close

Вход

Забыли?

вход по аккаунту

?

Non-contacting six-port reflectometers for in-situ measurement of microwave circuit modules

код для вставкиСкачать
Non-Contacting Six-Port Reflectometers
for In-Situ Measurement of Microwave Circuit
Modules
A Dissertation
Presented to
the Faculty of the School of Engineering and Applied Science
University of Virginia
In Partial Fulfillment
of the Requirements for the Degree of
Doctor of Philosophy in Electrical Engineering
by
DAN HUI
January 2008
UMI Number: 3289600
INFORMATION TO USERS
The quality of this reproduction is dependent upon the quality of the copy
submitted. Broken or indistinct print, colored or poor quality illustrations and
photographs, print bleed-through, substandard margins, and improper
alignment can adversely affect reproduction.
In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if unauthorized
copyright material had to be removed, a note will indicate the deletion.
®
UMI
UMI Microform 3289600
Copyright 2008 by ProQuest Information and Learning Company.
All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.
ProQuest Information and Learning Company
300 North Zeeb Road
P.O. Box 1346
Ann Arbor, Ml 48106-1346
APPROVAL SHEET
This dissertation is submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy (Electrical and Computer Engineering)
Dan Hui
The dissertation has been read and approved by the examining Committee:
sf<&U£~A4.<
CCSJULMS
Robert M. Weikle II (Advisor)
N. Scott Barker (Chair)
Stephen G. Wilson
Arthur W. Lichte/tberger
Bascom S. Deaver
Accepted by the School of Engineering and Applied Science:
H fi/L.
v
V"
Dean, School of Engineering and Applied Science
January, 2008
Ill
Abstract
Microwave circuits and devices, are commonly characterized using commercially
available vector network analyzers (VNA). For an operating frequency up to about
110 GHz, a device under test (DUT) that is usually connected to the VNA through
coaxial adapters which facilitate the transition from the DUT's transmission media
to the VNA's coaxial cables. A test fixture is usually required for such a transition.
Compared to the measurements using commercially available VNAs, In-Situ measurements allow the characterization of a DUT in the same environment where it
is designed to operate, with no need of precision connectors or test fixtures. This
approach is very attractive, particularly for those circuits operating at the upper
portion of the microwave spectrum (100—300 GHz) and at the submillimeter-wave
region (300—3000 GHz), where planar transmission lines are frequently used and
precision coaxial or waveguide adapters are largely unavailable.
A variety of non-contacting probing methods have been proposed and demonstrated for microwave circuit in-situ measurements. Most of them are focused on
electromagnetic field-mapping. However, these techniques suffer from drawbacks.
Some of them require quantification of the Pockels effect and require sophisticated
laser instrumentation that is typically not found in standard microwave electronics laboratories. The others utilize coaxial probes which can present over-moding
problems for high frequency operation and can be cumbersome to implement and
align.
In this work, a new approach for non-contacting in-situ measurements of microwave circuits is investigated and its concept demonstrated. This new approach
is a combination of a planar non-contacting probing structure and a six-port refiectometer architecture. The approach described in this work is a stand-alone
instrument that has the potential to be monolithic integrated and hence may benefit from low-cost compared to other non-contacting in-situ measurement systems.
In addition, a new calibration method based on null double injection technique
is demonstrated and studied as an alternative six-port calibration method that
does not require sliding terminations. This technique can be implemented and
IV
potentially automated using only a few widely-available microwave components,
resulting in a more convenient and frequency-scalable system solution.
V
Acknowledgments
I would like to express my deep appreciation to my advisor, Bobby Weikle.
He led me into the world of microwave engineering and his advice, support and
encouragement helped me through this project.
I also would like to thank Professor Stephen G. Wilson for his valuable suggestions and help on the part of the error analysis. I would like to thank Professor
N. Scott Barker as well for his suggestions and comments on the probing circuit
design.
Many thanks to the clean room personnel, Joe Beatrice, Professor Arthur Lichtenberger, Lei Liu, Specially, Hui Shen and Songbin Gong, who helped me a lot on
the circuit fabrication. I also want to thank the FIR lab personnel, Qun Xiao,
Haiyong Xu, Li Yang, Guoguang Wu for interesting discussions.
Finally, I would like to thank my family for their unconditional support, love,
and dedication. Without their support, I would not have finished this dissertation.
Contents
List of Figures
xiii
List of Tables
xiv
1 Introduction
1
1.1
Overview
1
1.2
Field Mapping Techniques
3
1.3
Non-Contacting S-Parameter Measurement Using Coaxial Probes
1.4
Contribution of This Work
7
1.5
Organization
8
2 Six-Port Reflectometers and Sampled Line Reflectometers
.
6
11
2.1 Introduction
11
2.2
Six-Port Reflectometer Calibration
14
2.3
Sampled-Line Reflectometers
17
2.4
Previous Sampled-Line Reflectometer Work at the University of Virginia
21
3 A Non-Contacting Sampled-Line Reflectometer
24
3.1
introduction
24
3.2
Principles of a Non-Contacting Reflectometer
26
3.3
Design and Simulation
31
3.4
Measurements and Analysis
35
3.4.1
36
Measurements
vi
Contents
vii
3.4.2
3.5
4
Measurement Sensitivity to Probe Position Error
44
Conclusions
44
Calibration of Six-Port Reflectometers Using Null Double Injection
53
4.1 Introduction
53
4.2
54
Background and Theory
4.3 Implementation
58
4.4
Measurement and Analysis
60
4.4.1
Measurements
60
4.4.2
Measurement Uncertainty
67
4.5
Discussion
71
5 A Non-Contacting Reflectometer With a Compact Coupling Prob-
6
ing Structure
75
5.1
Introduction
75
5.2
Compact Coupling Probing Structure
76
5.3
Modified Sampled-Line Reflectometer
79
5.4
Design and Simulation of the Modified Sampled-Line Reflectometer
82
5.5
Measurements of the Modified Sampled-Line Reflectometer
87
5.6
Preliminary Error Analysis
99
5.7
Conclusion
104
Summary and Future Work
106
6.1
Summary
106
6.2
Discussions and Suggestions for Future Work
107
List of Figures
1.1
Microwave test fixtures to facilitate transition from waveguide or
planar circuits to coaxial cables
1.2
A probe station to facilitate transition from planar circuits to coaxial
cables
1.3
3
A generic setup for mapping the electric field when an external
electro-optic probe is used
1.4
4
A generic setup for mapping the electric field when an inductive
co-planar probes is used
1.5
2
5
A non-contacting s-parameter measurement technique using capacitive and inductive coaxial probes
2.1
Generic configuration of a six-port reflectometer
2.2
Determination of T from the intersection of three circles represented
7
12
by equations (2.5)
13
2.3
Determination of T (|r| < 1) for a five-port reflectometer
14
2.4
Determination of w from three circles represented by equations (2.8)(2.10)
16
2.5
Architecture of a sampled-line reflectometer
18
2.6
Determination of w by two circles represented by equations (2.16a)
and (2.16b). The intersection point above the real axis is rejected. .
2.7
2.8
19
Extension of the operating frequency range of a sampled-line reflectometer by adding an additional power detector
20
An attenuator added for eliminating potential deep voltage nulls . .
20
viii
List of Figures
2.9
IX
Photograph of a sub-millimeter-wave sampled-line reflectometer presented in [5]
3.1
22
Measurement procedures for a non-contacting reflectometer, illustrating the source impedance difference between calibration and insitu DUT measurement
27
3.2
Generic block diagram of a four-port reflectometer
28
3.3
Reflectometer measurement setup with a 50-ohm source impedance.
30
3.4
Reflectometer measurement setup with a varying source impedance.
31
3.5
Magnitude and phase of the 0-dB attenuator measured under different source impedances (Ti corresponds to the situation without the
30fi transmission line and phase shifter, Tp\ and Tp 2 with the 30fi
transmission line and phase shifter at different phase shifts.)
3.6
. . . .
32
Basic configuration of non-contacting reflectometer based on sampledline reflectometer architecture
33
3.7
Photograph of the non-contacting reflectometer
33
3.8
Simulated couplings for a probe-to-through-line distance of 200/^m.
34
3.9
Simulated couplings for a probe-to-through-line distance of 300^m.
35
3.10 Measured and simulated couplings for a probe-to-through-line distance of 300^m
36
3.11 Measured V3, V4, V5, and V6 versus electrical length of the sliding
short at 1.2 GHz
37
3.12 Ellipse traced out by the sliding short on P 3 / P 4 versus P 5 / P 4 plane
at 1.2 GHz
37
3.13 Two circles on the w plane when DUT is a 6dB attenuator over the
frequency from 0.9GHz to 1.1GHz
38
3.14 Two circles on the w plane when DUT is a 6dB attenuatorover the
frequency from 1.2GHz to 1.4GHz
39
3.15 Comparison of reflection coefficients for a 6-dB fixed attenuator measured with the prototype reflectometer and an HP8720C network
analyzer
40
List of Figures
x
3.16 Comparison of reflection coefficients for a 10-dB fixed attenuator
measured with the prototype refiectometer and an HP8720C network analyzer
41
3.17 Comparison of reflection coefficients for a 0-dB fixed attenuator measured with the prototype refiectometer and an HP8720C network
analyzer
42
3.18 Measured reflection coefficient difference resulting from shifting the
probing structure in vertical direction (a) and in horizontal direction
(b) by 100/Ltm, 200/xm, 500//m for the 3-dB attenuator
45
3.19 Measured reflection coefficient difference resulting from shifting the
probing structure in vertical direction (a) and in horizontal direction
(b) by lOO/rni, 200^m, 500^m for the 6-dB attenuator
46
3.20 Measured reflection coefficient difference resulting from shifting the
probing structure in vertical direction (a) and in horizontal direction
(b) by 100/itm, 200/Ltm, 500/im for the offset short
47
3.21 Measured reflection coefficient difference resulting from shifting the
probing structure in vertical direction (a) and in horizontal direction
(b) by 10/Ltm, 20/izm, 30jum, 40/rni, 50^m for the 3-dB attenuator.
. 48
3.22 Measured reflection coefficient difference resulting from shifting the
probing structure in vertical direction (a) and in horizontal direction
(b) by 10/xm, 20/xm, 30^m, 40//m, 50^tm for the 6-dB attenuator.
.
49
3.23 Measured reflection coefficient difference resulting from shifting the
probing structure in vertical direction (a) and in horizontal direction
(b) by 10/j.m, 20^m, 30/xm, 40/im, 50/j.m for the offset short
50
4.1 Diagram of a general six-port refiectometer, the six-port network is
assumed to be linear
4.2
55
Illustration of the circles in the w-plane defined by equations (3)-(5). 56
List of Figures
4.3
XI
An experimental setup for implementing the null double injection
calibration technique.
The manufacturer part labels provided in
the figure correspond to those components used to implement the
method in this work
4.4
59
(a) Measured detector outputs as a function of relative phase-shift
between input signals at the source and DUT ports. The attenuation
for each arm of the calibration setup is fixed for this measurement.
Subscripts refer to the detector port, (b) Detail showing the variation of the sampled voltages in the vicinity of a null
4.5
Measured magnitude of the six-port network coefficients (K, L, M,
and N) as a function of frequency
4.6
61
62
(a)Comparison of reflection coefficients for 6 dB fixed attenuators
measured with the prototype reflectometer (circle) and an HP8720C
network analyzer (square). (b)(c) Difference between the measured
reflection coefficients ( A r ) as a function of frequency.
4.7
64
Comparison of reflection coefficients for 10 dB fixed attenuators measured with the prototype reflectometer (circle) and an HP8720C
network analyzer (square). (b)(c) Difference between the measured
reflection coefficients (AT) as a function of frequency.
4.8
65
(a) Measurement of the return loss for a 66.67 mm offset short with
the prototype reflectometer (circle) and the 8720C network analyzer
(square). (b)(c) Difference between the measured reflection coefficients (AT) as a function of frequency.
4.9
66
Annuli in the w-plane corresponding to measurements done on a 6
dB attenuator at 1.25 GHz. The region of overlap (detailed in the
inset) provides a measure of the precision with which w is known.
Mapping of this region to the T-plane allows the error in phase (A0)
and magnitude (Ap) of the reflection coefficient to be estimated. . .
68
List of Figures
xn
4.10 Measured reflection coefficient (a) magnitude and (b) phase of a 6
dB attenuator. The error bars show the standard deviation in the
measurement, corresponding to a confidence interval of 70%.
...
69
5.1
Basic configuration of the proposed compact probing structure. . . .
76
5.2
HFSS simulation results of the compact probing structure
77
5.3
Dimension of testing compact probing structure
77
5.4
Measured S-parameters of the testing compact probing structure.
5.5
A possible configuration of a non-contacting reflectometer with a
.
78
vector voltmeter
79
5.6
An optimized six-port vector voltmeter
80
5.7
A modified sampled line reflectometer
81
5.8
Sampled-line reflectometer with the proposed compact probing structure
5.9
81
A more detailed implementation of sampled-line reflectometer with
the compact probing structure
83
5.10 ADS simulation bench for the sampled-line reflectometer
84
5.11 ADS simulation results for the sampled-line reflectometer
85
5.12 Simulated eclipse traced out by a sliding short on the P3/P4—P5/P4
plane
86
5.13 A photograph of the fabricated reflectomter
88
5.14 TRL calibration standards for the HP8510C network analyzer. . . .
88
5.15 connection for TRL calibration
89
5.16 Sampled-line reflectomer placed on top of the THRU line
89
5.17 A photograph of the measurement setup
90
5.18 Comparison of reflection coefficients for a 0-dB fixed attenuator measured with the prototype reflectometer and a HP8510 network analyzer
91
5.19 Comparison of reflection coefficients for a 4-dB fixed attenuator measured with the prototype reflectometer and a HP8510 network analyzer
92
List of Figures
Xlll
5.20 Comparison of reflection coefficients for a 6-dB fixed attenuator measured with the prototype reflectometer and a HP8510 network analyzer
93
5.21 Comparison of reflection coefficients for a 9-dB fixed attenuator measured with the prototype reflectometer and a HP8510 network analyzer
5.22 Photograph of the matching circuit
94
95
5.23 Comparison of reflection coefficients for a matching circuit measured
with the prototype reflectometer and a HP8510 network analyzer. .
