and the measurement coefficients of DUT.
[DBl] I
521 Corrected Datai
Through
521 UrhCcrrected Data]
Reflection 511 DUTi
521 Corrected With S ill
:i Corrected With S ll
ilO.OO
181
Appendix C
' ™ lMATLABScriptT
%This Programm will calculate for the Insertio for the TWO PORT System.
%RT=Ratio of the Through power to the incident power
%Pi2= is the the Through power when comecteing through.
%Pi 1= is the the Incident power when comecteing through.
%Pd2= is the the Through power when comecteing Unkown device.
% Pdl= is the the Oncidet power when comecteing Unkown device.
if
521(dB
RT=pi2/pil;
nod 1 1
. P.d=pd2/pdl;
z iiJ n c o
RTcorrect=RdyRT;
M correct
S2 lUnco= 10*bg 10(Rd);
S21=10*log 10(RTcorrect);
error outi
sC
JCHEII
182
Appendix C
.TLAB Script F - —
%This progam calcJates the reflection coeffedent using MATLAB software
al= (pol-psl)/(4*pll);
a2'(po2-ps2)/(4*pl2);
-^21 a3=(po3-ps3)/(4*pl3);
p
P
^
c l-ab s(al+ b l* i)^ 2 ;
c2-abs(a2+b2*l)^2;
C3=abs(a3+b3*i)^2;
- - 11’
r
Theta=atan(imag(r)/real(r))*(180/pl)
L
Popenl= pll*abs(l+ cl)^2;
P shortl=pll*abs(l-cl)^2;
: %solylng for the 2nd metfiod of Rx and Ry
^ A 0 = cl* ((p d 2 /p l2 )-l)-(c2 * ((p d l/p ll)-X ));
I Al=2*(a2*cl-al*c2);
_ _ !^ iA 2 = 2 * (b l* c 2 -b 2 * c l);
RrftecttonCoef Maol
B 0=cl*((pd3/pl3)-l)-(c3*((pdl/pll)-l));
J ; ^ l - 2 ‘ (a3*cl-al*c3);
^ ' ‘“ ■2*(bl*c3-b3*cl);
Rx-(A2*BO-AO*B2)/(A2*B1-A1*B2);
_ ; Ry=(A0*Bl-Al«B0)/(A2*Bl-Al*B2);
I
BtunLossI
[PHll
r-Rx+Ry*i;
-bdllR=4bs(r);
Rloss--20*logl0(R)
:ZL=50*(l+r)/(l-r);
183
Appendix D
Appendix D
High Frequency
Multi-Probe
Reflectometer
In
MMIC
Design
184
Appendix D
il'”i
iimil
■i’ : n M
^
\
'
il#
V.S.s«vVsi.sl^V !i
■f f ' j j
I l il'
', ‘
1. 1
5Éwfch<ItUCOftM
.O'
D8(S11J,strlp_n0.cM 00(3121. strip_110.d-------
08(3221 strip n o . d i i
ntOMrxvtOHZ]
185
Документ
Категория
Без категории
Просмотров
0
Размер файла
16 469 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа