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Distributed broadband frequency translator and its use in coherent microwave measurement

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DISTRIBUTED BROADBAND FREQUENCY TRANSLATOR
AND ITS USE IN
COHERENT MICROWAVE MEASUREMENT
by
Prayoot Akkaraekthalin
A dissertation submitted to the Faculty of the University o f Delaware in
partial fulfillment of the requirements for the degree of Doctor o f Philosophy in
Electrical Engineering
Fall 1998
© 1998 Prayoot Akkaraekthalin
Ail Rights Reserved
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DISTRIBUTED BROADBAND FREQUENCY TRANSLATOR
AND ITS USE IN
COHERENT MICROWAVE MEASUREMENT
by
Prayoot Akkaraekthalin
Approved:
Neal C. Gallagher, Ph.D.
Chair o f the Department o f Electrical and Computer Engineering
Approved:
Andras Z. Szeri, Ph.D.
Interim Dean of the College of Engineering
Approved:
avanaugh, Ph.D.
'vost for Academic Programs'
id Planning
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I certify that I have read this dissertation and that in my opinion it meets
the academic and professional standard required by the University as a
dissertation for the degree o f Doctor o f Philosophy.
Signed:
Weide, Ph£>.
Professor in charge o f dissertation
I certify that I have read this dissertation and that in my opinion it meets
the academic and professional standard required by the University as a
dissertation for the degree of Doctor of Philosophy.
Signed:
Phillip Christie, Ph.D.
Member of dissertation committee
I certify that I have read this dissertation and that in my opinion it meets
the academic and professional standard required by the University as a
dissertation for the degree of Doctor of Philosophy.
Signed:
Dennis W. Prather, Ph.D.
Member o f dissertation committee
I certify that I have read this dissertation and that in my opinion it meets
the academic and professional standard required by the University as a
dissertation for the degree o f Doctor o f Philosophy.
Signed:
Thomas A. Goodwin, Ph.D.
Member o f dissertation committee
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ACKNOWLEDGMENTS
I would like to express my sincere gratitude to my advisor, Dr. Daniel van
der Weide, for his providing me the opportunity to work on this project, for his advice
and guidance, for his help in the laboratories, and for his full support and continuous
encouragement throughout the course o f my study and research.
I would like to thank Dr. Phillip Christie, Dr. Dennis Prather and Dr.
Thomas Goodwin for being my dissertation committee and for their useful discussions
and suggestions in this dissertation.
I would like to express my appreciation to Mr. Scott Kee for helpful
discussions, simulations and measurement throughout this work, for being a friend,
and for content and grammar checking o f the dissertation. A special thanks goes to Mr.
Thomas Clupper from W.L. Gore and Associates, Inc. for his valuable discussions and
for providing o f some materials and devices for this work. I would also like to thank
all other people in the van der Weide group, Dr. Vivek Agraval, Mr. Toralf Bork, Mr.
Jonathan Bergey, Mr. Robert March, Dr. Janusz Murakowski, Ms. Kelly Galvin, Mr.
Peter Pozsgai, and Mr. Bjom Rosner. I have benefited significantly from their help in
the laboratories and many useful discussions, as well as their friendship.
Also I would like to thank many other graduate students, past and present,
Dr. Yibin Bai, Dr. Daniel Aiken, Dr. David Smith, Dr. Brad Omer, Dr. Xiaoping
Shao, Mr. Michael Dashiell, Mr. Sean Rommel, Mr. Fen Chen, Mr. Hao Feng, Mr.
Shadi AbuGhazaleh, Mr. Dimitri Hits, Mr. Feng Liang, Mr. Kristofer Roe, Mr.
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Thomas Troeger, Mr. Thomas Adam, Mr. John-Mike Taylor, Mr. Feihua Zhang and
Ms. Ahmed Mumtuz, for valuable discussions, their help and their friendship.
I greatly appreciate all o f the invaluable and constant assistance from Mr.
William Rule, Mr. Chuck Hanavin, Ms. Barbara Shelton, Ms. Nancy Rash, Ms. Dian
Harper, Ms. Barbara Westog, Ms. Malinda Yamell and Ms. Dennis Lemon.
I would like to thank Mr. Vech Vivek and Dr. Suthi Aksomkitti at King
Mongkut’s Institute of Technology in North Bangkok, Thailand for encouraging and
supporting me to study here. I would also like to thank the Ministry of Science,
Technology and Environment in the Royal Thai Government for providing a
scholarship.
Finally, I would like to thank my parents for their love, endless support,
understanding and many helpful discussions.
This work was supported by the Office o f Naval Research Young
Investigator Program, a National Science Foundation PECASE award, the Federal
Aviation Administration and a University Research Award from Ford Motor Co.
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Dedication
To my parents,
whose endless love and supports have inspired my achievements.
vi
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TABLE OF CONTENTS
LIST OF FIGURES...........................................................................................................x
LIST OF TABLEES.......................................................................................................xiv
ABSTRACT.................................................................................................................... xv
Chapter
1 INTRODUCTION....................................................................................................... 1
1.1
1.2
1.3
1.4
Background........................................................................................................ 1
Motivation.......................................................................................................... 4
Organization of this dissertation........................................................................7
Original contributions........................................................................................8
2 NONLINEAR TRANSMISSION LINE..................................................................... 9
2.1
2.2
2.3
2.4
Theory o f nonlinear transmission line..............................................................10
NLTL characteristics........................................................................................ 13
Bond wire......................................................................................................... 17
Diodes in NLTL............................................................................................... 19
2.4.1
2.4.2
2.5
2.6
Varactor diode.................................................................................... 19
Why hyper-abrupt junction diode?....................................................20
Line loss........................................................................................................... 22
Design and simulation......................................................................................24
2.6.1
2.6.2
2.6.3
Basic design of NLTL........................................................................24
Simulation with PSPICE™ and Libra™ ......................................... 26
Results from simulation and measurement...................................... 27
3 MICROWAVE PHASE SHIFTER AND FREQUENCY TRANSLATOR..........31
3.1
Review o f microwave phase shifters............................................................... 31
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3.1.1
3.1.2
Mechanical phase shifters...................................................................31
Electronic phase shifters..................................................................... 34
3.1.2.1 Digital phase shifters............................................................ 35
3.1.2.2 Switch implementation for digital phase shifters................39
3.1.2.3 Analog phase shifters........................................................... 42
3.2
3.3
Distributed phase shifter using NLTL..............................................................45
Serrodyne frequency translation....................................................................... 46
3.3.1
3.3.2
3.4
Phase noise and frequency stability................................................................. 56
3.4.1
3.4.2
3.4.3
4
What causes phase noise?.................................................................. 57
Quantifying phase noise..................................................................... 59
Frequency stability concept.................................................................60
FREQUENCY TRANSLATOR IMPLEMENTATION AND
EXPERIMENTS......................................................................................................... 62
4.1
4.2
Controlling and processing for measurement................................................. 62
Simple heterodyne experiments....................................................................... 65
4.2.1
4.2.2
4.3
4.4
Measurement of mechanical frequency translator............................. 65
Measurement of distributed frequency translator without
compensation.......................................................................................68
Implementation of compensation circuits: a variable attenuator and a
gain controlled amplifier..................................................................................72
Experiment results after compensation............................................................76
4.4.1
4.4.2
5
Analysis of the effect o f flyback tim e...............................................48
Analysis o f the effect o f step-phase serrodyne modulation.............51
Measurement of distributed frequency translator with
sawtooth modulation........................................................................... 76
Measurement of distributed frequency translator with trianglewave modulation..................................................................................77
MICROWAVE REFLECTOMETER....................................................................... 85
5.1
Reflectometer and network analyzer background........................................... 85
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5.1.1 Reflectometer basics........................................................................... 85
5.1.2 Six-port reflectometer......................................................................... 87
5.1.3 Network analyzer................................................................................ 89
5.2
Heterodyne reflectometer using distributed frequency translator................ 90
5.2.1
5.2.2
5.2.3
5.2.4
5.3
6
Implementation o f heterodyne reflectometer.................................... 90
S-parameters........................................................................................ 92
Signal flow graph theory..................................................................... 95
Calibration..........................................................................................100
Experiments and results............................................................................... 101
CONCLUSION AND FUTURE STUDY..............................................................107
6.1
6.2
Conclusion.................................................................................................... 107
Suggestions for future studies....................................................................... 108
6.2.1
6.2.2
6.2.3
6.2.4
6.2.5
Improving the NLTL......................................................................... 108
Improving the controlling circuit...................................................... 110
Improving the reflectometer.............................................................111
Developing MMIC and MIC systems............................................. 111
Developing new applications...........................................................112
Appendix
A Specifications of a variable attenuator device........................................................113
B Specifications of a variable gain amplifier device................................................ 115
BIBLIOGRAPHY........................................................................................................... 122
ix
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LIST OF FIGURES
1.1
Application o f a frequency translator (FT) in electronic warfare to
deceive enemy Doppler radar. The plot of Doppler shift vs. target
velocity at various RF frequencies is also show n........................................... 2
1.2
Coherent microwave measurement (a) the present day system
employing two microwave synthesized sources with a phase-lock and
(b) the proposed system using a frequency translator..................................... 6
2.1
NLTL (a) a schematic diagram and (b) an equivalent circuit........................10
2.2
Equivalent circuit of a nonlinear transmission line unit cell..........................11
2.3
Equivalent circuit of periodic transmission line (partially distributed)
2.4
Bond wire structure for calculating inductance and capacitance..................18
2.5
Equivalent circuit of a reverse-biased varactor diode.................................... 19
2.6
Varactor diode (a) various doping profiles and (b) plot o f depletion
layer capacitance vs. reverse-biased voltage..................................................21
2.7
Lumped element equivalent circuit for a lossy transmission line unit
cell loaded with a varactor diode................................................................... 23
2.8
The scale model NLTL consisting of 30 (2.0 pF) and 20 (0.8 pF)
hyper-abrupt junction diodes interconnected by gold bond wires................ 25
2.9
Simulation o f the delay with PSPICE compared to measurement by
an HP 54750A high-speed digitizing oscilloscope....................................... 28
14
2.10 Schematic diagram o f the scale model NLTL in Libra simulation............... 29
x
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2.11 Simulation of the large scale model NLTL at zero bias using Libra
compared to measurement from an HP 8720D vector network
analyzer........................................................................................................... 30
3.1
The basic structure of rotary phase shifter and orientations between
dielectric plate and principle axes for decomposition o f fields.................... 33
3.2
Basic electronic phase-shifting circuits (a) switched-line phase
shifter, (b) reflective phase shifter with circulator, (c) reflective phase
shifter with 3-dB hybrid and (d) reflective phase shifter with multiple
short circuits, (e) lumped-eiement loaded-line phase shifter, (f)
distributed-element loaded line phase shifter, and (g) low pass highpass phase shifter............................................................................................36
3.3
Electronic switches using pin diodes and FETs for digital phase
shifters (a) series and (b) shunt circuits..........................................................41
3.4
Analog phase shifters (a) varactor diode phase shifter, (b) single dual­
gate FET amplified phase shifter, and (c) two dual-gate FET
amplified phase shifter....................................................................................43
3.5
Measurement of NLTL delay and transmission characteristic vs.
reverse bias voltage at 1 GHz RF................................................................... 46
3.6
Serrodyne modulation technique (a) a sawtooth-phase function and
(b) a step-phase function................................................................................ 49
3.7
Spectrums of serrodyne modulated signals for f j f m~20 (a) flyback
duration of 0.1% and (b) flyback duration of 1 % ........................................ 50
3.8
Spectral response of the serrodyne frequency translator with the 16step (4-bit digital) phase function.................................................................. 56
3.9
Sideband suppression level with respect to translated frequency vs.
the number of b its...........................................................................................57
4.1
Block diagram of a heterodyne experiment using rotary phase shifter......... 66
4.2
IF output (a) waveform from the oscilloscope HP 54750A and (b)
spectrum from the spectrum analyzer SR 780 (>52 dBc sideband
suppression obtained)......................................................................................67
xi
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4.3
Block diagram o f a simple NLTL heterodyne experiment at three
different RF frequencies.................................................................................. 69
4.4
Block diagram o f amplitude and phase variation measurement.................. 70
4.5
Measurement of the NLTL characteristics (a) amplitude and (b) phase
variations...........................................................................................................71
4.6
Variable attenuation circuit on microwave substrate.................................... 74
4.7
Variable gain amplifier on microwave substrate.......................................... 75
4.8
Measurement of the distributed frequency translator including
compensation circuits by using the heterodyne technique............................ 78
4.9
A LabVIEW program for controlling and processing (a) a front panel
and (b) a block diagram................................................................................... 79
4.10
Measurement atfa = 1 GHz and f m = 35 Hz using sawtooth scanning
signals (a) NLTL scanning signal (b) gain control signal and (c)
output waveform after mixer........................................................................... 80
4.11 Spectrum of downconverted signals at 35 Hz IF showing fundamental
and harmonic levels (>45 dBc suppression). Using a step-phase
function with amplitude and phase compensations (scanning
frequency f m = 35 Hz)...................................................................................... 81
4.12
Spectrum of signals at 1 GHz RF including original carrier, translated
frequency, and spurious sideband levels. Using a step-phase function
with amplitude and phase compensations (scanning frequency f m = 35
Hz).....................................................................................................................82
4.13
Phase noise measurement of the translated signal at 1 GHz RF
compared to microwave synthesized source (HP 83620A). The
difference is the additive phase noise created by the distributed
frequency translator..........................................................................................83
4.14
Measurement a t/, = 1 GHz and f m = 35 Hz using triangle-wave
scanning signals (a) scanning signal for phase compensation (b) gaincontrol voltage for amplitude compensation (c) output voltage after
mixer and amplifier and (d) output voltage after processing........................84
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5.1
Block diagram o f a conventional reflectometer.............................................86
5.2
Six-port reflectometer......................................................................................88
5.3
Schematic of a modem VNA consisting o f test set and front end
modules............................................................................................................91
5.4
Block diagram o f a heterodyne reflectometer using the distributed
frequency translator......................................................................................... 93
5.5
Schematic of the microcomputer controlling and processing....................... 94
5.6
N-port network illustrating scattered w aves..................................................96
5.7
Two-port network (a) block diagram showing incoming and outgoing
waves and (b) signal flow graph....................................................................98
5.8
Signal flow graph rules (a) Rule I, (b) Rule //, (c) Rule III, and (d)
Rule IV..............................................................................................................99
5.9
Complete signal flow graph o f the reflectometer....................................... 102
5.10 Simplified signal flow diagram for reflectometer system.......................... 103
5.11 Step-by-step to analyze signal flow graph (a) original simplified
signal flow graph o f the reflectometer (b) after Rule IV and / and (c)
after Rule III...................................................................................................104
5.12 Measurement of a 25 Q load compared to an HP 8720D network
analyzer, (note the expanded scale).............................................................. 105
5.13 Measurement of an arbitrary load (the inset picture) compared to
measurement from an HP 8720D network analyzer................................... 106
6.1
Planar transm ission lines (a) microstrip (b) slot line (c) coplanar
waveguide and (d) coplanar strip line..........................................................109
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LIST OF TABLES
2.1
Some important specifications of diodes........................................................ 26
4.1
Some important specifications of PCI-1200 [59].......................................... 63
4.2
Specifications of microwave substrates.......................................................... 72
xiv
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ABSTRACT
Digital and analog microwave phase shifters have been extensively used in
frequency translation applications, but they have rarely been used in microwave
coherent measurement systems because they usually lack adequate carrier and
sideband suppression. Increasing the carrier and sideband suppression on present day
phase shifters would be very expensive and complicated to integrate into microwave
integrated circuits (MICs) and monolithic microwave integrated circuits (MMICs). To
overcome these limitations, I have developed the first frequency translator based on a
nonlinear transmission line (NLTL) phase shifter, and demonstrated its application in a
high performance microwave coherent reflectometer. Rather than the more common
practice of forming shock waves on the NLTL with large signal excitation, this work
uses its voltage-variable delay, together with both amplitude and phase linearization,
to modulate the phase of a small 0.5-3.0 GHz microwave signal.
To demonstrate this concept, I designed and constructed a brassboard scale
model. I have calculated some important initial parameters of this scale model and
done many computer simulations using PSPICE and Libra. After investigating the
characteristics of the scale model NLTL, I designed and built additional circuits to
compensate delay (phase) nonlinearity and amplitude variation o f the output signal
from the scale model NLTL. I applied serrodyne (sawtooth) modulation, in which the
phase of the RF signal is varied linearly from 0 to 360° with time, to the scale model
NLTL to realize a novel distributed frequency translator. The resultant single sideband
modulator exhibits record > 45 dBc carrier suppression and > 50 dBc spurious
xv
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sideband suppression. The additive single sideband phase is also very low ( < 1 5
dBc/Hz), which confirms that the frequency translator has high frequency stability
comparable to commercial microwave synthesized sources.
With this high performance frequency translator, I created a coherent
microwave measurement system, resulting in an extremely low cost, lightweight and
small size system. I designed and built a heterodyne reflectometer for this purpose
using this new frequency translator, and it gave comparable performance to current
commercial network analyzers. This approach is expected to support coherent
microwave measurement techniques in the future because it offers a clear path toward
complete integration into MICs and MMICs. It will also have significant applications
in other instrumentation and sensors such as THz reflectometers and gas detection
systems.
xvi
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Chapter 1
INTRODUCTION
1.1
Background
Phase shifters find use in a variety o f communication and radar systems,
microwave instrumentation, and industrial applications. Although using mechanical
phase shifters is very simple and provides low loss, electronically tuned phase shifters
are now commonly used because of their potential utility in phased array antenna
systems for inertialess scanning. Passive phase shifters employ PIN or varactor diodes
as electronic switches for phase shift control, whereas active phase shifters use GaAs
FETs. In monolithic microwave integrated circuits (MMICs), MESFETs and varactors
are often used as electronic control elements for phase shifters. Even though electronic
phase shifters were invented in the 1950s, their evolution toward miniaturization and
utilization at higher frequencies continues.