95
5.24 Measured reflection coefficients for a matching circuit. The error
bar shows the perturbation from the radiation of the matching circuit. 99
5.25 Illustration of <7r on T plane
103
5.26 Measured reflection coefficient in magnitude of a 0 dB attenuator.
The error bars show the standard deviation in the measurement. . . 103
List of Tables
5.1
Simulated and true T for different DUTs
5.2
Maximum DC voltages detected from radiation of the matching circuit when input RF power is 16dBm
5.3
87
96
Maximum DC voltages detected from radiation of the matching circuit as input RF power changes
xiv
97
Chapter 1
Introduction
1.1
Overview
Microwave circuits and devices, which generally refer to those operating in the
frequency range from 300 MHz to 300 GHz, are commonly characterized using
commercially available vector network analyzers (VNA). A vector network analyzer is a microwave instrument designed to measure the scattering parameters
of a microwave network (i.e., the magnitudes and phases of the transmitted and
reflected waves from the network under excitation). For an operating frequency
up to about 110 GHz, a device under test (DUT) that is usually connected to
the VNA through coaxial adapters which facilitate the transition from the DUT's
transmission media to the VNA's coaxial cables. A test fixture is usually required
for such a transition, shown in Fig. 1.1 (a). For example, a rigid fixture that holds
a circuit and accommodates SMA panel-mount connectors at its flanges to interconnect microstrip lines to coaxial cables (shown in Fig. 1.1(b)). Alternatively, a
probe station (shown in Fig. 1.2) that utilizes coplanar waveguide probes to transition from planar transmission lines such as CPW's to coaxial cables can be used.
Such measurements can become problematic, however, when the device under test
(DUT) is a subsystem of a larger circuit that is integrated on a single chip. In
principle, separate, sacrificial test circuits can be fabricated on the same wafer,
and then diced and mounted in test fixtures equipped with standard connectors.
1
2
Chapter 1. Introduction
(a)
(b)
Figure 1.1. Microwave test fixtures to facilitate transition from waveguide or planar
circuits to coaxial cables.
This approach requires the fabrication of additional circuits, and usually does not
permit direct measurement of the module actually used in the system. Furthermore, careful calibration is needed to remove the uncertainty and error introduced
by the test fixture.
In-Situ measurements allow the characterization of a DUT in the same environment where it is designed to operate, with no need of precision connectors or
test fixtures. This approach is very attractive, particularly for those circuits operating at the upper portion of the microwave spectrum (100—300 GHz) and at the
Chapter 1. Introduction
3
Figure 1.2. A probe station to facilitate transition from planar circuits to coaxial
cables.
submillimeter-wave region (300—3000 GHz), where planar transmission lines are
frequently used and precision coaxial or waveguide adapters are largely unavailable.
1.2
Field Mapping Techniques
A variety of non-contacting probing methods have been proposed and demonstrated for microwave circuit in-situ measurements. Most of these are focused on
electromagnetic field-mapping and are based on two fundamental techniques. One
technique is to measure the electric field amplitude in the vicinity of a planar transmission line based on the Pockels effect that the application of an RF electric field
along certain crystal axes in electro-optic crystals produces a change in the indices
of refraction presented to an incident optical beam [1—4]. A GaAs substrate commonly used in Microwave Monolithic Integrated Circuits (MMIC's) itself exhibits
Pockels effect and can be used for field mapping of CPW lines [1]. Alternatively,
an electro-optic crystal probe external to (usually above) the circuit substrate can
be used to map the field above a planar transmission line [2-4]. Fig. 1.3 shows a
4
Chapter 1. Introduction
analyzer
-JHS
display
to-o
monitor
Figure 1.3. A generic setup for mapping the electric field when an external electrooptic probe is used.
generic setup for mapping the electric field when an external electro-optic probe
is used [2]. The probe is placed at the desired position where the electric field is
to be mapped. A polarized optical beam incidents into the crystal and emerges
back out from it. Because of the Pockels effect, the optic beam emerging out from
the crystal possess a component that is polarized along the direction orthogonal to
the incident beam polarization. The strength of this component is proportional to
the electric field amplitude and can be detected after passing it through another
polarizer aligned orthogonal the direction of the incident beam polarization.
A different field-mapping technique uses capacitive or inductive coaxial or coplanar probes to sample the electric and magnetic fields near the D U T [5-9]. Fig.
1.4 shows an example of such technique [5]. A small loop extended from a C P W
line is used to sense the magnetic flux density produced by the current flowing
in the transmission line that is below the loop. A network analyzer is used to
measure the transmission (S21) from the signal source to the C P W line, facilitated
by a SMA connector that transits from C P W line to the coaxial cable of port-2
of the network analyzer. The magnitude and phase of the measured 521 represent
the magnetic field magnitude and phase respectively. The C P W probe is moved
Chapter 1. Introduction
5
Port2
Portl
J
m
frn
s
Figure 1.4. A generic setup for mapping the electric field when an inductive coplanar probes is used.
with fine steps over an area using an automated motor to give an detailed field
map above the transmission line and the electromagnetic properties of the DUT is
then derived from this map for diagnosis purpose.
Both techniques suffer from a number of drawbacks. The first method requires
quantification of the Pockels effect and requires sophisticated laser instrumentation that is typically not found in standard microwave electronics laboratories.
Furthermore, it is only applicable for the measurement of electric field, not for
magnetic field. The second method utilizes coaxial or coplanar probes that require
highly accurate positioning and can be cumbersome to implement and align. Furthermore, the accuracy of measuring weak fields can be significantly degraded by
the polluting radiation fields from the probes and any other discontinuities in the
vicinity. In addition, both techniques require the probing to be done over some
spatial extension of the DUT, either simultaneously or by moving the probing
structure. Moreover, because most researchers focus on probing the electromagnetic field distribution near the DUT, great effort must be expended to quantify,
characterize, and minimize the invasiveness of the probes and their interference
with the measurement.
6
Chapter 1. Introduction
1.3
Non-Contacting S-Parameter Measurement
Using Coaxial Probes
From a circuit performance point of view, the electromagnetic field mapping actually yields more information than is usually needed. Typically, scattering matrices
(or s-parameters) or other terminal characteristics (such as an impedance matrix
or admittance matrix) of the network are sufficient to describe a circuit's behavior
for design and analysis purposes.
A non-contacting s-parameter measurement technique using a four-port reflectometer architecture demonstrated by Stenarson is shown in Fig. 1.5 [10]. Two
closely spaced coaxial probes are placed on top of an interconnecting transmission
line, one sampling the voltage on the transmission line through electric capacitive
coupling with an extended coaxial center line, the other sampling the current on
the transmission line through magnetic coupling with a loop connecting the coaxial
center line to the coaxial shield. The sampled voltage and current signals from the
coaxial probes are then processed with a microwave vector voltmeter where their
complex ratio is obtained. This complex ratio is basically equal to the impedance
of the device under test (DUT) except for a scaling factor if interference between
the probes and the interconnecting transmission line is ignored.
By using a four-port reflectometer calibration, this approach can remove the
aforementioned scaling factor and probe interference completely.
However, the
technique exhibits a number of drawbacks. The implementation demonstrated by
Stenarson is not a stand-alone instrument and requires an external vector network
analyzer to process the sampled waves.
In addition, The system described in
[10] utilizes a pair of manually shaped coaxial probes which limits its operation
frequency and introduces significant challenges with regard to probe placement and
alignment.
