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A microwave nonlinear network analyser

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THE U N IV ER SITY OF CALGARY
A M icrowave Nonlinear Network Analyser
by
Robert Walton
A THESIS
SUBMITTED TO THE FACULTY OF GRADUATE STUDIES
IN PARTIAL FULFILLM ENT OF TH E REQUIREM ENTS FO R T H E
DEGREE OF M A STER OF SCIENCE
DEPARTMENT OF ELECTRICAL ENGINEERING
CALGARY, ALBERTA
AUGUST, 2000
© Robert Walton 2000
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THE UNIVERSITY OF CALGARY
FACULTY OF GRADUATE STUDIES
The undersigned certify that they have read, and recommend to the Faculty of Graduate
Studies for acceptance, a thesis entitled, “A Microwave Nonlinear Network Analyser”,
submitted by Robert Walton in partial fulfillment of the requirement for the degree of
Master of Science.
Supervisor, Dr. R. H. Johnston*
Department of Electrical and Computer Engineering
Co-supervisbn Dr. L G ^ jb R o ry
Department of ElectricalVand Computer Engineering
Dr. E. P. Nowicki
Department of Electrical and Computer Engineering
^
v
Dr. D. J. I. Fry
/
Department of Physics and Astroriomy
2-1
Date
ii
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Abstract
There has been a dramatic increase in the demand for wireless communication services.
To be successful, a cell phone system must be cost effective and spectrally efficient, and
provide users with long battery life. To meet these demands, the nonlinear behaviour of a
system’s microwave components cannot be ignored. This thesis presents the development
and verification of a Nonlinear Network Analyser (NNA) that looks at the amplitude and
phase of the harmonics generated by a nonlinear microwave network up to 18 GHz. There
is no commercial tool that can do this, leaving designers with an incomplete view of how a
network is working. One use for the NNA is to measure the voltage and current waveforms
at a transistor, giving a designer a tool to tune the operation of power amplifiers. The NNA
also provides information useful to the development of more accurate nonlinear models,
which can reduce design time.
iii
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Acknowledgments
I would like to acknowledge my supervisors Dr. John McRory and Dr. Ron Johnston
for their help. I am especially grateful to John for the many hours he spent teaching me
about RF when I first started this project. Thanks for the time you spent with me talking
over problems, and introducing me to nonlinear RF analysis. And thanks for all your help
with writing and editing this thesis.
Thanks to all the staff and students at TRLabs. I don’t think there is a single person who
hasn’t helped me in some way or another. Thanks specifically to Rob Randall, Sean Hum
and Carl Conradi for the many fruitful discussions and your help tinkering in the lab.
Thanks to Anthony Lo for all the computer help and to Grant McGibney who explained
everything there is to know about fast Fourier transforms. Thanks to John McRory and
Chris Holdenreid for designing and laying out the test fixture for the MRF284.
From the University of Calgary, thanks to John Shelley and Ed Evanik for milling cir­
cuit boards. Thanks to Frank Hickli and Pat Wals.h for giving me free rein in the machine
shop, and showing me how everything works.
Thanks to George Squires, Leila Southwood and TRLabs for providing such a great
work atmosphere. Although the work on this thesis is quite specific, I feel that the open
atmosphere at TRLabs has let me learn about many aspects of the broad telecommunica­
tions field. This thesis would have been impossible to complete without the equipment sup­
plied by TRLabs’ sponsors.
Finally, thanks to TRLabs, NSERC and the University of Calgary for the financial sup­
port that made my studies possible.
iv
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For
Cindy and fo r my family.
Thanks fo r all the support.
v
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Contents
Approval Page...............................................................................................................
ii
A bstract.........................................................................................................................
iii
Acknowledgments.........................................................................................................
iv
Dedication......................................................................................................................
v
Contents.........................................................................................................................
vi
List of T a b le s ...................................
ix
List of Figures...............................................................................................................
x
List of Symbols and Abbreviations............................................................................
xiii
1 Introduction
1
2 Nonlinear Network Measurement
6
2.1 Measurement of Microwave Networks................................................................
7
2.2 Nonlinear Effects...................................................................................................
11
2.2.1
Microwave Power A m p lifiers...............................................................
12
2.2.2
Microwave Signal Distortion..................................................................
17
2.3 Nonlinear Network Analyser O verview ............................................................
20
2.3.1
Phase M easu rem en t...............................................................................
21
2.3.2
Sampling The W aveform s.....................................................................
22
vi
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3 NNA Implementation
24
3.1 System Overview......................................................................................................
24
3.1.1
Hardware Description and O p e ra tio n ......................................................
25
3.1.2
Systematic and Random Errors...................................................................
27
3.2 Removing Errors With Calibration..........................................................................
30
3.2.1
The System Error M odel............................................................................
30
3.2.2
Error Correction M a tr ix ............................................................................
34
3.2.3
Generating the Error M odels......................................................................
35
3.3 Linear Calibration T e c h n iq u e................................................................................
36
3.3.1
SOLT Calibration M athem atics................................................................
36
3.3.2
SOLT Calibration Standards M odelling...................................................
38
3.4 Absolute Calibration Technique.............................................................................
41
3.4.1
Absolute Amplitude Calibration...............................................................
41
3.4.2
Absolute Phase Calibration.........................................................................
42
3.5 D e-em bedding.........................................................................................................
44
4 NNA Verification
47
4.1 Flat Group Delay Assum ption...............................................................................
48
4.2 Timebase Error M easurem ent...............................................................................
52
4.3 Linear Calibration Verification...............................................................................
56
4.4 Schottky Diode M easurem ent...............................................................................
59
4.4.1
Fixture E x tractio n .....................................................................................
60
4.4.2
Diode Measurements..................................................................................
63
4.4.2.1 Comparison of Measured and Modelled W a v e s......................
63
4.4.2.2 Voltage and Current M easurem ent............................................
65
4.4.2.3 Comparison with Direct Voltage M easurements......................
67
vii
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5 Power Transistor Measurements
69
5.1 The Fixture D esign...............................................................................................
70
5.2 Fixture E x tra ctio n ...............................................................................................
72
5.2.1
Fixture Model Extraction.........................................................................
74
5.2.2
Fixture Parameter Verification................................................................
77
5.2.3
Calibration and Fixture De-embedding Verification.............................
80
5.3 Transistor Measurements.....................................................................................
83
5.3.1
Comparison with M o d e l.........................................................................
84
5.3.2
Matching with Tuners or Loadpull S y s te m .........................................
87
5.3.3
Verification of Waveforms with Ohm’s L a w ......................................
90
5.4 Proposed Amplifier Tuning T e c h n iq u e ............................................................
92
6 Conclusion
6.1 Thesis S um m ary..................................................................................................
96
96
6.2 Future W o rk ............................................................................................................ 100
A NNA Lab View Software Guide
102
References
117
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List o f Tables
Chapter 5
5.1
Scattering parameters of through with amplifier re m o v e d ............................
81
5.2
Scattering parameters of through with amplifier connected............................
82
5.3
Extracted Zload and measured Zioaci at different power levels........................
91
ix
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L ist o f Figures
Chapter 2
2.1
Voltage and current definitions of a two port n e tw o rk ....................................
8
2.2 Travelling wave and scattering parameter d e fin itio n s....................................
9
2.3
A typical single-stage microwave power amplifier...........................................
12
2.4
Typical FET class-A power amplifier load line................................................
13
2.5
Output against input power for linear and nonlinear am plifiers....................
14
2.6
Ideal voltage and current waveforms for a class-B amplifier...........................
15
2.7
Output spectrum of a nonlinear amplifier with a two tone inp u t.....................
17
2.8
Intermodulation distortion of a typical digital communicationsignal . . . .
18
2.9
NNA system schematic.......................................................................................
20
Chapter 3
3.1
NNA s y s te m .......................................................................................................
25
3.2
Picture of NNA showing a brass fixture and the oscilloscopeinputs...............
27
3.3
Signal flow graph describing one half of the NNA system ..............................
31
3.4
Simplified physical m o d e l ................................................................................
32
3.5
Greatly simplified error model for one measurementp o r t..............................
33
3.6
System error model for both measurement po rts............................................
33
x
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3.7
Definitions for a standard..................................................................................
39
3.8
A device in a fixture............................................................................................
44
3.9
Signal flow graph model for fixture extraction................................................
45
Chapter 4
4.1
Amplitude and phase deviation of the measured step from being ideal . . .
50
4.2
Oscilloscope phase error from Jan Verspecht’s dissertation [ 8 ] ...................
52
4.3
Repetitive waveform being sampled and then reconstructed..........................
53
4.4
Measured timebase distortion............................................................................
54
4.5 Spurious tones caused by timebase distortion in a sampled 3 GHz t one. . .
55
4.6 Connection of splitter for linear calibration verification.................................
56
4.7 Measured S\ i phasors from 200 MHz to 4400 M H z .......................................
58
4.8
Measured S2I phasors from 200 MHz to 4400 M H z .......................................
58
4.9
Schematic of the diode mounted in the test fixture..........................................
59
4.10 Model for the low reflection diode fix tu re ......................................................
60
4.11 Measured and simulated waves at the d io d e ...................................................
63
4.12 Voltage across the diode as the input voltage is sw e p t...................................
66
4.13 Current through the diode as the input voltage is s w e p t................................
66
4.14 Direct voltage measurement and NNA measurements...................................
67
Chapter 5
5.1
An MRF284 mounted in the fix tu re ................................................................
71
5.2
NNA system used to measure MRF284 .........................................................
73
5.3
Model used to describe the input and output fixtures......................................
74
5.4
Comparison of S21 amplitude of measured and extracted fixtures................
75
5.5
Comparison of 521 phase of measured and extracted fix tu re s.......................
76
xi
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5.6
Root choice of A 2\ parameter...........................................................................
78
5.7
Extracted real and imaginary output im pedance...........................................
79
5.8
Extracted real and imaginary input impedance...............................................
79
5.9
Modelled and measured drain w aveform s.....................................................
85
5.10 Modelled and measured gate waveforms........................................................
85
5.11 Load line at the package e d g e ........................................................................
86
5.12 Tuned and un-tuned external load lines...........................................................
88
5.13 Tuned and un-tuned internal load lines...........................................................
88
5.14 Simplified diagram showing the drain voltage, current, and l o a d ...............
90
5.15 Drain waveforms with two different load im pedances..................................
94
5.16 Gate waveforms with two different load im p ed an ces..................................
94
Appendix A
A.1
NNA interface hierarchy showing panel names and describing inputs. . . . 103
xii
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List of Symbols and Abbreviations
Chapter 1
CDMA
Code Division Multiple Access
LDMOS
Laterally Diffused Metal Oxide Semiconductor
NNA
Nonlinear Network Analyser
Chapter 2
di
forward travelling voltage wave at port /
b-t
reverse travelling voltage wave at port /
dB
logarithmic ratio of two powers; 101og(powerl/power2)
DC
Direct Current
fl
lower frequency for two tone test
fl
upper frequency for two tone test
FFT
Fast Fourier Transform
/drain
current entering drain
/,*
current entering port /
/load
current entering load
kSymbol/s
thousands of symbols per second
RF
Radio Frequency
xiii
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^yx
scattering parameter; reverse wave at porty over forward wave at port*
^drain
drain bias voltage (DC)
vgate
voltage from gate to ground
V
gate bias voltage (DC)
ygate
voltage across port i
v Ioad
voltage across load
vsource
internal voltage generated by source
system reference impedance; normally 50 Q.
Zjoad
load impedance offered to amplifier
z source
source output impedance; normally 50 Q.
Chapter 3
a-
measured forward wave at port i with standard s connected
b'im
measured reverse wave at port i with standard s connected
a ic
forward wave at port i calibration plane with standard s connected
b Sic
reverse wave at port i calibration plane with standard s connected
**1C
forward travelling wave at port i calibration plane
a id
forward travelling wave at port i device plane, within fixture
a im
measured forward travelling wave at port i
a,source
forward travelling wave available from source
scattering parameter describing port one fixture half
bic
reverse travelling wave at port i calibration plane
bid
reverse travelling wave at port i device plane, within fixture
b[m
measured reverse travelling wave at port i
'y x
scattering parameter describing port two fixture half
speed of light in a vacuum
XIV
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c^yx
port one error model scattering parameter
^ ^ Io ss
one way loss of line in calibration standard, measured in dB at 1 GHz
dBm
dB with respect to 1 mWatt
DUT
Device Under Test
Dyx
port two error model scattering parameter
£r
<D
relative dielectric constant of line in calibration standard
absolute phase calibration parameter
<f>a
phase from port one calibration plane to a l oscilloscope input
phase from port one calibration plane to b { oscilloscope input
r coup
A
reflection coefficient seen by DUT due to measurement hardware
r'load
reflection coefficient of load standard
rL open
reflection coefficient of open standard
rx
reflection coefficient of standard number x
^ sco p e l
reflection coefficient of oscilloscope channel one input
p
L scope2
reflection coefficient of oscilloscope channel two input
^sh o rt
reflection coefficient of short standard
rL source
reflection coefficient of source
GPIB
General Purpose Interface Bus
GS/s
giga samples per second
^scopel
gain of oscilloscope channel one input
^sco p e2
gain of oscilloscope channel two input
Gyx
measurement hardware coupling gains
K
absolute amplitude calibration parameter
I
length of line in calibration standard
NIST
National Institute of Standards and Technology
P [dBm]
incident power measured by power meter in dBm
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* [watts]
incident power measured by power meter in watts
R
resistance of load standard
R loss
effective resistance of the calibration standards’ line
R rc
row r, column c, of correction matrix
i Vcnorm
D
row r, column c, of correction matrix normalised with respect to i?33
SOLT
Short-Open-Load-Through
■^offset
one way delay of the calibration standards’ line
Vpm
peak incident voltage wave measured by the power meter
ZC
impedance due to fringing capacitance of open standard
Zl
impedance due to inductance of short standard
Chapter 4
A/
frequency difference between samples
N
number of frequency samples
A21est
estimated input fixture A2i scattering parameter
Cp
package capacitance between leads of diode package
<{>(00)
phase delay of through fixture
fn
frequency of nth sample
GaAs
gallium arsenide
bondwire inductance of diode package
Ll
lead inductance of diode package
^fixture
group delay of through fixture
tn
time delay between trigger and nth sample
co
radian frequency
xvi
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Chapter 5
/
!
reflection coefficient of perfect through terminated with Tjoad
FET
Field Effect Transistor
rload
reflection coefficient offered by NNA at port two calibration plane
^source
reflection coefficient offered by NNA at port one calibration plane
I
length of quarter wave transformer
X
wavelength of signal for quarter wave transformer
SMA
Sub Miniature type-A coaxial connector for DC-18 GHz signals
TRL
Through-Reflect-Line
impedance offered to quarter wave line
Zj
impedance looking into quarter wave line
Zijne
impedance of quarter wave line
xvii
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Chapter 1
Introduction
The last decade showed a dramatic increase in the demand for wireless communication
services. To meet this demand for system capacity, cell phone systems must use the avail­
able spectrum very efficiently. Unfortunately, adjacent channel interference limits how
closely communications signals can be packed together in the frequency domain. If a com­
munication signal on a carrier is amplified by a nonlinear power amplifier it will spread out
in frequency and will potentially interfere with adjacent channels. Guard bands, unused
areas of spectrum, separate the bands allocated to different channels, so that signals do not
overlap when they spread out. To reduce the size of this wasted spectrum the nonlinear dis­
tortion from the amplifier which results in adjacent channel interference must be very
small.
Unfortunately, power amplifiers must be operated in nonlinear regions to maximize
their efficiency. Up to two-thirds of the power used by a cell phone in talk mode, is used by
the power amplifier which amplifies the signal before it is sent to the antenna. An attempt
to operate an amplifier in a more linear region unfortunately reduces it’s efficiency, result­
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Chapter 1 Introduction
2
ing in a shortened battery life. For the power amplifiers used in base stations, inefficiency
results in waste heat. This heat must be removed using large heat sinks and cooling fans, or
it can result in decreased device life. More efficient power amplifiers are cheaper to build
and to maintain.
Another issue which makes it very, difficult to amplify modem communication signals
linearly is their digital nature. A Code Division Multiple Access (CDMA) signal is quite
wideband, and can have very high peak to average power ratios. The power in these signals
is very bursty, so, although they may have an average output power of about 25 W, for short
periods of time the output power can be 250 W. To manufacture an amplifier that can pro­
duce signals like these without producing nonlinear distortion is very expensive.
The above factors all indicate that nonlinear effects in cell phone systems, particularly
in power amplifiers, cannot be ignored. A 2 GHz signal amplified by an efficient, nonlinear
power amplifier, can contain harmonics above 10 GHz. Unfortunately, there is no commer­
cial tool which can look directly at the broadband waveforms produced by nonlinear micro­
wave networks. A spectrum analyser can measure, with limited accuracy, the amplitude of
these harmonics in the frequency domain, but cannot measure the phase. A linear network
analyser can measure the amplitude and phase of a single tone entering and leaving a net­
work. However, a linear network analyser assumes that the network is linear. It gives no
indication of the actual shape of the waveforms; it assumes they are single sinusoids. This
is, of course, an incredibly useful tool for characterising linear networks such as filters or
for characterising the small signal behaviour of amplifiers. The best way to look at the
shapes of the waveforms in a nonlinear microwave network is actually to use a simulator,
which uses nonlinear models of the network’s components to predict the network’s voltage
and current waveforms. However, nonlinear models are difficult to generate because it is
not possible to fully measure the output o f a nonlinear device. These models are often based
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Chapter 1 Introduction
3
on very large sets of data measured with a linear network analyser with different device bias
conditions and input powers. There are many techniques for designing nonlinear circuits
with limited information about how they are operating. However, not having all the infor­
mation is obviously a big disadvantage and greatly hinders the design process. An instru­
ment that can fully characterise the microwave signals entering and leaving a device would
increase model accuracy and allow new insight into nonlinear circuit operation.
In this thesis the development and verification of a Nonlinear Network Analyser (NNA)
is presented. This is a system that stimulates a two port microwave network with a signal,
and then looks at the amplitude and phase of the voltage and current waveforms at the net­
work edge. In the time-domain, it gives the actual shape of the waveforms; it does not
assume they are sinusoids as a linear network analyser does. The goal of the research under­
lying this thesis was to build and verify the operation o f an NNA capable of measuring har­
monics up to 18 GHz. This tool will likely be used b y students for device modelling and
microwave circuit design projects.
NNAs are not commercially available, although several prototypes with limited capa­
bilities have been built [1-3]. A simple but versatile design, based around a wide bandwidth
sampling oscilloscope, was proposed by Jan Verspechit working for Hewlett-Packard [4].
This thesis presents an implementation of an NNA sim ilar to Jan Verspecht’s. A modified
calibration routine is used that assumes the sampling heads of the wide bandwidth oscillo­
scope have flat group delays. This assumption simplifies the calibration routine, and
reduces the cost of the system gready. The NNA is a rack of mainly commercially available
equipment. A computer controls the equipment and provides a graphical user interface that
automates almost every aspect of the measurement process.
Chapter 2 contains a discussion about microwave network measurement, nonlinear
devices and the theory behind the NNA. This chapter includes an explanation of what the
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Chapter 1 Introduction
4
NNA is designed to do, and why it is useful. The reasons why it is difficult to look at microwave-frequency waveforms are discussed and a technique to determine the voltage and cur­
rent waveforms by measuring travelling waves is presented. The operation of microwave
power amplifiers and the various nonlinear effects discussed in the introduction are
explained. Finally, with the need to measure the nonlinear waveforms generated by net­
works established, the NNA measurement system is introduced.
Chapter 3 focuses on how the NNA works in detail. The NNAs hardware and operation
are presented. Sources of measurement error and some techniques used to reduce them are
examined. The bulk of this chapter deals with calibration, the removal of systematic errors
caused by the measurement hardware. The error model used to remove the systematic errors
in a measurement is derived, and a technique for determining these parameters is presented.
Some devices must be put in a fixture before they can be connected to the NNA. De-embedding, the process of removing the effects of a fixture from a measurement, is discussed.
In Chapter 4 results that verify the operation of the NNA are presented. This is difficult,
since there is no similar system that looks at waveforms directly to compare measurements
against. The procedure used was to test any assumptions made, each component part o f the
calibration routine, and finally the entire NNA. The flat group delay assumption used to
simplify the calibration routine is validated. A measurement of the timebase distortion of
the oscilloscope used in the NNA is presented. The effects of this error on a measurement
are shown and a technique for reducing the effects is discussed. Measurements of a splitter
taken with the NNA are compared with measurements taken using a linear network ana­
lyser, to verify that the bulk of the calibration routine is working. Measurements taken of a
Schottky diode using the NNA are compared with waveforms predicted by a model to dem­
onstrate that the other calibration procedures are working correctly.
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Chapter 1 Introduction
5
Chapter 5 is concerned with the measurement of a Motorola MRF284 Laterally Dif­
fused Metal Oxide Semiconductor (LDMOS) transistor. Characterising this device’s non­
linear behaviour is greatly complicated by the low input and output impedances the device
must be offered to operate correctly. The goals of this chapter are to present techniques used
to measure low impedance devices, and to show that the effects of tuners, used to change
the impedances offered to the device, can be removed from measurements. The fixture
which was designed to offer the device low impedances is described, and the extraction
technique used to model the fixture is presented. Measurements taken of the device using
the NNA are compared with predictions from a model. An iterative design technique
method for building an amplifier using the NNA is proposed, and some measurements
which show its validity are presented.
Finally, Chapter 6 gives a brief summary of the work presented. Some possible future
research which could be performed using the NNA is also discussed.
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Chapter 2
Nonlinear Network M easurem ent
In this chapter microwave network measurement, nonlinear devices and the theory behind
the Nonlinear Network Analyser (NNA) are discussed. An NNA measures the voltage and
current waveforms at a calibration plane. The NNA described in this thesis measures the
harmonics in a waveform up to 18 GHz. Although it has already been briefly discussed in
Chapter 1, this chapter contains an explanation of what an NNA is designed to do, and why
it is useful. In Section 2.1 reasons why it is difficult to look at waveforms at these micro­
wave frequencies are discussed, and a technique to determine the voltage and current wave­
forms by measuring travelling waves is presented. In Section 2.2 some nonlinear effects
seen in power amplifiers are described. It will be explained why amplifiers cannot always
simply be operated in a linear way. The effects of nonlinear amplification on digital com­
munication signals are also discussed. In Section 2.3 the NNA measurement system is
introduced, and some fundamental issues related to waveform sampling are presented.
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2.1 Measurement of Microwave Networks
7
2.1 Measurement of Microwave Networks
At low frequencies, an oscilloscope probe can be used to look at the voltage and current
waveforms in a circuit directly. At high frequencies it is not that simple because attaching
a probe affects a circuit’s operation, and because the voltage and current waveforms in a
network are a function of position. In this section these problems are discussed and a tech­
nique to measure waveforms in microwave networks is explained.
At microwave frequencies it is not possible to probe a circuit without affecting its oper­
ation. Microwave circuits are very sensitive to any change in either the input or the output
impedance they are offered. Even the effects of attaching a probe could greatly affect the
circuit’s operation, invalidating any measurements taken.
The distributed nature of microwave circuits means that the voltage and current on a
section of transmission line are a function of distance. Suppose a 1 GHz tone is connected
at one end of a transmission line. The wave travels at, or under, the speed of light depending
on the dielectric constant of the medium. Assuming free space, the voltage 6 inches down
the line was actually generated by the source 0.5 ns earlier. If the voltage is at the peak of
its positive cycle as the wave enters the line then 6 inches away the voltage will still be at
the peak of its negative cycle. Because the wavelength of the signals used in microwave
circuits is of the same order as the size of the circuits, microwave circuits are referred to as
being distributed. For low frequency circuits, components can be thought of as being
lumped together; only the topology of their connections is important, since the voltage
anywhere along a connecting line is approximately the same. If voltage and current
waveforms are measured in a microwave circuit or system they must be defined at a certain
cross-sectional reference plane.
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2.1 Measurement of M icrowave Networks
8
Both the impedance problem and the measurement reference plane problem can be
addressed if the device or system under test is treated as a two port network. Figure 2.1
shows how reference points are defined at the input and the output planes of a two port net­
work. In the diagram, v represents voltage, i represents current, and the subscripts indicate
port numbers.
fwStorBNewi/oi
Figure 2.1: Voltage and current definitions of a two port network
One definition of a linear network is simply that it adds no new tones to a signal. If a
sinusoidal voltage is applied to port one, then a sinusoidal current will flow into port one,
and the voltage and current at port two will also be sinusoidal, all at the same frequency as
the applied voltage signal. There are a number of different linear models that can be used
to describe a two port network in the frequency domain using four phasors at each fre­
quency of interest. These circuit models, which relate voltage and current, are determined
by shorting or leaving open one of the ports. These models can be used to indirectly deter­
mine the current from known voltages. However, this cannot be done at Radio Frequencies
(RF), firstly because it is very difficult to build a short or an open at RF, but also because
many microwave circuits will not work if they are offered a short or an open. In general
linear techniques for determining the current at each port from measured voltages are
invalid when dealing with nonlinear networks.
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2.1 Measurement o f Microwave Networks
9
Instead of measuring the voltage and current waveforms in a microwave network
directly, travelling voltage waves are measured and modelled. These travelling waves are
defined with reference to Figure 2.2 and are represented by complex phasors describing
bz
Two Port Network
£>1
a2
Figure 2.2: Travelling wave and scattering parameter definitions
their amplitude and phase. The a terms represent forward travelling voltage waves and the
b terms represent reverse travelling voltage waves. The subscripts denote the port number.
The S parameters are scattering parameters that model the ratios of the travelling waves at
a single frequency assuming that the network is linear and terminated with a defined refer­
ence impedance. The scattering parameters are defined as
Sn =
s
a,
21 " a,
c
°12
a2 = 0
a-, = 0
—
“
an
<2[ = 0
a, = 0
.
( 2 - 1)
Travelling waves behave like light waves. If a light ray is incident to a block of glass, some
light will be reflected back, and some will be transmitted through. The phasor
describes
the phase and amplitude of a tone incident to a two port network, b\ describes the tone that
is reflected, and 62 describes the tone that is transmitted.
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2.1 Measurement of Microwave Networks
10
To visualise how travelling waves relate to voltage and current, imagine a sinusoidal
voltage source injecting a signal into one end of a transmission line. This voltage results in
a travelling wave moving along the line toward an impedance terminating the other end.
Coaxial lines are easily built with an impedance of 50 Q , so this value is often defined as
the reference impedance. If the impedance at the end of the line is 50 £1, the same as the
reference impedance, all the power in the forward wave will be absorbed by the terminating
impedance, since there is no mismatch between the line and load impedances, and there will
be no reflected wave. However, if the load is a perfect short, all the power in the forward
wave is reflected, like light hitting a mirror. When light hits a mirror, the electric fields of
the incident and the reflected waves must add to zero at the mirror’s surface; the incident
and reflected waves must therefore have opposite signs. Similarly, when the forward wave
hits the short, the wave is inverted, or the phase changed by 180°, and it is returned as the
reflected wave. When the two voltage waves add at the short, they add out of phase giving
zero volts. Following the same reasoning, if the forward wave hits an open impedance, the
reflected wave will be reflected with no phase change. When the two travelling waves are
summed, the voltage at the open will actually be twice that of the voltage wave launched
into the line.
The voltage and current at a port can be calculated from the forward and reverse waves
using
v{- = ai + bi
i = ai ~ bi
z0
.
(2 - 2 )
where Z0 is the reference impedance, and vj and /; are the voltage and current at port i
respectively. It is standard to normalize ax and b[ with respect to the reference impedance,
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2.2 Nonlinear Effects
11
so that squaring them gives the the power in the forward and reverse waves respectively.
This thesis deals with the indirect measurement of the voltage and current through sampling
the travelling voltage waves. For these purposes it is best to leave the travelling waves un­
normalized. This way they can then be thought of as physical voltages moving down a line,
the sum of which, at any point, results in a real voltage.
The forward and reverse travelling waves are separated using directional couplers. As
will be discussed in Section 2.3, these waves can be sampled a distance from the device
being measured without affecting the impedances offered to the device. Due to the distrib­
uted nature of microwave circuits discussed above, these travelling voltage waves are a
function of where they are measured. A large part of this thesis deals with estimating the
waves at the network edge from the waves sampled a distance from it.
2.2 Nonlinear Effects
Linear microwave circuits can easily be modelled using the scattering parameters described
in Figure 2.2 and in (2-1). At each frequency of interest, four complex scattering parame­
ters completely model a linear circuit. These scattering parameters can be measured
directly using a linear network analyser. Although very expensive, linear networks analys­
ers assume a device is linear; they will not measure the shape of the actual forward and
reverse waves, but assume they are all pure tones. In this section some nonlinear effects
which, it will turn out, can only be fully characterised using an NNA are explained.
Section 2.2.1 focuses on explaining why microwave circuits, specifically power amplifiers,
must sometimes be operated in regions where they behave in a nonlinear way. In
Section 2.2.2 the unwanted signal distortion which results from this nonlinear behaviour is
explained.
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2.2 Nonlinear Effects
12
2.2.1 Microwave Power Amplifiers
Microwave signals are amplified by power amplifiers before being sent to antennas where
they are radiated into the air. Most of the signals are carrier tones modulated with informa­
tion which is relatively narrow band when compared with the carrier frequency. It is
assumed in this discussion that these signals can be treated as single tones; a pretty good
approximation to examine some nonlinear effects. Figure 2.3 shows a typical single-tranOutput Match
drain
gate
hoad
gate
Input Match
Figure 2.3: A typical single-stage microwave power amplifier
sistor microwave power amplifier. Vgate and Vdrajn are the DC bias voltages at the gate and
drain respectively. A voltage vsource is generated from a source which has an output imped­
ance zsource. The input match is a circuit which takes the impedance offered by the source,
and changes it to an impedance seen by the gate of the device in order to minimize any mis­
match. The changing gate voltage vgate sets up a changing current through the drain of the
device to ground. The drain DC bias inductor has a constant current flowing through it
which the load current ijoad and the drain current idrain must sum to. When the gate voltage
increases, idrajn increases resulting in decreasing qoad and a corresponding decrease in the
load voltage vjoad across the load impedance zload.
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2.2 Nonlinear Effects
13
A load line, shown in Figure 2.4, is used to show how vdrain and /drajn ^
related. The
curved lines are DC bias curves. Each curve represents /drain as a function of vdrairl, with
Vgate kept at a constant DC value. As Vgate is increased, more current flows for a given vdrain.
The thick line is the load line, which represents how vdrain is a linear function of /drain. The
slope of the load line is determined by zload- The plotted load line is that of a class-A ampli­
fier. The gate and drain DC bias voltages are chosen so that with no input voltage, the device
operates at the DC bias point indicated on the graph. Now, if a small input tone is applied,
the amplifier state is described by a point moving up and down the load line, only a very
small distance from the DC operating point. However, for the large gate voltage swing indi­
cated on the graph, the load line is compressed at each end. A certain incremental change
in vgate results in different changes in /drain, depending on where on the load line the tran­
sistor is operating. The current is clipped at the bottom as the device enters cutoff and the
current is clipped at the left as the device leaves the saturation region, entering the triode
region.
Triode- Saturation
'''gate
Cutoff
'''drain
Figure 2.4: Typical FET class-A power amplifier load line
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14
2.2 Nonlinear Effects
When the input to the device is small, the output is not compressed; the behaviour is
predominandy linear. However, when the input voltage increases and the full swing of the
load line is utilized, the device enters what is called compression; the behaviour is now pre­
dominandy nonlinear. Figure 2.5 shows the output power at the fundamental frequency as
a function of the input power. For an ideal linear amplifier, the gain is constant so the power
1 dB Compression
Nonlinear
Linear
Input Power (dB)
Figure 2.5: Output against input power for linear and nonlinear amplifiers
curve is a straight line. However, the power in the fundamental of the output does not
increase linearly in a real amplifier. A point called the 1 dB compression point is defined as
the point where the gain has been compressed by 1 dB. If driven much beyond compression,
most devices will suffer junction breakdown or overheat, and can fail if not shut off quickly.
When the device nears compression, any data modulated onto the input tone will become
distorted, as discussed in Section 2.2.2.
So, knowing that this compression occurs, why is the power into an amplifier not simply
backed off so it always behaves linearly? This is done for low output power amplifiers
which are are often used in receivers, or used to drive power amplifiers. Power amplifiers
cannot always be backed off due to issues of efficiency and cost:
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15
2.2 Nonlinear Effects
Modem digital communication signals have very high peak to average power ratios.
This means that the energy in the signal is not evenly distributed but has large spikes in the
time domain. A signal with a peak to average ratio of 10 dB that has an average power of
25 W, can have peak powers of up to 250 W for short periods of time. To make an amplifier
that could amplify signals like these linearly would be very expensive, since it must be
designed to amplify 250 W signals linearly.
The other issue that forces amplifiers to be operated nonlinearly is efficiency. The effi­
ciency of an amplifier is a measure of how well it produces output power from the DC
power supplied to it. As discussed in Chapter 1, wasted power reduces battery life in mobile
phones and increases the cost of base station amplifiers.
Looking at Figure 2.4, the actual power delivered to the load is a function o f the dis­
tance between the end points of the load line, or the voltage and current swing. There are
numerous classes of amplifier which are more efficient than the class-A amplifier whose
load line is presented. The DC bias point, the input power, and the output impedance at the
fundamental and harmonic frequencies can be tuned to change the load line. Figure 2.6
shows the drain voltage and current for an ideal class-B amplifier, obtained by adjusting the
Current
Voltage
C
£
3
o
CD
O
)
CO
I
c
2
Q
180
360
540
72I
Phase (degrees)
Figure 2.6: Ideal voltage and current waveforms for a class-B amplifier
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2.2 Nonlinear Effects
16
gate bias voltage to get a 180° conduction angle of the current. This amplifier is more effi­
cient than a class-A amplifier because when the voltage across the device is high, there is
no current flowing. This reduces the power dissipated in the device and increases the effi­
ciency of the amplifier.
Tuning the waveforms to produce amplifiers with certain characteristics is quite diffi­
cult, primarily because there is no commercial tool which can look at the shape of the load
line. A linear network analyser will only look at the linear, or small signal, part of the load
line. The current waveform in Figure 2.6 as measured by a commercially available linear
network would be sinusoidal. The best commercial tool to look at these waveforms is actu­
ally a simulator, which estimates the waveforms using nonlinear models. Unfortunately, the
models are difficult to generate and are often inaccurate, again because there is no tool to
measure nonlinear waveforms directly. These models are normally generated from a very
large number of linear measurements taken at different bias points. The NNA, discussed in
the next section, measures these voltage and current waveforms. It can be used to increase
the accuracy of the device models, and also to actually visualise the waveforms in an ampli­
fier or other network.
Other methods to estimate how a device is operating are based on evidence that can be
measured using existing tools. For example, when building a class-A amplifier, the DC
drain current gives a good indicator of what is happening. If the input power is increased,
and the DC current suddenly increases, this is an indicator that the bottom of the current
waveform is clipping more than the top. Another useful tool is the spectrum analyser. This
measures the power of all the harmonics in the output waveform. It won’t measure the phase
of the harmonics however, so it cannot actually measure their shape. There are a great
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2.2 Nonlinear Effects
17
number of ways to get around the problem of not being able to measure the waveforms
directly. However, all of these techniques are estimates and cannot ever fully describe how
a device is operating.
2.2.2 Microwave Signal Distortion
As described above, devices must sometimes be used in nonlinear regions of operation.
This can be desirable to tune an amplifier’s load line, but it will also distort the shape of the
signal being amplified. Figure 2.7 shows the output spectrum of a fifth order nonlinear
system excited by two tones spaced closely together at frequencies/! and/2. The order of
2fz
Frequency
Figure 2.7: Output spectrum of a nonlinear amplifier with a two tone input
a network, in the frequency domain, refers to the maximum number of tones which are
mixed together within the network to generate a new tone. Notice that there are groups of
tones in the output around the first, second, and third harmonic multiples of the input fre­
quency. The groups at the second and third harmonic frequencies are not a big issue,
because, although they may be required for the amplifier to operate correctly, they can be
filtered out before being sent to an antenna. The four unwanted tones around the tones at f i
and fa cannot be easily removed by filtering because they are so close to the desired tones.
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2„2 Nonlinear Effects
18
When a real communication signal is amplified by a nonlinear amplifier, the output
spectrum is spread as shown in Figure 2.8. A 125 kSymbol/s, DQPSK (Differential Quad­
rature Phase Shift Keying) input signal, centred at 1.8 GHz, was amplified by a Mini-Cir­
cuits ZFL-2500, 30 dB gain amplifier, and measured with a spectrum analyser. This is a
-30
Input
Output
-40
-50
-60
-70
-80
£
-90
-100
v A
f -
-110
-120
1.7996
1
1.7997
‘
1.7998
i
‘
'
1.7999 1.8000 1.8001
Frequency (GHz)
/ /a
‘----------
‘
1.8002
1.8003
1.8004
Figure 2.8: Intermodulation distortion of a typical digital communication signal
typical signal used in digital communication systems, and can be used to transmit two bits
o f information per symbol, without the need to estimate the carrier phase at the receiver.
The input signal was filtered with a 0.35 roll off raised square root cosine filter, to limit the
signal’s 3 dB bandwidth to around 125 kHz. Notice that the output signal is 30 dB larger
than the input signal, but that it has become spread in frequency. The first shoulders, around
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2.2 Nonlinear Effects
19
35 dB down from the desired signal, are third order intermodulation distortion products.
The second shoulders, about 6 dB above the noise floor, are 5th order intermodulation dis­
tortion products. This signal spreading is very undesirable, as the unwanted products often
fall within neighbouring frequency bands causing adjacent channel interference. Adjacent
channel interference makes it difficult to receive signals in the neighbouring bands, because
they have an unwanted signal imposed on them.
It is desirable to operate a device in a nonlinear way, to optimize amplifier efficiency
and minimize cost, but this results in intermodulation distortion which cannot be tolerated
if it interferes significantly with neighbouring frequency bands. There are many lineariza­
tion techniques which can reduce the distortion added by a nonlinear amplifier. However,
for wideband amplifiers it is difficult to model this intermodulation distortion using existing
techniques. This makes it difficult to investigate new linearization techniques, and to
improve the performance of existing ones. The NNA will give useful information about the
distortion in an amplifier, which can be used to produce models which would help with the
development of linearization techniques. The NNA can also be used to produce improved
models of the devices used in amplifiers. Current models can estimate the drain waveforms
for a single tone, with some degree of accuracy. However, for two tones, or real communi­
cation signals these models are not very accurate. Simulating how a nonlinear device will
operate, and the resulting signal distortion, may make it possible to design amplifiers which
operate nonlinearly, but which produce reduced levels of intermodulation distortion, even
without linearization.
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2.3 Nonlinear Network Analyser Overview
20
2.3 Nonlinear Network Analyser Overview
As indicated in Section 2.1, the NNA does not measure the voltage and current at the two
device ports directly. Instead, the forward and reverse voltage travelling waves are sampled
at each port and (2-2) is used to calculate the voltage and current waveforms. Figure 2.9
shows the basic NNA system. The signal source generates a signal which is connected to
Signal Source
Ref
Wideband Scope
"•>1
Directional Coupler
Fixture
Directional Coupler
Figure 2.9: NNA system schematic
either port one or port two of the Device Under Test (DUT) using a mechanical switch.
Whichever port is not connected to the source is terminated with a 50 Q load. Directional
couplers on the input and output separate the forward and reverse waves at each port and
tap off about 1% of each wave’s power. In the diagram, the a terms represent forward
waves and the b terms represent reverse waves. The subscripts indicate port numbers. The
four travelling waves are then sampled by a very fast oscilloscope which has a 50 GHz front
end bandwidth. The device under test must sometimes be connected within a fixture so it
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2.3 Nonlinear Network Analyser Overview
21
can be probed by the NNA. In Chapter 3 the details of the NNA implementation will be
presented. Most importantly calibration, the removal of systematic errors caused by the
directional couplers, cables, and oscilloscope inputs will be discussed, as well de-embed­
ding, the process of determining the waves at the device edge from the waves measured at
the fixture edge.
In this section some issues which are fundamental to the operation of the NNA are pre­
sented. In Section 2.3.1 it is explained how the NNA compares rotating phases between dif­
ferent frequency tones and in Section 2.3.2 the sampling technique used to measure the
signals is explained.
2 3 .1 Phase Measurement
Although the oscilloscope takes measurements in the time domain, the NNA calibration,
and most network modelling, is done in the frequency domain. A linear network analyser
need only measure the phase between a single incident tone and the fundamental of the
waveform that is either transmitted or reflected. A NNA must also measure the phase
between tones at different frequencies; for example, a single incident tone and the third har­
monic in the output waveform. It is quite difficult to see how we can measure the phase
between signals at different frequencies, since the phases between tones at different fre­
quencies rotate with time.
In order for a phase measurement to be useful, the position, or time on the waveform at
which it is taken must be defined. A wave that is increasing through zero volts at the refer­
ence time is defined as having zero phase. The choice of reference time is not as arbitrary
as it seems! Changing the reference time is equivalent to adding or removing group delay
to all four measurements. In the time domain, this is equivalent to simply moving the wave­
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2.3 Nonlinear Network Analyser Overview
22
form to the left or the right; the shape is unchanged. This reference time is defined at the
start of the time window sampled by the oscilloscope, which is determined by the oscillo­
scope trigger input.
2.3.2 Sampling The Waveforms
Every time the NNA acquires waveform data and takes a phase measurement the measure­
ment must be the identical. To achieve this, a stable trigger point on the repetitive wave­
form is required. The trigger frequency must be a common denominator of all the tones
present in the waveform being acquired. With this requirement met, an integer number of
cycles for any tone will pass before the next trigger. At the trigger point, each tone will
always be at the same angle in its cycle, resulting in a repeatable measurement. For most
measurements, the 10 MHz reference signal from the back panel of the signal source is used
as a trigger.
The time window over which the oscilloscope collects data must contain an integer
number of cycles of each tone present in a wave. The Fast Fourier Transform (FFT) used to
extract frequency spectra from the sampled waves assumes the data is cyclic. The FFT
effectively repeats the data in the time window out to infinite time, and takes a Fourier
series. A discontinuity between the last sample and the first sample will act like a step when
the data is repeated, causing frequency spreading in the extracted spectra. Since every tone
present must be a multiple of the trigger frequency, the time window length must be a mul­
tiple of the trigger period to prevent discontinuities. Windowing is the process of multiply­
ing the time domain data by some function, so that there are no discontinuities when the
FFT effectively lays the sampled windows end to end. These windowing functions tend to
remove data at the start and the end of a time sequence, and can affect the shape of the
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2.3 Nonlinear Network Analyser Overview
23
extracted frequency spectrum. For this application, the data does not need to be windowed
because the waveforms in the NNA are cyclic, and the oscilloscope is set up so there is no
discontinuity between the end of one window of data and the start of the next.
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Chapter 3
NNA Im plem entation
The previous chapters introduced the NNA, describing why it is useful and what it does.
The goal of this chapter is to describe how the NNA works. In Section 3.1 an overview of
the system is given and sources of error and the techniques used to reduce them are dis­
cussed. In Section 3.2 an error model used to remove the systematic errors from measure­
ments is developed. In Section 3.3 the linear part of the calibration routine which is very
similar to that performed by a commercial linear network analyser is discussed. In
Section 3.4 the absolute calibration, which can be thought of as correcting the shape of the
measured waves is described. Section 3.5 focuses on de-embedding, the process of remov­
ing the effects of a fixture from a measurement.
3.1 System Overview
In this section an overview of the NNA is given and some errors inherent to the system and
the techniques used to reduce them are described. The NNA is built using mainly off the
shelf measurement equipment. There are a number of components linked together over a
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3.1 System Overview
25
bus to a Macintosh computer. The Macintosh controls the system using an application writ­
ten with the National Instruments Lab View development package. The application has a
graphical user interface, which controls every aspect of the measurement process. This
Lab View application is described in Appendix A. In Section 3.1.1 the operation of the
NNA is presented and in Section 3.1.2 some errors present in the NNA measurements are
discussed.
3.1.1 Hardware Description and Operation
The NNA samples the forward and reverse travelling waves at the input and output ports
of a two-port Device Under Test (DUT). Figure 3.1 shows a diagram of the basic measure­
ment system. An HP-83650A signal sweeper generates a tone that can be connected to
Narda 4226-20
Directional Couplers
Fixture
Narda 4226-20
Directional Couplers
Figure 3.1: NNA system
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3.1 System Overview
26
either port of the DUT using an HP-8762C mechanical switch. The switch is controlled by
an HP-11713A switch controller, not shown on the diagram. Two Narda 4226-20, 0.5 to
18 GHz bandwidth directional couplers on each measurement port separate the forward and
reverse travelling waves. The four resulting signals are sampled by an HP-54750A, 50 GHz
sampling oscilloscope. The equipment is connected via a GPIB bus (General Purpose Inter­
face Bus) to a computer running software developed with Lab View. The sampled wave­
forms are transferred to the computer, and an FFT is performed to extract the amplitude and
phase o f all the harmonics. The waves at the device edge are then inferred from the meas­
ured waves by removing the systematic errors caused by the test system.
Figure 3.1 shows a single tone sweeper as the signal source. To fully characterise some
nonlinear systems, multi-tone or broadband probing signals are required. Two tone signals
are generated by combining the output of two single tone sources. Arbitrary wideband sig­
nals can be generated using an HP-8780A vector modulator controlled by in phase and
quadrature signals from a Tektronix AWG-520 1 GS/s arbitrary waveform generator.
If triggered by the 10 MHz reference signal from the source, the oscilloscope will be
able to sample any waveforms whose component tones are multiples of 10 MHz. This
10 MHz clock can be divided an integer number of times to sample signals that are not a
multiple of 10 MHz. For example, to test a device with two tones spaced 1 MHz apart, the
trigger signal must be reduced in frequency by a factor of 10. For a single tone measurement
the oscilloscope could be triggered directly with a portion of the probing signal. However,
the oscilloscope can only be triggered at a maximum rate 2.5 GHz, which often makes this
impossible. As described in Section 3.2, a calibration is performed by sampling a tone at
each frequency of interest. Most measurements will require calibration at frequencies
above 2.5 GHz, preventing the probing signal from being used to trigger the oscilloscope
directly.
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3.1 System Overview
27
3.1.2 Systematic and Random Errors
A measurement taken with the NNA includes many systematic and random errors inherent
in the measurement hardware. The effects of systematic errors can be removed, but the
effects o f random errors can only be minimized. This section discusses these errors and
some techniques to reduce or remove them.
The measured waves are linearly filtered by the NNA. Figure 3.2 shows part of the NNA
system. The waves which have been separated by the directional couplers are measured by
the oscilloscope a distance from the actual device. Each component tone in the waveforms
Signal
Source
O scilloscope
Inputs
Switch
Directional
Couplers
Directional
. Couplers
Device
Fixture
Figure 3.2: Picture of NNA showing a brass fixture and the oscilloscope inputs
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3.1 System Overview
28
is attenuated and phase shifted by the measurement system, resulting in a systematic meas­
urement distortion. The calibration routine, described in Section 3.2 removes the effect of
these errors.
The signals sampled by the oscilloscope are noisy. Some of this noise is thermal and
some is due to the quantizing of the signal by the 12 bit analogue to digital convertors in
the oscilloscope. This noise is random and essentially uncorrelated with the signal so it can
be removed by averaging. Around 64 waveforms are collected and averaged in the oscillo­
scope, resulting in a waveform with reduced noise. The full 4096 sample points in the oscil­
loscope are used, meaning that many cycles of each tone are stored. The FFT, used to
extract a waveform’s frequency spectrum, inherently takes the average phase and amplitude
of each of the cycles present in the sampled time window. These two sources of averaging
can reduce the noise floor of the final measurements to as much as 60 or 70 dB below the
maximum signal present.
There is a random error in the timing o f the oscilloscope samples. This jitter is inherent
in the oscilloscope, and is also caused by noise on the trigger signal. It results in a horizontal
smearing of the measured waveforms. The effects of jitter are largely removed by the aver­
aging performed to remove noise. However, averaging a signal with jitter is equivalent to
low pass filtering it. The attenuation caused by this effect is systematic and is removed by
the calibration described later. An amplitude calibration is therefore only valid if the jitter
present during a measurement is similar to the jitter present during the calibration. This is
true if the same source is used for both the measurement and the calibration. When a dif­
ferent source must be used for the measurement, the jitter from each source should be sim­
ilar. The oscilloscope can be used to statistically compare the jitter of the two sources. Jitter
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3.1 System Overview
29
is added by attenuating the trigger signal and reduced by increasing its amplitude. There are
also analytic techniques for characterising and removing the amplitude distortion caused by
jitter [5,6].
Temperature drift limits the repeatability o f measurements. The amplitude and phase
responses of the oscilloscope are a function of temperature. This effect is small, but over a
number of days the effect can result in inaccurate measurements. These errors are mini­
mised by calibrating the NNA shortly before it is used, and recalibrating if the temperature
changes. Linear network analysers suffer from the same problem.
Short term drifting effects also affect the system. If the phase of the probing signal
changes during the measurement time the results will be inaccurate. This has not been
observed to be a significant problem, but it may become so when using less accurate
sources or when taking averages over a long time period to reduce measured noise on small
signals. This problem can be minimized by averaging the frequency spectra from many
short measurements instead of averaging many samples taken over a long period together.
The many amplitude measurements of each tone are averaged together, as are the many
phase measurements. This removes the problem of averaging in the time domain where the
many different measurements with different phases can add up destructively to filter the
signal.
There is a systematic error in the timing o f the oscilloscope sampling. The oscilloscope
has a very high input bandwidth, but it can only take one sample for each trigger it receives.
After each successive trigger, it waits a longer amount of time before sampling. The wave­
form is constructed by combining these samples together. The clock used to time the sam­
pling has a systematic error which advances or retards the sampling times with respect to
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3.2 Removing Errors With Calibration
30
their ideal positions. This error is small and can be ignored for single tone, or narrow band
measurements. Section 4.2 in the verification chapter presents a method to measure and
reduce this distortion, and shows its effects on measurements.
3.2 Removing Errors With Calibration
A calibration is used to calculate the waves at a calibration plane from the measured
waves which has been distorted by the measurement system. The calibration generates a
model of the test system between a calibration plane and the oscilloscope’s samplers for
each frequency of interest. This is done by measuring waveforms while standards having
accurately known characteristics are connected to the NNA. The modelled waves at the cal­
ibration plane are then compared with the measurements to produce an error model at each
frequency of interest. These models are used to remove the systematic errors. The calibra­
tion plane is always defined at a connector. This allows simple calibration standards to be
used, and simplifies the absolute calibration routine described below. The model used to
characterise the errors in a measurement is derived in Section 3.2.1. In Section 3.2.2 a
matrix representation of the error model is presented and in Section 3.2.3 the calibration
routines used to determine the parameters in this matrix at each frequency of interest are
introduced.
3.2.1 The System Error Model
The goal of this section is to develop a simple error model whose parameters can be easily
determined. Figure 3.3 shows a model describing one half of the NNA system, assuming
there is no cross talk between the two NNA ports. Each black arrow represents a phasor
valid at one frequency. To characterise the test system a separate model must be generated
at every frequency of interest. This model is not compact; many of the phasors can be com-
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3.2 Removing Errors W ith Calibration
31
a1m A
A blm
rscope1 A L
scopel
scope2
1source
source
1c
Figure 3.3: Signal flow graph describing one half of the NNA system
bined together to simplify it. The inner box is a four port network describing the directional
couplers, the switch and the cables. The parameter aS0Urce *s
travelling wave available
from the source and r source is the source’s reflection coefficient. A reflection coefficient is
defined as the ratio of the reflected wave phasor to the incident wave phasor of a linear net­
work probed with a single tone. The parameters Tscopel and r
scope2
are the reflection coef­
ficients of the two oscilloscope inputs used to measure the incident and reflected waves.
GSCOpei and C?scope2 represent the gain of each of the oscilloscope inputs. The a \parameters
represent forward waves at port one, and the b j parameters represent reverse waves at port
one. The m subscripts denote measured waves, while the c subscripts denote waves at the
calibration plane.
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3.2 Removing Errors With Calibration
32
The model is greatly simplified by looking only at the outer dotted box indicated in
Figure 3.3. The system can now be described as having simply the source, the measured
waves and the device waves as inputs and outputs as indicated by the grey arrows in
Figure 3.4. The r source and r coup parameters model the reflection coefficients seen by the
DUT. The G parameters indicate the coupling gains between the two waves at the calibra­
tion plane and each of the two measured waves. If the directional couplers had perfect direc­
tivity then the GJ2 and G2i terms would be zero.
bc
Figure 3.4: Simplified physical model
To further simplify the model, the asource input can be written as a linear function of am
and bm, and treated as internal to the network. The new model now has am and bc as inputs
and bm and ac as outputs. Figure 3.5 shows the new two-port model, and relates the new C
parameters to the G parameters in Figure 3.4.
Figure 3.6 is a signal flow graph showing an error model for both ports of the NNA.The
subscript numbers represent the port number. The eight parameters are phasors which must
be determined at each frequency of interest. This model is very similar to the model used
in a linear network analyser which assumes that the two measurement ports are isolated [7].
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3.2 Removing Errors With Calibration
33
21
11
C21 ~ Q ~
^11
^
^
12
22
~
c 22 = r
^ 12^21
r
^11
source +1 r*• coup
- r" 12
^ II
Figure 3.5: Greatly simplified error model for one measurement port
Port 1 Error Box
Port 2 Error Box
A .
aim
b 2.:m
a2m
- '1/77
^1 c
a 2c
F igure 3.6: System error model for both measurement ports
The difference is the C2\ term. In a linear calibration, where only relative measurements are
required, this term is set to one. Only the ratio of the transmitted and reflected tones to the
incident tone is important in a linear measurement, so there is no need know the absolute
size of the incident wave. However, in order to measure a waveform’s shape, the NNA must
measure the absolute magnitude and phase of each tone present.
The four C terms describing the port one error model represent physical properties of
the couplers and lines. The C2\ term is inversely proportional to the gain of the measured
incident wave with respect to the wave incident to the calibration plane. The C\2 term rep-
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3.2 Removing Errors With Calibration
34
resents the gain of the measured reflected wave with respect to the reflected wave at the cal­
ibration plane. The Cn and C22 terms are leakage terms. The Cn term models the
component of the forward wave that is measured at the reverse port. The C22 term models
the component of the reverse wave that is measured at the forward port. The calibration will
remove the effect of all these errors.
Unfortunately, as shown in Figure 3.3, the C22 term also contains the two reflection
coefficient terms. In a linear network analyser these terms will correct for any mismatch
from the 50 Q. reference impedance in a measurement. In the NNA however, these terms
should not be included. The calibration routine attempts to extract what the measurement
would be without the mismatch. Unfortunately, this linear correction is not strictly valid
when measuring nonlinear networks. In practice this error can be ignored as long as the
mismatch from 50 Q. of the measurement system is not great. For weakly nonlinear circuits,
the error introduced is insignificant if the return losses looking into the measurement ports
are more than 20 dB.
3.2.2 Error Correction M atrix
The linear error model in Figure 3.6 can be represented with the following matrix equation:
a lc
b \c
=
K eJ°> *
a 2c
H c
1 Rn
0
0
a 1m
21 ^ 2 2
0
0
Im
0
0
r 33 r
0
0
/ ? 4 3
34
/? 4 4
l2m
'2 m
(3-1)
The R parameters are determined using a relative calibration similar to that performed in a
linear network analyser. The K and
parameters are absolute calibration parameters [4).
Once the R parameters and the absolute calibration parameters have been found at each fre-
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3.2 Removing Errors With Calibration
35
quency of interest, (3-1) can be used to determine the waves at the calibration plane from
the measured waves.
3.2.3 Generating the Error Models
To determine the parameters in (3-1) a calibration must be performed at each frequency of
interest. This calibration is divided into a relative calibration and an absolute calibration.
Although the absolute calibration is performed after the relative calibration, it is easier to
understand the process the other way around.
The goal of the absolute calibration can be viewed as correcting the shape of one wave.
Suppose a single tone is input to an ideal opamp configured to produce a square wave. Due
to systematic errors in the test system, each harmonic will be attenuated and phase shifted
by a different amount when measured. As a result, the measured transmitted waveform is
no longer a square wave even though the actual wave leaving the device is. The absolute
calibration makes sure that the amplitude of each harmonic in the <zlc waveform, and the
the phase of each harmonic in the &lc are measured correctly. Although the phase of one
waveform and amplitude of a different waveform are corrected, with the goal of determin­
ing the error model, this is equivalent to correcting the amplitude and phase of a single
waveform. In the time domain, the tones will combine together correctly resulting in a
waveform with the correct shape and amplitude.
For the sake of understanding the calibration routine, the absolute calibration can be
thought of as correcting the shape of a single waveform at the port one calibration plane.
The goal of the linear, or relative, calibration is to correct the shape of the other three cali­
bration plane waveforms with respect to this known waveform. For example, suppose that
the port two calibration plane is connected directly to the port one calibration plane using
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3.3 Linear Calibration Technique
36
a zero length through. In this case, the b2c waveform leaving the through must be the same
as the a\c wave entering it. Or if a short is connected to the port one measurement plane,
the reflected wave bic must be an inverted version of the incident wave a.\c. The linear cal­
ibration also corrects for the finite directivity of directional couplers.
3.3 Linear Calibration Technique
The linear calibration determines the R parameters in (3-1). A set of standards with pre­
cisely known characteristics is measured on the NNA. By comparing the measured waves
and the waves predicted by the standards’ models, the error parameters can be found. For
calibrating to a connectorised reference plane the Short-Open-Load-Through (SOLT)
method is well established. The SOLT calibration routine used to determine the R parame­
ters is described in Section 3.3.1 and the models which characterise the standards are
described in Section 3.3.2.
3.3.1 SOLT Calibration Mathematics
The R l2, Z?2i> ^
R i 2 terms are first determined by making measurements of the wave­
forms at port one with a short, an open and a load connected [8]. This must be done at each
frequency of interest. The three standards have known reflection coefficients
r l5 r2, and
r 3 respectively. The modelled forward and reverse waves for each of the three measure­
ments are related by
(3-2)
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3.3 Linear Calibration Technique
37
where the superscripts indicate the measurement number. Substituting parts of (3-1) into
(3-2) gives
= R 2la lm + R 22b lm
+
^2 (a lm + R l2b lm) = R 2la lm + R 22b lm
T 2{a\m + R l2b \m) = R 2A m + R 22 b\ m
(3-3)
which can be written in matrix form and solved for the unknown R parameters, yielding
r
R 2\
-1
1
12
~ a lm ~ b \m
2
~ a lm - A m
=
3
r 22
—a,1m ~bL
p 1
r ia lm
T' 2
T 2a \m
p
3
_ 3 a lm
(3-4)
Measurements of the same standards are then taken at port two. Using a similar devel­
opment, the following matrix equation is written to determine three more R parameters
from these fourth, fifth, and sixth measurements:
•pi , 4
^34norm
^ 4 3 norm
D
44norm
=
4
-1
I 2m ~ a 2m
~bL
■pi 1 5
5
2 2m ~ a 2m
~bL
pi 1 6
6
h6
3 2m ~ a 2m ~ b 2m
p
1
4
^2m
5
p
2a 2m
p
6
r 3 a 2m
where RXY = R xYnormR 33• The Rxy parameters are normalized at this point because they
cannot be fully determined until /?33 is known. A measurement of a through with power
incident to port one is used to determine R 3 3 . For this seventh measurement, the incident
wave at port one is equal to the reverse wave at port two, or
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3.3 Linear Calibration Technique
38
Substituting parts of (3-1) and (3-5) into (3-6) gives
a \ m + R \ 2 b lnt -
^ 3 3 (-^ 4 3 n o rm a 2 /n + a 22m
m ^ 44norm __
(3-7)
which can be solved for R 3 3 , yielding
^43norm^2/n
??
L
(3-8)
2m44norm2m
To sum up, the Z? parameters from (3-1) can be completely determined at each fre­
quency by taking seven measurements: a measurement of a short, an open, and a load on
port one and port two, followed by the measurement of a zero length through with power
incident to port one.
3.3.2 SOLT Calibration Standards Modelling
The short, open, and load standards are very accurately machined. They are described by
models whose parameters are traceable to the National Institute of Standards and Technol­
ogy (NIST). The model parameters are supplied by the manufacturer of the standards, who
has measured them on a machine calibrated with standards verified to be accurate in a NIST
lab. This section describes the models for the Hewlett-Packard standards used to calibrate
the NNA [9].
Figure 3.7 shows a diagram of the standards. The standards have a delay line before
being either shorted, left open or connected to a broadband load. An offset is a length of
line connecting either the short, the open or the load to the standard’s connector. The con-
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3.3 Linear Calibration Technique
39
Calibration / connector plane
^offset
Figure 3.7: Definitions for a standard
nector plane is defined for male and female connectors so that when they are connected
together, the connector’s reference planes lie on top of each other. The offset delay is the
one way delay from the connector reference plane to the internal standard. It is given by
If i r
offset
(3-9)
where I is the length of the offset, c is the speed of light, and er is the relative dielectric con­
stant of the line. For accurate standards the dielectric is normally air.
The resistance i?[OSS models the skin effect in the line, and is calculated using
J f [G H z|
Rios, = 10
(3-10)
where d!Bloss is the one way loss in dB along the line at 1 GHz. The factor of a half is equiv­
alent to taking the square root of the power lost, and the frequency /[GHz]> given in GHz
accounts for the frequency dependence of skin loss.
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3.3 Linear Calibration Technique
40
The open standard is modelled as a lossy delay line left open at the end with a capacitive
impedance Zc to account for fringing. The open standard’s reflection coefficient is given by
r
open
= R,
ZJ Z c ~ 50. e- j ^ / T oaxl
50 *
* lo s s _ yZ ^ +
(3-11)
^
l)
where i?joss and r offset are given above, and Zc is modelled as a third order polynomial func­
tion of frequency given by
Z c = C0 + C J + C2f 2 + C3/ 3.
(3-12)
The short standard is modelled as a lossy delay line shorted to ground at the end with
an inductive impedance Z^. The short standard’s reflection coefficient is given by
T ,= R,
short
•/2'l ~ 50e-J2nf Ti°»
loss j z L _j_ 5 0
(3-13)
L
J
where i?|OSSand T0ffset are given above, and ZL is modelled as a third order polynomial func­
tion of frequency given by
ZL = L0 + L J + L2/ 2 + L 3f .
(3-14)
The load standard is the simplest to model. The broadband load used in the standard is
assumed to be ideal. Therefore the load’s reflection coefficient is simply given by
r,oad = 0 •
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(3 -1 5 )
3.4 Absolute Calibration Technique
41
3.4 Absolute Calibration Technique
The absolute calibration parameters in (3-1), K and d>, have yet to be determined. The K
term relates the amplitude of the measured waves to the amplitude of the waves at the cal­
ibration plane at a given frequency. The angle O corrects for any frequency dependent
phase shift, or deviation from a flat group delay, present in the system. In Section 3.4.1 it
is explained how the K term is found and in Section 3.4.2 how
is found.
3.4.1 Absolute Amplitude Calibration
K is determined by simply connecting a power meter to the port one calibration plane. A
tone is applied to port one at each frequency of interest. Measurements are taken using the
NNA and the power meter. K is chosen such that the extracted incident power at port 1 is
equal to the value from the power meter.
The FFT used by the NNA returns the peak voltage of each tone in a waveform. Since
the travelling waves are not normalized to 50 Q. they are essentially voltage waves. The
power meter, which is calibrated to account for its return loss, measures the power that is
incident, or available, to it. Therefore the forward voltage wave at the calibration plane
should equate to the peak voltage measured by the power meter. The measured power in
watts Pfwatts] *s a function of the peak voltage wave incident to the power meter Vpm
p
[watts]
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(3-16)
3.4 Absolute Calibration Technique
42
Converting P into dBm, since this is what the power meter normally measures, gives
= 30+ lO log
= 30 +
'V„
(3-17)
20,0g,o ( l^ )
which is solved for Vpm which is the same as |a Ic|
f P [dBm| ~
V " K J = 10x 10
20
30^
■
(3-18)
To calculate K, (3-18) is equated to the relevant part of (3-1) giving
^pm = * « L + *12*L|
(3-19)
which is then solved for K yielding
K = ,- Q
- ypm 8Q
- :.
lm
(3-20)
3.4.2 Absolute Phase Calibration
Theoretically, the phase calibration can be performed by connecting a wideband source
with a known signal shape to the port one calibration plane. The angle <£> would then be
chosen at each frequency so that the calibrated measured phase agrees with the known
phase of that harmonic. A “golden diode” with a model assumed to be perfect can be used
as a phase standard [2]. A more traceable solution is to use a wide bandwidth sampling
oscilloscope [4], A wideband oscilloscope is calibrated using a “nose to nose” method that
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43
3.4 Absolute Calibration Technique
estimates the impulse response of the sampling heads. The output from a wideband source
is measured using this calibrated oscilloscope, and used as a standard to calibrate the NNA.
The “nose to nose” calibration method requires two or three wideband scopes which
would greatly increase the cost of the system. Instead, the oscilloscope inputs used in the
NNA are assumed to have flat group delays. A typical oscilloscope response has only a
±0.75° deviation from this assumption up to 18 GHz [8]. Using this assumption a simple
phase calibration routine is possible. This assumption will be discussed in Section 4.1
where the phase response of the oscilloscope is estimated and compared with published
results obtained using the “nose to nose” method. By assuming the oscilloscope inputs have
flat group delays, the phase calibration problem is reduced to finding the phase response
between the calibration plane and the oscilloscope inputs using a linear network analyser.
The relative calibration will account for any difference in the length of the oscilloscope
group delays.
One lead of a linear network analyser is connected to the port one calibration plane. The
other lead is connected to the lines that enter the
and b\ oscilloscope channels sequen­
tially. The resulting S2i phase measurements, <J)a and
are identical to those that would
have been obtained by the NNA with an ideal impulse generator connected to the port one
calibration plane. To develop the equation for <£, the values measured with the linear net9
9
work analyser are treated as if they actually were measured by the NNA as a lm and b len.
Parts of (3-1) are used to relate these “measured” waves to the reverse wave at the calibra9
9
tion plane b lc . The parameter b lc is defined to have zero phase at all frequencies to prop­
erly calibrate the NNA, giving
(3-21)
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3.5 De-embedding
44
This can be solved for <E>, yielding
<f>
= angle
(3-22)
3.5 De-embedding
The calibration method discussed above only removes errors up to a connectorised calibra­
tion plane. This is sufficient to measure connectorised devices, but not for a device mounted
in a test fixture or other circuit. For example, many transistors must be mounted in a test
fixture that provides transmission lines for the input and output connections. Chapter 5 dis­
cusses measurements of a device that requires a fixture that not only physically connects
the device but also includes impedance transforming networks. One use for the NNA is to
help build and tune amplifiers. In this case, the device is embedded within the amplifier
matching networks, bias tees and other components. De-embedding is the process of cal­
culating the waves inside the fixture from the waves measured at the calibration plane.
Figure 3.8 shows the various measurements planes.
Port 1 Fixture
r"
Port 2 Fixture
r
T est Lead
Connector
\
Port 1 Cal Plane
Port 2 Cal Plane
Port 1 D evice Plane
Port 2 Device Plane
Figure 3.8: A device in a fixture
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3.5 De-embedding
45
De-embedding effectively moves the calibration plane from the connectors to the
device edge. This is done using the model in Figure 3.9. The c subscripts indicate waves at
the calibration plane and the d subscripts indicate waves at the device plane. Notice that the
port two fixture is defined with its port one to the right instead of at the left as is standard.
This is done so the two fixtures both have port two at the device plane and port one at the
calibration plane. This symmetry allows the same equations to be used for removing the
effects of both the fixtures from the measurements.
Port 1 Fixture
Port 2 Fixture
Figure 3.9: Signal flow graph model for fixture extraction
In parts of Chapter 4 and Chapter 5 methods for extracting the fixture models will be
discussed. The models are simply a set of scattering parameters at each frequency of inter­
est. The signal flow graph in Figure 3.9 is solved to determine the de-embedded waves from
the waves at the calibration planes yielding
a id = a icA u + b idA 22
(3_23)
^ic = a \cA \ \ + b \dA \2-
(3-24)
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3.5 De-embedding
gives
U
_
Solving (3-24) for
46
b ld =
^ 1C ^ 1CA 11
A------------ •
a 12
f
(3 ~2 5 >
Substituting (3-25) into (3-23) gives
b l c ~ a l cA ll
i -12
"—
si
•
( 3 “ 2 6 )
Due to the symmetry added by reversing the port two fixture model, the equations at port
two are the same, but with the A parameters exchanged for B parameters
,
2d. =
b 2 c ~ a 2cS l l
A
~
12
7— ci'jB 11
a2d = «2 A l + 2-c•
rrt
O 27)
(3-28)
12
For measurements where tuners or other components are insertedas well as a fixture,
the scattering parameters of the components can be chained togetherto produce a single
combined fixture model at each port.
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Chapter 4
NNA Verification
In this chapter experiments that verify the operation o f the NNA are discussed. This is dif­
ficult, since there is no similar system that looks at waveforms directly to compare meas­
urements against. The procedure used was to test any assumptions made, each component
part of the calibration routine, and finally the entire NNA. In Section 4.1 the flat group
delay assumption used to simplify the calibration routine is discussed. Measurements taken
of a 15 ps rise time step are presented, as well as a measurement of an oscilloscope impulse
response taken by Hewlett-Packard. The timebase error in the oscilloscope is plotted in
Section 4.2. The effects of this error on a measurement are shown and a technique for
reducing the effects is discussed. In Section 4.3 experiments used to verify the linear cali­
bration routine are discussed. The linear part of the calibration determines seven-eighths of
the error model, so this verification is very important. Results in Section 4.4 show that the
absolute calibration is working correctly. Measurements taken of a Schottky diode using
the NNA are compared with waveforms predicted by a model. Because the diode circuit
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4.1 Flat Group Delay Assumption
48
tested was very simple, the voltage across the diode could be measured directly with the
oscilloscope. The absolute calibration routine was tested by comparing a voltage measured
with the NNA with this direct voltage measurement.
4.1 Flat Group Delay Assumption
As described in Section 3.4.2, the absolute phase calibration was greatly simplified by
assuming that the oscilloscope inputs have flat group delays. This means that the signal
sampled by the oscilloscope is simply a delayed version of the signal connected to the input
on the front o f the oscilloscope. Obviously, for this to be completely true, the inputs must
have infinite bandwidth. Real circuits cannot be built with infinite bandwidth. This section
examines the flat group delay assumption. Measurements are presented which give an idea
of the error introduced by assuming a flat group delay, and give a maximum frequency at
which this assumption is valid.
The HP-54750A wide bandwidth oscilloscope used in the NNA has two 20 GHz inputs,
used to measure the waves at port one, and two 50 GHz inputs used to measure the waves
at port two. The specified bandwidth is the frequency at which the input signal is attenuated
by 3 dB before being sampled. The amplitude response is not an issue for the NNA because
the absolute amplitude calibration will correct for any errors it introduces in a measuremenent. However, the phase responses of the oscilloscope inputs are not corrected by the cal­
ibration, because they are assumed to act as a simple group delay. The phase response of
the oscilloscope is not specified by Hewlett-Packard, but it cannot be too bad or the oscil­
loscope would be useless. The oscilloscope was designed primarily to look at time domain
pulses, where small deviations in the phase response would go largely un-noticed. How­
ever, the NNA makes frequency domain measurements of multi-tone signals, where errors
at certain frequencies may cause more drastic problems.
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4.1 Flat Group Delay Assumption
49
To get an initial estimate of the oscilloscope inputs’ phase responses, a very high speed
step was measured. Any deviation from a perfect step response could be attributed to either
an imperfection in the pulse, or the phase response of the oscilloscope. An HP-8130 pulse
generator was used to trigger aTD-1108A tunnel diode supplied by Picosecond Pulse Labs.
A tunnel diode behaves like any other diode. If the voltage across it is slowly increased, at
some point it will turn on and start conducting current. However, when a tunnel diode first
turns on, it produces a very fast step, even if the voltage that turned it on changed only
slightly. The TD-1108A was biased until it almost fired and was then triggered with the
pulse generator, producing 15 ps rise time voltage steps. A perfect step is described by the
Fourier transform pair
u(f) <->7c8(cd) +
7©
(4-1)
where t is time, co is radian frequency, u(r) is the step function, and 8(co) is an impulse
function. The impulse part of the frequency representation is at DC and represents the aver­
age voltage of the step. The 1/jco part indicates that the phase of every frequency component
is at -90° but that the power falls off asymptotically with frequency. Note that the frequency
domain representation indicates that at DC there is an infinite imaginary component. How­
ever a phasor at DC does not rotate with time, so the imaginary component can be ignored
or set to zero.
Figure 4.1 shows the amplitude and phase response of the measured pulse. The plots
where normalized so that they indicate the deviation of the pulse from being ideal. This was
obtained in the frequency domain by dividing the measured frequency data by simulated
data from the right side of (4-1). It could have also been obtained by correlating the meas­
ured time domain response with the step from the left side o f (4-1). The first thing to note
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4.1 Flat Group Delay Assumption
50
T3,
T<33D *4
*5. "6
-10
10
Frequency (GHz)
CO
cn
CD
9, 0
CD
co _o
CO *
.e
CL
0
1
2
3
5
6
4
Frequency (GHz)
7
8
9
10
Figure 4.1: Amplitude and phase deviation of the measured step from being ideal
is that the amplitude response was attenuated by 7 dB at 10 GHz. This indicates that the
step was not ideal, since the oscilloscope input used was specified to have a 3 dB bandwidth
of 50 GHz. The finite rise time of the pulse, the impulse response of the diode, and timing
jitter all cause errors in the pulse shape. The phase plot shows a ±2.5° deviation up to
8.5 GHz. It is possible that this error is due to the oscilloscope impulse response, but it is
more likely due to the impulse response of the diode. At 8.5 GHz the measured signal
power was -80 dB smaller than at DC. The response up to about 8 GHz was almost identical
for a large number of measurements. Above this frequency, different measurements gave
different responses indicating that the power was too small at these frequencies to obtain an
accurate measurement. Measurements taken using all four oscilloscope input were almost
identical. If this phase error were caused predominantly by the oscilloscope inputs, it would
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4.1 Flat Group Delay Assumption
51
likely differ between the 20 GHz and the 50 GHz inputs. From these measurements, the
only conclusion that can be made is that the oscilloscope likely has less than ±2.5° o f phase
error up to 8.5 GHz. The very bad amplitude response of the measurement, which is defi­
nitely not due to the oscilloscope, suggests that the oscilloscope response is actually a lot
better than this worst case limit of ±2.5° u p to 8.5 GHz.
Jan Verspecht, working with the Hewlett-Packard Network Measurement and Descrip­
tion Group in Brussels, has taken more accurate phase response measurements. With the
goal of actually developing a traceable phase standard they came up with the “nose to nose”
calibration technique [10]. The input of one oscilloscope is connected to the input of
another. The first oscilloscope is set to sample continuously. With each sample, due to the
way sampling circuitry works, a small impulse is created which is then measured by the
second oscilloscope. This impulse is distorted by the impulse response of the first oscillo­
scope and then by that of the second. By connecting the three possible combinations of
three oscilloscopes two at a time, the impulse response of each can be determined.
Figure 4.2 shows the phase error for the HP-54120, an earlier, 20 GHz version, of the
oscilloscope used in the NNA [8]. There is only a ±0.75° error in the phase up to 18 GHz.
Notice that the phase error starts rapidly increasing beyond the 20 GHz specified bandwidth
for the oscilloscope. This result is a lot m ore conclusive than the one obtained by measuring
the step response of the diode. It indicates that the flat group delay assumption is valid up
to about 18 GHz for the 20 GHz inputs used to measure the port one waves. M ost likely,
the assumption is valid up to an even higher frequency for the 50 GHz inputs used to meas­
ure the waves at port two.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.2 Timebase Error Measurement
52
8
6
Q
c<D
n
1 2
CL
0
-2
0
5
10
15
20
25
Frequency (GHz)
Figure 4.2: Oscilloscope phase error from Jan Verspecht’s dissertation [8]
4.2 Timebase Error Measurement
There is a systematic error in the timing of the oscilloscope sampling. The clock used to
time the sampling has a repeatable error which advances or the retards the sampling point
with respect to its ideal position. In this section an estimation of this error is presented, and
its effects on a typical NNA measurement are shown. A technique to reduce this error is
also discussed.
The oscilloscope has a very high input bandwidth, but it can only take one sample for
each trigger it receives. After each successive trigger, it waits a longer amount of time
before sampling, as shown in Figure 4.3. In the diagram, the vertical dashed lines are trig­
gers which occur, in this case, once for each repetition of the signal to be sampled. The
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.2 Timebase Error Measurement
Trigger
Trigger
Trigger
53
Trigger
>
Time
Time
Figure 4.3: Repetitive waveform being sampled and then reconstructed
times ti to r4 indicate the increasing offset between the trigger and each successive sample
time. The waveform on the right shows how the sampled signal is reconstructed by com­
bining these samples together with the correct timing. For legibility the diagram shows one
trigger for each cycle of the waveform. When measuring real signals there are normally
many cycles for each trigger.
Figure 4.4 shows this error as a function of the time delay between the trigger edge and
a sample being taken. This plot was obtained by sampling a single 10 GHz tone. The timebase error in the oscilloscope acts to modulate this tone. Down converting the measured
signal in software and low pass filtering it resulted in a complex signal describing the error.
Integrating the phase of this error signal to a given time, gave the timing error for that sam­
pling delay.
The error is cyclic with a period of 4 ns. This is due to the internal timing mechanism
of the oscilloscope. After receiving a trigger edge a 250 MHz oscillator is started [11].
Then, after an integer number of cycles, a ramp generator is started. When the ramp reaches
a specified value the sample is taken. The clock results in a coarse timing offset with mul-
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4.2 Timebase Error Measurement
54
CO
CL
CO
60
64
72
68
Time Delay (ns)
76
80
Figure 4.4: Measured timebase distortion
tiples of 4 ns, and the ramp produces the remaining portion of the desired delay. The main
error is due to an error in the slope of the ramp, resulting in the observed 4 ns cyclic error
as the ramp is used to provide between 0 and 4 ns of delay.
The effect of this timebase distortion in the frequency domain is to add spurious tones
spaced at 250 MHz multiples from a tone being sampled. For a single tone or narrow band
measurements, the effects of this timebase distortion on the real tones are removed by the
calibration routine. For measured waveforms with more than 250 MHz bandwidth around
any harmonic, this distortion may cause errors and can be reduced if required [12,13]. The
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4.2 Timebase Error M easurement
55
frequency domain data is extracted from the time domain data, taking into account the
known sample times. A standard FFT assumes the samples are evenly spaced, which is
what causes the spurious tones.
Figure 4.5 shows the frequency domain representation of a 3 GHz tone sampled with
the oscilloscope. The circles were obtained by taking a standard FFT. The crosses were
obtained using the technique which takes into account the actual time the samples were
taken. The corrected transform has reduced all the spurious tones down into the noise at
around -65 dBm, a reduction of up to 25 dB or by a factor of over 300 times.
-0
:
:
:
:
:
:
:
£
-10 ............ ;........... ; ........... -j.............; ........... : .............
:
:-------------
x Corrected
d Uncorrected •
O
X
...
-
:............ •:............ :............ i .............:............i .............
-20 - ......... :...............
-30 ........... : ............; ........... : ............: ............j ............ i............ j .............j............ i ............
"E
cn -40
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- 6 0 :L........^ .......... !•........... -i.............>...........i ...........- - i ........................:............x
* Xx
o
9?
-70 ^ x
o
o x
^
X
:c ® £.
x x o i xx
;
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. r...........: ........... ........................................... :.......... . : .......... ..............................
X
X
: O°
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:•........... ...............:............ i .............:............ :•............ ■'
:
:
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r
»i_______ i_______ i_______
-_L
... ii_______
... . -ii_______ ii_______ 1i_______
_gQ _______ i_______
i_______
2.5
2.6
2 .7
2.8
2.9
3
3.1
3.2
3.3
3 .4
3.5
Frequency (GHz)
:
:
.
Figure 4.5: Spurious tones caused by timebase distortion in a sampled 3 GHz tone
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.3 Linear Calibration Verification
56
4.3 Linear Calibration Verification
The linear calibration accounts for seven-eighths of the error parameters that must be deter­
mined by the calibration routine. This section, which verifies that the linear calibration is
working correctly, goes a long way toward indicating that the NNA takes valid measure­
ments.
The linear calibration was tested by comparing measurements taken of a Mini-Circuits
ZFRSC-42 splitter using the NNA with measurements taken using a linear network ana­
lyser. The splitter was chosen because it had a simple response and because it was lying
around on a bench and no one else wanted it. It was designed to take a signal from DC to
4200 MHz at port three and split it evenly between ports one and two. For the purpose of
the verification, the splitter was connected in the NNA as shown in Figure 4.6. Between
i
I
I
Calibration plane 1
i
I
I
Calibration plane 2
Figure 4.6: Connection of splitter for linear calibration verification
port one and two of the splitter there is a specified 7 dB isolation if port three is terminated
in 50 Q . To make the response a little more interesting, port three of the splitter was left
open.
The scattering parameters of the splitter were measured on an HP-8510 linear network
analyser, between 200 MHz and 4400 MHz in 200 MHz steps. The same measurement was
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4.3 Linear Calibration Verification
57
then taken using the calibrated NNA. Figure 4.7 and Figure 4.8 show the resulting Si i and
S2i measurements respectively. Note that as the frequency increases the points move anti­
clockwise. The NNA and HP-8510 measurements agree quite accurately. As the frequency
increases, the magnitude of 5 ^ increases, indicating less power is entering port one. Cor­
respondingly, ^21 decreases as the frequency goes up indicating that less power is leaving
port two.
Small deviations between the measurements are due to the way the NNA calculates the
scattering parameters compared with the way the linear network analyser calculates them.
The NNA calculates the waves at one port and completely ignores any mismatch at the
other port. It then calculates Si t from these waves. The linear network analyser calculates
S n from the waves at port one, removing the effect of any mismatch at port two. This is not
done by the NNA, because it is designed to measure what the actual waves are, not what
they would be if the other port were terminated with exactly 50 £2.
These results are very encouraging and indicate that the linear part of the calibration is
working correctly.
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4.3 Linear Calibration Verification
58
120
60
0.2
150
30
0.1
180
210
330
240
300
x NNA
O HP-8510
270
Figure 4.7: Measured
phasors from 200 MHz to 4400 MHz
90
120
0.2
60
0.15
150
30
0.1
0.05
180
210
330
240
300
x NNA
O HP-8510
270
Figure 4.8: Measured S2i phasors from 200 MHz to 4400 MHz
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.4 Schottky Diode M easurement
59
4.4 Schottky Diode Measurement
In order to verify that the entire NNA was working correctly, measured waveforms were
compared with waveforms predicted using a model. The HSMS-8101, a high frequency,
gallium arsenide (GaAs) diode, was chosen as a test device because it has an accurate
model [14]. A test fixture was built with a connector on both ends of a 50 Q. transmission
line. The diode was soldered in the middle of this line, shunting it to ground, as shown in
Figure 4.9. The device model included a PSpice chip model and the lead inductance Lp, the
M easurem ent plane
Connector
Connector
-
MHSMS-8101 GaAs Diode
Figure 4.9: Schematic of the diode mounted in the test fixture
bondwire inductance
and the package capacitance between the two leads Cp. For this
diode Ll = 1nH, Lb = 1nH and C/>=80fF. The diode model was simulated using the
HP-EEsof harmonic balance microwave simulator software. The NNA was connected to
this fixture, and a 1 GHz tone applied to port one. The diode clipped the bottom of this
waveform, producing harmonics which could be seen with the NNA. In Section 4.4.1 the
extraction technique used to model the fixture is described. Finally, in Section 4.4.2 results
o f a number of experiments performed with the diode are presented.
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4.4 Schottky Diode Measurement
60
4.4.1 Fixture Extraction
The NNA calibration routine removed errors up to calibration planes which were defined
at the fixture connectors. The effects of the fixture on the measurements were removed as
described in Section 3.5 on de-embedding. In this section the technique used to model the
fixture halves is presented.
Four scattering parameters are required to thoroughly describe a fixture half. However,
for low reflection, symmetrical fixtures, this model can be simplified. A fixture model
resulting from assuming that there is little reflection is shown in Figure 4.10. This is a simPort 1 Fixture
Port 2 Fixture
C--------^ --------V -------- ^
a1d
^2d
Port 2 Cal Plane
Device Plane
Port 2 Cal Plane
Figure 4.10: Model for the low reflection diode fixture
plified version of the model which was first presented in Figure 3.6. The A parameters refer
to the port one fixture and the B parameters refer to the port two fixture. The a terms repre­
sent forward waves while the b terms represent reverse waves. The subscript numbers rep­
resent the port number, a subscript c denotes waves at the calibration plane, while a d
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4.4 Schottky Diode Measurement
61
subscript denotes waves at the device, or measurement, plane. Note, that in keeping with
the de-embedding equations developed in Section 3.5, the port two fixture file is flipped left
to right from the way scattering parameters are normally defined.
To extract the fixture model parameters, the fixture was measured without the diode on
a linear network analyser. This gave a set of four scattering parameters at each frequency
of interest: Sj j, Sj2, S2X and S22, where port one is on the left and port two on the right. The
following equations are used to determine the A and B parameters from the measured S
parameters:
All = 5 11
-
5 22 =
Id
II
A 22
CO
*11
21
b
+1
II
A12 =
14
+1
II
A l\ = B X2
0.
The parameters A 22 and B22 are not shown in Figure 4.10, because they are assumed to be
zero as indicated in (4-2). Equation (4-2) involves taking the square root of the forward and
reverse fixture scattering parameters. This leaves a single sign common to A21( AI2, B2X,
and B i2 unknown. The sign is determined by assuming the entire fixture can be approxi­
mated by a simple delay. This delay is used to estimate A2i and the sign is chosen so that
the error between this estimated value and the extracted value is minimized.
Assuming that the whole fixture can be modelled as a simple delay, the phase of the S2I
measurement <j) is a function of the radian frequency © and the fixture delay Xfixture:
<K©) = coxflxture .
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(4-3)
4.4 Schottky Diode Measurement
62
Unfortunately, xfixture cannot be determined simply by dividing both sides by
CO because
<{>
wraps around every 2tc radians. Instead, both sides are differentiated, giving
^ ((0) =
(4-4)
which can be rearranged to obtain the fixture’s group delay
•
(« )
The linear network analyser takes samples every A/ Hz. If A / is small, so that <f>does not
wrap around between frequency samples, this differentiation can be treated discretely using
25 a ? ------
C4^
where/„ is a frequency between the second and the last frequency measured. In practice, to
minimize the effect of measurement error, Tfjxture is calculated between the first and the last
frequency samples, using
_ W W ) -<»(/,)
fixatn
2H<VA/
k
‘
where N is the number of frequency points sampled. A 2 \qSI is then estimated using
j ^ Kf 9 ^ fix tu r e
A2i
= «
(4-8)
where the factor of a half is required since A2 1 describes onlyhalf the fixture. The sign of
the square roots in (4-2) ischosen to minimize the error E, where
£ = I A 21- A 21„ J .
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C4-9)
4.4 Schottky Diode Measurement
4.4.2
63
Diode Measurements
The diode was soldered into the test fixture which was connected to the NNA. A 1 GHz
tone was applied to port one of the fixture. The calibration removed errors up to the edge
of the test fixture, and the effect of the fixture on the measurements was removed to give
the waves at the diode package. In this section three experiments performed with the diode
in order to verify the operation of the NNA are discussed.
4.4.2.1 Com parison of M easured an d Modelled Waves
Figure 4.11 shows a comparison between the measured and the modelled waves with a
1.8 V peak incident tone. When the input voltage goes negative, the diode starts to conduct,
shorting the incident wave to ground. The reverse wave b\ is small when the diode is off,
b. NNA
b , NNA
1.5
-o-
s<D °-5
o
O
)
CO
Q— - o
I
0
-0.5
-1.5
0
0.5
1
* 1.5
Time (ns)
Figure 4.11: Measured and simulated waves at the diode
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2
4.4 Schottky Diode Measurement
64
and large when the diode turns on. The positive part of the transmitted b2 wave is not
greatly affected by the diode when it is off, but is clipped when the diode turns on.
These waveforms agree well with those predicted by a model. There are small differ­
ences which can be attributed to errors in the model, and are unlikely to be caused by inac­
curacies in the NNA. Two differences, and their possible causes are described below:
First, the ringing in the measured b { waveform is at a lower frequency than the model
predicts. This could only be attributed to massive errors in the NNA measurement which
would greatly change the shape of the overall measurement. Since the general trends of the
measurement are correct, it is more likely that this is a small error in the model.
Second, the measured transmitted waveform has a greater peak-to-peak value than
modelled, but the reflected waveform is smaller than modelled. This was verified not to be
an error in the calibration routine by applying power to port two of the fixture. The reflected
and transmitted waves were identically shaped to those in the first measurement, despite the
ports being switched. The reflected
wave from the first measurement was now seen at
b2, and the transmitted b2 wave was now seen at
This experiment ruled out the discrep­
ancy between the measured and modelled waves being caused by a systematic error in the
NNA. In the first measurement the by reflected wave was too small but in the second meas­
urement the bi transmitted wave was too big. The difference in the wave shapes is likely
due to an error in the model.
A small resistance or inductance between the diode and ground not accounted for in the
model could cause both the errors. A series resistance in the fixture would increase the cir­
cuit’s time constant, decreasing the ringing frequency as observed. A series resistance or
inductance would prevent the diode from shorting the incident wave as well as the model
predicted. The reverse wave would then be smaller and the forward wave not as well clipped
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4.4 Schottky Diode Measurement
65
as the model predicted. The model does not take into account the width of the transmission
line, or the vias to ground in the circuit; both of which could be the source of the error.
4.4.2.2 Voltage and Current Measurement
The voltage across and the current entering the diode are calculated using
vi = ai + b i
ai - b i
1‘ ~
7
(4-10)
0
where v{- and it are the voltage and current at port i, Z q is the reference impedance, and at
and bi are the forward and reverse waves at port /. Recall that the a and b waves are not
normalized as is often done, so are defined as voltage waves, not power waves.
The input voltage was swept from 0.25 to 2.5 V peak. Figure 4.12 shows the voltage
across the diode and Figure 4.13 shows the current through the diode. The current is actu­
ally the sum of the currents entering port one and port two. For small input voltages, the
diode hardly turns on; the voltage is-sinusoidal and there is little current flowing. As the
input voltage increases, the diode conducts more during the negative part of the input tone;
more current flows and the voltage across the diode is clipped. These measurements are,
again, consistent with the operation of a diode.
To further confirm the correct operation of the NNA, the voltage measured at port one
of the device plane is identical to the voltage measured at port two. This is to be expected,
since the port one and port two device measurement planes are both where the diode con­
nects to the transmission line.
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4.4 Schottky Diode Measurement
66
0.25 V
0.50 V
0.75 V
1.00 V
1.25 V
1.50 V
1.75 V
2.00 V
2.25 V
2.50 V
_2 _____________i_____________ I--------------------!_____________ I
0
0.5
1
Time (ns)
1.5
2
Figure 4.12: Voltage across the diode as the input voltage is swept
40
0.25 V
0.50 V
0.75 V
1.00 V
1.25 V
1.50 V
1.75 V
2.00 V
2.25 V
2.50 V
-2 0
0
'
0.5
'■
1
Time (ns)
■---------------------------------
1.5
2
Figure 4.13: Current through the diode as the input voltage is swept
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4.4 Schottky Diode Measurement
67
4.4.2.3 Comparison with Direct Voltage M easurements
When power is incident to port one of the test fixture the a2 wave has a very low amplitude.
This is because most of the b2 wave leaving the test fixture is absorbed by the load at port
two of the NNA and not reflected back. Because a2 is approximately zero, the voltage
across the diode, calculated using (4-10), can be assumed to equal the b2 wave. This pro­
vides an opportunity to further verify the operation of the NNA.
Port two of the fixture is connected directly to an input of the wideband oscilloscope.
Figure 4.14 compares this oscilloscope measurement with measurements taken using the
calibrated NNA. A measurement taken with the NNA but without the systematic errors
removed is also shown. This un-calibrated measurement was scaled in amplitude to make
Uncalibrated NNA
Oscilloscope
— — Calibrated NNA
1.5
0.5
-0.5
-1.5
1
1.2
1.6
1.4
1.8
2
Time (ns)
Figure 4.14: Direct voltage measurement and NNA measurements
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.4 Schottky Diode Measurement
68
a fair comparison since it is attenuated 20 dB by the directional couplers. The calibrated
NNA measurement agrees almost precisely with the voltage measurement taken directly
with the oscilloscope. Assuming that the oscilloscope has a flat group delay, this is another
indicator the calibration technique is working correctly. This was very good evidence that
the absolute phase and the absolute amplitude calibrations were working correctly.
The un-calibrated b2 wave deviates only slightly from the calibrated wave. Even if this
deviation were acceptable, the linear calibration is required to correct the other waveforms
with respect to b2. For a device with a greater mismatch from 50 Q., a2 would be of similar
size to b2, and the waves would add incorrectly to give the voltage at port two. So, although
it may appear that the calibration only has a small effect, for other measurements its effect
can be significant. This will be seen in Chapter 5, where a device with a three ohm output
impedance in measured.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 5
Power Transistor M easurements
In this chapter the measurement of a Motorola MRF284 Laterally Diffused Metal Oxide
Semiconductor (LDMOS) transistor is described. This is a 30 W device designed for base
station applications at frequencies from 1000 to 2600 MHz. LDMOS transistors, like Field
Effect Transistors (FETs), have a gate next to a channel which is sandwiched between the
drain and source regions. In a regular FET, where the drain and source are both on top of
the substrate, a bondwire connects the source to the package ground. An LDMOS device
has the source on the bottom of the substrate and the drain on the top of the substrate. This
makes it possible to directly connect the source to the package ground. Removing the
source bonding wires greatly reduces source parasitics minimizing loss and feedback in the
device.
Although the MRF284 is a high power device, signals in modem systems will still drive
it into nonlinear modes of operation. Characterising this nonlinear behaviour is greatly
complicated by the low input and output impedances that the device must be offered to
operate correctly. The goals of this chapter are to develop techniques to measure the wave­
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5.1 The Fixture Design
70
forms of low impedance devices, and to show that the effects of tuners, used to change the
impedances offered to the device, can be removed from measurements. The waveforms at
the edge of the MRF284 were measured with a single 1.97 GHz tone incident to the gate.
The fixture which was designed to offer the device low impedances is described in
Section 5.1. In Section 5.2 the extraction technique used to model the fixture is developed.
In Section 5.3 measurements taken of the device using the NNA, are compared with pre­
dictions from a model. Finally, a method for building an amplifier using the NNA instead
of nonlinear models is proposed in Section 5.4.
5.1 The Fixture Design
The fixture holds the MRF284 so it can be connected to the NNA. It is basically a simple
amplifier circuit, providing electrical connections, DC bias, and impedance matching at the
gate and drain. Tuners on each measurement port change the impedance offered to the
MRF284 to affect its operation. Mechanical tuners have loss so they cannot offer low
impedances directly to the MRF284. Instead, the fixture has impedance translating trans­
formers to map impedances from the centre of the smith chart, which can be offered with
tuners, to low impedances.
Figure 5.1 is a picture showing the device mounted in the fixture. The thick lines con­
nected to the gate and drain leads are quarter wave impedance transformers. The optimum
impedances that should be offered to the device, provided by Motorola, are 1+j 1.4 £2 at the
input and 2.5-j0.9 £2 at the output. The fixture was not designed to optimally load the gate
and drain, but to map the impedances which can be offered by a tuner or load pull system
into low impedances. The quarter wave transformer was designed to perform this imped­
ance translation at 1.97 GHz and at odd harmonics multiples. With no tuners, it was
designed to offer around 3 Cl to the transistor at the odd harmonics, and around 50 £2 at the
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5.1 The Fixture Design
71
Gate Bias
Drain Bias V,drain
DC Bias Network
50 Q line
X / 4 Transformer
SMA Connector
Gate
Drain
Source
Figure 5.1: An MRF284 mounted in the fixture
even harmonics. The following equation was used to calculate Z^ne the impedance of the
quarter wave lines:
Z line ~ J Z l Z 2
where
and
l = X/4-
(5-1)
are the desired impedances at each end of the line and I = A./4 indicates
that the length of the line is one quarter of the wavelength. For this design, Z\ was 50 £2 and
must be translated to Z2 which was 3 £2. This gave a line impedance of 12.25 £2.
The short traces connecting the transformers to the coaxial SMA connectors are simply
50 £2 lines. The networks running from the device edge to the big wires are for DC bias.
They supply the gate bias Vgate and the drain bias Vdrajn. The bias networks were designed
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5.2 Fixture Extraction
72
to offer an open to the device at every harmonic multiple of 1.97 GHz. Note that the series
capacitors required to block DC from leaving the amplifier are not in the fixture; they are
external to the fixture and are not shown in Figure 5.1.
The circuit board contained many plated-through vias connecting the ground plane on
top of the board to the bottom of the board. The bottom of the circuit board was soldered to
a brass plate by using a hotplate and solder paste. The brass plate was then screwed to a
large heatsink cooled with a fan. The flange of the MRF284 was bolted directly to a milled
groove in the brass plate to supply a source ground connection, and also to provide a good
path for heat to leave the device.
Figure 5.2 shows a schematic of the entire measurement system used to measure the
waveforms at the edge of the MRF284. It is similar to the low power NNA measurement
system described earlier. The four 20 dB attenuators reduce the sampled waves so the oscil­
loscope can measure them safely. The 10 dB attenuator is rated for 100 W and prevents the
directional coupler on port two from being over driven. The 6 dB attenuator is the smallest
that can be used to limit the power entering the switch to the specified 1 W. The capacitors
are part of the bias network, external to the fixture. The tuners are not always present, but
can be used to offer the device different impedances. The 40 dB amplifier boosts the tone
from the sweeper so that the device can be driven into compression. If the device input is
matched, about 4 W is needed to reach compression.
5.2 Fixture Extraction
As shown in Figure 5.2, the device is separated from the calibration planes by a fixture half,
a capacitor and possibly a tuner. It is important that the calibration planes offer close to
50 Q.. A deviation from 50 Q. can cause a small error in the calibration, as discussed in
Section 3.2.1. If no tuners are used, the capacitors can be included in the calibration if they
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5.2 Fixture Extraction
73
50 GHz Sweeper
RF
Wide Bandwidth Oscilloscope
Ch.1
20dB
Ch.2
Ch.3
Ch.4
;20dB
20dl
20dB
Fixture^
Tuner
>
ro
40dB
Blocking Capacitor
Calibration Plane
Calibration Plane
OD
Figure 5.2: NNA system used to measure MRF284
are not too reflective. Due to the reflective nature of the tuners it is important that they are
not included in the calibration.
The de-embedding process will remove the effects of the fixture and possibly the capac­
itor and tuners from the measurements. When de-embedding, the fixture parameters are
chained together with the scattering parameters of the tuners and capacitors if required.
This technique is good when using tuners, since they can be adjusted, quickly measured on
a linear network analyser, and then replaced in the system. The NNA does not need to be
completely re-calibrated just because the tuners have been adjusted.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5.2 Fixture Extraction
74
The technique used to extract the fixture parameters is described in Section 5.2.1, and
in Section 5.2.2 and Section 5.2.3 some measurements that verify the extracted fixture
models are presented.
5.2.1 Fixture Model Extraction
In this section a technique to determine the scattering parameters describing the fixture
is developed. Scattering parameters at each frequency of interest model the input and output
fixture halves. The frequencies of interest are 1.970, 3.950, 5.910, 7.880, 9.850, and
11.820 GHz; multiples of the fundamental up to the sixth harmonic.
The MT956 fixture characterisation and measurement software package from Maury
Microwave was used to extract the fixture models [15]. Figure 5.3 shows the fixture model
which was first presented in Section 3.2.1. For this highly reflective fixture, a Through-
Port 2 Fixture
Port 1 Fixture
r
a 1d
au
r
S12
®22
^22 J
*11
J\C
&2d
A2i
+-
®11
S21
*12
b td
tb2c
. a 2c
a2d
Figure 5.3: Model used to describe the input and output fixtures
Reflect-Line (TRL) calibration routine was used to determine the A and B scattering param­
eters [16]. Three similar fixtures were built with different standards between the fixture
halves [17]. The through standard was made by butting both fixture halves together. The
line standard was built be connecting the two halves by a short piece of 12.25 Cl transmis-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5.2 Fixture Extraction
75
sion line. The reflect standard, needs only to be modelled to within 180° to help with a
square root sign choice, so the fixture without the device soldered in was used as an open.
It was decided that three separate fixtures be built, each with a different calibration
standard, instead of building just one fixture and connecting different standards. The advan­
tage is that the standards don’t have to be connected and disconnected to the fixture. The
disadvantage is that the fixtures must all be built identically. The brass was machined to
within less than a thousandth of an inch, and the fixtures were built as carefully as possible
so that standards were identical except for the way the two halves were joined. The software
generated a model of the input and output fixture from measurements of these standards
made using a linear network analyser.
To verify the fixture extraction was working correctly, the extracted input and output
fixture models were chained together. Figure 5.4 compares the amplitude of this extracted
0
Q.
E
<
-20
-25
o
Measured
Extracted
-30 ---------------<-------------- i-------------- i-------------- 1---------------1-------------- 1-------------0
2
4
6
8
10
12
14
Frequency (GHz)
~0~
F igure 5.4: Comparison of S2\ amplitude of measured and extracted fixtures
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5.2 Fixture Extraction
76
model ’s ^21 and the amplitude obtained by measuring the through fixture directly with a
linear network analyser. Note that only every tenth point on the lines is marked.The two
measurements lined up exactly. This should be expected since one part of the TRL algo­
rithm used to extract models of the fixture halves took a measurement of the through. This
test, however, helped indicate that the extraction was working correctly.
The fixture extraction includes taking a square root which leaves the sign of the A21 and
A12 pair, and the B2l and B l2 pair unknown. Figure 5.5 compares the S2i phase of the meas­
ured and the extracted fixture models, arbitrarily choosing both signs to be positive. The
bottom graph shows the error between the two signals. There is no error at most frequen­
cies. However, there are some large errors, all multiples of 90°. These errors are caused by
choosing the wrong signs for the square roots. Actually, the problem is worse than indi200
CO
100
o>
CO
j§ -100
CL
-200
0
2
4
6
8
10
12
14
12
14
Frequency (GHz)
400
200
-400
Frequency (GHz)
Figure 5.5: Comparison of S21 phase of measured and extracted fixtures
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5.2 Fixture Extraction
77
cated: if both fixture halves have the wrong sign, when they are combined together the
resulting model will actually have the correct sign. Statistically, half of the frequency points
have the wrong sign chosen. The visible errors were at frequencies where only one of the
signs was incorrect.
These signs cannot be determined by assuming the fixture has a simple group delay, as
was done in Section 4.4.1; over the 1.97 to 11.82 GHz frequency range of interest, the fix­
ture has many resonance points. Instead, the fixture parameters from 50 MHz to 11.82 GHz
were extracted taking the positive roots. At the low frequencies, where the fixture is short
compared to the wavelength, the phase delay must be less than 180° so the signs must be
positive. The sign at each successive frequency point was chosen to prevent any large dis­
continuities from appearing in the extracted A21 or fl21 parameters. Figure 5.6 shows the
phase of A2j . The phases resulting from positive and negative root choice are shown in grey.
For simple fixtures, choosing the phase to minimize large discontinuities is easily auto­
mated. For this fixture, with its many resonance points, this was done by hand. The resulting
phase is shown with the thick black line. Although there are frequencies where the signs
could not be chosen with absolute certainty, these points are not at frequencies o f interest.
The goal of the extraction was only to model the fixture halves at 1.97 GHz and harmonic
multiples. At these frequencies the phase is well determined.
5.2.2 Fixture Parameter Verification
To verify the extraction technique, the impedances looking into the fixture halves were cal­
culated from the extracted models. Figure 5.7 and Figure 5.8 show the impedance offered
to the device output and input respectively. The output fixture offered a real impedance at
each frequency of interest, indicating that the quarter wave transformer was working cor-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5.2 Fixture Extraction
78
100
—
50
—
Correct
Incorrect-ve
Incorrect+ve
® -50
o>
Q.
-150
-2 0 0 - v
-250
-300
10
12
14
Frequency (GHz)
Figure 5.6: Root choice of A2j parameter
rectly. The real impedance offered was around 3 Q at the odd harmonics and 50 Q. at the
even harmonics. This agreed with the simulation used to first design the fixture. The input
fixture behaves as expected but with a fundamental frequency of 2.2 GHz instead o f the
desired 1.97 GHz. Unfortunately, the input quarter wave transformer was built slightly
shorter than designed. This error will change the input match slightly, but, since the fixture
was not designed to offer an optimum input match, this is not too important. For measure­
ments with the device driven into compression, an input tuner is required anyway.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5.2 Fixture Extraction
79
60
Real
Imag
50
40
20
o
i/
-10
-20
-30
12
14
Frequency (GHz)
Figure 5.7: Extracted real and imaginary output impedance
60
Real
Imag
50
40
20
a
10
-10
-20
-30
14
Frequency (GHz)
F igure 5.8: Extracted real and imaginary input impedance
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5.2 Fixture Extraction
80
5.2.3 Calibration and Fixture De-embedding Verification
To verify that the calibration and de-embedding routines were working correctly, a meas­
urement was taken of the through fixture standard using the NNA. The through fixture has
the input and output fixture halves butted directly together. An input tone was swept from
1.97 GHz to 11.82 GHz and applied to port one. The errors up to the fixture edge where
removed using a calibration. The effects of the fixture and the external blocking capacitors
on the measurements were then de-embedded, to give the forward and reverse travelling
waves at the device plane where the two fixture halves were butted together.
The calibration must be performed with the 40 dB amplifier shown in Figure 5.2
removed from the NNA. The amplifier was tuned to operate at 1.97 GHz and was quite
narrow band. The calibration could not be performed with the amplifier present because it
blocks the signals used to calibrate at the higher harmonic frequencies. This will not affect
the measurement of signals at port two at all. However, the calibration at port one is only
valid at 1.97 GHz. At other frequencies, the return loss looking into the amplifier output is
only one or two dB. This large reflection coefficient may invalidate the calibration at these
frequencies.
Table 5.1 shows the scattering parameters where the fixtures butt together with the
amplifier not connected. The impedance offered by the fixture at port one r source, and the
impedance offered at port two T[oad are also shown. The S2i and S 12 parameters are approx­
imately one, as would be expected. The
1 and S22
parameters would normally be zero for
a good through. However, scattering parameters are defined with both ports terminated in
a reference impedance. In this case, port one of the through is terminated with r source, the
reflection coefficient looking into port two of the input fixture half, and port two is termi-
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5.2 Fixture Extraction
81
Freq (GHz)
Sn (£2)
Hoad (£2)
^ (a )
f source ( a )
S12 (a)
521 (a)
1.970
0.867
Z179.19°
0.860
Z178.33°
0.883
Z - 174.55°
0.857
Z-175.03°
0.994
Z-2.28°
0.989
Z0.52°
3.940
0.061
Z-98.100
0.123
Z58.63°
0.407
Z123.84°
0.554
Z 1 17.32°
0.998
Z-1.17°
0.998
Z0.70°
5.910
0.885
Z-179.19°
0.830
Z - 179.71°
0.861
Z - 167.55°
0.816
Z -166.90°
1.054
Z-2.300
0.996
Z1.23°
7.880
0.084
Z - 129.79°
0.177
Z123.94°
0.692
Z141.24°
0.774
Z142.19°
1.006
Z-3.34°
1.007
Z-0.95°
9.850
0.868
Z 178.20°
0.726
Z 173.04°
0.689
Z-150.14°
0.656
Z-138.06°
1.089
Z-5.85°
0.940
Z4.26°
11.820
0.208
Z 169.31°
0.266
Z150.380
1.056
Z 147.79°
0.829
Z140.590
0.967
Z-3.18°
0.980
Z-2.77°
Table 5.1: Scattering parameters of through with amplifier removed
nated with Vload, the reflection coefficient looking into port two of the output fixture half.
/
The equation for S j !, the reflection coefficient that should be measured at port one is
*11 = s n + / y v - -
(5 -2 )
1 - 0 22i load
where the S parameters describe the ideal through. Since S 12 = S21 = 1, and S 11 = S22 ~ 0»
/
then
= r load. A similar argument shows that the reflection coefficient that should be
measured at port two is
rsource The results are excellent for the first four harmonics, but
show small errors at the higher frequencies. This is most likely due to the fact that the NNA
calibration plane does not offer exactly 50 £2 to the fixture. This results in a slight error for
the r estimations. Also, as discussed in Section 3.2.1, the error model is only strictly valid
assuming that the NNA ports offer 50 £2. The calibration will try to correct the waves to
remove the effect of any mismatch from 50 £2. The calibrated waves are estimates of what
the actual waves would be if there where no mismatch. Other possible sources of error are
physical differences between the fixture part of the standards, and of course repeatability
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5.2 Fixture Extraction
82
errors. A final possible source of error is a frequency offset between sources in the NNA
and in the linear network analyser used to model the fixture. The linear network analyser’s
clock may be slow or fast with respect to the NNA source’s clock. The fixture extraction
may have actually been performed at slightly different frequencies than the measurements.
The errors observed are only up to 3° in phase and about 5% in amplitude. To put the angle
error in perspective, light travels 0.25 mm in the time it takes a 10 GHz waveform to
change by 3°!
Table 5.2 shows the scattering parameters and offered impedances at the device plane
when the amplifier is connected. Connecting the amplifier has two effects. First, the
Freq (GHz)
[ and
Hoad (£2)
S22 (G)
^source C^)
S12(G)
S2l (G)
1.970
0.870
Z179.030
0.860
Z178.33°
0.862
Z-176.11°
0.857
Z -175.03°
1.060
Z-0.04°
1.043
Z-3.28°
3.940
1.065
Z-47.62°
0.123
Z58.63°
0.424
Z 134.05°
0.554
Z 1 17.32°
0.957
Z-3.20°
0.813
Z76.41°
5.910
1.449
Z 126.49°
0.830
Z-179.71°
0.887
Z-163.81°
0.816
Z -166.90°
1.015
Z-2.120
6.003
Z109.840
7.880
1.091
Z - 135.37°
0.177
Z123.94°
0.754
Z141.75°
0.774
Z142.19°
0.888
Z-1.92°
0.556
Z51.19°
9.850
0.840
Z138.63°
0.726
Z 173.04°
0.718
Z - 132.23°
0.656
Z-138.060
1.039
Z -13.31°
6.608
Z -4.11°
11.820
1.314
Z-131.61°
0.266
Z150.380
0.492
Z139.000
0.829
Z 140.59°
1.143
Z-8.96°
0.706
Z - 142.7°
T able 5.2: Scattering parameters of through with amplifier connected
S2i measurements, which were taken with power incident to port one, are only valid at
1.97 GHz. At other frequencies no power leaves the amplifier. Second, the waves sampled
at port one are not properly calibrated. The amplifier output offers a very reflective load at
any frequency but the fundamental, which partially invalidates the calibration. These
effects are seen in the measurements. The scattering parameters at 1.97 GHz are not as pre­
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5.3 Transistor Measurements
83
cise as the ones without the amplifier. The trends of 5 j2 are correct, but due to the reflective
nature of the amplifier output, are not as good as the measurements taken without the ampli­
fier. The S 2 2 measurements are quite accurate, which is good since the most important part
o f the MRF284 measurements will be the voltage and current at the drain. The errors in s22
are due to the reflection coefficient of the amplifier being ignored when calculating rsource.
To conclude, the scattering parameter measurements of the through taken with no
amplifier match the predicted values well. The measurements taken with the amplifier are
not as good as those taken without it, as was to be expected due to the large mismatch the
amplifier adds at port one. The waveforms taken at the gate of the MRF284 will not be per­
fect, although the fundamental components will be measured accurately. The amplifier will
not affect the measurements taken at port two, where the interesting drain waveforms are.
5.3 Transistor Measurements
This section presents measurements of the MRF284 taken using the NNA. The goal was to
demonstrate the variety of measurements that can be taken, as well as to gather further evi­
dence that the NNA was working correctly. Once the fixture parameters were extracted, the
device was soldered into the fixture. A single tone at 1.97 GHz was applied to the input port
and the NNA was used to measure the harmonics up to 11.82 GHz. Above this frequency
the waveforms had little power.
Section 5.3.1 compares the voltage and current measurements with predictions from a
model. Section 5.3.2 presents measurements of the drain waveforms taken when the device
is matched for maximum output power. Section 5.3.3 further verifies that the NNA is work­
ing correctly by calculating the impedance offered to the drain from the measured current
and voltage waveforms.
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5.3 Transistor Measurements
84
5.3.1 Comparison with Model
For this measurement, no tuners were used so the fixture was translating the 50 Q offered
by the NNA to low impedances at the gate and drain. Around 3 Q. was offered at the odd
harmonic frequencies and around 50 Q. was offered at the even harmonic frequencies. The
gate was biased at 2 V and the drain at 26 V, resulting in a 200 mA drain current The gate
voltage was chosen so the device would be almost off with no input signal present. This
class-AB configuration produced many harmonics when the device was driven with a
36 dBm, or 4 W, tone.
The MRF284 was modelled using a Root model and package parasitic parameters sup­
plied by Motorola. The simulation embedded this model between the scattering parameter
files which describe the two fixture halves. Figure 5.9 compares the measured and modelled
drain waveforms at the package edge. The model predicts the measured waveforms surpris­
ingly well. The measured and predicted drain voltage waveforms are both clipped at the
bottom. This asymmetrical clipping is caused by the high impedance offered to the drain at
even harmonics. Although the second harmonic current is significantly smaller than the cur­
rent at the fundamental, it results in a voltage of similar magnitude. This large second har­
monic voltage combines with the fundamental to produce the observed clipping.
Figure 5.10 compares the measured and modelled gate waveforms at the package edge.
The gate current was modelled correctly, but the measured gate voltage was 30% larger than
modelled. This is likely due to an error in the input fixture model. The TRL extraction algo­
rithm did not take into account the large step from the transformer to the gate flange. The
source connection to the fixture ground was very near to this step which caused an
increased fringing capacitance. The voltage predicted by the model was found to be very
sensitive to any small change in input impedance. This sensitivity, combined with the step
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
85
5.3 Transistor Measurements
35
3000
30
2000
O25
1000
<D
03
3
"o
>
20
Current (mA)
^
-1000
measured
'drain simulated
'drain
0
'drain
'drain
600
400
200
measured
simulated
800
J -2000
1000
Time (ps)
Figure 5.9: Modelled and measured drain waveforms
3000
2000
1000
©
OJ
o
as
-1000
>
-1C-15r
-
20
-2000
o
•o
igate measured
igate simulated
'gate measured
rgate simulated
-
0
200
600
400
800
Time (ps)
Figure 5.10: Modelled and measured gate waveforms
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-3000
- -4000
1000
Current (mA)
s
86
5.3 Transistor Measurements
that wasn’t modelled, could explain the discrepancy between the measured and modelled
gate voltages. Another source of error at the input, is the assumption that the calibration
which must be performed without the 40 dB amplifier connected, is still valid when it is
connected.
Figure 5.11 shows that the measured and modelled load lines compare favourably. As
described in Section 2.2.1, a load line is simply a plot which shows the voltage on the hor­
izontal axis versus the current on the vertical axis. It is a useful tool to gain insight into how
a device is operating. The slope of each harmonic component in the load line is determined
by the impedance offered to the drain at that frequency. Increasing the resistance compo­
nent of the impedance will increase the voltage swing for a given current swing. Increasing
2500
Measured
2000
- - Simulated
1500
C
1000
500
-500
-1000
20
22
24
28
26
30
32
vdrain
Figure 5.11: Load line at the package edge
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
34
5.3 Transistor Measurements
87
the reactance portion of an offered impedance increases the hysteresis of the curves. This
will be seen in Section 5.3.2 and Section 5.3.3.
5.3.2 Matching with Tuners or Loadpuli System
The gate bias voltage was adjusted to around 2 V to get a 200 mA drain current. The input
was then matched using a tuner. Matching the input reduces the power reflected back from
the gate and maximizes the power entering the gate lead of the device. A tuner at the output
was used to load the drain to get maximum output power. The input power was increased
until the output power was 1 dB lower than it would be if the device was linear. This is the
1 dB compression point of the device. The output was then matched for maximum power.
This changed the 1 dB compression point, so the input power was swept to find it again.
The output was then tuned again for maximum power. This iterative procedure of tuning
the output, and finding the 1 dB compression point was repeated until the tuner setting did
not change. The input tuner was not changed throughout this procedure.
Figure 5.12 shows the external load line for measurements with the un-tuned output and
the optimally loaded output. The tuners were characterised using a linear network analyser,
and their scattering parameters chained with those of the fixture and blocking capacitors.
These combined models were used to de-embed the effect of the tuners, the capacitors and
the fixture from the measurements to obtain the load line at the device edge.
The tuned load line has a much greater current swing than the un-tuned line. The power
in the fundamental of the output wave was 30 W, the rated power for the device. The tuned
load line is closer to a linear, oval shape than the un-tuned line for two reasons. First, the
tuned impedance offered at the fundamental frequency resulted in a large fundamental com­
ponent in the voltage. Second, the un-tuned fixture offers around 50 Cl at the even harmon­
ics, whereas the tuner offers essentially random impedances at the harmonic frequencies.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
88
5.3 Transistor Measurements
10
Not tuned
Tuned
5
0
•5
0
10
20
30
40
50
60
v drain 0 0
Figure 5.12: Tuned and un-tuned external load lines
10
Not tuned
Tuned
5
<
c
CD
0
■5
0
10
20
30
40
50
vdrain 0 0
Figure 5.13: Tuned and un-tuned internal load lines
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
60
5.3 Transistor Measurements
89
In this case, the magnitude of the impedance offered at the second harmonic frequency was
around 10 £2 which produced a small second harmonic component in the voltage for the
tuned measurement.
Figure 5.13 shows the tuned and un-tuned internal load lines. The MRF284 package
was assumed to have no coupling between the gate and the drain. With this assumption,
input and output scattering parameter models were generated from Motorola’s models
which described the gate and drain parasitics respectively. These parasitic models were
chained with the fixture, the tuner and the capacitor models and used to de-embed the meas­
ured waves up to the chip substrate.
The drain to source parasitics for the MRF284 are quite small. Because o f this, not
much current should be lost between the internal and the external drain connection. Indeed,
the current swing of the external measurement is only very slightly smaller than the internal
measurement. As would be expected for a transistor tuned for maximum power and driven
into compression, the voltage is clipped at the left where the device leaves the saturation
region. The current is not clipped hard at the bottom of the load line because the impedances
offered at the drain are not real. This means that when the channel stops conducting, and
the voltage at the drain is pulled up by the inductance of the DC bias supply, the capacitive
load will draw current to try and keep the voltage the same. Positive current is defined as
entering the drain, so the current which charges the capacitor will be negative.
The effects seen when the output was matched for maximum power are consistent with
those predicted by a model. These effects are also consistent with the theoretical operation
of amplifiers, and are further indicators that the NNA is working correctly.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5.3 Transistor Measurements
90
5.3.3 Verification of Waveforms with Ohm’s Law
To further confirm that the NNA was operating correctly the voltage, current and imped­
ance at the drain were investigated. Figure 5.14 is a simplified schematic showing the drain
connections. The Vdrajn parameter is the DC drain bias voltage, vgate is the input gate volt-
drain
gate
3oad
Figure 5.14: Simplified diagram showing the drain voltage, current, and load
age, vdrain is the drain voltage, idrain is the drain current, and Z(o a d is the impedance offered
to the drain. From the diagram, Ohm’s law
v drain
<5-3>
should be valid at each multiple of the fundamental frequency. The negative sign is
required because /drain is defined as leaving the load.
The MRF284 was biased with 4 V at the gate and 26 V at the drain. No tuners were used
in the measurement. The load impedance was estimated from B22, the reflection coefficient
seen by the device looking into the output fixture using
1+
= iI—
5s
- t S 22
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(5-4)
5.3 Transistor Measurements
where B22
91
defined in Figure 5.3. A 1.97 GHz tone was swept from 10 dBm to 36 dBm.
The six harmonic components of vdrain and
were extracted and zIoad was estimated at
each frequency using (5-3). Table 5.3 compares the values of zjoad extracted from the fix­
ture model using (5-4) with the values from the measurements calculated using (5-3). The
Frequency
2[0ad ( ^ )
(GHz)
(Extracted)
(36 dBm)
(30 dBm)
(20 dBm)
(10 dBm)
1.970
3.3053+j0.0510
3.069l-j0.0426
3.0682-j0.0421
3.0680-j0.0423
3.0686-j0.0424
3.940
49.253-j2.4757
49.975-j7.0602
49.974-j7.0043
49.976-j7.0209
49.966-j7.0184
5.910
3.2426-j0.6532
3.3907-J0.6396
3.3897-J0.6393
3.3944-j0.6407
3.3917-j0.6136
7.880
45.665-j 1.8636
45.932-j5.0364
45.936-j5.0562
46.018-j5.0633
48.551+j 1.4925
9.850
3.8404-j0.2310
2.8626-j0.0297
2.8659-j0.0337
2.8426-j0.0521
3.1275-j0.0476
11.820
26.821+j8.0560 27.735+j 10.859 27.748+j 10.862 27.854+j 10.857 27.534+j 10.097
Table 5.3: Extracted Zioad and measured Zjoad at different power levels
extracted and the measured impedances agree well. The small error between the two is due
to the way zIoad was calculated from the extracted output fixture model. It is assumed in
(5-4) that the impedance offered to port one of the output fixture half at the calibration plane
is exactly 50 £2. In reality, the return loss of the 100 W, 10 dB attenuator is only specified
to be greater than 15 dB.
The measured Zjoad values are very consistent as the power is swept. The gain of the
oscilloscope inputs was increased for the smaller input signals to minimize the effect of
dynamic range limitations. The only differences between the measured impedances at dif­
ferent powers is for the higher harmonics. When the input power is low, the drain and volt­
age waveforms have almost no higher harmonic frequency components. The effect of
random errors in the measurement begin to effect the accuracy of the calculated values.
However, even these very low power measurements are quite consistent.
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5.4 Proposed Amplifier Tuning Technique
92
5.4 Proposed Amplifier Tuning Technique
The capability to measure the load line right at the chip substrate is one of the most power­
ful things the NNA can be used for. The shape of the load line at the device channel, which
is very close to the chip edge, determines the efficiency, gain, output power and linearity
of an amplifier.
The shapes of the voltage and current waveforms at the drain can be manipulated to
make different kinds of amplifiers. For example, to make a class-F amplifier, the gate bias
is changed to get a 180° current conduction angle, so the current is a rectified sinusoid. The
voltage waveform is made square so that when the current is high the voltage is low, and
when the current is low the voltage is high. This reduces the power dissipated by the device
as waste heat. The tuned load line shown in Figure 5.13 could be from a prototype amplifier
on the bench. To create a class-F amplifier, the impedance offered to the channel at the fun­
damental frequency should be made real, so that the current does not go negative and the
device turns off completely. The impedances offered at the harmonic frequencies must be
changed to produce a square voltage wave which is low when the device is conducting cur­
rent. For an ideal device with no parasitics, the odd harmonics should be offered an open
and the even harmonics should be shorted. The fundamental should be matched for maxi­
mum power or gain. Obviously for a real device, these theoretical impedances will have to
be changed a little. The NNA can be used to look at the voltage and current waveforms to
determine how the impedances should be changed.
Assuming the device is ideal, changing the load impedance will not affect the drain cur­
ren t The device can be thought of as supplying a current which produces a voltage across
the output load. In this case, Ohm’s law can be used at each frequency to calculate the
impedance required to produce the desired voltage from the given current.
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5.4 Proposed Am plifier Tuning Technique
93
The assumption that the drain current is not affected by changing the load impedance
was tested. The input was matched with a tuner on the input. The drain bias Vdrain was set
to 26 V, the gate bias Vgate to 4 V and the input power was set to 20 dBm. The output was
tuned for maximum gain. Measurements were then taken with and without the output tuner.
Figure 5.15 and Figure 5.16 show the drain and gate waveforms for the tuned and un­
tuned measurements. The gate current and voltage did not change greatly by changing the
load impedance. The drain current advanced by about 30° and increased in amplitude by
about 10% when the load impedance was changed. As would be expected, the drain voltage
changed quite dramatically.
The change in drain current is larger than expected, and appears to slightly disprove the
hypothesis that the drain current is not a function of load impedance for the MRF284. How­
ever, the fundamental of the load impedance was changed from 3.0743-j0.0651 Q to
2.0984-j3.7896 Q; a very large change. It is proposed that for smaller changes, the hypoth­
esis is valid to a certain degree.
The marginal truth to the assumption that the drain current is not a function o f the load
impedance, suggests that an iterative design approach may be valid. A first cut of an ampli­
fier would be built using nonlinear models if available, or by assuming the device is ideal.
The voltage and current waveforms at the drain would be measured with the NNA. Assum­
ing the drain current will not be affected, new load impedances are calculated at each fre­
quency of interest to obtain the desired voltage shape. This new amplifier would then be
built and again measured on the NNA. The amplifier will likely not behave exactly as pre­
dicted, so a new set of impedances would be calculated to get the desired voltage waveform
at the drain. On this second design iteration, the impedance changes should be much
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5.4 Proposed Am plifier Tuning Technique
94
32
3.5
o
30
Current (A)
Voltage (V)
2.5
26
/ ? '•
24
1.5
-•o-
22
rdrafn tu n e d
'drain
drain
'drain
200
600
400
tuned
800
0.5
1000
Time (ps)
Figure 5.15: Drain waveforms with two different load impedances
6
o
2
0.5
o
0
-0.5
■2
-4
rg ate tu n e d
igate tuned
rgate
'gate
200
600
400
800
-1.5
1000
Time (ps)
Figure 5.16: Gate waveforms with two different load impedances
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Current (A)
Voltage (V)
4
5.4 Proposed Amplifier Tuning Technique
95
smaller than for the first iteration, so the drain current should change less. A new amplifier
would be built and another design iteration performed if the waveforms were not shaped as
desired.
This iterative approach initially seems wasteful in terms of the number o f prototypes
that may need to be built. However, when building a high power amplifier, it is normal to
go through several design prototypes until everything works correctly. The proposed itera­
tive technique could likely be performed with each prototype that is built. By understanding
exactly how the device is operating, and making changes based on this knowledge, better
amplifiers can be built in less time than it currently takes.
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Chapter 6
Conclusion
This thesis described a Nonlinear Network Analyser (NNA), and some tests that verified
that it works correctly. The NNA excites either port of a device under test with a microwave
signal. It measures the amplitude and phase of the harmonics in the travelling waves inci­
dent to, reflected by, and transmitted by a network. The NNA has a measurement band­
width of about 18 GHz. Above this frequency an assumption used to calibrate the NNA,
that the oscilloscope inputs have flat group delays, begins to cause phase errors. The system
has a graphical user interface that controls the measurement hardware. The work presented
in this thesis is summarised in Section 6.1 and some ideas for future work related to the
NNA are presented in Section 6.2.
6.1 Thesis Summary
In Chapter 2 it was explained what an NNA does, how it works, and why it is useful.
Because the wavelength of microwaves is on the same order as the circuit size, it is quite
difficult to measure the voltage and current waveforms at the ports of a network. Direc­
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6.1 Thesis Summary
97
tional couplers separate the forward and reverse travelling voltage waves without affecting
the operation o f the network under test. A calibration is used to estimate the waves at the
network edge from these waves which are sampled a distance away from the network. The
voltage and current waveforms can be calculated from the travelling waves.
The NNA samples the forward and reverse waves at two measurement ports using a
50 GHz bandwidth sampling oscilloscope. Since, in the frequency domain, the phases of
different frequency tones rotate with respect to each other, a phase measurement must be
defined at a certain time. This reference time is defined by the oscilloscope’s input trigger.
For the phase measurements to be repeatable, every tone to be measured must be at a mul­
tiple of the trigger frequency. The start and end of the sampled waveforms must be contin­
uous so they do not need to be windowed before their spectra are estimated using an FFT.
This is guaranteed by making the time window length a multiple of the trigger period.
The NNA measures the amplitude and phase of all the tones generated by a nonlinear
network, essentially providing the shape of the waveforms. This information will be useful
for characterising most nonlinear microwave networks. It will be especially useful for look­
ing at the current and voltage waveforms in a transistor, to determine how an amplifier is
working, or to improve device models.
Unfortunately, to operate efficiently, power amplifiers must be driven into compression,
and offered loads and biased so that theyhehave nonlinearly. Increased efficiency lengthens
the battery life in mobile power amplifiers, and reduces the cost of building and maintaining
power amplifiers in base stations. It is very difficult to amplify some digital communication
signals with high peak to average power ratios linearly. These factors mean that amplifiers
must often work in nonlinear ways, resulting in signal distortion. Intermodulation distortion
causes a signal to spread in frequency. This distortion causes adjacent channel interference
which limits how efficiently spectrum can be used. The NNA is the only tool that fully char­
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6.1 Thesis Summary
98
acterise this nonlinear behaviour by measuring the waveforms entering and leaving a non­
linear network directly.
The NNA implementation was described in detail in Chapter 3. There are a number of
sources of error in measurements taken with the NNA. Noise and jitter are the biggest
causes of random error and are reduced by averaging many waveforms together in the oscil­
loscope. Systematic linear distortion introduced by the NNA is removed with a calibration.
An eight parameter error model at each frequency of interest describes the measurement
system. A linear calibration, similar to that performed in a linear network analyser, deter­
mines seven of the error parameters. An absolute calibration at each frequency of interest
determines the last parameter in order to correct the shape of the measured waveforms in
the time domain. The absolute phase calibration assumes the oscilloscope inputs have flat
group delays. This reduces the phase calibration problem to that of characterising the NNA
between the port one calibration plane and the oscilloscope inputs. The NNA is always cal­
ibrated to connectors. To measure a device that is in a fixture, the NNA is calibrated up to
the edges of the fixture, and the effect of the fixture on the measurements is de-embedded.
In Chapter 4 experiments were described that demonstrate the NNA works correctly.
The flat group delay assumption, used to simplify the absolute phase calibration routine,
was examined. A measurement taken by Jan Verspecht, working for Hewlett-Packard, indi­
cates that the phase error of an earlier version of the oscilloscope used in the NNA was only
±0.75° up to 18 GHz. The magnitude of this phase error is very small, and is not an issue
affecting the accuracy of the NNA.
A measurement of the oscilloscope’s time base distortion, a systematic error in the
timing of the samples, was taken. For single tone measurements, or measurements where
the bandwidth around each harmonic is less than 250 MHz, this distortion can be ignored
since its effect is removed by the calibration routine. For measurements where this error is
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6.1 Thesis Summary
99
a problem, it can be reduced by using a modified Fourier transform which takes into
account the timing of the samples.
The linear part of the calibration was tested by measuring a splitter with a linear net­
work analyser and with the NNA. The results agreed very well, indicating that the linear
part of the calibration routine works correctly.
To verify the entire operation of the NNA, measurements taken of a Schottky diode
were compared with predictions from a model. The measurements agreed well, but some
discrepancies indicated that the simulations did not take into account a resistance or induct­
ance in the fixture. Because the diode fixture was essentially a 50 Cl line, the voltage across
the diode is approximately the same as the voltage travelling wave leaving the fixture. The
oscilloscope was used to measure this wave directly. This measurement lined up exactly
with a measurement taken using the NNA, where the effects of the cables and directional
couplers were removed using a calibration. This verified that the absolute calibration rou­
tine works correctly.
In Chapter 5 measurements taken of an MRF284 were discussed. The MRF284 is an
LDMOS transistor which must be offered low impedances at the gate and drain to operate
correctly. The NNA was modified to operate with the 30 W signals required to test the tran­
sistor. A fixture was built which supplied the device with bias voltage and also had quarter
wave transformers which translated the impedances from tuners into low impedances. A
TRL extraction technique determined the fixture half models, but left two signs for root
choices unknown. A new technique was used to determine these signs. The extracted fixture
models agreed well with simulations used to design the fixture.
Measurements of the through fixture taken with the NNA verified that the calibration
and de-embedding processes work as expected. Because the calibration must be performed
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6.2 Future Work
100
without the driver amplifier at port one, measurements at port one were only valid at the
fundamental. The drain measurements at port two were not affected by the amplifier.
The drain voltage and current measured with the NNA agreed well with predictions
made using a simulator. The gate voltage was 30% larger than predicted; likely due to
capacitive fringing in the fixture not included in the extracted fixture models. A tuner was
used to match the device for maximum output power. The load lines at the device edge, and
at the chip substrate edge, were measured with and without the output tuner. All the effects
seen were consistent with the theoretical operation of amplifiers.
The measurement accuracy was further confirmed by calculating the load impedance
from the measured voltage and current waves. At each frequency of interest, these meas­
ured impedances agreed very well with the load impedance calculated from the output fix­
ture half model.
6.2 Future Work
There are a number of research topics that could be investigated, either to improve the oper­
ation of the NNA or to demonstrate that the NNA is a useful design tool. In this section a
number of them are discussed.
In Section 5.4 a technique for building amplifiers was proposed, based on the assump­
tion that a small change in load impedance effects the drain voltage substantially more than
the drain current. An iterative approach could be used to tune the drain waveforms for a
desired shape. After a few iterations of changing the load to get a desired voltage waveform,
the impedance changes will be small and any deviation from the assumption will be negli­
gible. It is proposed that this technique could be tested by building a highly efficient classF amplifier.
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6.2 Future Work
101
The NNA provides a lot of information that would be useful for generating device mod­
els. This could be a very fruitful area of research. The NNA should also be a useful tool for
system-level, black-box modelling. System level models could be used for simulating lin­
earization techniques or could be included in simulations of proposed systems that predict
bit error rate curves and other system properties.
In Section 3.2.1 an approximation made while developing the error model was
described. A calibrated measurement returns what the waves at a port would be if the NNA
offered exactly 50 Q. to that port. The technique it uses to remove the effect of the deviation
from 50 Q. is only strictly valid for linear networks. This effect was ignored because the
NNA actually offered very close to 5012. A technique was developed to remove the effect
of this error, but it has not been tested so was not discussed in this thesis. This work could
improve the routines used to calibrate NNAs.
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Appendix A
NNA Lab View Software Guide
This appendix is a guide to the software that runs the NNA measurement system. The NNA
software controls most aspects of the measurement process from calibration to displaying
results. It is written using the National Instalments LabView programming language. This
language was chosen because of its excellent support of the National Instruments GPIB
card used to interface with the NNA’s components, and the tools it provides for developing
graphical user interfaces.
Overview of Software
Figure A .l shows the hierarchy of panels visible to the user. Each box gives the panel’s
name at the top and a summary of the inputs required from the user underneath. The panels
are shown vertically in the order in which they would first be used. This section gives a
brief overview of how these panels are used. The section after will give precise details of
how the panels work and what they do.
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NNA LabView Software Guide
103
SetupEquipment
‘ PowefeMeterTable
Set-up scope tim ebase
S et memory position
Open power meter panel
Enter calibration data
Acquire*Calibrations
i- /^D3t3Zrif;-f'~ rxT
Open calibration panel
C hoose cal frequencies
S et cal pow ers / sco p e
Extract Calibration_
sf^ P aram etersf”"®-
SOLE Nonlinear.
BgggM
C hoose cal frequencies
f|gf€llcIP®Iil
S e t GPIB add resses
-••A?^Eortur^gilttK w y
C h oose folders
Select number of files
C hoose fixture files
Prompted for files
S et cal powers / scop e
Open panels
AcquireMeasiirement
- $ & sjg ^ & £ 8 ^ 2 ^ ‘xSAi
:"if ~
Open measurement panel
Choose frequencies
Set m eas power / scope
rass^
, Measurement^ Sc
^Extraction
Choose frequency
■
2
;K/'?
; ViewWaveforms:'
Prompted for file nam e
Set m eas power / scope
4i:i&StobTone •!'- . -a
Choose display type
Set scales
Choose frequencies
Write data files
Set m eas power / scope
Figure A .l: NNA interface hierarchy showing panel names and describing inputs
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NNA LabView Software Guide
104
The Front panel is used to set some parameters and to open sub-panels. When using the
NNA for the first time, the GPIB addresses of the equipment should be set on this panel.
The directories used to store calibration and measurement information are also selected
here. There is an option to de-embed the effects of a fixture from the measurements. Press­
ing the run button GE1will start the main panel running. Once the panel is running, pressing
one of the large buttons will bring up the corresponding sub-panel. Pressing the STOP
button will halt the program.
Before the NNA can be used the Set-up Equipment panel should be run by pressing the
SETUP button on the Front panel. It will reset the oscilloscope and the GPIB bus so that
everything is in a predictable state. The oscilloscope timebase is set here and the Calibrate
Power Meter panel can be called to load the power meter head’s calibration data into the
power meter. On this panel, and all other sub-panels, the required fields should be filled in
and the run button
the reram button 0
pressed to start the panel. When the panel has completed, pressing
will go back to the next panel up in the hierarchy.
Before a measurement can be taken the NNA must be calibrated. The Acquire Calibra­
tion Data panel is first used to measure the standards, and the Extract Calibration Param­
eters panel then used to extract the calibration parameters from this data.
The Acquire Calibration Data panel is opened by pressing the CAL DATA button on
the Front panel. It gives the option of selecting either a linear or nonlinear calibration. The
resulting SOLT Linear and SOLT Nonlinear panels have fields to enter the calibration fre­
quencies. The selected panel will prompt the user to connect standards and it will record
the waveforms from each measurement it takes in the calibration data directory.
Pressing the CAL EXTRACT button on the Front panel will bring up the Extract Cal­
ibration Parameters panel. It takes the raw data from the calibration data directory and
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NNA LabView Software Guide
105
generates the error correction matrixes which are saved in the calibration parameters direc­
tory.
After connecting the DUT the Acquire Measurement Data panel should be opened with
the MEAS DATA button on the Front panel in order to take a measurement. From here
either the Frequency Sweep, Single Tone, or Two Tone panels can be opened. The Frequency
Sweep panel will perform a frequency sweep measurement similar to that performed by a
linear network analyser. The Single Tone or Two Tone panels will take a single measurement
with power incident to a specified port. These panels record uncorrected data in the meas­
urement data directory. The Measurement Extraction panel removes the systematic errors
from the measurement and de-embeds the effects of a fixture from the measurement if
required.
The waveforms that result from a single tone or two tone test can now be viewed with
the View Waveforms panel by pressing the VIEW WAVEFORMS button on the Front panel.
Various time-domain or frequency-domain modes can be selected to display the results in.