A phase shifter with a linear phase change as a function of time operates
as an ideal frequency translator. Microwave frequency translators are widely used in
electronic countermeasure systems (jam m ing) for electronic warfare. By shifting the
incoming carrier frequency such a device can provide deceptive information to enemy
Doppler radar. Figure 1.1 shows this technique and Doppler shift vs. target velocity
plot at several carrier frequencies. A good frequency translator should have the
original carrier frequency as well as all other spurious signals suppressed. The first
frequency translator using mechanical rotary phase shifter was built in 1940s by Fox
1
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[1]. Although his work used a mechanical device, it perhaps comes closest to the ideal
frequency translator, but its use is limited by its bulk, inertia, and small frequency
shift. Cacheris [2] introduced an electronic version of Fox’s frequency translator which
used a ferrite plate with a pair of coils oriented at right angles to each other. By driving
the coils 90° out of phase, continuous rotation of the magnetic field will result in a
shifted frequency at the output o f the device. Using this technique, frequency shifts in
excess of 20 kHz can be obtained with carrier suppression greater then 20 dB, and
spurious sideband suppression greater than 35 dB. Instead o f using a continuous phase
OH ! No problem
Antenna
carrier frequency
frequency shifted
by FT
f Doppler shift
faAf -
Target velocity (m/sec)
Figure 1.1:
Application of a frequency translator (FT) in electronic warfare to
deceive enemy Doppler radar. The plot o f Doppler shift vs. target
velocity at various RF frequencies is also shown.
2
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shift, Sohoo [3] proposed a new approach in which linear sawtooth modulation
(serrodyne modulation) is used to drive a ferrite phase shifter (Faraday rotation type).
Only a small magnetic field is required for Faraday rotation using this technique. This
technique has also been applied to a varactor diode phase shifter by Hardin [4], but the
device presented only a small range o f frequency shift.
Advances in semiconductor technologies have brought about new methods
of microwave frequency translation. JafFe and Mackey [5] introduced a stepped phaseshift approach, employing a semiconductor-switching technique to achieve microwave
frequency translators. The step-phase shift is employed to yield a staircase
approximation of the continuous ideal sawtooth phase shift. Several authors [6-12]
have demonstrated frequency translators utilizing this technique.
Topi
[8]
demonstrated 15 dB of carrier and spurious sideband suppressions by employing a
hybrid 3-bit PIN diode phase shifter with the serrodyne modulation technique. A
previous effort utilizing a monolithic 5-bit digital phase shifter achieved carrier and
spurious sideband suppressions of 22 dB from 7 to 12 GHz [9,10], Mazumder and
Isham [11-12] also showed the same values of carrier and spurious sideband
suppressions when they employed a 5-bit MMIC phase shifter for the frequency range
of 6 to 18 GHz. In the present day, this technique has become a standard for producing
digital microwave phase shifters due to its small size requirement and low cost even
though it provides low carrier and spurious sideband suppression.
Analog microwave phase shifters have also been extensively studied to
improve carrier and sideband suppressions, but most analog phase shifters provide
phase change less than the 360° required for serrodyne modulation. Varactor diodes
and dual-gate FETs are usually used in passive and active analog phase shifters
3
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respectively, however, only dual-gate FET phase shifters have been able to obtain a
complete 360° phase change. An active 11.5 GHz frequency translator using four dual­
gate FETs has been developed [13]. This system achieved carrier and spurious
sideband suppressions o f more than 20 dB for translation frequency of up to 1 MHz.
The first 360° analog phase shifter in MMIC technology was presented by Lucyszyn et
al. [14], employing a coplanar waveguide (CPW) structure with varactor diodes and 3
dB couplers. With serrodyne modulation, their frequency translator provides a carrier
suppression of 30 dB and low sideband suppression o f 13 dB at 24 GHz over a narrow
bandwidth of 200 MHz. Many researchers [15,16] have integrated an analog phase
shifter as a tuning element in a digital phase shifter in order to improve the resolution
of phase steps, but this typically limits the operational bandwidth of the frequency
translator.
1.2
Motivation
As the capabilities of communication, computation and radar systems
continue to rise, the ability to evaluate them must always stay one step ahead.
Conventional logic systems are reaching clock rates in the 1 GHz regime, while new
devices and architectures-both for computation and wideband radar-aim for 100 GHz
operation, so there is a clear need for instruments to test these systems, particularly in
the field. Furthermore, new sensors using micro- and millimeter-wave reflection and
transmission often depend on coherent generation and detection of these signals.
What has been less clear is the best approach to develop such
instrumentation. In THz measurement systems, two microwave synthesizers are
required to generate a coherent output signal, as shown in Figure 1.2(a). Commercial
vector network analyzers (VNAs) are very accurate and can now measure network
4
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parameters to 100 GHz. These measurement systems are bulky, expensive, and
provide only narrow instantaneous bandwidths, so their use is limited to the laboratory
and to linear devices and systems. Short-puise lasers have been proposed and pursued
by several groups using a wide variety of methods to test ultrafast or wideband devices
and circuits in the time domain, but laser-based approaches will not likely become
portable, low-power, low-cost solutions for measuring 1-100 GHz signals.
A promising alternative to these short-pulse laser systems is a purely
electronic one using picosecond pulses from integrated circuit (IC) nonlinear
transmission lines (NLTLs) [17-20]. This is a much more design- and technology­
intensive approach than the laser-based systems, thus limiting the number of groups
pursuing it. One o f the most significant barriers to their widespread deployment,
however, has been their need for coherent (phase-locked) microwave synthesizers to
drive them, placing their total bulk and expense on par with the laser systems. Similar
economic concerns drive the design o f commercial VNAs: they rely on only one
synthesized source and use a sampling detector, rather than using two sources and a
mixer, thereby trading dynamic range for lower cost
A new solution proposed here can generate a coherent microwave signal
using only one microwave source and a frequency translator, as displayed in Figure
1.2(b). This technique can enable a complete, possibly monolithic, integration of
wideband network analyzers, directly addressing the need for instruments to
characterize 100 GHz devices, circuits, and systems, as well as the growing
opportunities for sensors in this regime. Driving a NLTL phase shifter with serrodyne
(sawtooth) modulation results in a distributed frequency translator that can be used
with an inexpensive (ultimately integrated) microwave source to coherently convert a
5
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wideband microwave signal directly to baseband. This invention, coupled with
improved directional sampling circuits [17,19], could enable high-performance,
inexpensive, and field-capable 100 GHz vector network analysis. In addition, several
other new military and commercial applications such as THz reflectometers which
would benefit from a monolithic coherent generation/detection system [21-24]. This
approach is the first to present a clear path to complete integration o f a coherent microand millimeter-wave measurement system.
Microwave
source
Mixer
Phase-lock
Microwave
source
Output
Linear
DUT
(a)
fo ~ fm
translator
Microwave
source
,|
Splitter
Mixer
1
Output
(b)
Figure 1.2:
Coherent microwave measurement (a) the present day system
employing two microwave synthesized sources with a phase-lock
and (b) the proposed system using a frequency translator.
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This dissertation aims to study characteristics o f a NLTL in frequency
translating for coherent microwave measurement systems. The use of the NLTL as a
phase shifter or phase scanner would overcome the disadvantages o f the present day
digital and analog microwave phase shifters. This technique is expected to reduce
phase noise and improve phase stability. The details of the NLTL, microwave phase
shifter and frequency translator, and its application in a microwave reflectometer are
described in the later chapters.
13
Organization of this dissertation
This dissertation is organized into six chapters. The next chapter describes
basic concepts of a NLTL and its characteristics such as frequency cutoff, input
impedance, and insertion loss. The design and simulation o f the scale model NLTL on
a brassboard are clearly detailed.
Some measurement results are illustrated and
compared to the simulations.
A basic review of microwave phase shifters is presented in Chapter 3. This
is intended mainly to highlight their limitations when used as phase scanners in
frequency translators. The analysis of the frequency translator using serrodyne
modulation technique is also described.
Chapter 4 discusses how to implement the distributed frequency translator
and amplitude and phase compensation circuits. Experimental results including
translated output waveforms, spectrums and phase noises are illustrated.
Application of the frequency translator in an inexpensive microwave
reflectometer is proposed in Chapter 5. The design and calibration technique for this
reflectometer are clearly explained. The reflection coefficients o f various devices are
7
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tested with the proposed reflectometer and the results compared to those obtained from
a commercial network analyzer.
The conclusion and some directions for further research to improve the
distributed frequency translator and the heterodyne NLTL reflectometer are described
in the last chapter.
1.4
Original contributions
This work is concerned with the development of a new frequency
translator using a NLTL phase shifter and its application in a coherent microwave
measurement system. The following original contributions are contained herein:
1. Development of a scale model NLTL for microwave phase shifting.
2. Application of the serrodyne modulation technique to the scale model
NLTL for creating a new distributed frequency translator.
3. Analysis o f the carrier and sideband suppression from the effects of
flyback time and step-phase modulation.
4. Design o f compensation circuits to correct the amplitude and delay
(phase) variations of the output signals from the distributed frequency translator.
5. Design o f a microcomputer-based heterodyne microwave reflectometer
with the distributed frequency translator.
6. Development of a calibration technique using three standards (short,
open and matched load) to eliminated the systematic error in the reflectometer.
8
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Chapter 2
NONLINEAR TRANSMISSION LINE
The type o f nonlinear transmission line (NLTL) used in this work is a high
impedance transmission line periodically shunted by reverse biased varactor diodes to
produce a synthetic structure on which the small signal propagation velocity depends
on the voltage-variable capacitance. A NLTL can be realized as a large scale model or
an integrated circuit o f diodes and transmission line sections. Figure 2.1 gives a
schematic diagram and an equivalent circuit of a NLTL. On this structure the phase
velocity vp is modulated by the diode capacitance, vp = l/^ L C (V ) , where L is the
inductance and C(V) is the sum o f the diode and parasitic capacitance o f the line, all
per unit length. For a large signal wave, the dependence of phase velocity or delay on
the voltage of the traveling wave leads to wave compression and shock wave
formation because a wave travels slowly at voltage levels near zero but quickly at
reverse-bias voltages where the depletion depth of the diode is large. Several authors
[17-24] have studied the behavior of NLTLs to generate subpicosecond pulses for uses
in many applications, especially for high-speed sampling and wide bandwidth
instrumentation. However, when a small-signal signal propagates through a NLTL, the
wave compression or shock wave formation is not significant because the voltage
differences o f the traveling wave are too small for it to modulate its own phase
velocity. Therefore, a NLTL is expected to be useful as a small-signal device in the
microwave phase shifting by applying an appropriate bias voltage for a certain phase
9
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nnnn noon
nnnn
o
(b)
Figure 2.1:
NLTL (a) a schematic diagram and (b) an equivalent circuit
shift. In this work, only the small-signal mode with specific applications in phase
shifting and frequency translating for coherent microwave measurement will be
studied.
2.1
Theory of nonlinear transmission line
To analyze the characteristics of a continuous NLTL, the equivalent circuit
o f a differential element dz of a NLTL (a unit cell) is displayed in Figure 2.2. When V
and / are differentiable single-valued functions of z and t, the nodal equations then can
be expressed as
(2.1a)
(2.1b)
10
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Ldz
0000
r
Ih
C(V)dz
Figure 22:
dl ^
dZ
dZ
V + — dZ
dZ
Equivalent circuit of a nonlinear transmission line unit ceU.
where L is the inductance per unit length and C(V) - dQ(V)!dV is a variable nonlinear
shunt capacitance (diode capacitance) per unit length.
These nonlinear differential equations can be solved using the method of
characteristics [25-27], by forming a pair of linear combinations o f the two equations,
as shown in the following.
I ; +A.lLI,+A.xVz +QvVl = 0
(2.2a)
I.+ ^ U '+ W + Q y ,
(2-2b)
= 0
where the partial derivatives with respect to the variables z and t are denoted by lower
case subscripts, and A./ and Aj are the combining multipliers. By introducing an
auxiliary pair of variables, a and /?, we separate these equations so that, in each, all
derivatives of I{cL.f3) and V(a,P) are with respect to a common variable. To accomplish
this, the multipliers A./ and 2? are chosen to be
11
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K = jQ J L
(2.3a)
Aj = - 4 Q J L
(2.3b)
The nonlinear mapping from (z,/) to (a,/3) then can be expressed as
Id a = dz + —]===
(2.4a)
2dp =
(2-4b)
where
dz = d a + dp
(2.5a)
dt = J.LQvd a - 4 LQvdp
(2’5b)
Substituting (2.4) and (2.5) into (2.2), yields two wave equations
l. =
i,
-
(2.6a)
J
q
J
lv,
(2<Sb)
It is apparent thatV(a,P) isseparated into forward and backwardtraveling waves, V(JJ)
and V(a),respectively.Solving(2.4b), it is found that the forward
wave travels at a
voltage-dependent propagation velocity, v(F), expressed as
4
~
LC(V)
(2'7)
Integrating (2.6b) with respect to P, the relation o f the voltage wave and the current
wave called a voltage-dependent characteristic impedance is given in the following
equation.
■
J5
12
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2.2
NLTL characteristics
It is possible to create an integrated circuit from a fully distributed NLTL,
however, line losses could be significant due to lossy dielectric material under the
lines. Therefore, only partially distributed NLTLs have been studied in this work.
Many partially distributed NLTL structures have been investigated, but a very
promising technique to reduce the line losses is the integration o f diodes connected
with suspended (air bridged) transmission lines. The suspended lines reduce dielectric
loss and increase line impedance for better impedance matching after loading with
varactor diodes. The remainder o f this section will discuss the key characteristics of a
partially distributed NLTL.
In the earlier section, it was found that a section o f the fully distributed
capacitive loaded transmission line has the phase velocity v = 1/VLC . However, the
effect of the periodic spacing o f the diodes may affect the performance of the NLTL,
so its characteristics including phase and group velocities, frequency cutoff and
characteristic impedance will be analyzed [28].
Consider a transm ission line with characteristic impedance Z/ periodically
loaded with shunt susceptance b with spacing d. The equivalent circuit of a unit cell
and a cascade of unit cells are shown in Figure 2.3. The relationship between the input
variables Vn, I„ and the output variable Vn*i, In*i are found by utilizing the ABCD
transmission matrix. If we break down the unit cell into three circuits in cascade
including a section of transmission line of length d! 2 (or electrical length
&2
= kd/2 ,
where k is the propagation constant), a normalized shunt susceptance j b at the middle,
followed by another section o f transmission line. Then the voltage and current
relationship at the unit cell can be expressed as
13
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,«+/
d/2
d/2
Figure 23:
Equivalent circuit of periodic transmission line (partially
distributed).
9
. . 9
cos—
y
sin—
0
2
2
.. 9
9
1 /s
in — cos—
2
2 .
#
.. 9
cos— y sin— 1
2
2
9 jb
. . #
/s in — cos—
2
2
c o s # - —sin#
2
(_
_\
J —cos# + sin# + —
2
2
n+l
n+l
*
a + sin#
■ a —b
—cos#
2
2
/I+I
n+l
(2.9)
c o s # - —sin#
2
For wave propagation on the transm ission line, the voltage and current at
the («+l)th terminal must be equal to the voltage and current at the nth terminal except
for a propagation term. This gives
K +l = e-"Vm
(2.10a)
(2.10b)
14
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where y= jP + a is the propagation constant for the periodic structure. Combining the
equations (2.15) and (2.16) with ABCD matrix representation provides
f
V
■A
C
*
I-F*"
D . I LO
Lo
o
'
\
X * . '
J-
= 0
(2 . 11)
C . .
Solving the eigenvalue e^, we obtain
coshjt/ = coshad cos fid + j svahad sin f3d
= c o s # - —sin#
2
(2.12)
The right-hand side o f this equation m ust be purely real, hence either a = 0 or ft = 0. If
a = 0 and
* 0, this case will corresponds to the passband which the waves can
propagate without losses. Then the equation (2.12) can be written as
passband:
£
cos fid = c o s # - —sin#
(2.13)
The values of /? in (2.13) can be solved if the magnitude of the right-hand side is less
than or equal to unity, but there will be an infinite number of solutions (passbands)
that can satisfy this equation. If a * 0 and /?= 0 or it, the wave does not propagate, but
attenuates along the line and this frequency is said to be in the stopband. When
substituting the value of fi into (2.12), we obtain
stopband:
cosh otd = c o s# — sin#
(2.14)
The equations (2.13) and (2.14) hold for any shunt susceptance. If the shunt element is
a capacitor C* b = coCdZi = toCd^jL, 1C, where C/ and Li are the capacitance and
inductance of a unit cell of transmission line respectively, and c o = 2 n f We know that
# =kd= cot]L,C, , therefore the equation (2.13) can be written as
15
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✓'iC* 7
cos (3d —cos kd h-------—- sin led = 0
2
(2.15)
Solving this equation yields the phase velocity
cod
CO
Vp
'
1
~
{
cod
ooC.Z,
.
cod'
arccoa cos----------- — - s m —
\
v
2
v
(2.16)
while the group velocity is
dco
sin(/3d)d
rd CdZ A . cod aCdZ td
cod
—+
cos
sm — +
v
2v
i/
2
(2.17)
From the above, it is readily seen that for low frequencies {i.e. much below cutoff
frequency), the calculated phase velocity and group velocity are essentially frequency
independent. The cutoff frequency can now be determined.
If the periodic cutoff frequency fper, where fper - ooperlljt is the highest
frequency in the first passband, the equation (2.15) can be written as
(2.18)
LL,
Expanding the cosine and sine in their series expansions we have
f
r
,
1
1
+ 2—
+
—
2 - 1 i + Z - L,Cloooer
2
C, ' I K r 24
ci.
_ _
For Ci «
(2.19)
Cd, the third and higher terms can be neglected, and the periodic cutoff
frequency can be approximated to be
fper ~
1
x jL ^ C j+ C ,)
16
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( 2 .20 )
Another important parameter of the periodic structure is the characteristic
impedance Zr presented to the voltage and current waves at the input terminals o f a
unit cell. For a symmetrical network, A = D, the normalized impedance of a unit cell
can be obtained from (2.11), which yields
_
I2 sm 0 + bcos 0 - b
(2.21)
V2sia0 + bcos0 + b
For frequencies well below cutoff frequency of the periodic structure, sin 0 =
sin {(oyjL lCl ) « q)-JL,C,
and cos 0 = cos (o)-yjL,C, ) ~ 1, so that the characteristic
impedance becomes
( 2 .22 )
2.3
Bond wire
In microwave circuit systems bond wires are frequently used as parts of
transmission lines for connecting devices. In this work, gold bond wires are employed
for connection between diodes because their structure is simple and easy to
characterize and implement. A generalized structure o f bond wire can be seen in
Figure 2.4. This bond wire can be modeled using lumped elements and the bond wire
inductance is found to be [29]
17
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Bond wire
Bonding pad
Substrate
or device
Groud plane
d
Figure 2.4:
Bond wire structure for calculating inductance and capacitance.
L(nH)
=
10 J* 2ln(p(x))tf6c
(2-23)
where
i 1/2
P(x) = r
—x~
— esc B
'
d
0
h - —cot/3
.2
(2.24)
d is the distance between two bond connections, h is the minimum average height of
the pads, r is the radius o f the bond wire, fi is the bonding angle in radians, and all
units are in inches.
The corresponding incremental capacitance is given as
dC =
1.4337
p F I inch
ln(/>(x))
18
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(2-25)
2.4
Diodes in NLTL
To achieve the required voltage-variable capacitance, varactor diodes can
be used in NLTLs. The basic element of a varactor diode is the capacitance o f its
junction space-charge region, therefore, it can be either a prt junction, a Schottky
barrier, or even a metal insulator semiconductor diode.
2.4.1
Varactor diode
Electronic properties of varactor diodes have been studied and can be
found elsewhere [30]. An equivalent circuit of a packaged reverse-biased varactor
diode is shown in Figure 2.5. Q is the diode capacitance, Rj is the small-signal
junction resistance resulting from the generation recombination and leakage current,
Rd is the diode series resistance, Ls is the inductance of bond wire, and Cp is the
capacitance of the diode package. Usually, the resistance Rj is very high, and if the
effect of Ls and Cp can be neglected. The quality factor Q of the diode is
Q
1
=
a>cRdCd(V)
Equivalent circuit of a reverse-biased varactor diode.
19
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(2.26)
The intrinsic cutoff frequency f c, where f c = qjJ2 k is defined as the frequency at which
Q= 1 is given to be
/
=
--------
2nRdCd(V)
(2.27)
In order to obtain a high cutoff frequency, the value o f Rd and C*(F)must
be very small. The resistance Rd can be reduced by using a semiconductor material
with high carrier mobility and high doping, which means that n-type is preferred over
the /7-type semiconductors. Further reduction in Rd requires a low resistivity
semiconductor and a large cross-sectional area for the diodes, but these features tend to
increase CJiV), and hence, a compromise is required. Note that the capacitance CJ^V)
depends on the reverse voltage, and thus an increase in the reverse bias causes an
increase in f c. Most o f practical varactor diodes are fabricated on an n-type epitaxial
layer grown on n+-substrates with epilayer thickness providing the optimization
between foand Q (F ) to meet the desired value of cutoff frequency. Nevertheless, the
epilayer thickness need be carefully considered to avoid punchthrough.
2.4.2
Why hyper-abrupt junction diode?
Consider a varactor diode with various doping profiles in the n-side, where
as /7-side is assumed to be very heavily doped, as shown in Figure 2.6(a). The carrier
concentration follows the one-dimensional Poisson equation
d*v _
dx 2
qN(x)
es
(2.28)
where N(x) is the generalized doping distribution approximated as N(x) = B x q is the
electron charge (1.602xl0'l9C), and es is permittivity of semiconductor. For m = 0, the
doping profile corresponds to the uniformly doped case. The device will have a oneside linearly graded profile, if m = 1, and hyper-abrupt junction, if m < 0. A hyper-
20
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abrupt junction can be achieved by an epitaxial process or by ion implantation.
Integrating Poisson’s equation with the appropriate boundary conditions provides the
capacitance per unit area [31].
m+l
qB{es )
(m + 2)<Y + V J
C„(F) =
(2.29)
where Vb, is the built-in voltage.
An important parameter used to characterize the varactor diodes is
^
sensitivity defined to be
s =
y
^
Cd(V) dV
(2.30)
m +2
Larger values of sensitivity indicate larger changes in capacitance with
varying-bias voltage. For linear graded junctions, m = 1 and s = 1/3; for abrupt
junctions, m = 0, s = lA; for hyper-abrupt junctions with m = -1, -3/2, and -5/3, the
Nn-N,
InC
n-side
p-side
heavily
doped
Hyper-abrupt
junction
m=-5/3
5=3
Abrupt
-3/2
5= 1/2
Graded
5= 1/3
x
0
► In V
(b)
(a)
Figure 2.6:
Varactor diode (a) various doping profiles and (b) plot o f depletion
layer capacitance vs. reverse-biased voltage.
21
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values of j are 1,2 and 3 respectively, as illustrated in Figure 2.6(b). It is evident that
hyper-abrupt junction diodes with high sensitivity are desirable in the NLTL as the
variable capacitance so that the large capacitance change can be obtained using a small
number of varcator diodes and small voltage swing.
2.5
Line loss
The loss of a NLTL is primarily caused by two contributions, the loss from
all diodes and the resistive loss in the transmission line. The loss from radiation is
usually negligible because the capacitive loading of the diodes is assumable large
enough so that the wave velocity on the NLTL is too slow to couple the energy into a
substrate mode. This section discusses the loss of a NLTL in detail.
To analyze the loss characteristic in a NLTL, the series resistances of
diodes and transmission line have been added into the unit cell model. We start by
analyzing the loss by the diodes. The shunt susceptance when the series diode
resistance is included can be expressed as
Zs
1/ ja C d + Rd
(2.31)
(2.32)
or
Substituting (2.32) into (2.12), where Q = a x , produces a pair of coupled equations for
ad and fid
coshadcosfid = cos cor -
coCjZ,
1
sin tar
2
nl/^2
2 1+ a 2R2
dC*
svdh.adsm.pd =
(2.33a)
(2.33b)
22
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For low frequencies (eo «
afar), the approximations sinh a d « ad, sin fid * fid, and
sin car^ car can be made. Thus the equation (2.33b) reduces to
,
1 2r,2o 7 car
a d * -eo CdRdZ, —
(2 J 4 )
It can also be found that fid * ca^L,CT or carlfid « ca^jC, / CT at frequencies much
less than the cutoff frequency, therefore equation (2.34) becomes
ad * ^ca 2 C]RdZ T
(235)
This equation can also be derived directly from the lumped circuitmodel, as shown in
Figure 2.7. We then include the loss effected by a series resistance Ri of transmission
line, and assume that R t« oaLi and R< j« 1/ coC
yd
t
so
that
= V z F a j(R , + jcoL, )(1 - jcaRdCd)jcaCT
£.36)
Thus we obtain
ad * -c a 2C 2dRdZT + - ^ ~
2
22j
Figure 2.7:
Neper
(2.37)
Lumped element equivalent circuit for a lossy transmission line unit
cell loaded with a varactor diode.
23
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The first term o f this equation accounts for the resistive loading of the
diodes. In order to make this component of the loss small, the cutoff frequency of the
diode needs be very high. The second term, which is caused by the ohmic loss of the
transmission line conductor, can be extremely important at high frequencies where the
skin depth is small.
2.6
2.6.1
Design and simulation
Basic design of NLTL
A scale model NLTL (100 times larger than an integrated version) with a
bias tee and coupling capacitors has been constructed (Figure 2.8). The scale model
NLTL consists of a series of two NLTL sections on a brass block, with 30 hyperabrupt junction diodes (Diode 1) at 0.185 inch interval spacing for the first section and
20 hyper-abrupt junction diodes (Diode 2) at 0.025 inch interval spacing for the
second. The scale model NLTL has been intentionally designed to increase a cutoff
frequency o f the second section, however, this would only be useful when operating in
large signal mode to increase pulse compression and decrease fall times.
The specifications of both diodes are in Table 2.1. The intrinsic cutoff
frequencies determined by means o f (2.27) are found to be 49.7 GHz for Diode 1 and
99.5 GHz for Diode 2. Gold bond wires with the diameter of 0.0003 inch have been
used for connections between diodes, as shown in the expanded picture o f Figure 2.8.
The angle /? o f the bond wire structure (Figure 2.4) is approximately 15° or 0.083 ?r
radian. Using (2.23), (2.24) and (2.25), the values o f bond wire inductance and
capacitance can be numerically calculated to be 4.735 nH and 0.052 pF for the first
section o f the scale model NLTL and 0.549 nH and 0.008 pF for the second. The
24
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periodic cutoff frequencies for each section, therefore, can be readily calculated by
utilizing (2.20) with these values and diode capacitances. The periodic frequency
cutoffs of 6.4 and 30.2 GHz are obtained for the first and the second sections
respectively.
By employing (2.8), the characteristic impedance of the first and the
second sections of the bond wire transmission lines are then computed to be 300 and
260 Q respectively.
However, when including the effect of periodically loaded
varactor diodes at zero bias, these characteristic impedances are then dropped to 50
10 m m
Figure 2.8:
The scale model NLTL consisting o f 30 (2.0 pF) and 20 (0.8 pF)
hyperabrupt junction diodes interconnected by gold bond wires.
25
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.1
Some important specifications of diodes.
Parameters
Ohmic contact, Rs
Zero-bias junction capacitance, Cjo
Junction potential, Vj
Grading coefficient, M
Chip size
Diode 1
1.6
2.0
1
0.5
20x20x5
Diode 2
2.0
0.8
1
0.5
15x15x5
Unit
Q
pF
V
mil
and 25 Q respectively calculated by (2.22). The bond wire resistances
approximated to be 2.51 and 0.34 Q for the first and the second section respectively.
Using (2.37), the loss o f a unit cell can be also calculated to be 0.280 and 0.062 dB for
the first and the second section respectively at an operating frequency of 1 GHz. A bias
tee consisting of large valued coupling chip capacitors and a shunt toroid inductor was
placed at the input o f the scale model NLTL. At the output, only coupling capacitors
were installed. Then SMA connectors were connected at the input and output coupling
capacitors.
All necessary characteristics of the NLTL were determined and some
initial calculations were done at an operating frequency of 1 GHz and zero bias. The
further important parameters have been extensively studied by employing powerful
software packages as described in the next section.
2.6.2
Simulation with PSPICE™ and Libra™
Computer simulations with Microsim/PSPICE and HP/EEsof Libra have
been used to characterize the scale model NLTL. PSPICE is usually used for
simulating low frequency circuits, whereas Libra is more suitable for some high
frequency characteristics such as scattering parameters (definitions explained in
26
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Chapter 5). The diode parameters for simulating with PSPICE and Libra are shown in
Table 2.1.
2.6.3
Results from simulation and measurement
The simulation of the delay time for the scale model NLTL with diode and
bond wire parameters from the previous sections was performed at an operating
frequency o f 1 GHz using PSPICE. The results agree well with measurements using
HP 54750A high-speed digitizing oscilloscope, as illustrated in Figure 2.9. This result
confirms that employing 50 varactor diodes provides the complete cycle delay (1 ns)
needed for a frequency translator (detailed in the next chapter). Using an HP 8720D
vector network analyzer in conjunction with the Libra software, linear network
parameters were measured. The measurement o f scattering parameters and the group
delay at bias voltages ranging from zero to -10 V over the frequency range of 0.05 to
3.0 GHz band were compared with the results from simulation simultaneously. Figure
2.10 shows the schematic diagram of the scale model NLTL in Libra simulation. There
are good agreement between simulations and measurements for scattering parameters,
Si i (or reflection coefficient) and S 21 (or transmission coefficient), and the group delay
at all bias voltages form zero to -10V, but only the result at zero bias is shown in
Figure 2.11.
A fitting between results from a model o f the NLTL and from
measurement (scattering parameters and group delay) at several biases has been done
using an HP 8720D vector network analyzer in conjunction with a microcomputer and
Libra. The resulting diode parameters (i.e. series resistance and capacitance) are in
good agreement with its specifications from the manufacturer.
27
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A NLTL integrated circuit is expected to have improved performance and
reduced size and cost To progress toward full integration of the NLTL circuits on a
chip, certain device parameters should be optimized and timed in Libra simulation, but
the details of integration are not included in this work.
2.0
•
#
•
M e a su re m e n t
1
1.5
/
O)
<D
E
>
1.0
1
~
IS
a>
I
a
0.5 -
V^
o.o
I1
0
‘. ------1
1------.'
2
Ii
4
», _
. v
Ii
6
.,
v _
• • Vw
.1i
8
a
—
• •
i-------1
I-------10
R e v e rse bias voltage (V)
Figure 2.9:
Simulation of the delay with PSPICE compared to measurement by
an HP 54750A high-speed digitizing oscilloscope.
28
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
f-rzHpTTjl
LIBRA S im ulation o f S c a le M odel NLTL
lit ••
JR
&?.•,■"**'
as:'.. &
I*. .«
n«i
W
H
lKM
■
M
Iimi
III
im
t r t""t" i
S)
I ■ t ■ | ■ t '
j ' |
t r T 't
j
)
I
]
VO
r n
'v r
t r :~i
r
•Ml
Figure 2.10: Schematic diagram of the scale model NLTL in Libra simulation.
Sim ulation
DS11
O S21
M easu rem en t
V
S 11
A
S21
D elay
X
O D elay
o.o
10000
- 2 0 . 0
8000.0
- 4 0 . o
5000.0
- 60.0
4000.0
0
ffl
~E
q
.
u,
o
^
to
• 80 . 0
-
100.0
0.0
2000.0
3 . 0
Frequency (0.5 GHz/div)
Figure 2.11: Simulation of the large scale model NLTL at zero bias using Libra
compared to measurement from an HP 8720D vector network
analyzer.
30
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Chapter 3
MICROWAVE PHASE SHIFTER
AND FREQUENCY TRANSLATOR
A microwave phase shifter is a two-port device whose basic function is to
provide a change in the phase o f a microwave signal. Phase shifters can be broadly
classified as being either mechanical or electronic, and also can be categorized as
analog and digital phase shifters depending on the type of operation. Analog phase
shifters change the phase continuously, whereas digital phase shifters allow variation
o f phase shift only in discrete steps, employing a sequence o f binary bits to control the
desired phase steps. In the following sections, the basic operational features of
mechanical and electronic phase shifters will be briefly described. Also a new
electronic phase shifter called a distributed phase shifter will be proposed in this
dissertation.
3.1
3.1.1
Review of microwave phase shifters
Mechanical phase shifters
Mechanical phase shifters are often built in coaxial lines or metallic
waveguides with dielectric or ferrite plates [1,32,33]. The phase of these phase shifters
can be changed by means of mechanical tuning, such as a variation in the physical
length o f the line or rotation displacement of a dielectric slab inside a waveguide. The
mechanical phase shifters have several advantages when compared to electronic phase
31
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
shifters including very low loss (typically 0.5 dB for a 360° phase shift), easy
fabrication, and ruggedness. Figure 3.1 shows the basic structure o f rotary phase
shifter, a widely used mechanical phase shifter introduced by Fox [1]. This phase
shifter consists o f two rectangular-to-circular waveguide tapered transitions, together
with an intermediate section of circular waveguide that is free to rotate. A thin half­
wave dielectric plate is located at the intermediate section and two similar quarterwave plates are placed at the ends. At tapered transitions of both ends the TEio mode
in the rectangular waveguide is transformed into the TEu mode in the circular
waveguide, and the quarter-wave plates oriented at an angle of 45° relative to the broad
wall of the rectangular waveguide convert a linearly polarized TEu mode into a
circularly polarized mode, and vice versa. The ends of the dielectric plate are typically
tapered to reduce reflections. The half-wave plate produces a phase shift based on the
angle, which it is rotated.
Assuming that the incoming TEu mode (linear polarized) incident on the
first quarter-wave plate can be represented by Ea suuaf, then this wave can be
decomposed into two modes, polarized parallel and perpendicular to the quarter-wave
plate. These components can be written in the form o f Euj = £v/ = (E J
)sinax. The
propagation constant /?/ o f the parallel polarized mode is greater than the propagation
constant /S? of the perpendicular mode. The length I o f the quarter-wavelength plate is
chosen so that
)l = rc/2. After propagation through the first quarter-wavelength
plate, the fields are the circularly polarized, and can be decomposed into components
along U2 and
axes, as shown in the following equations [33].
32
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Rotating section
'3
TE10
TE 10
A/4 p la te
Figure 3.1:
A/2 plate
A/4 p la te
The basic structure of rotary phase shifter and orientations between
dielectric plate and principle axes for decomposition o f fields.
(3.1a)
(3.1b)
Next, this wave propagates through the half-wavelength plate with length
21
and the output fields written as components along the 113 and v? axes become
- —j=Gos(pct - 3 /?,/ 4-Iff)
(3.2a)
(3.2b)
33
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Finally, after propagating through the second quarter-wavelength plate, the output field
can be expressed as
(3.3a)
where
(3.3b)
(3.3c)
The output field from the rotary phase shifter is again a linearly polarized
TEu mode on output, having the same direction of polarization as the incident field.
However, the resultant phase has been shifted by an amount 4/?// + 20 which means
that the rotation o f the half-wavelength plate through an angle
0
produces a phase shift
equal to twice the angle (20). This simple dependence of the phase change on a
mechanical rotation is the key advantage o f the rotary phase shifter. Therefore, the
rotary phase shifter has been used in this work to verify the concept of an ideal
frequency translator (explained the next chapter).
3.1.2
Electronic phase shifters
Compared to mechanical phase shifters, electronic phase shifters can
provide inertialess phase change with minimal switching time. Digital electronic phase
shifters generally use switches to alter the electrical phase length, while analog
electronic phase shifters vary a device reactance continuously to control the phase
change. The principles of electronic analog and digital phase shifters are presented in
the following sections.
34
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3.1.2.1 Digital phase shifters
In all types o f digital phase shifters the desired phase shifts are introduced
by changing the bias state of the control devices or switches, which are typically PIN
diodes [34-39] or GaAs FETs [40-45], PIN diodes and the GaAs FET switches are
extensively used either as series or shunt switches. There are four main types o f digital
phase shifters: switched-Iine, reflective, loaded-line and low-pass high-pass. Figure 3.2
shows these basic types of digital phase shifters suitable for planar circuit realization.
The switched-line phase shifter in Figure 3.2(a) operates by simply switching between
two transmission lines of different physical lengths to provide a relative change in
electrical length. This phase shifter is quite simple to implement on a planar substrate,
but the physical length o f the transmission lines becomes too large for a low operating
frequency. The insertion loss of this phase shifter is normally high, since the switching
devices are in the transmission path.
Figure 3.2(b), (c) and (d) illustrate reflective phase shifters, where short
circuit switches control phase changes through the circuits. The phase shifter in Figure
3.2(b) relies on a circulator brought the microwave signal down to a section of
transmission line or a short circuit, which reflects the microwave energy back to the
circulator. The circulator then directs the reflected microwave energy to the output port
with a shifted phase depended on the location of the switch. This kind of phase shifter
is only unidirectional and requires a circulator. Another reflective phase shifter in
Figure 3.2(c) uses a 3-dB hybrid power splitter to direct a half of the microwave
energy down to each of two transmission lines with short circuits controlled by
switches. The reflected microwave signals recombine in phase at the output port
providing a variable phase based on the location of short circuits on the transmission
lines Figure 3.2(d) shows a reflective phase shifter extended from Figure 3.2(c) to
35
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(a)
(b )
Output
iT L
Output
Input
(d)
(C)
Input
Figure 3.2:
Input
Input
Output
Output
Basic electronic phase-shifting circuits (a) switched-line phase
shifter, (b) reflective phase shifter with circulator, (c) reflective
phase shifter with 3-dB hybrid and (d) reflective phase shifter with
multiple short circuits, (e) lumped-element loaded-line phase shifter,
(f) distributed-element loaded line phase shifter, and (g) low pass
high-pass phase shifter.
36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 3.2:
Continued.
37
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obtain more phase-steps, employing a 3-dB hybrid with multiple short circuits. All of
the reflective phase shifters are based on variable length transmission lines, which may
become too large at a low operating frequency. Also mismatches and insertion loss in
the circulator and the 3-dB hybrid can cause to errors in the amount of phase shift.
Figure 3.2(e) and (f) display loaded-line phase shifter types for both
lumped-element loads and distributed-element loads [38,39]. These phase shifters
consist of two identical reactive loads placed at quarter-wavelength intervals on the
transmission line. The reflection from the two loads will destructively combine (180°
out of phase), resulting in a good input match. The distributed-element loaded-line
phase shifter uses transmission line stubs as the reactive loads which enable a simple
switch to be employed to provide either an open or a short circuit stub. The stubs
transform the terminations into reactive components, where the short circuit stubs look
inductive and the open circuit stubs look capacitive. The advantages of this type of
phase shifter are simplicity and low loss, however, the quarter-wavelength
transmission line can be too large for some particular uses. The loaded-line phase
shifter is usually restricted to applications with phase shift of 45° or less.
The last important structure is a high-pass low-pass phase shifter operated
by switching between a high-pass filter and a low-pass filter. This phase shifter is
illustrated in Figure 3.2 (g). Both filters are amplitude matched at the operating
frequency but have different insertion phase lengths. A low-pass filter comprised of
series inductors and shunt capacitors provides a phase delay, and a high-pass filter
comprised of series capacitors and shunt inductors provides a phase advance.
Therefore, the relative difference between these states gives the desired phase shift, for
instance, a 180° phase shifter may be composed of a circuit that switches between +90°
38
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and -90° phase length filters. By arranging switches between low-pass and high-pass
filters, this phase shifter can be very small due to the use o f lumped elements
compared to the other types for the same bandwidth, but tend to have more insertion
loss. At low frequencies, lumped elements can be used to implement the filters,
however, the parasitics o f the semiconductor switches effect the filtering functions at
high frequencies.
3.1.2.2 Switch implementation for digital phase shifters
A step-phase change in a digital phase shifter is usually obtained by using
switches, as described in the previous section. In the present day, PIN diodes and
GaAs FETs are often used either as series or shunt electronic switches in most
microwave systems, as shown in Figure 3.3 (a) and (b).
A PIN diode is a PN junction device that has an intrinsic region (i region)
located between the p and n-doped contact regions. The intrinsic region gives a very
high value of diode breakdown voltage, whereas the device capacitance is reduced by
the increased separation between the p and n regions. In forward bias the conductivity
of the intrinsic region is controlled or modulated by the injection of charge from the
end regions. The PIN diode is a current-controlled resistor with excellent linearity and
low distortion. It is very useful, therefore, for high frequency and high power switch
applications. When the diode acts as a switch at microwave frequencies, the switching
speed from a low-impedance (on state) to a high-impedance (off state) is very crucial
if high IF is required. The switching time is composed of two components: a time
required to remove most o f the charge from intrinsic region called a delay time, and a
time during which the diode is changing from a low-impedance to a high-impedance
state called a transition time. The delay time is inversely proportional to the charge
39
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
carrier lifetime. If the diode has a short carrier lifetime, it will have a fast switching
speed, but will suffer from high forward bias resistance (high insertion loss). The
transition time depends on geometry and doping profile o f the diode, but it is not
sensitive to the amount of forward and reverse bias. Another design parameter of a
PIN diode as a switch is a switching cutoff frequency, which is defined in terms of
series resistance and capacitance. Typically, PIN diodes have the cutoff switching
frequency in range of a few hundred GHz to several hundred GHz, however, they are
usually used in a frequency range around one-hundredth to one-fiftieth o f the
switching cutoff frequency to avoid high insertion loss.
For the GaAs FET switch, two different modes o f operation can be used:
active and passive modes. In active mode, ether single-gate or dual-gate FETs can be
used as three-terminal devices identical to those operated in amplifier mode. In passive
mode, GaAs FETs are used as passive two-terminal switches with the gate acting as a
control terminal only. In another words, the impedance between the drain and the
source terminals depends upon the DC control voltage at the gate terminal. The highimpedance state is attained by applying a DC voltage on the gate greater than the
pinch-off voltage (typically - 3.5 V). The low-impedance or conducting state occurs
with zero DC bias applied to the gate. The channel from source to drain is opened and
it presents a very low resistance (typically ~ 1.5 to 3.5 Q per mm of gate periphery).
The DC currents (typically small) that flow between gate-source and gate-drain are
functions of the fabrication process, device periphery, and magnitude of applied
voltage. Since no further external bias, coupling and matching circuits is required, the
GaAs FET switch is inherently broadband.
40
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Digital phase shifters using PIN diodes are quite simple and suitable for
high power application, whereas GaAs FETs phase shifters can work at lower power
but higher operating frequencies. The resolution of phase change (step-phase
increment) in digital phase shifters depends on the number of digital-controlled bits,
for example, a 4-bit, 360° digital phase shifter will have only 22.5° step-phase
increments. The value of the step-phase increment is obviously limited by the structure
o f digital phase shifter. Phase shifters with very small step phase increments are very
difficult to realize due to the large number of transmission lines and switches required.
Due to these difficulties, such devices have never been realized.
Bias
Ideal switch
PIN diode
FET
“o------
(a)
Ideal switch
PIN diode
FET
i
Bias
(b)
Figure 3.3: Electronic switches using PIN diodes and FETs for digital phase
shifters (a) series and (b) shunt circuits.
41
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3.1.23 Analog phase shifters
An analog phase shifter usually provides a high phase resolution limited
only by the control circuits. Typically, analog phase shifters are categorized into those
which operate in passive and active modes.
In passive mode, varactor diodes are
usually used as the tuning elements of the phase shifter [4,46,47]. Figure 3.4(a) shows
a conventional type of varactor diode phase shifter. The varactor diodes provide a
varying reactance to the circuit which is a function o f the negative bias voltage.
Although this varactor diode phase shifter provides an accurate tuning of phase shift
the range o f phase change is limited (typically -
1 0 0 °)
by the tuning range of the
varactor diodes.
In active mode, dual-gate FETs have been extensively studied for realizing
analog phase shifters by numerous authors [48-50]. A simple dual-gate FET amplifier
circuit acting as an analog phase shifter is shown in Figure 3.4(b). One gate (G?) of the
FET is used as the signal input gate, and the second gate (G/) is used as the control
gate. The output phase change is obtained by the interaction between voltagecontrolled source capacitance at gate G/ and the external tuning impedance, however,
the gate-controlled voltage results the variation in gain. A continuous variation of
phase change up to -
100°
with gain has been reported, but in principle only a narrow
bandwidth could be achieved from this type o f phase shifter. Figure 3.4(c) displays
another 90° analog phase shifter using two dual-gate FETs as variable-gain amplifiers.
The operation o f this phase shifter scheme is based on the complex summation of two
variable-amplitude quadrature signals from both FET amplifiers. The input signal is
divided into two equal parts by using a 90° hybrid, then these quadrature signals are
fed into variable-gain FET amplifiers. The amplified outputs of the FETs then are
added in an in-phase power combiner resulting the vector sum \Qs}* at the output port,
42
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Output o ——<
3 dB, 90°
hybrid or
coupler
Input o— ►
Varactor
diodes
(a)
Matching
circuit
Input
o
1
L
Controlled
voltage
K ls
I
i Output
Matching
circiut
Tuning
impedance
(b)
A L0°
0°
input
90°
power
divider
B L9QP
In-phase
power
conbiner
o Output
90°
Dual-gate FET
amplifiers
(C)
Figure 3.4:
Analog phase shifters (a) varactor diode phase shifter, (b) single
dual-gate FET amplified phase shifter, and (c) two dual-gate FET
amplified phase shifter.
43
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where
|C| = yjA2 + B2 and <p= tan' 1 (B/A). The output phase shift, therefore, can be
controlled by properly adjusting the gain o f each FET amplifier independently, thus an
output signal of any phase and amplitude can be generated. This phase shifter has
several advantages such as large bandwidth (octave), high gain capability, and fast
response. However, to obtain a 360° phase shifter the vector sum o f four quadrature
vectors are required. Those quadrature vectors can be realized by a 180° power divider,
two 90° hybrid, four dual-gate FET amplifiers, and an in-phase four-way power
combiner. These FET amplifiers need four control voltage signals, but two amplifiers
operate at a time resulting in variations o f amplitude and phase of the output signal by
the effect o f combiner.
These analog phase shifters can provide high resolution for small amounts
of phase change, whereas digital microwave phase shifters are appropriate when a
larger step phase change is required. Many researchers, therefore, have developed
some techniques to improve the characteristics of electronic phase shifters by means of
combination of analog and digital phase shifters. Andricos et al. [15] have proposed a
new electronic phase shifter by mixing a 6 -bit digital phase shifter (combining the
loaded-line and reflective types) with an analog phase shifting circuit to provide
accurate tuning of phase from 0° to 360°, however, their complicated phase shifter
circuit works only over a narrow frequency band and exhibits high insertion loss. A
reflective phase shifting circuit with a frequency multiplier has been introduced by
Klymyshyn et al. [16] to realize a 360° linear microwave phase shifter. A sub­
harmonic signal o f 1/N frequency is injected into their phase shifter, then the
frequency multiplier translates the output to the desired carrier frequency and restores
the fiill 360° phase shift range. Their circuit has been implemented on microstrip at an
44
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operating frequency of 18 GHz, but it operates for only over a narrow bandwidth (200
MHz).
3.2
Distributed phase shifter using NLTL
The mechanical phase shifter can work as an ideal frequency translator,
but it provides very low frequency shifts and narrow bandwidth, and its structure is
limited to only hollow waveguides. This phase shifter is bulky and requires a rotating
part (inertia is a concern), therefore it has never been used as a frequency translator in
any modem microwave system. All electronic phase shifters using both passive and
active components (z.e. PIN diodes and FETs) are generally employed as microwave
frequency translators in the present day, but they provide low resolution of step-phase
change causing low carrier and spurious sideband suppression.
In order to achieve broadband operation, however, a low-Q structure is
required. To reduce losses, the structure should be distributed rather than simply
resistive. To achieve monolithic integration, varactor diodes rather than ferromagnetic
components should be the variable phase elements. When operated in small-signal
mode, the nonlinear transmission line (NLTL) satisfies all these requirements,
therefore a distributed phase shifter with the NLTL structure has been proposed and
applied to frequency translation for the first time. Using this phase shifter would
overcome the drawbacks of both mechanical and the present electronic phase shifters.
The scale model NLTL was built on a brassbroad, as shown in Figure 2.7,
the details of which were discussed in the previous chapter. The NLTL offers voltagevariable delay to the RF signals as bias is changed, hence it can work as a phase shifter
and a frequency translator when its phase is modulated. The NLTL characteristics,
time delay and transmission coefficients, have been comprehensively measured at an
45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.8
1.5
— • — Time delay (ns)
0.7
— ■— Transmission (V/V)
CO
c
1.0
0.6
>*
I
ra
<D
T3
0.5
0.5
0.4
0
>
0
O
‘to
CO
'E
CO
c
CO
0.0
cr
0.3
-0.5
0.2
0
5
10
15
20
Reverse bias voltage (V)
Figure 3.5:
Measurement of NLTL delay and transmission characteristic vs.
reverse bias voltage at 1 GHz RF.
operating frequency of 1 GHz using a digitizing oscilloscope (HP 54750A), as shown
in Figure 3.5. The results show the expected decrease in delay with increasing reverse
bias voltage, as well as the variation in transmission through the circuit.
33
Serrodyne frequency translation
A frequency translator is a device used for shifting up or down the
frequency o f an input signal by some desired amount A good frequency translator
should provide an output of only the shifted carrier frequency with minimum power
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
loss and without generating spurious frequencies. One way to create a frequency
translator is to use a phase shifter as a phase modulator. When the phase angle of an
input RF signal is varied linearly with time, a frequency o f the resultant output signal
is translated to a new frequency. This frequency shift is similar to the familiar Doppler
frequency shift caused by a wave reflection from a moving object. A constant Doppler
frequency shift is produced by a constant rate of change in electrical phase between
waves from the microwave source and the reflector. An ideal frequency translation
can be accomplished by using a phase shifter controlled by a linear phase function of
modulation frequency f m. Mathematically, the linear phase function can be expressed
as
m
=
2
(3-4)
The output waveform o f the phase shifter is given by
= £sm [ 2 ^ 0/+^(r)]
= £sm [ 2 s-(/„ + / .) ( ]
(3-5)
where E is the signal amplitude, f 0 is the microwave carrier signal frequency, and
(fQ +
is the new shifted frequency. A simple ideal frequency translator has been
studied using a mechanical rotary phase shifter providing a linear-phase function,
however, only a small frequency shift on the order of ten cycles per second could be
obtained. The results o f the experiment for this scheme will be presented in the next
chapter.
As illustrated in Figure 3.6(a), a frequency translation can also be achieved
by driving a phase shifter with a periodic sawtooth phase function, varying the phase
linearly between zero and 360°, then flying back to zero instantaneously. This phase
modulation method is also known as the serrodyne technique. This technique was first
47
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
applied by Sohoo [3] to a ferrite Faraday rotation phase shifter to accomplish a
frequency translation. Although it was already being explored in the 1950’s, the
serrodyne modulation technique using the periodic sawtooth phase function has never
been realized for lack of an analog microwave phase shifter to change the phase
linearly over 360° efficiently. Several authors [5-14,51,52] have utilized a step-phase
or staircase phase function to approximate the continuous sawtooth phase function, as
shown in Figure 3.6(b). The frequency translators then can be implemented by means
o f the digital phase shifters explained in the previous section. However, only coarse
staircase phase functions have been used to implement frequency translators in the
literature, and so their frequency translators usually suffer from insufficient carrier and
spurious sideband suppression. Also, their frequency translators are usually realized by
integrating hybrid couplers with variable capacitances or gains arising from diodes or
transistors. These techniques usually limit the bandwidth o f the frequency translators.
Recently, a new method o f integrating fixed-delay transmission line segments,
switches and drivers has enabled a 6-18 GHz digital phase shifter which, when
serrodyne modulated, has yielded the highest record o f 22 dB for both carrier and
spurious sideband suppressions [ 1 2 ].
3.3.1
Analysis o f the effect of flyback time
A sim ulation of a serrodyne frequency translator using a continuous
sawtooth scanning signal has been performed under a variety o f modulation conditions
to observe how frequency translators would respond at increasingly higher modulation
rates. Figure 3.7(a) and (b) show two representative results o f the simulation using
MATLAB®, pointing out one limitation to achieving high-speed modulation: as the
48
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Phase
fo
180°
fo+fn,
1
tim e
P hase
s h ifte r
t_
s in [ 2 * (£ + /J t]
s in (2 ^ t)
-180°
Sawtooth-phase function
(a)
P hase
kf.+fm
t
T/2
-T/2
tim e
■iiiTii,
P hase
sh ifte r
. • -180°
Step-phase function
(b)
Figure 3.6:
Serrodyne modulation technique (a) a sawtooth-phase function and
(b) a step-phase function.
retrace transient (flyback) time becomes increasingly signficant in the period o f the
sawtooth waveform, sidebands become more prominent.
For example, to build an ultrawideband 500 MHz frequency translation
with the near-ideal results of Figure 3.7(a) would require a 2 ps flyback in the 2 ns
period. One approach to achieve such ultrawideband performance would be, in fact, to
49
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CO
TO,
<D
•o -20
i
i
"O t
(0 6
®
4
CO
2
1
CL
E
0- „
”0
(0
*o -40
<D
_N
20
40
Time (1 = RF period)
75
E
-60
lllh.
,ll
0
2
1
3
Normalized frequency
(a )
CQ
2 ,
0)
TJ
3
"5.
E
co
128828^004846234355311
-o
<
D
N
75
E
fc -60
o
z
1
2
Normalized frequency
(b)
Figure 3.7:
Spectra of serrodyne modulated signals for fo/fn-20 (a) flyback
duration of 0.1% and (b) flyback duration of 1 %.
50
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
use another NLTL to modulate the frequency translator, since the large signal NLTL
output waveform is a sawtooth with a < 2 ps falling edge. Another approach would be
to build a nonlinear control system to achieve minimum transition time during flyback.
Many systems, however, do not require such high frequency translation, though carrier
and spurious sideband suppressions remain important. An alternative to circuit-based
approaches for coherent measurement applications is to allow a longer flyback time
and pause the baseband digitizing circuitry and/or Fast-Fourier Transform (FFT)
calculation, allowing the circuit to fly back while ignoring the resultant spurious
products that are generated (only) during this time. A similar approach demonstrated
later is to use triangle-wave phase modulation and run the FFT forwards during one
cycle and backwards during the second, eliminating the retrace transient entirely.
3.3.2
Analysis of the effect of step-phase serrodyne modulation
The following will detail the Fourier series analysis of serrodyne
frequency translation by means o f the step-phase function [6,7]. From equation (3.5)
we obtain
eou, = £ [cos <f>(t) sin I j t f j + sin <f>(t) cos 2nf0t]
= E [cos <f>(t)sin o)0t + sin <p(t) cos Q)at]
(3.6)
where co0 = 2nf0. For a periodic modulation signal over the interval T and eom = 2rrfm,
the functions sin <f>(t) and cos <f>(t) can be represented by Fourier series
(3.7a)
n« 1
(3.7b)
51
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where
= f £ > * '> *
c° =
f
o -sb )
a" =
(3. 8c)
= ^ j^ s ^ O s in n a ^
c» = | O
4
(3.8a)
0S^ (f)c0S" ^
, = ^ £ '* c o s 0 ( t ) s m n a j d t
T
(3 8 d )
(3.8e)
( 3 .gf)
<p(t) is an odd function and 0 = 2 ;ra tr = T. Therefore,
= C0 = att = dn = 0
Then, the equations (3.7a) and (3.7b) can be written as
sin 0(f) =
s in n e r
(3.9a)
00
cos 0 ( 0 =
X cos ncomt
n*1
2
(3
9b)
Substituting (3.9a) and (3.9b) into (3.6), we then find that
T I [ ( c „ + ^ ) sin (ffl0
/l=l
- 6 Jsin (ffl 0 + n a j f ]
(3.10)
From this equation, it can be seen that the carrier frequency is completely
suppressed. However, there are two sidebands, which have the amplitudes o f
52
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
E(c„+bn)/2 for the upper sidebands at frequency (eoo+notm) and E(c„-b„)/2 for the lower
sidebands at frequency (eOo-neOm). In order to find the amplitude of these sidebands, the
coefficients cn and b„ have to be firstly determined. Assume the phase function is
divided into N steps, which each have magnitudes equal to 2 jdN. If the phase varies
with time between —772 and T/2, a magnitude of the phase function at the /nth step can
be written as
(3.11)
<t>m = ^ -[2 m —(JV + l)]
N
T
N~
T_r
a/-!
(/w -l)—— < t < — m ----2 .
N
N
2 .
and
(3.12)
Inserting (3.11) and (3.12) into (3.8d) and (3.8e), we can obtain
b» = f t
c = —V
(3.13a)
N>2) cos— [2m -(N + l)]cosncojdt
Evaluatingthe integrals inequations (3.13a) and (3.13b), and substituting
into (3 . 1 0 ),the spectral line
(->.13b)
b„ and cn
magnitude of the upper and lowersidebands can be
expressed as
=
£
- ^ ( Cn + K )
= £ ( ~ 1)n 1 V sin— [2 /n(w —1) + l] - s in — [2 / n ( n - l ) - 2 n+ l]
N
2nn 6
Nl
”
E ( - 1)/»+l
2rm
A . 2nm
cos— —cos— (1 - 2 n) L sm —> r(n ~ l)
N
N
Jm «l
sin— - sin —
N
N
(1 - 2 /z)
-A
2 Jtm
z , cos- r r (" - |)
m*I
iy
53
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(3.14a)
" o u tji
r y 1'\n+l N
ir
ir
= ----------- V" sin— [2m(n + 1) - 1]—sin— [2 m(n + l ) - 2 « - l ]
^
N
N
/M*l
E ( - 1)
2 rue
. 2nm ,
cos— - c o s — (1 + 2 /z) > sin
(n + 1)
^
M
N
JV
Jm=l
sin— - s i n —
N
N
(1
(3.14b)
+ 2 /z) V c o s ^ ^ ( /z + l)
S
iv
From a trigonometric series, we can find that
sin - ^
(n ± 1) =
0
(3.15a)
ff»=l
N
t
sm — (n ± l) ,
v2 nm , ^
1
> cos
(n± l) = ----- —-------------^nsl
N
„ . n , ^
2
2 sin — (n± l)
N
(3.15b)
Inserting (3.15a) and (3.15b) into (3.14a) and (3.14b), we obtain
£ ( - l ) n+l ( . K
. Kn ^ ^
----------- sm ----- sm — (1 —2 «)
2nit \
N
N
'o u tjt
sin— (/7 - 1 )
N
2 sin — (/7 - 1)
N
sin— (/7+ 1)
£ ( - i r l f . k .. . ,
. k\
N
— —-— sm — (1 + 2 /7)—sm —
2njt \
N
N j 2sin— (/7 + 1)
outjt
(3.16a)
(3.16b)
n k
Let k be any positive integer from 0 to oo. If (n ± 1)IN * k, we can see that
e±0ut.n= 0. If
(/7
± 1)/N = k and from (3.16a) and (3.16b), there will be an output at a
harmonic of the modulation frequency/* found to be
54
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
+
_
£ ( —l ) w ~*z
“ 2x(kN + \)
2sin— JV
N\
£ ( - 1) kN
2jc{kN—1)
2
(3.17a)
sin — 1 N
(3.17b)
or the normalized spectral output magnitude of the translated RF signal can be
expressed as
I=
1
. 7t
sm—
.
1
N ____ L_
(kN ± l) n_
kN ±1
N
.
(j I g )
These spectral lines appear at output frequencies
f Q+ fm
foul
fo r translation frequency
f Q+ (k N + 1 ) f m
, k =1^2................,oo
fo r upper sidebands
f 0 - (kN -1 ) f m
, k =1,2............. ,oo
fo r lower sidebands
(3-19)
From (3.18) and (3.19), the normalized spectral magnitude o f translated
frequency and spurious sideband levels can be determined at any spectrum number of
harmonic n (the number of modulation frequency increments away from the input
frequency f 0), where n = 1 ± kN. For (n±l)/N=k, the output components appear at the
harmonic o f the modulation frequency/*, as shown in Figure 3.8, when N = 16. Using
&=1, the spurious sideband suppression level is calculated to be -24.6 dBc for a 4-bit
digital frequency translator (N = 16). The spurious sideband suppression level with
respect to the translated frequency as a function of the number o f bits is given in
Figure 3.9. The spurious sideband suppression level will be improved by every additional bit.
55
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6
dB for
0
CD
-10
0
"O
§Q.
-20
E
n
T3
0
-30
N
0
E
-40
-50
-79
-63
-47
-31
-15
0
17
33
49
65
81
Spectrum number (n)
Figure 3.8:
3.4
Spectral response of the serrodyne frequency translator with the 16step (4-bit digital) phase function.
Phase noise and frequency stability
The undesired phase (or frequency) modulation imposed on a carrier
frequency limits the frequency stability o f microwave sources. Phase noise, which is
the fluctuation o f phase in a random fashion, will modify the spectrum at the output of
microwave sources. Today, measuring and specifying phase noise has become
increasingly important as phase noise is often the limiting factor not only in
microwave sources but also in many other RF and microwave systems such as
56
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On
a
*20-
£<>o S10
■®o «£
-
-
60-
100 -
Number of bits
Figure 3.9: Sideband suppression level with respect to translated frequency vs.
the number of bits.
amplifiers, frequency multipliers, and dividers. A frequency translator also has phase
noise associated with it that should be measured. This section describes the concepts
o f phase noise and frequency stability.
3.4.1
What causes phase noise?
Electronic devices such as resistors, capacitors, diodes, and transistors
usually inject noise into the systems. Three main types o f fundamental noise
m echanisms causing phase noise are thermal noise, shot noise, and low frequency ( 1/f)
noise.
57
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Thermal noise, also called Johnson noise, is caused by the random
thermally excited vibration of the charge carriers in conductive and resistive devices.
The available thermal noise power is proportional to the absolute temperature and to
the bandwidth of the system. In equation form this is N, = kT&f, where k is
Boltzmann's constant (lJSOSxlO'^J/K), T is the absolute temperature in Kelvin, and
A/"is the bandwidth in Hz. The spectrum o f thermal noise is independent o f frequency
{i.e. white noise).
The second common noise, shot noise, is caused by the quantum effects
(current fluctuation) of the semiconductor devices. The rms value of the shot noise
current is proportional to the square root o f the noise bandwidth. This means that it is
white noise containing constant noise power per hertz o f bandwidth.
Low frequency (1/f) noise (also known as flicker noise) is associated with
contact and surface irregularities in semiconductors. It appears that 1I f noise is caused
by fluctuations in the conductivity of the medium. At high frequencies, this noise is
not usually significant and can be somewhat reduced by proper processing of
semiconductor surfaces.
These kinds of noises may contribute amplitude and phase noise power
into the frequency translator. However, phase noise is considered to be an important
parameter for frequency stability o f the frequency translator. The thermal and shot
noise in the NLTL and amplifier are expected to generate significant phase noise in the
NLTL frequency translator. In addition, noise in the scanning signal is also anticipated
to generate phase noise around the translated frequency. A measurement of phase
noise from the NLTL frequency translator, therefore, will be presented in the next
chapter.
58
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3.4.2
Quantifying phase noise
Due to the random nature of the instabilities, the phase deviation is
represented by a spectral density distribution. The term spectral density describes the
energy distribution as a continuous function, expressed in units o f energy within a
given bandwidth. A measure of phase instability often used is SJJ), the spectral
density of phase fluctuations on a per-Hertz basis. The voltage fluctuations caused by
phase noise, A(pms, can be expressed as
(3 2 0 )
where K# is a constant, therefore we obtain
B
s' ( / )
I l T
s r_ ( D
(321)
V
where B is a bandwidth, and SvmJJ) is the power spectral density of the voltage
fluctuations.
However, the single sideband phase noise, Mf), is the most commonly
used expression for phase noise. This value relates the energy in a single phase
modulation sideband to the total signal power and can be defined as
A /)
_ Power density (one phase modulation sideband)
/-* •
Carrier power
(j .z z )
£{f) is usually presented logarithmically as a plot o f phase modulation
sidebands in the frequency domain, expressed in dB relative to the carrier per Hertz of
bandwidth (dBc/Hz). £{f) can be derived from S^J) using the phase modulation
technique [53]. This is found to be
59
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A ft
3 .4 3
=
^
S
/ / )
(3.23)
Frequency stability concept
A relatively simple model o f the instantaneous output that was introduced
in the early 1960’s and has found wide acceptance is [54,55]
y (t) = ((Va +£•(/“)) sin[2/z£, +0(t)]
(3.24)
where <p(j) is a random process denoting phase noise, V0 and f 0 are the nominal
amplitude and frequency respectively, and s(t) is the amplitude noise. If it is assumed
that e(t) and rate of change o f Aiffj) is small, the deviation o f frequency from the
nominal frequency can be defined as [53,56]
ATM =
2k
at
(3.25)
Transforming this equation into the frequency domain by the Laplace
transform, we obtain
Af ( f ) =
or
A /l(/)
$K/)
Lk
=
(3.26a)
(3.26b)
A proposed definition for the measure o f frequency stability is the spectral
density, Sj(f), where the spectrum is considered to be one-sided on a per hertz basis
(the spectral density is the Fourier transform o f the autocorrelation function). The
function SJf) has the dimensions of Hz2/Hz. If the spectral density of phase noise in
the system is known, then
S v( f )
4 fL(f)
=
B
60
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(3.27)
To describe the frequency stability o f different carrier frequencies, the
spectral density of fractional frequency fluctuations, Sy(f), is utilized. Sy(f) is also
related to S jf) and Sj(J). If we define the fractional frequency fluctuation y(0 =
where f 0 is a nominal carrier frequency, use o f the same Laplace transform approach
yields
*S) - S - W )
(3-28“>
f 2
or
Therefore,
yL( f ) =
7 7
Jo
WLif)
$ ( / ) = ^ W rm sif) _ f__g ^
y
fo
B
fo
(3.28b)
(3.29)
It is apparent that the spectral density of fractional frequency fluctuations
is equal to the spectral density of frequency fluctuations divided by f 02 and has unit of
Hz'1. In practice, only the phase noise spectral response can be accurately measured to
determine the frequency stability using various techniques such as double-balanced
mixing, phase-detection, autocorrelation, and phase-locked loop methods [57,58]. A
commercial phase noise instrument usually characterizes the phase noise as the ratio of
the measured power in one noise sideband component, on a per hertz of bandwidth
spectral density basis, to the carrier signal power (dimensions o f dBc/Hz). This phase
noise spectral response from measurement, however, will indicate the frequency
stability.
61
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Chapter 4
FREQUENCY TRANSLATOR IMPLEMENTATION
AND EXPERIMENTS
This chapter explains how to implement the frequency translator with the
scale model NLTL. The system is automatically controlled and processed by using a
microcomputer with LabVIEW® software. A key part of this system is the design o f
the hardware and software o f the amplitude and phase compensation circuits. All tests
and measurements have been done by employing a high-speed digitizing oscilloscope,
a network analyzer, and a spectrum analyzer with phase noise measurement utility.
4.1
Controlling and processing for measurement
A microcomputer with a DAQ card (data acquisition board), GPEB
interface (general purpose interface bus) and LabVIEW program has been used to
control the scanning signals and instruments, and to process the data. The DAQ board
(PCI-1200 from National Instruments) has been employed to control the NLTL and a
variable attenuator or a variable gain amplifier, and to process the output data from the
heterodyning system. The important specifications of the DAQ card for this work are
shown in Table 4.1.
The differential inputs (± 5 V) have been chosen to reduce noise because
the common-mode noise picked up by the leads is canceled out. This card uses a
multiplexing technique for measuring the input signals, therefore the sampling rate for
each individual channel will be limited to 12.5 kS/s. To properly digitize the signals
62
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Table 4.1
Some important specifications o f PCI-1200 [59].
Parameter
Analog input
Analog output
Configuration
single-ended,
4 differential channels
100 kS/s
1 to 1 0 0
0-10 V, ± 5 V
60 ps full-scale (typical) at
2 channels
1 2 bits
0-10 V , ± 5 V
5 ps full-scale
Channel input
8
Sampling rate
Gains
Range
Setting time
Channel output
Resolution
Range
Setting time
100
gain
for analysis, the maximum input frequency must be less than 6.25 kHz (from the
Nyquist
sampling theorem). The precision o f the measured signal (the smallest
detectable change in voltage) is calculated from the range, resolution, and gain o f the
DAQ board. This change in voltage represents 1 LSB of the digital value, and it is
often called the code width. The ideal code width is found by dividing the voltage
range by the gain times two raised to the order o f bits in the resolution. A gain o f 100
has been selected in this work, so the code width can be determined to be 24.4 pV,
which means the theoretical resolution of one input bit in the digitized value is
24.4 pV.
Both output channels were used in the unipolar mode to apply the control
signals for the NLTL and the attenuator/amplifier. The resolution of the output voltage
can be determined to be 10/ 2 12 = 2.44 mV. The setting time o f 5 ps (full-scale) affects
the rise and flyback times of the NLTL scanning signal, limiting the amount of
suppression o f the undesired sideband levels on the RF output.
63
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A GPIB interface (NI-488.2M from National Instruments) [60], with the
LabVIEW program has been installed into the microcomputer to control and obtain
data from the instruments. All o f the instruments in the experiment including a
microwave synthesizer, a high-speed oscilloscope, and a spectrum analyzer have been
connected in parallel to the GPIB bus, but only one can be actively controlled at a
time.
LabVIEW is a program development application
from National
Instruments [61], much like other commercial program development systems.
However, LabVIEW uses terminology, icons, and ideas familiar to scientists and
engineers and relies on graphic symbols (graphic programming language, G) rather
than the textual language found in other programs. LabVIEW has extensive libraries o f
functions and subroutines for most programming tasks, designed specifically for
instrument control such as for DAQ, GPIB, serial instruments, data analysis, data
presentation, and data storage. LabVIEW programs are called virtual instruments (Vis)
because their appearance and operation are meant to imitate front panel of actual
instruments. It is easy to write and debug the LabVIEW programs because it includes
conventional program debugging tools, including breakpoint, single-step debugging,
and program execution animation (to see data flow).
LabVIEW programs contain an interactive user interface (called the front
panel) and a block diagram. The front panel can contain knobs, push buttons, graphs,
and other controls and indicators. Data can be input using the keyboard and mouse,
and the results viewed on the computer screen. The structure o f the LabVIEW program
is created in a block diagram, containing the sequence of subroutines (graphical source
codes) which makes up the program. LabVIEW programs use a hierarchical and
64
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modular structure, therefore can be used as top-level programs, or as subprograms
within another programs or subprograms. An example picture o f the front panel and
the block diagram are shown in Figure 4.9.
4.2
Simple heterodyne experiments
The
microwave
heterodyne
technique
is
commonly
used
in
communication systems and instrumentation. This technique utilizes a mixer to
convert (heterodyne) an original frequency (RF) and a frequency from local oscillator
(LO) to new shifted frequencies. The output frequencies from the mixer are the sum
of RF and LO (upconverter) and the difference (downconverter), and the desired
frequency could be recovered by filtering. Mixing is achieved by applying the RF
signal and the LO signal to a nonlinear microwave device such as a diode. Usually, the
level of the LO signal must be higher than that of the RF signal to pump the mixing
device into a nonlinear region.
The block diagram for the experiment setup is shown in Figure 1.2(b).
Both a mechanical rotary phase shifter and a new distributed phase shifter using the
scale model NLTL have been employed to perform a frequency translation in the
experiments.
4.2.1
Measurement o f mechanical frequency translator
Figure 4.1 shows a block diagram o f a heterodyne experiment using rotary
phase shifter (HP J885A) controlled by a stepper motor as a frequency translator. The
signal from a microwave source (HP 83620A) at
8
GHz is separated into two signals
by using an Anaren 40267 splitter. One of the split signals is a LO and another is
translated into a new RF frequency by the rotary phase shifter. After downconverting
65
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Motor
Splitter
Microwave
source
.1
1
Mixer
shifter
= o
Microcomputer
Oscilloscope/
Spectrum --------------------► controlling and
processing
analyzer
Figure 4.1:
Block diagram of a heterodyne experiment using rotary phase
shifter.
using a mixer (DMI-18AN65 from RGH), the output signal (IF) is then measured by
an oscilloscope (HP 54750A) and a spectrum analyzer (SR 780).
A microcomputer with LabVIEW has been used to control the stepper
motor (Model 5000) from Technology 80, Inc., and receive the output signals from an
oscilloscope and a spectrum analyzer through the GPIB. The shifted frequency from
the original carrier depends upon the speed of stepper motor. Figure 4.2 (a) and (b)
show a waveform and the spectrum of the IF signal after downconverting. It is
apparent that this signal is a sinusoidal waveform with high sideband suppression
(> 52 dBc). This sideband suppression level is comparable to the value obtained from
a heterodyne system using two phase-locked microwave synthesized sources.
66
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100
u_
—
-
100 -
-
200 -
-300 0
50
100
150
200
250
300
time (ms)
(a)
aim
100 Hz
Fundamental
.Second harmonic
SOrs
(b)
Figure 43:
IF output (a) waveform from the oscilloscope HP 54750A and (b)
spectrum from the spectrum analyzer SR 780 (>52 dBc sideband
suppression obtained).
67
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However, only a maximum o f 7 Hz IF output can be obtained from the
frequency translating system utilizing a rotary phase shifter as a phase scanner due to
low mechanical speed. Furthermore, sub-harmonics appeared in the spectrum by the
effect o f having two cycles o f phase change in one completed turn of rotation (see
equations (3-3)). The limitations o f low frequency shift, short lifetime (mechanical
wear), bulk and high expense are also the drawbacks of this frequency translator,
hence it has never been realized for any modem application.
4.2.2
Measurement of distributed frequency translator without compensation
The use of a NLTL as a phase scanner to realize a frequency translator has
been described earlier. A simple coherent measurement, as shown in Figure 4.3, has
been performed at several RF and modulation frequencies by using a system with a
continuous sawtooth scanning frequency f m o f 500 Hz from a function generator (HP
33120A). The voltage level o f the sawtooth scanning signal is determined from Figure
2.9 for 1 GHz RF so that the total delay is equal to one period o f the RF frequency
(1 ns in this case). Although the circuit works as anticipated when modulated at f m
through
2
n radians at the fundam ental microwave frequency fo, distortion in the output
waveforms (also at the RF frequencies o f 2 and 3 GHz), as well as the retrace (flyback)
transient are apparent on the oscilloscope traces. The distortion is caused by nonideal
NLTL characteristics of phase nonlinearity and amplitude variation.
The phase and amplitude characteristics of the scale model NLTL have
been carefully studied. The measurement o f amplitude and phase variations as bias
voltage is adjusted was performed using a heterodyne technique with two phase-locked
microwave synthesized sources, as given in Figure 4.4. One o f downconverted signals
was used as a reference and another was used to measure the characteristics o f the
68
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Splitter
Microwave
source
Mixer
Sawtooth
scanning
signal
Trigger
i
to
CM
r
/ \
1
1
✓
i
\
/
J
1 GHz RF
Figure 4.3:
A
>
E
£
8
1
■
\
o
CO
\jl
/
2 GHz RF
'\j
3 GHz RF
Block diagram o f a simple NLTL heterodyne experiment at three
different RF frequencies.
NLTL. These signals were fed into the inputs of the DAQ for processing with
LabVIEW, while the microwave sources were controlled through the GPIB. The
results from the measurement o f amplitude and phase variations over the operating
frequency range o f 0.5 to 3 GHz vs. the NLTL scanning voltage from 0 to 10 V are
plotted in Figure 4.5 (a) and (b).
It can be seen that the variations of the delay (or phase) are nonlinear
with bias voltage but almost linear with frequency. These variations are caused by the
capacitance-voltage nonlinearity of varactor diodes, a characteristic that could be
modified, but probably not eliminated, in the fabrication processes by compensating
the doping profiles o f the diodes. The variations o f output amplitude at various
69
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frequencies and bias voltages are due to the inherent voltage-dependent impedance
mismatch between the scale model NLTL and the source and load. Compensating
these amplitude variations using varying doping profiles would be very difficult, and
would preclude using the substrate for other purposes, such as integrated amplifiers
with active devices. However, external amplitude compensation circuits can be
designed to correct for these variations with similar results and much fewer
difficulties. This is the route chosen to take for this work.
Using the measured phase and amplitude data, a look-up table was created
to generate waveforms to drive the NLTL phase scanner and the variable
attenuator/amplifier. This will compensate the nonlinearlity of the delay and amplitude
variation. A compensation circuit, however, must be carefully designed and built. A
12-bit digital-to-analog converter (DAC) from DAQ has been utilized to output the
waveform to drive the circuit In order to keep output amplitude constant either a
variable attenuator or a gain-controlled amplifier can be employed.
Splitter
Microwave
source
Phase-lock
NLTL
Mixer
Microwave
source
Reference
Mixer
Microcomputer
controlling and
processing
Splitter
Figure 4.4: Block diagram of amplitude and phase variation measurement.
70
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® 0.4
<*
10
^
(a)
at
O
o
<D
J3
E
3
Z
(b)
Figure 4.5:
Measurement of the NLTL characteristics (a) amplitude and (b)
phase variations.
71
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43
Implementation of compensation circuits: a variable attenuator and a gain
controlled amplifier
Voltage controlled variable attenuators have been widely used for
automatic gain control and switch circuits. Both PIN diodes and GaAs FET devices are
often employed for design of variable attenuators. However, GaAs FETs are
compatible with GaAs monolithic circuits and provide higher frequency performance.
The GaAs MMIC FET variable attenuator (AF002N2-32) from Alpha Industries Inc..
therefore, has been chosen for designing a variable attenuator in this work. The data
sheet for this device is included in Appendix A. The basic operation of GaAs FET
attenuator is very simple because its structure consists of only one FET operating in
passive mode. The RF input and output are connected to drain and source of the FET,
and the channel resistance will be controlled by the gate voltage. There is a nonlinear
relationship between the control voltage and channel resistance. There have also been
complicated circuits reported which use GaAs FETs to increase attenuation and
bandwidth [62].
A two-stage variable attenuator has been designed on a microwave
substrate (GML 1000) with sr = 3.05 and 30 mil thickness (d) from GIL (see
specifications in Table 4.2). 50-ohm microstip lines have been used for input and
output RF lines in each stage o f the attenuator. For a given characteristic impedance
Table 4.2
Specifications of microwave substrates.
Substrate
GML 1000
RT/Duroid 6010.5
Frequency
(GHz)
2.5
10.0
10.0
Dielectric constant
Sr
3.05±0.05
3.05±0.05
10.5±0.25
Dissipation factor
tan S
0.003
0.004
0.0028
72
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(Z0), the width of microstrip (W) can be approximated by the following equations [63]:
8eA
W_
d
fo r W /d < 2
el A - 2
2
5 - l - l n ( 2 5 - l )+ % -![-\ In (5 -l) + 0.39~ —
2 s.
where
J
-
Z 0
lS r + l
60 V 2
t
Sr
\
Sr +l
0.23 +
fo r W !d> 2
0.11
'r
(4.1a)
(4.1b)
J
(4.1c)
B =
The width of microstrip is then calculated to be 73.3 mil for Zq=50Q using
this substrate. The variable attenuator has been constructed on microwave substrate
using attenuator chips, coupling capacitors, SMA connectors at input and output ports,
and a BNC connector for the control signal, as shown in Figure 4.6 (see schematic of
the circuit in Appendix A).
Using a variable attenuator causes a reduction of the RF power, therefore a
variable gain amplifier has also been studied for a second generation system. This
amplifier will allow the NLTL frequency translator to have constant high power output
at all frequencies.
GaAs FETs are now widely used as standard devices for designing
amplifiers, especially in micro-millimeter wave ranges. Compared to bipolar junction
transistors, GaAs FETs have simpler structure, smaller size, and higher operating
frequency and temperature, however, bipolar transistors offer higher gain and they are
inexpensive and durable. A GaAs FET with a dual-gate structure is very attractive as a
gain controlled amplifier with low noise characteristic and low power dissipation [64].
73
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 4.6: Variable attenuation circuit on microwave substrate.
The gain of a dual-gate GaAs FET can easily be controlled by varying the second gate
bias voltage. Using a commercial dual-gate FET, an ultra-wideband (0.1-17 GHz) flatgain amplifier with 15-dB gain-controlled range has been reported [65], A very lownoise and wide gain control range (—50 dB) amplifier (MMIC) has also been obtained
by means of a silicon bipolar transistor with the operating frequency up to 6 GHz [66].
This work needs a variable gain amplifier to maintain the constant
amplitude at the output of the NLTL over the frequency range of I to 3 GHz, therefore
the silicon bipolar MMIC variable gain amplifier (IVA-14208) from HP has been
selected. This device has particular advantages such as wide gain control range (34
dB), fast gain response (<10 ns), large bandwidth (~ 3 GHz), and extremely low cost.
The detailed specifications o f this device can be seen in Appendix B. In order to
design the amplifier circuit, the Rt/Duroid 6010.5 substrate with sr = 10.5 and 25 mil
thickness from Rogers Corporation (see specifications in Table 4.2) has been chosen
74
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because the 50-ohm microstrip line width will be compatible to the device contact
spacing, which is very small (~50 mil). This substrate also has an advantage o f having
lower losses than the GML 1000 substrate, but it is more expensive. The width of a
50-ohm microstrip line has been calculated to be 21.7 mil by using equations (4.1).
Implementation of the device has been done with microstrip lines on the microwave
substrate. Coupling capacitors were installed to block DC bias and bypass capacitors
were required on the gain control pin. SMA connectors were used for the input and
output RF signals and a BNC for the gain control voltage. Figure 4.7 shows a
photograph o f the variable gain amplifier circuit and the schematic can be found in
Appendix B.
Gain-control
voltage
Output
Figure 4.7:
Variable gain amplifier on microwave substrate.
75
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4.4
4.4.1
Experimental results after compensation
Measurement o f distributed frequency translator with sawtooth
modulation
Either a variable attenuator or a variable gain amplifier can be
implemented after the NLTL in order to compensate the output amplitude, as shown in
Figure 4.8. A microcomputer with a DAQ and LabVIEW provides the scanning signal
and the attenuator or gain control voltage to the NLTL and variable attenuator or
amplifier simultaneously. The front panel and the block diagram o f the LabVIEW
program are shown in Figure 4.9 (a) and (b). Even though a 12-bit DAC has been
utilized, only 360 phase steps (1° step-phase resolution) have been implemented in the
distributed frequency translator. With this step-phase resolution, the downconverted
output frequency o f 35 Hz EF is obtained. The limitation of step-phase resolution is
caused by the data speed of the DAQ, however, higher resolution (phase steps) could
be chosen, but a lower IF output frequency would have to be used.
The downconverted output signal (35 Hz IF) from the measurement at 1
GHz RF after compensations is clearly sinusoidal, but exhibits a flyback transient
(Figure 4.10). The sideband suppression level of > 45 dBc was measured from the
spectrum analyzer (SR 780), as illustrated in Figure 4.11. This confirms that the
resultant output is a sinusoidal waveform. The similar results for other RF frequencies
(2 and 3 GHz) have also been obtained from the measurement.
To measure how nonsinusoidal the output is, a microwave spectrum
analyzer (HP 8565E) has been utilized to determine the original carrier and sideband
levels directly from the output o f variable gain amplifier. Figure 4.12 shows the result
from measurement in which > 45 dBc carrier suppression and > 50 dB spurious
sideband suppression have been obtained when driven at 0 dBm. The spurious
76
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
sideband suppression level from the measurement is comparable to the 51.2 dB
calculated from (3.18), where k= 1 and N = 360.
The stability of the distributed frequency translator has been investigated
by measuring the phase noise characteristic directly from the output of the variable
gain amplifier using the spectrum analyzer (HP 8565E) with a phase noise
measurement utilities. The resultant phase noise at 1 GHz RF when driven with a stepphase function at a scanning frequency of 35 Hz is given in Figure 4.13, as is the phase
noise measured directly from the microwave synthesized source (HP 83620A). The
phase noise measurement at other frequencies (2 and 3 GHz) has also performed, but
the results do not vary significantly over RF. It is obvious that the additional phase
noise caused by the frequency translator is comparatively low which means that the
system has high frequency stability.
4.4.2
Measurement of distributed frequency translator with triangle-wave
modulation
To improve the output, a triangle-wave scanning signal has been used
instead of the sawtooth scanning signal. By using the triangle-wave scanning signal,
the spikes at the flyback times could be eliminated. However, a post signal processing
is required to reverse the second period of IF signal (in time domain). The resultant
output and the scanning signals are depicted in Figure 4.14. Obviously, the output is
sinusoidal with no spikes, but appearance of strong sub-harmonics was found in the
spectrum. This was due to using two cycles o f the waveform with imperfect matching
o f the waveforms.
77
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
fo
Splitter
Microwave
so u rce
Scanning
signal
NLTL
[>
L
r
fo
Control
Variabl eattn .
or am|ilifier
voltage
fn
Mixer
fo
fm
Spectrum
analyzer
fm
Microcomputer
controlling and
processing
O scilloscope
GPIB
Figure 4.8:
Measurement of the distributed frequency translator including
compensation circuits by using the heterodyne technique.
78
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
mtnooo«iii<Mtaci
awrtfc-^
(b)
Figure 4.9:
A LabVIEW program for controlling and processing (a) a front
panel and (b) a block diagram.
79
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5
©
CO
(D
©
© 2
JS
.q
(a)
^
<D
7.20
a>
S
o
7.15
o 7.10
oo 7.05
co
CD
7.00
(b)
25
20
E
15
15
10
c
gj
(O
i""
£ .10
lO n s/d iv
5
0
-5
-10
-30
-20
-10
0
10
20
(C)
30
time (ms)
Figure 4.10: Measurement a t /fl = l GHz and f m = 35 Hz using sawtooth scanning
signals (a) NLTL scanning signal (b) gain control signal and (c)
output waveform after mixer.
80
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Ai>e
-117.0*6
200 Hz
dBVpk
-15
dBVpk
SRS
Fundamental
Second harmonic
■' '■p'Pbvyer lirfe"
^ (6 0 H z o ffe e t)
-165 _______ .
:
100 Hz
dBVpk 0 Hz
FFTchi Log Mag BMH
200 Hz
Figure 4.11: Spectrum of downconverted signals at 35 Hz IF showing
fundamental and harmonic levels (>45 dBc suppression). Using a
step-phase function with amplitude and phase compensations
(scanning frequency f m- 35 Hz).
81
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0
Relative amplitude (dB)
-20
Translated f
35 Hz offset
T r a n s la te d fr e q u e n c y
1 .0 0 0 0 0 0 0 3 5 G H z '
2 _ Original carrier
§
1 GHz
1
-4 0
Power line
/ 60 Hz
id
Frequency (50 Hz/div)
-6 0
F irst s p u rio u s s id e b a n d
-8 0
-100
Frequency (20 kHz/div)
Figure 4.12: Spectrum of signals at 1 GHz RF including original carrier,
translated frequency, and spurious sideband levels. Using a stepphase function with amplitude and phase compensations (scanning
frequency f m= 35 Hz).
82
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-6 0
Phase noise (dBc/Hz)
-70
-80
-90
-100
-110
-120
-130
NLTL frequency translator
HP 8 3 620A
100
10k
100k
1M
Offset frequency (Hz)
Figure 4.13: Phase noise measurement of the translated signal at 1 GHz RF
compared to microwave synthesized source (HP83620A). The
difference is the additive phase noise created by the distributed
frequency translator.
83
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(a)
> 7 .2 0
<
D
0)_
jg 7.15
•k 7.10
o 7.05
qi 7.00
(b)
5) -5
-10
” -15
£
-20
(c)
o» -5
to
it
._
-10
“ -15
-20
(d)
10
20
30
40
50
60
time (ms)
Figure 4.14: Measurement at f 0 = 1 GHz and f m = 35 Hz using triangle-wave
scanning signals (a) scanning signal for phase compensation (b)
gain-control voltage for amplitude compensation (c) output voltage
after mixer and amplifier and (d) output voltage after processing.
84
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Chapter 5
MICROWAVE REFLECTOMETER
The most fundamental concepts of high-frequency transmission lines and
devices involve incident, reflected and transmitted waves. Often it is very important
that these waves be measured to ensure efficient transfer o f RF energy. A network
analyzer (scalar or vector system) is usually used to measure these waves in terms of
scattering parameters (S-parameters).
Key components o f a network analyzer are
reflectometers, used for measuring a reflected wave or reflection coefficient of
devices. This chapter explains the basic concepts of a reflectometer and a network
analyzer, then a new reflectometer is proposed using the distributed frequency
translator, allowing the use o f the heterodyne technique to measure both the amplitude
and phase of the reflection coefficient. The proposed reflectometer system provides
high accuracy, high stability, easy system realization, and potential for low cost. This
technique can also be readily extended to a network analyzer.
5.1
5.1.1
Reflectometer and network analyzer background
Reflectometer basics
Reflectometers form the core of microwave network analyzers, and are
typically based on power sensing (using diodes or bolometers) or coherent sampling
front ends. A basic block diagram o f a conventional reflectometer primarily consisting
of a microwave source, a dual directional coupler and detectors is shown in Figure 5.1.
85
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Calculation
and display
Det
DeL
reflected
Microwave
source
DUT
incident
Dual directional
coupler
Figure 5.1:
Block diagram of a conventional reflectometer.
A dual-directional coupler is a four-port device that enables the incident
wave and reflected wave to be measured separately. The phasor ratio o f
(reflected
wave) and 6./ (incident wave) sampled by the dual-directional coupler is the voltage
reflection coefficient o f the DUT. In practice, this ratio is only approximately realized
because o f imperfections in the dual-directional coupler and other factors. However, a
dual-directional coupler having very high directivity and low VSWR is now
commercially available over a broad frequency range, allowing the reflection
coefficient to be measured accurately. Nevertheless, this method is still not suitable for
measurement o f very small reflection coefficients. Several techniques have been
86
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proposed to measure these smaller reflections [67-69]. Using standard loads to
calibrate a conventional reflectometer has been proposed by Hollway and Somlo [70].
This technique contains no critical components and requires no tuning adjustments,
and therefore it is very simple, accurate, and useful for automatic operations. However,
the phase angle of the reflection coefficient cannot be measured using this technique
because the detectors yield just the amplitude or power response o f the microwave
signals.
5.1.2
Six-port reflectometer
In order to obtain the amplitude and phase o f the reflection coefficient,
additional couplers or hybrids and detectors can be added. This measurement scheme
was introduced by Cohn and Weinhouse [71], followed by Hoer [72], then developed
into a six-port reflectometer (requiring four detectors) by Engen [73,74]. Figure 5.2
shows a schematic of a six-port reflectometer consisting of a six-port junction with a
microwave source, a DUT and four power detectors attached to each port. The main
task of this reflectometer is to determine an unknown complex reflection coefficient
based on knowledge of the scalar values o f the power from four detectors. Weidman
[75] implemented a six-port junction using six waveguide directional couplers to
measure a complex reflection coefficient in a WR-15 waveguide for the frequency
range from 55 to 65 GHz. The calibration procedure for this reflectometer was done by
means of five sliding short positions, three sliding load positions, and one reflection
coefficient standard. In another work [76], three waveguide quadrature hybrids and
one 180° hybrid have been utilized to implement the six-port. A microstip six-port
reflectometer was investigated by Collier and El-Deeb [77-78] for the first time.
87
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By employing a six-port reflectometer, the reflection coefficient can be
calculated accurately, but this method has disadvantages due to its complex structure
and the lack o f a well-developed calibration technique. Recently, several authors [7982] have developed techniques to calibrate the six-port reflectometer and ended up
with a minimum o f four standards (for instance, matched load, open, short, and offset
short) needed. Their calibration methods involved the solution o f twelve nonlinear
equations for eleven system unknowns. Because of mathematical difficulties, some
researchers have opted to simplify the analysis by imposing various constraints on the
design of their reflectometers.
Cullen and Belfort [83] proposed a reflectometer operating in millimeterwave range, employing a seven-port junction (requiring five detectors). Even though
their reflectometer structure is more complicated, it provides an easier calibration.
Det 1
Det 2
ii
Microwave
source
Six-port
junction
Det 3
Figure 5.2:
DUT
Det4
Six-port reflectometer.
88
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5.13
Network analyzer
A linear two-port network can be characterized by a matrix of four
complex quantities, called scattering parameters, which are functions of frequency
and describe the relationship between forward and reverse waves at the ports of the
device. A vector network analyzer (VNA) is an instrument that measures the scattering
parameters o f a two-port network at selected frequencies. A simpler kind of network
analyzer is a scalar network analyzer, which can measure only network parameter
magnitudes. An automatic VNA with error calibration working in a multi-octave
bandwidth o f 0.1 to 12.4 GHz was first developed by Hackbom [84] from Hewlett
Packard in 1960s. This VNA system used two conventional reflectometers, and diode
detection technique. In the present, a new detection scheme, known as a tuned
receiver, has been developed and installed in many modem commercial VNAs.
Figure 5.3 gives a schematic o f a tuned receiver VNA consisting of two
modules [85, 86]. In the first module, known as a test set, the signal from microwave
synthesizer is delivered to the DUT at the measurement frequency. Directional
couplers sample the incoming signal a/ as well as reflected 6/ and transmitted b?
signals from the test port. Then reflection (bj/ai) and transmission (b ja i) coefficients
can be calculated. The other two parameters are obtained by repeating the
measurement in the reverse direction. These parameters usually are determined by
measuring the sample signals at a low frequency after down conversion using a front
end. To down convert all microwave signals to the same IF, a local oscillator and a
harmonic generator are used to generate a signal at a tunable frequency f a. A harmonic
generator produces a comb of harmonics o f the local oscillator signal, thenj/0 is picked
so that IF = fmeas ± nfia, where fm-as is the measurement frequency and n is the harmonic
number. The IF can be fixed (i.e. 20 MHz) by using phase-locking technique.
89
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Nevertheless, the phase-Iock algorithms for locking to the various comb teeth are
complex and time consuming. The IF signals are bandpass filtered to improve
sensitivity and dynamic range. The magnitude and phase information from the IF
signals can be extracted by using an analog-to-digital converter (ADC) and digital
signal processing (DSP).
A network analyzer incorporating two six-port reflectometers has been
developed [87-90], however, the dynamic range of this system is limited due to the
very low signal levels in each detector. Meanwhile, heterodyne reflectometers as
employed in modem commercial network analyzers use sampling front ends, which
improve upon the dynamic range limitations o f the six-port approaches. These could
be further improved, however, by use of mixers in the front end, but the expense of an
additional microwave source is prohibitive. Homodyne network analyzers [91-96],
while not commercially available, bear the strongest similarity to the architecture
proposed here in that they usually employ a variable-phase and reference arm derived
from a single source, and they use balanced mixers as detectors. Their dynamic range
is limited, however, by DC detection.
5.2
5.2.1
Heterodyne reflectometer using distributed frequency translator
Implementation o f heterodyne reflectometer
This dissertation proposes a new reflectometer by using the NLTL
heterodyne technique to measure both amplitude and phase of the reflection
coefficients providing an extremely low cost system and easy system realization. This
technique can be readily extended to a two- or more-port vector network analyzer.
Figure 5.4 depicts a block diagram of this measurement scheme. The signal from the
90
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Reference
-► <3,
Reflected
Transmitted
Port 1
+ b,
-► b-,
Port 2
£
Forward
Directional
coupler
Directional
coupler
Backward
Test set
20 MHz IF
Harmonic
generator
Frequency "comb
Tuning
Front end
Figure 5 J :
Schematic of a modern VNA consisting o f test set and front end
modules.
91
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microwave source is split into the NLTL input and mixer LOs. The microcomputercontrolled NLTL serrodyne phase modulation and variable-gain amplifier result in a
frequency translation. A dual-directional coupler (HP 1I692D) has been used to
couple the incoming signal from the frequency translator and the reflected signal from
a DUT. These signals are fed into mixers (RF), which results in downconvertion to
35 Hz IF. The spectrum o f the IF signals (20 periods) are taken by FFT using a
LabVIEW program on the microcomputer, from which the amplitude and phase of the
incident (channel 1) and reflected (channel 2) waves are obtained. The calculation of
complex reflection coefficient is then performed by the microcomputer. The schematic
o f the microcomputer controlling and processing is clearly shown in Figure 5.5. The
NLTL scanning signal and gain-control voltage are obtained from a look-up table and
then output through 12-bit DACs at the same time as the signal data from the mixers
(IF) are received. The microwave source is also controlled by a LabVIEW program
through the GPIB to sweep the frequency from 1 to 3 GHz with 0.2 GHz incremental
step.
5.2.2
S-parameters
As we know, the voltages, currents, and impedances cannot be measured
in a direct manner at microwave frequencies. The quantities that are directly
measurable are reflection coefficient or standing wave ratio, transmission coefficient,
and power. The measurement o f power is required only if the absolute value of the
electromagnetic field in the device needs to be known. The transmission coefficient
through a circuit and the reflection coefficient from a port or junction are the relative
measurement o f amplitudes and phases of the transmitted wave and the reflected wave
respectively as compared with the incident wave. In other words, the directly
92
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Mixer
Splitter f 0
Splitter
Reflected wave
Mixer
Incident wave
Microwave
source
ii
NLTL
Control
Figure 5.4:
AMP
Microcomputer
controlling and Scanning
processing Gain control
DUT
Dual directional
coupler (20 dB)
Block diagram of a heterodyne reflectometer using the distributed
frequency translator.
93
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Microcomputer with LABVIEW
DAQ
Input
channel 1
(incident)
FFT
Ch.1
Channel
splitter
Input
channel 2
(reflected)
FFT
Ctl.2
Output
channel 1
(NLTL)
Calculation
Digital
control
Output
channel 2
(amplifier)
to control
microwavef
synthesizer'
Figure 5.5:
logic
controlling
and display
GPIB
Schematic of the microcomputer controlling and processing.
94
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
measurable quantities are the amplitudes and phase angles o f the wave reflected, or
scattered, from a junction relative to the incident wave amplitudes and phase angles.
For many microwave devices, the scattered wave amplitudes are linearly related to the
incident wave amplitudes. This linear relationship can be described by scattering
parameters.
Consider the Af-port network o f Figure 5.6. If a wave with an associated
voltage ai is incident at port 1, it will result a reflected wave b\ = 5 //a/, where S u is
the reflection coefficient o f port 1. The incident wave may also be transmitted, or
scattered, out o f the other ports. The transmitted waves will have amplitudes
proportional to at/ which can be expressed as b„ = S„jaj, n = 2, 3 ,... ,N , where S„i is a
transmission coefficient to port n from port 1. In general, waves will be incident at all
ports so the scattered waves from each port will be produced. By superposition
1
1
principle, these scattered waves can be written in a matrix form as
b2
P
n
=
.
■^tl
^12
$2i
$22
’IN
a.
(5.1a)
S Nl
S N2
•— $NN_
[6] = [S][b]
or
(5.1b)
where [S] is called the scattering matrix.
5.2.3
Signal flow graph theory
A signal flow graph is a graphical representation o f the relationships
between a set of independent input variables that are linearly related to a set of
dependent output variables. A signal flow graph has been widely applied to solve
95
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Figure 5.6:
N-port network illustrating scattered waves.
linear systems in many application areas. Hunton [97] has applied signal flow graphs
to the scattering matrix to solve microwave transmission line problems. His signal
flow graphs have been improved, making clearer, simpler, and easier to use by Kuhn
[98]. The use o f signal flow graphs for the solution of microwave transmission line
problems is easily shown by considering the scattering matrix method o f writing the
network equations. For a two-port network in Figure 5.7 (a) with wave at entering port
1
and wave c*2 entering port 2 , the scattered waves at port1and 2 represented by bt and
62
respectively are given by the following equations:
b{ = S u a t + S l2a 2
b2 = 5*21^1 ^”*^2 2 ^ 2
96
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(5*2)
A signal flow graph representation o f equation (5.2) is shown in Figure 5.7
(b). On this graph, each port has two nodes, a„ and b„, where node a„ represents the
wave incident to the device at port n and node b„ represents the wave leaving the
device at port n. A direct branch running from each a node to each b node has a
certain scattering coefficient associated with it. This coefficient shows how an
incoming wave gets transformed into an outgoing wave at a node b. The value at node
b is a superposition of the individual waves arriving from each of the a nodes. Because
the value of the wave at node b relies on superposition, only linear systems can be
analyzed. Consider the graph in Figure 5.7 (b) and equation (5.2), it is can be seen that
S n = bi/ai is the reflection coefficient looking into port
transmission coefficient from port
load (a2 = 0 ). Similarly, S22 =
1
6 2 /^ 2
1,
and S 21 = b ja i is the
to port 2 , when port 2 is terminated by a matched
and S12 -
6 7 /0 2
can also be found, when port 1 is
terminated by a matched load (0 / = 0 ).
A signal flow graph will be more complicated when a device has a larger
number of ports such as a dual-directional coupler which has four ports. In practice, a
number of devices will often be cascaded, raising the complexity of the signal flow
graph, therefore reducing a signal flow graph to a simpler form is necessarily required.
An iterative method to simplify a signal flow graph is based on the following four
rules [98]:
RULE I: Two branches, whose com m on node has only one incoming and one
outgoing branch (branches in series), may be combined to form a single
branch whose coefficient is the product of the coefficients of the original
branches. Thus the common node is eliminated.
RULE II: Two branches pointing from a common node to another common node
(branches in parallel) may be combined into a single branch whose
coefficient is the sum o f the coefficients of the original branches.
97
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b,
a,
b,
(a)
(b)
Figure 5.7:
Two-port network (a) block diagram showing incoming and
outgoing waves and (b) signal flow graph.
RULE III: When node n possesses a self loop (a branch which begins and ends at n)
of coefficient Sm the self loop may be eliminated by dividing the
coefficient of every other branch entering node n by 1-5OT.
RULE IV: A node may be duplicated, i.e., split into two nodes which may be
subsequently treated as two separate nodes, so long as the resulting signal
flow graph contains, once and only once, each combination of separate
(not a branch which forms a self loop) input and output branches which
connected to the original node. Any self loop attached to the original node
must also be attached to each of nodes resulting from duplication.
Figure 5.8 depicts all signal flow graph rules in detail. These rules will be
employed to simplify the signal flow graph of reflectometer system in the next section.
The final solutions solved from the signal flow graph will be used for calibrating the
reflectometer system to eliminate some of the measurement errors.
98
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p,
s l>
9------- ►
p2
s"
• -------•
Pj
=
p,
•
S 3 I ~ S 2 I S 32
►
P 3
•
(d)
Figure 5.8:
Signal flow graph rules (a) Rule I, (b) Rule II, (c) Rule III, and (d)
Rule IV.
99
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5.2.4
Calibration
There are mainly two basic sources o f measurement error: systematic and
random. Systematic errors are due to imperfections in the reflectometer system (i.e.
signal leakage and crosstalk), therefore they are time invariant and predictable. These
errors may be characterized during the calibration process and mathematically
removed during measurements. Random errors uncorrelated to the measured signals
are caused by instrument noise and are unpredictable since they vary with time in a
random fashion, and thus they cannot be removed by calibration. However, random
error in the reflectometer system can be reduced by signal averaging. The following
discusses the calibration technique used to remove the systematic errors for the
proposed heterodyne reflectometer system.
From the block diagram of the heterodyne reflectometer system (Figure
5.4), the complete signal flow graph is shown in Figure 5.9. If we assume there are no
reflections from the detection ports to the main line o f the dual-directional coupler, we
obtain the simplified signal flow graph of the reflectometer, as illustrate in
Figure 5.10, where A and B are detection factors. If the microwave source is matched,
then Ts= 0, and if the dual-directional coupler is symmetrical, then S 31 = S 42 and S 32 =
S 41. Solving the simplified signal flow graph, as shown in step-by-step (Figure 5.11),
will provide the ratio o f Pnf and Pinc,
p
=
Pmc
0
B
S 32 -~ ^ 2 2 ^ L )
a
s 3l( i - s nr L)+s2ls,2r L
^2 1 ^3 1 ^L
2)
Three c o m m ercial 3.5-mm coaxial standards (matched load, short and
open circuits) have been utilized to calibrate the reflectometer. From the above
equation, we substitute P = PM for matched load (T*. = 0), P = Ps for a short circuit
100
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(Ti = -1), P = Po for an open circuit (T/. = 1), and P = PL for an arbitrary load or DUT,
then obtain the following equations.
= 7A ' Sf 3L
1
(54a)
(54b)
?
A S 3l(\ + S 22) - S 2lSn
-
P
°
& S n ( l - S 72) + S 2lSn
A 5 3, ( l - 5 22) + 52IS32
PL = l . S n Q ~ S 22r L) + S2lS 3ir L
a s na - s 22r L) + s ns nr L
and
Solving these equations yields the measured reflection coefficient,
r
L
(P y-W o-P s)
(5S)
(Pm +P lXP0 +P s )-2(P0Ps + W
Theoretically, using this error calibration technique, the directivity of the
dual-directional coupler need not be very high, but well-matched source and mixers
are required. This reflectometer, however, can be employed for accurately measuring
very small reflections.
5J
Experiments and results
Equation 5.5 has been programmed into LabVIEW, then the calibrated
reflectometer has been used to measure the complex reflection coefficient of two
different DUTs. Figure 5.12 shows the swept measurement o f reflection coefficients
for a 25 Q load from 1 to 3 GHz compared to the result from an HP 8720D vector
network analyzer. For this comparison, a maximum 0.03 dB difference in magnitude
101
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and 0.5 degree in phase are obtained. An arbitrary load with large variations in
reflection coefficient has also been measured against the HP 8720D, with results
shown in Figure 5.13. Again, a good agreement is obtained between the proposed
reflectometer and network analyzer. Finally, the 50 Q standard used for calibrating to a
zero reflection has been measured and the result (~ 80 dB) is also comparable to the
HP 8720D. This result reflects the dynamic range o f the proposed reflectometer
system.
Detector
i r
Connector
ik
Dual directional
cou p ler
Source
Cable, adapter
& connector
Connector
i r
Connector
11
Detector
i r
Figure 5.9:
Complete signal flow graph of the reflectometer.
102
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
DUT
Dual-directional
c o u p le r
Standard lo a d s
or DUT
P.in
Figure 5.10: Sim plified signal flow diagram for reflectometer system.
103
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
<32
(a)
(b)
<32
(C)
Figure 5.11: Step-by-step to analyze signal flow graph (a) original simplified
signal flow graph of the reflectometer (b) after Rule IV and / and
(c) after Rule III.
104
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Phase
•
HP 8 7 2 0 D
NLTL R eflectom eter
180
-9.5
- 179
-9.6
- 178
-9.7
177
Magnitude
■
(Ajp/oO eseijd
Magnitude (0.1dB/div)
-9.4
HP 8 7 2 0 D
NLTL R eflectom eter
176
-9.8
1.0
1.5
2.0
2.5
3.0
Frequency (GHz)
Figure 5.12: Measurement of a 25 Q load compared to an HP 8720D network
analyzer, (note the expanded scale)
105
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
25-ohm
Connector
200
Short
Airline
Tee
-
Airline
CQ
100
Connector
T3
<D
3
4-^
T3
1
2
Input
-12
-100
Phase (degrees)
^ H O n
-16
-200
1.0
1.5
2.0
2.5
3.0
Frequency (GHz)
Magnitude
■
HP 8 7 2 0 D
NLTL R eflectom eter
Phase
------HP 8 7 2 0 D
•
NLTL R eflectom eter
Figure 5.13: Measurement of an arbitrary load (the inset picture) compared to
measurement from an HP 8720D network analyzer.
106
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 6
CONCLUSION AND FUTURE STUDY
6.1
Conclusion
A novel design using a serrodyne modulated NLTL for phase shifting and
coherent microwave measurement has been proposed. This new technique is simple,
and the process for fabricating NLTLs involves only diodes, transmission lines,
capacitors and resistors, so it can be easily integrated in future single-chip designs.
There are significant applications for this device in both instrumentation and sensing,
particularly because it offers a clear path toward complete integration o f a coherent
measurement system. This modulated NLTL (distributed) frequency translator is also a
viable candidate for integration with NLTL pulse generators and diode sampling
bridges, enabling for the first tim e the foundation o f a complete m onolithic wideband
micro- and millimeter-wave network analyzer system.
Some preliminary designs, simulations o f the delay time and the scattering
parameters using PSPICE and Libra, and experiments have been done on the scale
model. From measurements, the distributed frequency translator exhibits > 45 dBc
carrier suppression and > 50 dBc spurious sideband suppression. This verifies that the
output waveform is very sinusoidal without significant distortion caused by harmonics
and sidebands. The single sideband phase noise of the distributed frequency translator
has been measured to be < 15 dBc/Hz more than the synthesized source. This confirms
that the frequency translator has high frequency stability.
107
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The application o f the distributed frequency translator in a heterodyne 1-3
GHz reflectometer has been studied. The results show that this new reflectometer has
high performance comparable to that o f a commercial network analyzer. While this
technique lays a promising foundation for inexpensive coherent microwave
instrumentation, it can be further extended to other micro- and millimeter-wave
sensors, such as handheld reflectometers operating in the THz regime for applications
such as sensing gasses, nonmetallic weapons and explosives.
6.2
Suggestions for future studies
Although the results from this study on the distributed frequency translator
and its application in a microwave reflectrometer are promising, there remains a
tremendous amount o f further research. Here are only a few thoughts for future studies
on this object.
6.2.1
Improving the NLTL
Instead o f using bond wire transmission lines interconnecting the diodes,
planar transm ission lines summarized in Figure 6.1 could be utilized. These
transmission lines have superior characteristics, especially low losses at very high
frequencies [99-103]. Slot lines are rarely used in microwave circuits because they
suffer from high radiation loss, high dispersion, and low power-handling capabilities.
Microstrip and coplanar waveguide (CPW) lines are most commonly used in MICs
and MMICs since they offer low dispersion and loss. The use o f microstrip or CPW
sections with varactor diodes to be a NLTL, therefore, is expected to increase the
performances at higher frequencies, and also lower cost if done monolithically.
108
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 6.1:
(a)
(b)
(c)
(d)
Planar transmission lines (a) microstrip (b) slot line (c) coplanar
waveguide and (d) coplanar strip line.
In MICs microstrip lines are the most commonly used because their
configurations are very simple and easy to fabricate. The microstrip lines can easily be
fixed on a metallic mount providing an efficient heat sink due to the back metalization.
However, they are not suitable for the planar fabrication in MMICs since they require
thinned substrates (100-200 pm) to avoid the substrate mode excitations. Furthermore,
highly inductive via-hole connection to the backside ground plane is necessary for
shunt elements.