7
Chapter 1. Introduction
Coaxial Cables
/"^Microwave
V^ySynthesizer
'
' * ^^
Measurement Reference
Plane
Figure 1.5. A non-contacting s-parameter measurement technique using capacitive
and inductive coaxial probes
1.4
Contribution of This Work
In this work, a new approach for non-contacting in-situ measurements of microwave
circuits is investigated and its concept demonstrated. This new approach is a combination of a planar non-contacting probing structure and a six-port reflectometer
architecture. The planar probing structure significantly reduces positioning error while enhancing the measurement repeatability (compared to separate coaxial
probes). In addition, the planar structure is suitable for monolithic integration
using micro-fabrication technology and facilitates the integration of the probing
structure with other microwave processing circuitry. The six-port reflectometer,
which was pioneered by Engen and coworkers at the National Bureau of Standards
[11], sample the magnitudes of travelling waves at a DUT's ports using power detectors (Schottky diodes in this work) and derive the DUT's scattering parameters
from those power measurements.
The approach described in this work is a stand-alone instrument that has the
potential to be monolithic integrated and hence may benefit from low-cost compared to other non-contacting in-situ measurement systems. In addition, a new
calibration method based on null double injection technique is demonstrated and
Chapter 1. Introduction
8
studied as an alternative six-port calibration method that does not require sliding
terminations. This technique can be implemented and potentially automated using
only a few widely-available microwave components, resulting in a more convenient
and frequency-scalable system solution.
1.5
Organization
This dissertation proposal consists of five chapters. Chapter 2 is a brief introduction to the six-port reflectometers with emphasis on the theory and calibration
of the sampled-line reflectometer, which is a special type of six-port reflectometer
originally proposed by Williams [12]. The sampled-line reflectometer is adopted in
the prototype work of this research for its simplicity and its amenability for being
scaled to the sub-millimeter-wave region.
Chapter 3 describes a prototype non-contacting in-situ measurement system
that is based on a CPW planar probing structure and commercially available zerobias diode detectors. Its design, fabrication, calibration and measurements will be
discussed in detail.
Chapter 4 presents the null double injection technique as an new six-port calibration method. It is based on the power measurements as one of power detectors
is tuned to zero. This is done by using adjustable (and potentially programmable)
phase shifters and attenuators at the excitation port and the measurement port of
a six-port reflectometer.
Chapter 5 demonstrates a modified sampled-line reflectometer integrated with
a novel compact planar probing structure. Its operation principle, design, measurement and error analysis will be presented.
Chapter 6 gives discussion and conclusion of this work.
Bibliography
[1] G. David, W. Schroeder, D. Jager, and I. Wolff,
"2D electro-optic probing
combined with field theory based multimode wave amplitude extraction: a
new aaproach to on-wafer measurement," IEEE Int. Microwave Symp. Digest,
1995.
[2] M. Shinagawa and T. Nagatsuma, "Electro-optic Sampling using an External
GaAs probe tip," Electron. Lett, vol. 26, pp. 1341-1343, Aug. 1990.
[3] R.M. Reano, K. Yang, L.P.B. Katehi, and J.F. Whitaker, "Simultaneous Measurements of electric and thermal fields using an electrooptic semiconductor
probe," IEEE Trans. Microwave Theory Tech., vol. MTT-49, no. 12, pp. 25232531, Dec. 2001.
[4] K. Yang, G. David, S.V. Robertson, J.F. Whitaker,and L.RB. Katehi, "Electrooptic mapping of near-field distributions in integrated microwave circuits,"
IEEE Trans. Microwave Theory Tech., vol. MTT-46, no. 12, pp. 2338-2343,
Dec. 1998.
[5] G. Yingjie, and I. Wolff, "A miniature magnetic field probe for measuring fields
in planar high-frequency circuits," IEEE Int. Microwave Symp. Digest, 1995.
[6] G. Yingjie, and I. Wolff, "A miniature magnetic field probe for measuring threedimensional fields in planar high-frequency circuits," IEEE Trans. Microwave
Theory Tech., vol. 44, no. 6, pp. 911-918, 1996.
9
10
Bibliography
[7] G. Yingjie, and I. Wolff, "Measurements of field distributions and scattering
parameters in multiconductor structures using an electric field probe," IEEE
Int. Microwave Symp. Digest, 1997.
[8] S.S. Osofsky, and S.E. Schwarz, "A non-contacting probe for measurements on
high-frequency planar circuits," IEEE Int. Microwave Symp. Digest, 1989.
[9] S.S. Osofsky, and S.E. Schwarz, "Design and performance of a non-contacting
probe for measurements on high-frequency planar circuits," IEEE Trans. Microwave Theory Tech., vol. 40, no. 8, pp. 1701-1708, 1992.
[10] J. Stenarson, K. Yhland, C. Wingqvist, "An in-circuit noncontacting measurement method for s-parameters and power in planar circuits," IEEE Trans.
Microwave Theory Tech., vol. 49, no. 12, pp. 2567-2572, Dec. 2001.
[11] G.F. Engen, "The six-port reflectometer: an alternative network analyzer,"
IEEE Trans. Microwave Theory Tech., vol. 25, no. 12, pp. 1075-1080, Dec.
1977.
[12] W.L. Williams,
"Computer Aided Measurements of Microwave Circuits,"
Ph.D. Dissertation, California Institute of Technology, Pasadena, CA 1989.
Chapter 2
Six-Port Reflectometers and
Sampled Line Reflectometers
2.1
Introduction
Six-port reflectometers were pioneered by Hoer, Engen and coworkers at the National Bureau of Standards in the late 1970s [1-3]. These instruments were proposed as an alternative to commercially available VNA's t h a t were based on mixing
the microwave frequencies to a low IF frequency and using a vector voltmeter at
the IF frequency to measure the magnitude ratio and phase difference between the
incident and scattered waves. Six-port reflectometers are based on direct power
detection and do not require heterodyne detection and vector signal measurements,
resulting in significantly reduced system complexity. Figure 2.1 shows the canonical
configuration of a six-port reflectometer. It consists of a phase-locked, frequencytunable microwave source, a six-port linear network and four power detectors.
The wave amplitudes into and out of the linear six-port network can be expressed as a linear combination of two independent excitations to the network. If
the incident wave (02) and the reflected wave (62) at the measurement plane are
chosen as the two independent excitations to the network, then the wave amplitudes (bi, i = 3,4, 5, 6) incident onto each detector can be expressed as:
bi = Aia2 + Bib2,
11
i = 3,4,5,6
(2.1)
Chapter 2. Six-Port Reflectometers and Sampled Line Reflectometers
P3
P4
o
e
12
o
ai<
Six-Port Linear
Network
DUT
Microwave
Synthesizer
0
0
P5
P6
Figure 2.1. Generic configuration of a six-port reflectometer.
and the power associated with each wave amplitudes
Pi = \bi\2,
1 = 3,4,5,6
(2.2)
Taking the power ratios with respect to P 4 , (2.2) yields:
Aia2 + Bib2
A4a2 + Bib}
i = 3,5,6
(2.3)
Noticing that
r=
«2
(2.4)
(2.3) can be simplified to:
AtT + Bi
IA4T + B4 I
3,5,6
(2.5)
For a given set of power measurements equations (2.5) represent three circles on the
T plane with their intersection point representing the DUT's reflection coefficient
(as illustrated in Figure 2.2) where the centers of the circles are denoted as q3, q5,
and q6.
Fundamentally, the DUT's reflection coefficient (r) is an implicit function of
the detected powers P 3 , P 4 , P 5 and P6 as indicated by (2.5). This function is only
dependent on the coefficients {A} and {Bi}, which are a property of the six-port
Chapter 2. Six-Port Reflectometers and Sampled Line Reflectometers
13
U.T)
Figure 2.2. Determination of T from the intersection of three circles represented
by equations (2.5).
linear network and the power detectors. After proper calibration, the A,'s and Bi's
(normalized with respect to 5 4 ) can be completely determined and any DUT's
reflection coefficient can thus be solved from (2.5) with power measurements P 3 ,
P4, F 5 and P 6 .
If the DUT is known apriori to be passive (|T| < 1), a simplified class of six-port
reflectometers that only require five power detectors can be used [2]. These are
called five-port reflectometers and include the sampled-line reflectometers that will
be discussed later in this chapter. As shown in Figure 2.3 where power detector
PQ has been omitted, five-port reflectometers are designed in such a way that the
straight line between q$ and q& does not intersect the unit circle on the T plane and
the intersection point beyond the unit circle can thus be rejected. However, fiveport reflectometers suffer from degraded precision compared to properly designed
six-port reflectometers because the intersection point, in a direction perpendicular
to the line between q3 and q5, has high sensitivity to power measurement errors [3].
Chapter 2. Six-Port Reflectometers and Sampled Line Reflectometers
14
Im(r)
- k'\
unit circle
Figure 2.3. Determination of T (\T\ < 1) for a five-port reflectometer.
2.2
Six-Port Reflectometer Calibration
There are many algorithms that have been developed for calibrating six-port reflectometers, a brief survey will be presented in Chapter 4. The calibration by means
of sliding terminations given by Engen is among the most widely used [3] [4]. This
method divides the calibration procedure into two steps: first, a reduction from
the six-port to a virtual four-port reflectometer that is accomplished using sliding
terminations; second, calibration of this virtual four-port reflectometer using the
well-known technique based on three known standards. The theoretical foundation
of this calibration method will be summarized next.
If the wave amplitudes incident onto detectors 3 and 4 (63 and 64) are chosen
as the two independent variables of the six-port network, the wave amplitudes into
ports 5 and 6 (65 and 66) can be written in terms of linear combinations of them:
65 = Kb3 + LbA
(2.6)
b6 = Mb3 + Nbi
(2.7)
Chapter 2. Six-Port Reflectometers and Sampled Line Reflectometers
15
where the complex coefficients K, L, M, and TV are constants of the network. With
(2.2), these relations are readily manipulated into the well-known form,
M2 = §
where wx = -L/K,
(2-8)
\w-Wl\2
= Cji
(2.9)
\W-W2f
= p^
(2.10)
w2 = -N/M,
( = 1/|K|2, p = 1/|M| 2 , and
w=^
(2.11)
Equations(2.8-2.10) describe a set of three circles in the w-plane (Figure 2.4), the
intersection of which determines the complex ratio w. Solving w in (2.8-2.10)
yields its real and imaginary parts
Re\w\ = —•
;—;
!
——
(2.12a)
2|wi|
,m{w} _ fl/fl-Aft/f. + h > l ' - i t / m W - f e { « }
(2126)
It can also be shown from (2.1), (2.4) and (2.11) that w is a bilinear transformation
where A = ^ 3 / ^ 4 , B = B3/Bi
and C = A4/B4.
Equation (2.13) illustrates
that the six-port is converted to a four-port reflectometer, with w regarded as the
"indicated" (or pre-calibrated) reflection coefficient. It should be noted in Figure
2.4 that w\ can be placed on the positive part of the real axis because the phase
of wi may be arbitrarily set to zero [4] [5]. The phase of w\ does not have effect
on the six-port to four-port reduction because it amounts to rotating the entire
w-plane and the form of (2.13) is invariant under w plane rotation.
The calibration step of reduction from the six-port to the virtual four-port
reflectometer involves determining the coefficients (wi, w2, (, and p) in (2.12). Once
this calibration step is done, the calibration of the virtual four-port reflectometer is
performed by finding coefficients (A, B and C) in (2.13) by one of several standard
Chapter 2. Six-Port Reflectometers and Sampled Line Reflectometers
16
Im(W)
Re(W)
Figure 2.4. Determination of w from three circles represented by equations (2.8)(2.10).
techniques [6]. The typical approach uses three calibration standards: an open
load (r o = 1), a short load (r s = — 1) and a matched load ( r m = 0). Letting their
corresponding w's be w0, ws and wm, then A, B, and C can be solved from a set
of three linear equations produced by (2.13):
( r
B
1
-Wo • r 0 V
I w
wss \
• Ys
W0
-ws
J
(2.14)
\wW„
m J
To determine w\, (, W2, and p, Engen has suggested using a sliding termination
that traces out a circle on the (r) plane. Since it; is a bilinear transformation of T
as in (2.13), the sliding termination also traces out a circle on the w plane:
\W - Rr? = R2
(2.15)
where it is not necessary that Rc and R to be known for the purpose of calibration.
With (2.8), (2.9) and (2.15), the sliding termination traces out on the P3/F4—
Chapter 2. Six-Port Reflectometers and Sampled Line Reflectometers
17
P5/P4 plane an ellipse of which the shape and position can be found from a leastsquares fit. w\ and ( are determined from the shape and position of the ellipse
[4] [5]. However, several sign ambiguities are encountered in this process and they
must be resolved by either additional measurements or detailed prior knowledge
of the six-port network architecture [3-5]. The sign ambiguities are dependent on
two considerations: first, whether the origin of w-plane lies inside the circle traced
out by the sliding termination; second, whether the point wi lies inside the same
circle. Five-port reflectometer architectures usually resolve the sign ambiguities by
requiring in their design that the circle and the line between the origin and Wi do
not intersect [4]. As for general six-port reflectometers, additional measurements
that are independent of the sliding termination measurements are performed to
resolve the sign ambiguities as well as to solve w2 and p [4].
2.3
Sampled-Line Reflectometers
The sampled-line reflectometer is an example of a six-port reflectometer and was
first demonstrated by Williams in 1989 [7]. As shown in Figure 2.5, it consists of
a transmission line with one end connected to a signal source and the other end
to a DUT. A set of power detectors are placed along the transmission line, each
tapping a small amount of power from the transmission line and thus sampling
the magnitude of the standing wave on the line. For a five-port reflectometer
implementation, a set of three detectors are used.
If the distance between the power detectors P4 and P5 is less than a half wavelength at the operating frequencies, then it can be shown the u;'s corresponding to
passive DUT's (|r| < 1) lie below the real axis (or Im{w} < 0) [11] [5].