The Cascade Fixture Files panel is opened by pressing the CASCADE FILES button
on the Front panel. It chains a number of Touchstone format scattering parameter files into
a single file. This is useful for generating a de-embedding file describing a number of com­
ponents connected between the calibration plane and the Device Under Test (DUT).
Panel Details
This section gives a detailed explanation of the panels shown in Figure A. 1. Many of the
sections refer to Touchstone format scattering parameter files. For this reason, these files
are described first.
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NNA Lab View Software Guide
106
Touchstone Scattering Parameter Files
This standard file format contains a number of header lines followed by a number of data
lines:
! <comments>
# <frequency units> <parameter> <format> R <n>
<data line>
<data line>
where
!
= delimiter indicating a comment line
#
= delimiter indicating the line that specifies the data format
frequency units
= units of frequency: Hz, kHz, MHz or GHz
parameter
= parameter type of data: S, Y, Z, G or H; normally S
form at
= parameter format of data:
DB for dB-angle
MA for magnitude-angle
RI for real-imaginary
n
= real reference impedance in ohms; normally 50
Although Touchstone format files can contain different kinds of parameters, the NNA uses
only scattering parameters so the parameter type will always be S. Each data line contains
numbers separated by some form of white space. The first column gives the frequency in
the units indicated by frequency units. The eight columns that follow are organised into four
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NNA Lab View Software Guide
pairs normally describing the ^ n . 52i» ^i2> ^
107
S 22 parameters in the format indicated by
format. For example, if the file contains scattering parameters in the real-imaginary format
a single data line would be:
/
Re{5 n }
Imf^u}
Re{S2i}
R e fs 'll
frnfS^} ^e (^22}
Front Panel
The Front panel is automatically opened when the NNA software is started. It has a number
of buttons which bring up sub-panels. There are also fields that determine the operation of
the NNA.
When using the NNA for the first time the GPIB addresses of the equipment should be
set on this panel. After setting this information, or any other permanent information, the
‘Make Current Values Default’ option from the ‘Operate’ menu should be selected so that
the information does not have to be re-entered when Lab View is restarted. Note that this
option is only available when the software is stopped.
The MAIN SOURCE ADDRESS field sets the GPIB address of the main source used
for calibration and for taking measurements. The MAIN SOURCE TYPE field selects the
type of the main source. It is a list of the three sources which were available in the lab at
the time of writing: the HP-83650, the HP-8780A and the HP-865x series. The MAIN
SOURCE POWER LIMIT field is used to limit the power from the source; if a request is
sent to the source for a power higher than this limit, an alarm will sound and the software
will stop. This is to reduce the likelihood of accidentally applying too much power to either
the DUT or the NNA measurement system.
The 437B ADDRESS field sets the GPIB address of the HP-437B power meter used in
the absolute calibration routine. The 437B SENSOR NUMBER specifies the memory posi­
tion in the power meter that holds the calibration table for the connected power meter head.
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NNA Lab View Software Guide
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Finally, the 11713A ADDRESS field sets the GPIB address of the HP-11713 switch con­
troller and the 54750A ADDRESS field sets the GPIB address of HP-54750A oscilloscope.
This panel contains four fields under the header of DIRECTORIES for specifying the
directories used by the main parts of the software. These are changed by clicking on the
button above them while the panel is running, opening a dialogue box from which a folder
can be chosen. The calibration data directory stores the waveforms that the NNA measures
during the calibration routine. The calibration parameters directory stores parameters
extracted from this data to model the errors in the NNA system. Note that a directory can
only contain one set of either calibration data or calibration parameters. There is an indica­
tor on the front panel that describes the calibration parameters that will be used for correct­
ing a measurement. The measurement data directory is used to store the uncorrected
waveforms acquired by the NNA when taking a measurement. The measurement results
directory stores the results obtained by using the parameters in the calibration parameters
directory and the specified de-embedding files to remove the errors from the raw data in the
measurement data directory. The measurement data and measurement results directories
can both contain a number of different measurements. The measurements in the measure­
ment data directory are listed under the heading MEASUREMENTS. The name of the
measurement that will be either taken or corrected should be entered in the SELECTED
MEASUREMENT field under this list.
If measurement de-embedding is to be performed, the FIXTURE DE-EMBEDDING
box should be selected and the names of the input and output fixture files specified in the
INPUT FIXTURE and OUTPUT FIXTURE fields. Note that these fields are hidden unless
the box is on. The diagram above the input fields indicates that port two o f the fixture halves
is the port that connects to the DUT.
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NNA Lab View Software Guide
109
Set-up Equipment
This panel should be run when the NNA is first turned on. It will reset the GPIB bus and
the GPIB buffers of the equipment connected to it, so that everything is in a known state.
There are fields to set the oscilloscope timebase, acquisition type and triggering. Notice
that there are no fields to set the vertical settings of the oscilloscope; these are set individ­
ually for each part of the calibration and measurement process. The TIMEBASE SCALE
is normally set to 10 ns per division. This gives a total measurement time window of 0.1 ps
which is long enough to capture any tone which is a multiple of the 10 MHz reference
which is normally used for triggering the oscilloscope. The RECORD LENGTH, which is
the number of samples stored by the oscilloscope, should normally be set to its maximum
value of 4096 points. The AVERAGING field should normally be on. For the experiments
performed in this thesis, the NUMBER AVERAGES field was set to 64 to reduce the noise
floor to -65 dB without resulting in too long a measurement time.
The TRIGGER SLOT field is used to select which one of the two trigger inputs is active.
The input on the 20 GHz module is in slot two and the input in the 50 GHz module is in slot
four. The trigger LEVEL and SLOPE settings are the same as those in most other oscillo­
scopes. When the trigger either increases or decreases past the trigger level, a trigger
occurs. To minimize jitter the level should be set so that the trigger occurs during the fastest
changing part of the trigger waveform. In the case of a typical sinusoid this is at zero volts.
The trigger slope can normally be set as either positive or negative. The BW LIMIT switch,
limits the trigger input bandwidth to 100 MHz. If the trigger input is less than 100 MHz this
option should be enabled to reduce noise on the trigger signal and the resulting jitter.
The FLATNESS button turns on the flatness calibration in a HP-54750A sweeper. This
assumes that the sweeper has already been calibrated for flatness as described in its manual.
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NNA Lab View Software Guide
110
This option keeps the amplitude of the signal applied to the DUT constant as the frequency
of the sweeper is swept. It essentially accounts for any frequency dependent loss in the
NNA cables and directional couplers. The LOAD CAL TABLE button opens the Power
Meter Table panel.
Power Meter Table
This panel is used to load the calibration data shipped with a power meter head into the
power meter. This needs only be performed if the data has not already been entered. The
calibration data is essentially a list of percentages given at a number of frequencies that
describe the response of the power meter head. Power meter heads are shipped with a
detailed printout showing this calibration data. An abbreviated version of this data is also
shown on a sticker attached to the power meter head. The calibration data pairs are entered
in the FREQ and CAL FACTOR columns. The REF CAL FACTOR gives the response of
the power meter head at the 50 MHz calibration frequency.
The power meter has ten sensor positions that can each hold a different table of calibra­
tion factors. The SENSOR NUMBER field determines which of these is to be loaded, and
the SENSOR NAME field can be used to give a seven-character name for the table. The
SENSOR NUMBER and GPIB ADDRESS fields are initially the values set on the front
panel, but can be overridden. Tables 0-7 can contain up to 40 entries and tables 8 and 9 can
each contain up to 80 entries. Note that this panel does not calibrate the power meter; this
must be done manually before the power meter is used.
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NNA Lab View Software Guide
111
Acquire Calibration Data
This panel is used to take measurements of standards which will be used to generate the
error correction matrixes. The CAL TYPE field can be used to select either a linear or non­
linear calibration. WhSn run, this panel will open either the SOLT Linear or SOLT Nonlin­
ear panels. The linear calibration does noes not include the absolute calibration routine
included in the more complete nonlinear calibration. The linear calibration is useful when
only a frequency sweep measurement is to be performed to verify that a set of calibration
standards is working correctly or that de-embedding is being performed correctly.
SOLT Linear
This panel will prompt the user to connect a number of standards. It will then record raw
measurements of these standards into the calibration data directory. The FREQUENCIES
field is used to enter a list of calibration frequencies. The two power settings, SOURCE
POWER PORT 1 and SOURCE POWER PORT 2, control the source power independently
when the power is incident to port one and port two. This is useful when taking high power
measurements with driver amplifiers and attenuators included in the calibration. There are
also two sets of vertical oscilloscope settings, VERTICAL PORT 1 and VERTICAL
PORT 2, for when power is applied to port one and port two by the NNA respectively. As
is the case for any of the NNA measurements, the oscilloscope should be set to get the max­
imum swing on the screen without clipping. If the oscilloscope clips while the NNA is
taking calibration measurements, the resulting error parameters will be invalid. Averaging
should be turned off to visualy verify that the data is not clipped for any of the calibration
frequencies. Selecting the BW LIMIT fields reduces the bandwidth of the 20 GHz inputs
to 12.4 GHz, and the bandwidth of the 50 GHz inputs to 26.5 GHz when power is incident
to both port one and port two. It is recommended that for most measurements under
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NNA Lab View Software Guide
112
15 GHz, the 20 GHz modules be left unlimited, and the 50 GHz modules be limited. When
run, the panel will ask for a short, an open, and a load to be connected to port one and then
to port two, followed by a zero length through connecting the two calibration planes.
SOLT Nonlinear
This panel behaves exactly the same as the SOLT Linear panel, having the same input
fields, but also takes measurements to implement the absolute portion of the calibration
routine. It will ask for a calibrated power meter to be connected port one. It will then prompt
the user to put two files in the calibration data directory before the Extract Calibration
Parameters panel is run. The ‘!portl_al_phase’ and ‘!portl_bl_phase’ files are Touch­
stone format scattering parameter files taken using a linear network analyser. They describe
the response of the measurement system from the port one calibration plane to the cables
that enter the channel one and channel two oscilloscope inputs respectively.
Extract Calibration Parameters
This panel has no inputs and will run automatically when opened. It takes the raw calibra­
tion data from the calibration data directory and calculates an error correction matrix at
each calibration frequency. These are stored in the calibration parameters directory. Indi­
cators describe the calibration details, show the progress the calculations, and display the
calculated correction matrixes.
Acquire Measurement Data
This panel is used to open either the Frequency Sweep, Single Tone or Two Tone measure­
ment panels in order to take a measurement. The MEAS TYPE field is used to select the
measurement type. The measurement name from the Front panel is passed to the opened
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NNA Lab View Software Guide
113
panel as the default measurement name. However, this measurement name can be changed
within the panels so that a number of measurements can be taken without returning to the
Front panel every time.
Frequency Sweep
This panel will perform a single tone frequency sweep measurement putting the raw data
into the measurement data directory. The main source, specified in the Front panel, is used
for this measurement. The FREQUENCIES field sets the frequencies to take measurements
at. The two power settings, SOURCE POWER PORT 1 and SOURCE POWER PORT 2,
control the source power independendy when the power is incident to port one and port two
of the DUT. There are also two sets of vertical oscilloscope settings, VERTICAL PORT 1
and VERTICAL PORT 2, for when power is applied to port one and port two respectively.
When the Measurement Extraction panel is run it creates a Touchstone format scattering
parameter file with the name ‘<measurement_name>.freqswp\
Single Tone
This panel will perform a single tone, single power measurement putting the raw data into
the measurement data directory. The main source specified in the Front panel is used for
this measurement. The incident power level, frequency, and port can be specified with the
POWER, FREQUENCY, and PORT fields respectively. The vertical oscilloscope settings
can also be set for the measurement using the VERTICAL fields. The measurement name
is set using the MEAS NAME field. When the Measurement Extraction panel is run it cre­
ates a Touchstone format scattering parameter file with the name ‘<meas_name>.single’.
This file does not contain scattering parameter data however. It contains a single row for
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NNA Lab View Software Guide
114
each frequency of interest. The first column gives the frequency. The next four pairs of col­
umns give the real and imaginary parts of the ax, b Xj a2, and b2 Pea^ voltage phasors at that
frequency.
Two Tone
This panel will perform a two tone measurement, putting the raw data into the measurement
data directory. It assumes that the outputs from two microwave sources are combined
together and connected to the switch. There is a set of five fields to control each of the two
sources, SOURCE 1 and SOURCE 2. The frequency and power are controlled using the
FREQUENCY and POWER fields respectively. Both o f the sources have a PHASE BUMP
field. This will advance the phase of the source’s output by a given angle. This is useful to
line up the phases of the incident tones so the results are easier to visualise. This is actually
equivalent to changing the reference time of the measurement, but is more intuitive to use.
The GPIB address and the type of source are specified using the ADDRESS and SOURCE
TYPE fields. To aid in specifying the source details, an indicator displays the address and
type of the main source specified on the front panel. The vertical oscilloscope settings are
set with the fields in the VERTICAL box. The measurement name is set using the MEAS
NAME field. When the Measurement Extraction panel is ran it creates a Touchstone format
scattering parameter file with the name ‘<measurement_name>.2tone’. This file does not
contain scattering parameter data however. It contains a single row for each frequency of
interest. The first column gives the frequency. The next four pairs of columns give the real
and imaginary parts of the a x, b x, a2, and b2 peak voltage phasors at that frequency.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
NNA Lab View Software Guide
115
M easurement Extraction
This panel will run automatically when opened. It takes a measurement from the calibra­
tion data directory, specified on the Front panel and uses the calibration parameters from
the calibration parameters directory and the specified de-embedding information to
remove the systematic errors. The result is placed in the measurement results directory. The
result’s format is described in either the Frequency Sweep, Single Tone or Two Tone section
depending on the measurement type. Indicators on this panel show the details of the meas­
urement and calibration.
View Waveforms
This panel will show the results of either a single tone or two tone test. Pressing the LOAD
RESULTS button will bring up a file selection box used to select a single file from the
measurement results directory. The PLOT switch selects either a four plot overlay or four
individual plots. The DISPLAY TYPE switch selects one of the following results to view:
the time domain waves, the time domain voltage and currents, the power of the waves at
each harmonic, or the phase of the waves at each harmonic. Underneath the main display
is a plot that shows the load line at port two when the voltage and current are being dis­
played. The MAX TIME field sets the time that the time domain results are showed up to,
and the POINTS field sets the number of points displayed in time domain waveforms. The
GROUP DELAY COMPENSATION slider adds group delay to or removes group delay
from the measurement. In the time domain this simply moves the waveforms to the left or
the right. In the frequency domain, this can be used to change the slope of the phase
response, or to set the incident tone phase to a desired reference value. The AUTOSCALE
button turns autoscale on or off. With autoscale off, a number of fields control the time
domain and frequency domain scales independently. Since the NNA does not measure the
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NNA Lab View Software Guide
116
DC components of a signal, there are vertical offset fields for the time domain displays.
These are most useful when displaying the voltage and current waveforms: the DC bias
voltage and current from the DC supply can be entered, so that the waveforms are offset
correctly.
The SAVE TD WAVES button saves the time domain data to a text file who’s name is
selected from a file selection box that pops up. The first column of this file contains the time
of each sample in ns. If displaying the voltage waves, the following columns contain the aq,
by, a2, and b2 samples. If displaying voltage and current, the columns contain the vj, v2, ij,
and i2 samples. The SAVE FD WAVES button, saves frequency domain data to a text file
who’s name is selected from a file selection box that pops up. No matter which format is
set to display, a Touchstone format file is created where each row represents a single fre­
quency. The first column gives the frequency in MHz. The next four pairs of columns give
the magnitude in dBm and the angle in degrees of the
a2, and b2 waves respectively.
Cascade Fixture Files
This panel is used to help create scattering parameter files for de-embedding the effect of a
fixture combined with other devices such as tuners. It takes one or more Touchstone format
scattering parameter files, picks out a set of desired frequencies and chains them together
to produce a single scattering parameter file. If only one file is specified, the panel creates
a new file containing only the desired frequencies. The FREQUENCIES field describes the
frequencies which will be picked out of the input files. The NUMBER FILES field speci­
fies the number of files to cascade together. When the panel is run, file selection boxes will
prompt for the input file and output file names. The diagram on the panel indicates that the
files are numbered from the DUT outwards. The files are all defined with port two oriented
toward the DUT.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
References
[1J Markku Sipila, Kari Lehtinen and Veikko Porra, “High-Frequency Periodic TimeDomain Waveform Measurement System”, IEEE Transactions on Microwave The­
ory and Techniques, Vol.36, No. 10, pp. 1397-1405, October 1988.
[2] Urs Lott, “Measurement of Magnitude and Phase of Harmonics Generated in Non­
linear Microwave Two-Ports”, IEEE Transactions on Microwave Theory and Tech­
niques, Vol.37, No.10, pp. 1506-1511, October 1989.
[3] Gunter Kompa and Friedbert van Raay, “Error-Corrected Large-Signal Waveform
Measurement System Combining Network Analyzer and Sampling Oscilloscope
Capabilities”, IEEE Transactions on Microwave Theory and Techniques, Vol.38,
No.4, pp. 358-365, April 1990.
[4] Tom Van den Broeck and Jan Verspecht, “Calibrated Vectorial Nonlinear-Network
Analyzers”, Conference Record o f the IEEE Microwave Theory and Techniques
Symposium 1994, San Diego, California, USA, pp. 1069-1072, May 1994.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
References
118
[5] T. Michael Souders, Donald R. Flach, Charles Hagwood and Grace L. Yang, “The
Effects of Timing Jitter in Sampling Systems”, IEEE Transactions on Instrumenta­
tion and Measurement, VoI.IM-39, pp. 80-85, February 1991.
[6] W.L. Gans, “The Measurement and Deconvolution of Time Jitter in EquivalentTime Waveform Samplers”, IEEE Transactions on Instrumentation and Measure­
ment, Vol.IM-32, pp. 126-133, March 1983.
[7] Stephan Adam, “A New Precision Automatic Microwave Measurement System”,
IEEE Transactions on Instrum entation and Measurement, Vol.IM-17, No.4, pp.
308-313, December 1968.
[8] Jan Verspecht, “Calibration of a Measurement System for High Frequency Nonlin­
ear Devices”, Doctoral Dissertation, Vrije Universiteit, Brussel, September 1995.
[9] “Specifying Calibration Standards for the HP-8510 Network Analyzer”, HewlettPackard product note 8510-5A.
[10] Ken Rush and Jan Verspecht, “Individual Characterization of Broadband Sampling
Oscilloscopes with a ‘Nose-to-Nose’ Calibration Procedure”, IEEE Transactions on
Instrumentation and Measurement, Vol.IM-43, No.2, pp. 347-354, April 1994.
[11] “HP-54120B Digital Oscilloscope Mainframe - Service Manual”, Hewlett-Packard
Part No. 54120-90908, 1989.
[12] Jan Verspecht, “Accurate Spectral Estimation Based on Measurements With a Distorted-Timebase Digitizer”, IEEE Transactions on Instrumentation and Measure­
ment, Vol.IM-43, No.2, pp. 210-215, April 1994.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
References
119
[13] E. Van der Oudera and J. Renneboog, “Some Formulas and Applications o f Nonuni­
form Sampling of Bandwidth-Limited Signals”, IEEE Transactions on Instrumenta­
tion and Measurement, Vol.37, No.3, pp. 353-357, September 1988.
[14] Raymond Waugh, Hewlett-Packard WSD Diode Applications, personal correspond­
ence, November 1998
[15] “Fixture Characterization and S-Parameter Measurement Using M aury’s MT956D
Software”, Maury Microwave Application Note 5C-038, May 1998.
[16] Glenn F. Engen and Cletus A. Hoer, “‘Thru-Reflect-Line’: An Improved Technique
for Calibrating the Dual Six-Port Automatic Network Analyser”, IEEE Transactions
on Microwave Theory and Techniques, Vol. MTT-27, No. 12, pp. 987-993, Decem­
ber 1979.
[17] “Applying the Agilent 8510 TRL Calibration for Non-coaxial Measurements”,
Hewlett-Packard Product Note 8510-8 A, Part No. 5091-3645E.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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