CPWs offer the advantages o f very low dispersion and the elimination of
via holes. Also, they are not sensitive to layer thickness and allow easy fabrication of
series and shunt elements. CPWs are considerably more appropriate when fabricating
MMICs because they require only a single lithographic definition and metal
evaporation.
109
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Coplanar strip (CPS) lines are also favorable for the NLTLs due to their
balanced nature. High characteristic impedance up to ~ 300 Q can be made, resulting
better matching when fabricated with varactor diodes. In addition, CPS lines are easier
to fabricate compared to the CPWs.
A further development step is to fabricate the NLTL on a single chip. This
not only reduces the cost o f the NLTL, but also reduces the parasitics associated with
commercial diode packages. The most important improvement is the reduction in
diode area, resulting in the improvement o f cuttoff frequency and loss. The NLTL
chips can be fabricated on silicon [104], but GaAs NLTLs have been extensively
investigated by a number o f researchers [17-24, 105-109] because o f their superior
characteristics such as higher carrier mobility and breakdown field. However, a novel
CPW NLTL with the suspended structure using silicon CMOS technology is
promising and now being developed by the van der Weide group in the Department of
Electrical and Computer Engineering, University o f Delaware. This suspended CPW
NLTL provides lower loss and higher operating frequency when compared to other
NLTL chips made from silicon, but higher loss than GaAs NLTLs. This new approach
could also allow to create extremely low cost NLTL systems.
6.2.2
Improving the controlling circuit
A DAQ with 16- or more bit resolution and more than 1 Mbit/sec data rate
is now commercially available. The use o f a high-resolution DAC to control the
distributed frequency translator could allow a high step-phase resolution to be built.
This could further reduce the carrier and spurious sideband suppressions at the output
o f the frequency translator. Using the ultra-high speed DAQ could reduce the spikes at
the flyback times and also other spurs. Moreover, with high-speed DAQ, a higher IF
110
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
could be obtained resulting in faster measurement. The size and speed o f the
LabVIEW programs are considered to be important parameters limiting the
performance o f the controlling circuit. Actually, the LabVIEW package is a generalpurpose program, therefore considerable program overhead is included. To improve
the speed, a specific application program in C or assembly language could be written.
Nevertheless, carefully implementing most parts o f the controlling circuit in a single
chip IC could definitely increase the speed o f the system. This could also reduce noise,
weight and cost o f the system.
6.2.3
Improving the reflectometer
Improving the distributed frequency translator results in a higher
performance reflectometer. However, other parameters of the reflectometer should also
be considered to increase the number o f measurement points, and speed. Increasing the
number o f measurement points will definitely decrease the speed o f the reflectometer,
hence very high speed hardware and software are necessarily required.
In order to reduce cost o f the NLTL heterodyne reflectometer system, a
non-phase locked microwave source should be employed. Using a non-phase locked
source can reduce noise by the effect o f phase-locking, however, this will also reduce
the frequency accuracy.
6.2.4
Developing MMIC and MIC systems
Most o f the frequency translator and reflectometer circuits could be
integrated into MMICs and MICs. The motivations are embedded in the following
promising attributes o f the integrated circuits approach:
111
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1. low cost;
2. small size and weight;
3. broadband performance;
4. improved reliability and reproducibility; and
5. circuit design flexibility and multifunction performance on a chip.
A single chip containing a frequency translator and a reflectometer (or a
network analyzer) could be developed in silicon, silicon-on-sapphire (SOS) or GaAs
foundries. Silicon is a well-defined technology, but silicon substrate is very lossy at
high frequencies because o f the instability o f semi-insulating silicon to maintain its
semi-insulating properties through the high-temperature processes. The use o f sapphire
as a substrate could eliminate the losses associated w ith semi-insulting silicon.
However, GaAs (n-type) has higher carrier mobility (over six times that of silicon),
GaAs on semi-insulating GaAs substrate, therefore, is operable at higher frequencies
(>100 GHz) with low losses.
6.2.5
Developing new applications
While improving the speed and accuracy o f the NLTL reflectometer, the
Web-accessed NLTL reflectometer has been developing by the van der Weide group.
Other interesting applications o f the distributed frequency translator in micro- and
millimeter-w ave ranges should be studied, for example, an inexpensive two-port
vector network analyzer, and a portable gas sensor. Also, the NLTL phase shifter itself
could be utilized in several applications (non-frequency translator) in microwave
instrumentation and com m unication systems.
112
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Appendix A: Specifications of a variable attenuator device
GaAs 15 dB MMIC FET Voltage
Variable Attenuator In SOT 143 DC-2GHz
pha
AF002N2-32
Single Voltage Control
Low Cost
Small SOT 143 Package
15 dB Range
Jt O
Very Low DC Dissipation
Easily Adapted for Positive Control
Non-fleflecnve
Absolute Maximum Ratings
T he AF002N2-32 is a singfe control non-rellective W A
ideal far AGC applications, lb law DC drain
characteristic and stze m ake it suitable far th e PCN and
portable cellular m arkets. A positive control voltage
m ay be used by adrfing 2 DC blocking capadtore (C at)
and 1 bypass capacitor (Cep).
10mW>500MHz(V-av
4mW @ 50 MHz 0/-8V
Control VfrStagaw
+0.2V, -10V
Operating Temperature: -40 to S5°C
Storage Temperature: -& tol50*C
0 jc :
25*C/W
(Note: Operating this device above any of these
parameters may cause irreversible damage.)
Electrical Specifications at 2S°C
Operating Characteristics at 25°C
HP Input I
Description
Insertion Ian
OC-OSOHz
OC- 1 GHz
0C-2G H Z
XI
X3
XS
dB
dB
dB
Max
Max
Max
Attanuanon
OC-OSGHz
O C -t GHz
0C-2GHZ
IS
11
dB
dB
dB
Mki
Mkl
Min
VSWR
0C-2GHZ
dB
Max
7
2.0:1
bnpeam e
SOOhmsNemnal !
SwKMng Ctiancarada
RISE. FALL(10/90%or 90/10%RF1
ON. OFF (30%CTLto 90/10% RF)
VUeoFaadtau
Const* Votaoea
V0 (Low)
V0 (Hgh)
7
10
20
|
na tVp |
na Typ i
mV Typ i
1
1
1
Oto-0£VQ20|iAMax
-SVOSOiiAMax
Comgraawon Pont Idrall Aaanuanen Lava*
SB MHz
800 MHZ
x i da
-e
-«
1.0 dB
-3
0
113
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
dBm Typ
dBm Typ
Typical Performance Data
1
i
1
1
i
i
r 0^
!
!
1
1
oc
1
;
1
1
I -
1
1
25
20
as
as
15
2S
10
20
5
\S
0C
GHz
1
GHZ
Insertion Loss vs. Frsqusney
Attenuation S tstss vs.
IP
2
OC
'•3 0 0 MHz
2
VSWR vs. Frsqusney
Frsqusney
S
1
GHz
♦15
3S
>
O'
-2
-1
i
3
£
g 25
20
SIOMTIMHI “I
IS
3
Attenuation vs. Bias
Pin Out
8 9 12 IS
AOsution (08)
12
18
Attenuation vs. IP3
Attenuation vs. 0.1 dB
Compression Point
Bias Configurations
J1
J2
GNO
VI
1 i
GMO
Poattlvs
VoM
sqs
OoarsMow
Jt
Cbl
vt
Truth Table
VI
-5
0
♦5
0
J2 H f - o
Cbl
GNO
N w ttm Vottag* Opmtton
VI
o TZZ TO
Stats
liraarnon u a a
FuaAoanuaoon
Portiiv® Vottag* Opmtton
FOiAnanuanon
fnaaraon Loss
15
KdS)
^7
Cop
0 to «3V Control
Cqi_£ 0.01 nF
Capa iooo pF
■ —~h"t—inn i f e n iii»mm
114
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
18
Appendix B: Specifications of a variable gain amplifier device
Silicon Bipolar MMIC 2.5 GHz
Variable Gain Amplifier
MhtjM
HEWLETT
PACKARD
IVA-14208 and IVA-14228
Features
Description
• Differential Input and
Output Capability
• DC to 2.S GHz Bandwidth:
3.4 Gbits/s Data Rates
• High Gain: 24 dB Typical
• Wide Gain Control Range:
34 dB Typical
• 6 V Bias
• 5 V Vqc Control Range.
<3 inA
• Fast Gain Response: < 10 nsec
Typical
• IVA-14208: Low Cost Plastic
Surface Mount Package
• IVA-14228: Hermetic Ceramic
Surface Mount Package
The IVA-14 series MMICs are
variable gain amplifiers. The
IVA-14208 is housed in a miniature
low cost plastic surface mount
package. The IVA-14228 is housed
in a miniature hermetic ceramic
surface mount package. Both
devices can be used in any
combination of single-ended or
differential inputs or outputs (see
Functional Block Diagram). The
lowest frequency of operation is
limited only by the values of user
selected blocking and bypass
capacitors.
175 V
Figure 1. IVA-14228 Typical Variable
Gain vs. Frequency and
at
Vcc = 6V .Tc_ « 2 5 0C.
Typical applications include
variable gain amplification or
limiting for fiber optic systems
(e.g. SONET) with data rates up to
3.4 Gbits/s. mobile radio and
satellite receivers, millimeter
wave receiver IF amplifiers and
communications receivers.
The tVAseries of variable gain
amplifiers is fabricated using
Hewlett-Packard’s 10 GHz fT.
25 GHz
ISOSAT™-1 silicon
bipolar process. This process uses
nitride self-alignment, submicrometer lithography, trench
isolation, ion implantation, gold
metallization and polyimide inter­
metal dielectric and scratch
protection to achieve excellent
performance, uniformity and
reliability.
IVA-14208
Plastic SO-8 Package
IVA-14228
Ceramic ‘28’ Package
Functional Block
Diagram and Pin
Configuration
t.
2.
3.
4.
n M o e s c m rn o M
# ut*
■*
V e t, AC GROUND
7.
C.
Vn , AC GROUND
M TUT*•
i
!
vac
OUTPUT ♦
OUTPUT*ee
|
I
IVA>t4ttt FAOCAQCSOTTOM t t V caAC GROUND
115
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IVA-14208, -14228 Absolute Maximum Rating^1!
i Symbol
1 Mr-'fa
i Pm
'fcc-%
! T,
! ^sg
i P.
Parameter
Device VoltaRe. T™. = 25°C
Input Power.
= 25°C
Control Voltage.
= 25°C
Junction Temperature-tStorage Temperature
Total Device Dissipation
Units
IVA-14208
IVA-14228
Volts
dBm
Volts
12
13
10
150
-65 to -*-150
I000'21
12
13
10
200
65 to -*200
1000<3'
•c
•c
mW
Thermal Resistance:
| IVA-14208 Thermal Resistance Junction to Case141: 9^ = 68°CAV
IVA-14228 Thermal Resistance Junction to Case141: 0^ = 63°C/W
j
Notes:
1. Operation In excess of any one of these conditions may result in pexuim a damage to the device.
2- T _ „ - 2S*C. Derate at 14.7 mWfC for T ,„. > 82**C.
3.
» Z5*C. Derate at 15.9 mW/”C for
> i 2TC
4.T,- i50“c.
IVA-14208. -14228 Guaranteed Electrical Specifications AH measurements reflect single-ended
(unbalanced) performance. T ^ = 25°C. VJ;C= 6 V. V^ = 0 V. Vfcc = 0 V, ZL= 50 Q
i Symbol
1 GP
' AGP
]
GCR
: ISO
VSWR
NF
to
Ic c
i
i
dB I
GHz I 2.0
Reverse Isolation (|S12j2). f = 1 GHz.
\fcc=0to5 V
dB
IVA-14208
IVA-14228
Typ.. Max. Min. Typ. Max.
22
24
24 j
Min.
20
|
dB
! 30
±0.7
±1.2 |
2.5 j
2.2
2.5
34
30
34
1
1
!
37
40
Input VSWR. f = 0.05 to 2.0 GHz.
\fcc * 0 to 5 V
j
2:1
2:1
Output VSWR. f = 0.05 to 2.0 GHz.
V^c = 0 to 5 V
!
!
2:1
2.5:1
Output Power at 1 dB Gain.
Compression f = 1 GHz
t
Units
dB
Gain Control Range121, f = 1 GHz.
\fcc= 0to5V
50 Q Noise Figure, f = 1 GHz
P u iB
IP 3
Gain Flatness, f = 0.05 to 2 GHz
3 dB Bandwidth
fjd B
Mju
Parameter
Power Gain flSj,!2). f = I GHz
1
dB
dBm
i
9.0
9.0
-2.0 :
-2.0
450
450
i
Pk-Pk Single-ended Output Voltage,
f = 1 GHz
tnVpp
Third Order Intercept Point, f = 1 GHz
Group Delay, f = I GHz
Supply Current
dBm j
psec 1
mA | 28
!
i
8
450 ;
38 ; 48
8
450
38
28
48
Notes:
1. The recommended operating voltage range for these devices is 5 to 8 V. Typical performance as a function of voltage is shown in the
graphs on the following pages.
2. The recommended gam control range for these devices for dynamic control is 0 to 4.2 V. Operation at gam control settings above 4 2V
may result in gam control increase rather than gam decrease See figures 4 and 19.
116
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IVA-14228 Typical Performance Curves
soa
OUTPUT*
-3 0 <
8.1
. . . . . .
tO
hw ouw cy
Figure 2. IVA-I42X8 Connection Diagram Showing Balanced Inputs and
Unbalanced Outputs. Inputs and Outputs May Be Either
or Unbalanced.
9
S
O
uX
B
I0
Figure 3. IVA-14228 Gain vs.
Frequency and Va ; Vcc * 6 V.
2S°C.
*
20
3
i0
•to
a.
•20
1
— ■»
3-0
to n o
•40
9
Ml
Iz
0
t
2
3
V0C(V0CTS)
4
Figure 4. IVA-14228 P (dB and Gain vs.
vcci vcc 3 6 v- T « b * 2S°C
s
nmueicrtoHz)
Figure 5. IVA-14228 N oise Figure vs.
Frequency and Vcc: V c c - 6 V . T ^ .
25®C-
VoctVOCTS)
Figure 6 . IVA-14228
8V .Tea-.a 2 5 ° C .
vs. V^s
Vc c =
*1
X
a 2:1»■
B
>
x
a
B
>
meouoicv iomu
Figure 7. IVA-14228 VSWR vs.
Frequency; Vcc « 6 V. V ^ * 0 V. Ta
25°C
F*eOUe4CY(OKl)
Figure 8. IVA-14228 VSWR vs.
Frequency; Vcc * 6 V. Vcc * 5 V. Ta
2S°C
FHffQUmCT(OHH
Figure 9. IVA-14228 Group Delay vs.
Frequency; Vcc * 0 V. Vcc * 6 V.
*
2S°C
117
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IVA-14228 Typical Performance Corves (cont.)
2
2S
0
s
24
£
22
I
20
!•
to
•4
14)
(XI
0.1
FREQUENCY (OHU
Figure 10. IVA-14228 Gain vs. Fre­
quency and Temperature; Vrc * 6 V.
Vcc-OV.
meaueicvtGHx)
0
XO
29
0
Figure 12. IVA-14228 Gain and PldB vs.
Temperature: Vcc * 6 V. V ^ »0V .
Frequency * 1 GHz.
Figure 11: IVA-14228 PldB vs. Fre­
quency and Temperature: VCC-6 V .
'fcc-O V.
•0:
Mi
| ts|------■
ci
3
■i
\
I
9
i
401
2S*C
Mi
20
IS
0.1
FREQUENCY (GMz)
20
27
20
S
24
Figure 15. IVA-14228 Icc vs. Vcc and
Temperature: Vcc * 0 V.
Figure 14. IVA-14228 ICc vs*
Temperature; Vcc s 0 V.
* 0 V.
Frequency * 1 GHz.
2
0
1S *C
■2
2S-C,
U
(VOLTS)
TEMPERATURE (*C)
Figure 13. IVA-14228 Noise Figure vs.
Frequency and Temperature: Vfcc a 6 V.
\^ c * 0 V.
■4
a
a
21
20S
IS
7
Vfcc (VOLTS)
Figure 16. IVA-14228 Gain vs.
Temperature; V cc 3 0 V.
Frequency » 1 GHz.
and
•10
5
U
(VOLTS)
125
TEMPERATURE (*C)
7
Figure 17. IVA-14228 PldB vs. \fec *nd
Temperature; Vcc * ® V,
Frequency * I GHz.
118
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IVA-14208 Typical Performance Curves
is
■OV
OJUW
I
a
i
X7SV
o
s
10
S
<
O
nmue«CY(GHi}
5
•40
10
0.1
10
0.1
FflCQUeNCVlQm
Figure 19. IVA-14208 Gain and P l t f vs.
VGO VCC * 6 V* Frequency » 1 GHz.
Figure 18. IVA-14208 Cain vs.
Frequency and \fec; V^c * 6 V.
TCMr 3 25°C.
- 25°C.
Figure 20. IVA-14208 Noise Figure vs.
Frequency: V<x « 6 V.
*0V.
Tcm.* 2 5 ° C
4
3
2
1
2
3
4
soo
10
&
►
<
M
an
I
00
u
HI
c
a(0
>
o
0.1
9
&0
meouoicv (QHu
FucoueicrtcME)
(VOLTS)
Figure 22. IVA-14208 VSWR vs.
Frequency; Vcc » 6 V . Vqq * ® V.
* 25*C.
Figure 21. IVA-142081 ^ vs. V^;
\fcc * 6 V. T
* 25°C.
Figure 23. IVA-14208 Group Delay vs.
Frequency; Vcc * ® V.
* 0 V.
To m * 25®C.
20
o
US
■i
25
-2
<
24
-3
E
-4i
23
4
•4
10
FRSMJCNCYtGHU
Figure 24. IVA-14208 PldB vs.
Frequency »nd Vcc; VCC * 6 V.
Frequency * 1 GHz.
* 25°C.
22
Tewewiuntrci
Figure 25. IVA-14208 Gain and P !dB vs.
Temperature: Vc c * 6 V. Ifcc * 0 V.
Frequency * 1 GHz.
TEMreuTunero
Figure 26. IVA-14208 Icc vs.
Temperature: V c c -6 V .V c c .0 V .
119
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IVA-14208 Typical Performance Curves (cont.)
27
SO
*$
a
40
a
a
a
a
a
Vq . (VOLTS)
Figure 27. IVA-142081,
I c e **■ vc c :
Vcc - 0 V. T
* 25°C.
25°C-
(VOLTS)
V cg (VOLTS)
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