For an ideal sampled-line reflectometer, the wave amplitudes incident onto each
detector (6j, i=3,4,5) are proportional to the standing wave amplitudes on the
transmission line:
63 = h3(a2 • e*fc+fc) + b2 • e -^+*3))
b4 = h4{a2 • e ^ + ^ 3 )
+ b2
. e-j(*+«a+fc))
(2.16)
(2.17)
Chapter 2. Six-Port Reflectometers and Sampled Line Reflectometers
h e, -+- e2 + e3
18
i-^-a2
K-b2
•€
0
Microwave/"^
Synthesizeiky
P4
0
0
P3
P5
V
MDUT
V
Figure 2.5. Architecture of a sampled-line reflectometer.
h = h5(a2 • ej9s + b2 • e-jf>3)
(2.18)
where h3, /i 4 , and /i5 represents the ratio between wave amplitude to each power
detector and standing wave voltage on the through line. a2 and b2 can be solved
from equations (2.16) and (2.17) as linear combinations of b3 and 64:
a-2
^
h3
hi
(ej(02+03-0i) _ ej(02+03+0i))
/l4
h3
(e-j(«2+«3-ei) _ e-j(02+03+<?l))
(2.19)
(2.20)
Substituting equations (2.19) and (2.20) into (2.18) yields:
0
ej(82+e3-6i) _ ej(02+03+0i)
' e-j(e2+e3-e1) _ e-j(82+o3+6i)
(2.21)
After some algebraic manipulations, equation (2.21) can be simplified to
h5sm(di + 82),
h5 sin 62
°5 = I
^~a ° 3 ~~ 7 — r _ 5 - 6 4
ri3 sin &i
hi sin #i
(2.22)
Comparing equation (2.6) and (2.22), we have for this idealized case of a sampled•¥^-, and
line reflectometer K = £5 5in(*l+M L
«4 sin 0i '
h3
sin 6*i
'
h« sin 0o
(2.23)
Wl
K
/i4 s i n ^ + 02)
From (2.23), u;i is a positive real number for 9X + 82 < n.
From equations (2.16) and (2.17), we have
_ 63 _ /l3
W
e.7(02+03) +
~ b4 ~ hA ' ej(«i+02+03) +
Ye-j(e2+e3)
Te-^+e*+e*)
(2.24)
Chapter 2. Six-Port Reflectometers and Sampled Line Reflectometers
19
Im(W)
Re(W)
solution
Figure 2.6. Determination of w by two circles represented by equations (2.16a)
and (2.16b). The intersection point above the real axis is rejected.
Equation (2.24) can be rewritten as
w=
(2.25)
hi 1 + re-ASi+fc+fc)
From Equation (2.25), the imaginary part of w can be expressed as
Im{wx
h
=
>
(iri2-!)^^
(2.26)
It is easily seen from equation (2.26) that Im{w} < 0 for |T| < 1 and s i n ^ > 0.
With this property, w\ and £ can be solved without ambiguity from the measurements of a sliding termination, (as mentioned in the proceeding section, this
is common for a five-port reflectometer.) This property also makes it possible to
solve for w in terms of P3, P4, and P5 from (2.8) and (2.9) (illustrated by Figure
2.6):
Re{w}
P3/P4-CP5AP4+KI
Im{w} = -Jj-
2K|
(2.27a)
- (Re{w})2
(2.276)
The reduction from the six-port to a virtual four-port reflectometer is achieved by
(2.27) with known w\ and (.
Chapter 2. Six-Port Reflectometers and Sampled Line Reflectometers
I
6
Microwave,
Synthesize
6
P6
P3
P5
20
0
DUT
T
V
Figure 2.7. Extension of the operating frequency range of a sampled-line refiectometer by adding an additional power detector.
i-»a2
x-b2
HNM
Microwave,
Synthesize:
6
0
P3
P5
attenuator
0
DUT
V
Figure 2.8. An attenuator added for eliminating potential deep voltage nulls
The power detectors are usually uniformly spaced along the transmission line
(#i = 62 in Figure 2.5). To extend the operating frequency range of a sampled-line
reflectometer, a fourth power detector (P 6 ) can be placed halfway between a pair of
adjacent power detectors (P3 and P5, for example) as shown in Figure 2.7 [11] [5].
The new power detector triplet (P 3 , P6 and P5) can be used at twice the operating
frequency of the original triplet (P 4 , P 3 and P 5 ). This procedure can be continued
on to extend the operating frequency range provided room exists for the detector
sampling probes.
One practical issue in implementing a sampled-line reflectometer is that deep
voltage nulls might occur on the transmission line when the standing wave ratio
(SWR) is very high (i.e. the magnitude of the reflection coefficient is close to 1
because SWR
= (1 + | r | ) / ( l — | r | ) ) . This requires the ability to detect accurately
Chapter 2. Six-Port Reflectometers and Sampled Line Reflectometers
21
very low levels of microwave power, which can present serious difficulties and result
in higher measurement uncertainty. To address this problem, an attenuator can be
placed between the sampled-line reflectometer and the DUT which effectively reduces the SWR on the transmission line. Because the attenuator can be considered
as part of the overall six-port, its effect can be calibrated out of the measurements.
However, the attenuator also increases the minimum reflection coefficient (|r| m j„)
that can be measured with prescribed accuracy if the measurement noises (Ar)
for both cases are assumed equal. More specifically, the | r | m j n for the case with an
attenuator of X dB attenuation is 2X dB higher than that for the case with no attenuator because r'no-attenuator = S^ • ?with-attenuator where S2i is the transmission
coefficient of the attenuator.
Compared to most six-port reflectometer architectures, the sampled-line reflectometer is simple, requires few components is amenable to planar integration.
This is especially advantageous and attractive for scaling to millimeter-wave and
sub-millimeter-wave frequency bands.
2.4
Previous Sampled-Line Reflectometer Work
at t h e University of Virginia
Due to the simplicity and capability of being scaled to higher frequency, Ulker et.
al. have implemented sampled-line reflectometers in the millimeter-wave and submillimeter-wave bands [5]. Fig. 2.9 shows a split-block view of one implemented
sampled-line reflectometer operating up to 300GHz. The sampled line itself is
a waveguide channel with three equally-spaced identical channels perpendicular
to it. Placed in these three channels are quartz-supported microstrip circuits that
sample the traveling waves in the sampled-line waveguide (or stated in another way,
tap a small amount of RF power from the sampled-line waveguide). A Schottky
detector diode chip is mounted to each quartz circuit. One side of the diode is DCconnected to the block (ground) using a bond wire. The bond wire is approximately
quarter-wavelength long to present an open circuit to the diode at the frequency
Chapter 2. Six-Port Reflectometers and Sampled Line Reflectometers
22
Figure 2.9. Photograph of a sub-millimeter-wave sampled-line reflectometer presented in [5].
of operation. On each quartz circuit, there is a stepped-impedance low pass filter
following the detector diode and DC voltages are measured at the end of the low
pass filter.
The six-port to four-port reduction is performed using a custom-made sliding
waveguide short and the four port calibration is done with three off-set short-ended
waveguides. The capability of sampled-line reflectometers using this approach has
been demonstrated up to the 300 GHz region
Bibliography
[1] C.A.Hoer,K.C.Roe, "Using an arbitrary six-port junction to measure complex
voltage ratios," IEEE Trans. Microwave Theory Tech., vol. MTT-23, pp. 10751080, Dec. 1975.
[2] C.A.Hoer,
"Using six-port and eight-port junctions to measure active and
passive circuit parameters," National Bureau Stand. Tech., note 673, Sept.
1975.
[3] G.F. Engen, "The six-port reflectometer: an alternative network analyzer,"
IEEE Trans. Microwave Theory Tech., vol. 25, no. 12, pp. 1075-1080, Dec.
1977.
[4] G.F. Engen, "Calibrating the six-port reflectometer by means of sliding terminations," IEEE Trans. Microwave Theory Tech., vol. 26, no. 12, pp. 951—957,
Dec. 1978.
[5] S Ulker, "Sampled-line reflectometer for millimeter and submillimeter-wave
network measurements,"
Ph.D. Dissertation, University of Virginia, Char-
lottesville, VA 2002.
[6] Application Note 8510-5B, "Specifying Calibration Standards for the Agilent
8510 Network Analyzer," Agilent Technologies, Inc., P.O. Box 50637, Palo
Alto, CA 94303-9511; website: www.agilent.com.
[7] W.L. Williams, "Computer Aided Measurements of Microwave Circuits," Ph.D.
Dissertation, California Institute of Technology, Pasadena, CA 1989.
23
Chapter 3
A Non-Contacting Sampled-Line
Reflectometer
3.1
introduction
The method used for sampling travelling waves at the port(s) of a DUT and the
measurement system architecture are the two key issues for the design of noncontacting s-parameter measurement systems. Non-contacting reflectometers (i.e.
one-port s-parameter measurement systems) were pioneered by Stenarson and et.
al. [1]. Their system was based on suspended coaxial sampling probes connected
to a commercial vector network analyzer and accurate measurements up to 20 GHz
were demonstrated [1]. However, this method requires precise probe positioning
(especially along the vertical direction), which presents difficulties in terms of measurement precision and repeatability for these systems. The repeatability is related
to exact placement of the probe above the circuit as well as precise alignment of the
relative positions of the probes. Using separate probes will always introduce some
uncertainty and this uncertainty become more severe as the operating frequency
is increased. In addition, the measurement system demonstrated by stenarson is
typically not stand-alone and requires a commercial vector network analyzer to
measure the sampled voltage ratios.
In this chapter, a planar probing structure that significantly reduces position-
24
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
25
ing error while enhancing the measurement repeatability (compared to separate
and manually-assembled coaxial probes) is utilized to sample the travelling waves.
In addition, the planar structure is suitable for monolithic integration. A fiveport sampled-line reflectometer architecture that uses zero-bias Schottky detector
diodes is described in this chapter - providing the additional advantage that the
measurement system is stand-alone, eliminating the requirement for a commercial
vector analyzer. Schottky detector diodes are utilized as power detectors in this
work and care is taken that they are operated in their square law detection region where the DC voltage response is proportional to the input RF power. An
advantage of this approach is that schottky diodes have the potential for being
monolithically fabricated with other circuitry to form a completely integrated noncontacting measurement system.
Before presenting the design and measurements used to characterize the sampledline non-contacting reflectometer, a basic and critical principle of non-contacting
refiectometers will be described first. Specifically, it will be shown analytically
that the measured reflection coefficient by a non-contacting reflectometer is independent of the source impedance. Although this principle is fundamental to circuit
theory, its importance lies in the fact that, for non-contacting in-situ measurement
in particular, the impedance of the source driving the calibration standards may
be significantly different from that driving an in-situ DUT. It is pointed out in [1]
(and is evident from fundamental circuit theory) that, if the voltage across and
the current into a DUT are measured simultaneously, then the DUT impedance is
simply the ratio of the two, independent of the source impedance. In practice, the
sampled voltages (Ki and V^2)are different linear combinations of the voltage and
current:
Vai=PfV
+ qi-I
VS2 = P2 • V + q2 • I
This leads to a bilinear transformation between impedance (Z — X-) and the ratio
of the sampled voltages:
v
V.2~
Ei.z + ^
a
•Z+1
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
26
The procedure of calibration is to obtain the coefficients in this bilinear transformation (pi/q2, Qxlli
an
d V2lli)- However, in order to perform a meaningful
calibration, the coefficients in this bilinear transformation (pi/<?2, Qi/o.2 and P2/92)
have to be independent of load impedance (Z) and the impedance of the RF source.
This property is not yet proven formally in literature to author's knowledge and
will be derived in the following section.
3.2
Principles of a Non-Contacting Reflectometer
Before the measurement of an in-situ DUT, a non-contacting reflectometer must
be calibrated. As shown in Figure 3.1., the signal source that drives the calibration
standards may have a different impedance than the preceding stage of an in-situ
DUT. Thus successful non-contacting measurement demands the independence of
the raw (or un-calibrated) reflection coefficient on the source impedance (Za), which
will be demonstrated next.
Shown in Figure 3.2. is a generic block diagram of a four-port reflectometer
measurement system where the raw reflection coefficient (w — 63/64) can be either
measured with a vector voltmeter as in [1] or derived from a five-port/six-port
power detector measurements. Ports 3 and 4 of the reflectometer are terminated
with impedances (Z3 and Z\) that are not necessarily matched to the reference
impedance (Zo) for the s-parameters. Depending on the actual implementation
of the non-contacting reflectometer, these impedances represent either the input
impedances of a vector voltmeter or those of the power detectors. Let's define the
associated reflection coefficients as:
rfc = § ^ | ^
= 3,4)
(3.1)
The 4 by 4 s-matrix of the reflectometer yields
61 = Snai + 5i 2 a 2 + Sua3 + 5i 4 a 4
(3.2)
62 = S2\ai
(3.3)
+ S22d2 + S23a,3 + 52404
27
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
flfc
9bJ
Non-contacting
reflectometer
signal
source
for
calibration
calibration
standards
ib3
pb'
W=
Non-contacting
reflectometer
preceding stage
—I
1 >
in-situ DUT
1Zs
Figure 3.1. Measurement procedures for a non-contacting reflectometer, illustrating the source impedance difference between calibration and in-situ DUT measurement.
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
28
zsh nz4
a3b3
Mi
|atb4
'it.
Non-contacting
reflectometer
biai •
-&2
• b2
Zs
DUT
^
Figure 3.2. Generic block diagram of a four-port reflectometer.
h = S3idi + 5 3 2 a 2 + 53303 + 5 3 4 a 4
(3.4)
64 = 54iai + 54202 + ^4303 + 544O4
(3.5)
with two boundary conditions:
«3 = r 3 o 3
(3.6)
a 4 = Tibi
(3.7)
Plugging (3.6) and (3.7) into (3.4) and (3.5) and solving 63 and 64 in terms of ai
and 02 yields
M-
a\
(3.8)
a-2
where
M
( 1 - 5 33 r 3 )
—534r4
-543r3
(1 — 5441^4)
(3.9)
On the other hand, substituting (3.6) and (3.7) into (3.3), ai can be expressed as:
1
a\ = -^-h
o2i
522
523
524
- — o 2 - — r 3 6 3 - —r4fe4
o2i
o2i
o2i
,,.„>
(3.10)
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
29
Substituting 63 and 64 in (3.10) with a\ and a2 using (3.8), equation (3.10) becomes
ai = ^-b2
021
- - ^ a 2 - ^ r 3 ( M 1 1 a 1 + M12a2) - - ^ r 4 ( M 2 1 a 1 + M22a2)
o2i
o2i
o2i
(3.10)
Solving ai in terms of a2 and b2 in (3.10) yields:
Ol = £l&2 + 6 « 2
(3.11)
where
6=
6=
1
521 + S23T3Mn + S2iT4M21
S22 + S^T^M^ + S ^ ^ - A ^
(3.12)
(3.13)
Subsequently we have
(3.14)
Combining (3.8) and (3.14) gives:
(3.15)
where
N =M •I ^
^2 I
(3.16)
Prom (3.15), the raw measured reflection coefficient (w = 63/64) can be obtained
Nu + iv12rL
W
= N21
+
N22TL
^
where FL = a2/b2 is the reflection coefficient of the DUT. It can be observed from
(3.17) that the raw measured reflection coefficient is a bilinear transformation of the
true reflection coefficient of the DUT. Furthermore, this transformation is only dependent on the reflectometer and NOT dependent on the source impedance. Thus,
the raw measured reflection coefficient is independent of the source impedance.
To verify this property experimentally, a four-port reflectometer measurement
system is set up as in Figure 3.3. The four-port network itself is a 3-dB directional
coupler. Due to the lack of a separate, stand-alone vector voltmeter, a calibrated
30
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
]4r switch
port2
Vector
Network
Analyzer
portl
3dB
directional
coupler
i
DUT
Figure 3.3. Reflectometer measurement setup with a 50-ohm source impedance.
vector network analyzer (VNA) is used to act as the signal source as well as the
vector voltmeter. Port-1 of the VNA is fixed and acts as the signal source. Port2 of the VNA switches between the port-3 and port-4 of the directional coupler.
For each DUT, two sets of s-parameters are measured with the network analyzer
and the ratio of the measured S2\ is taken as the raw reflection coefficient of the
DUT. A short, an open and a matched load are used to calibrate the four-port
reflectometer. A 0-dB attenuator (with the un-connected port left open) is then
measured and its raw reflection coefficient is converted to the calibrated one.
To vary the source impedance, the refletometer measurement system is modified
as shown in Figure 3.4. The source impedance is varied by using a phase shifter
following a section of 30Q, transmission line. The same 0-dB attenuator is measured
again with this setup. The same bilinear transformation for the setup in Fig. 3.3
is used to convert the raw reflection coefficient to the calibrated one.
Figure 3.5. shows the magnitude and phase of the reflection coefficients for the
0-dB attenuator measured under different source impedances. These data show
very good agreement with one another and the small discrepancies between them
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
31
switch
Vector
IJEEE.
Network
Analyzer >
portl
y
30Q Mine
0^H
phase shifter
Figure 3.4. Reflectometer measurement setup with a varying source impedance.
are probably due repeatability issues related to the flexible cables used in the
measurement.
3.3
Design and Simulation
Figure 3.6 shows the basic configuration of the prototype non-contacting reflectometer studied initially in this work. This instrument configuration is based on
the sampled-line reflectometer architecture and figure 3.7 shows a photograph of
the circuit. Its center design frequency is chosen to be 1 GHz such t h a t the circuits
are large enough to be easily assembled and controlled by a positioner. The reflectometer consists of a section of 50 Q microstrip line and a set of four sampling
probes. The microstrip line is fabricated on a Roger's RT/Duroid
6010.2 substrate
(er — 10.2, thickness = 1.27 mm) with panel-mount SMA connectors attached to
the input and DUT ports. The sampling circuit, which is mounted on an X-Y-Z
positioner (Newport 460P-XYZ) and is fabricated on a Roger's RT/Duroid
5880
substrate (e r — 2.2, thickness of 1.575 mm), consists of four rectangular probes.
The probes feed C P W transmission lines that are terminated with zero-bias Schottky diode detectors (Pasternack PE8013). The input to the microstrip throughline is connected to a microwave synthesizer (Systron Donner, model 1626) and
32
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
~ -1
m
I -2
c
o>
n
II
-*-n
->-r_pi
-«-r_P2
6.5
5.5
Frequency(GHz)
180
120
-60
-120
-180
Frequency(GHz)
Figure 3.5. Magnitude and phase of the 0-dB attenuator measured under different
source impedances (Ti corresponds to the situation without the 30Q transmission
line and phase shifter, Tpi and Tp2 with the 30Q transmission line and phase shifter
at different phase shifts.)
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
33
diode detector
positioner
SMA flange
RF signal]
CAL
EZB-DUT
standards
attenuator
microstrip thru line
Figure 3.6. Basic configuration of non-contacting reflectometer based on sampledline reflectometer architecture.
Figure 3.7. Photograph of the non-contacting reflectometer.
34
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
m
•D
"C
0)
»
E
2
(S
Q.
^^°°°
0.75
0.90
-*-|S31| -o-|S41| -*-|S51| -"- |S6111
1.05
1.20
1.35
1.50
Frequency(GHz)
Figure 3.8. Simulated couplings for a probe-to-through-line distance of 200/um.
the output connects to coaxial calibration standards or DUT's. The outputs of
the diode detectors are measured with a data acquisition instrument (IOTECH
DAQ/55) which is controlled by a notebook computer for automatic data collection. Although only three detectors are necessary for measuring passive loads, an
additional detector is employed as a backup. A 2-dB attenuator placed between the
probing structure and the DUT's/standards eliminates deep voltages nulls from occurring on the microstrip through line. It should be noted that, for a true "in-situ"
measurement environment, the calibration standards and the DUT's should be of
planar form. Nevertheless, the general approach and method of this technique can
be readily investigated using coaxial adaptors and loads for this proof-of-concept
demonstration.
Figure 3.8 and Figure 3.9 show the simulated coupling (l-S^I, i=3,4,5,6) from the
excitation port to the detector ports using Ansoft's High Frequency Structure Simulator (HFSS). These s-parameter simulations are used to determine the distance
from the probes to the circuit that yields a sufficient amount of power coupling to
each detector. Note, however, the operating principle of the sampled-line refiec-
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
35
-15
-16
17
m
•D
I
18
19
20
21
22
-^>-|S31| -o-|S41| - * - | S 5 1 | -»-|S61|
23
•24
0.75
0.90
1.05
1.20
1.35
1.50
Frequency(GHz)
Figure 3.9. Simulated couplings for a probe-to-through-line distance of 300/^m.
tometer is based on the assumption that Im{w} < 0 (where w is the "indicated"
reflection coefficient) for |T| < 1. Strictly, this is only valid for an ideal sampledline in which the probes do not influence the standing waves on the transmission
line. Consequently, to reasonably approximate a true sampled-line reflectometer,
the amount of power coupled to each detector should be large enough for precise
(high SNR) detection while preventing the probe structure from significantly disturbing the waves on the through line. Measurements have shown that a coupling
of less than 15 dB yields a minimum DC voltage of approximately 100/xV with an
RF source power of 5 dBm, which presents a signal to noise ratio of approximately
16 with a measured 6/xV standard deviation of the DC measurement noise.
3.4
Measurements and Analysis
The non-contacting sampled-line reflectometer described above was calibrated using Engen's sliding termination technique and the resulting virtual four-port network was subsequently calibrated using an open, short, and matched termination
from a Hewlett-Packard 85052D calibration kit. To evaluate the operation of the
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
0.75
0.90
1.05
1.20
36
1.35
1.50
Frequency(GHz)
Figure 3.10. Measured and simulated couplings for a probe-to-through-line distance of 300/xm.
reflectometer, a set of sample loads with various magnitude and phase responses
were measured, including a variety of fixed attenuators. Measurements of the same
loads were performed with a Hewlett-Packard 8720C Vector Network Analyzer to
serve as a reference for comparison.
3.4.1
Measurements
The coupling from the excitation port to the detector ports were measured with
HP8720C. In Figure 3.10, they are compared to the simulation results. The measured couplings are less than 15 dB and there is general agreement between the
simulated and measured results in terms of overall magnitude. Differences between
the measured and simulated values, on this scale, can be attributed to several factors, including the open structure of the instruments and small difference in the
source or load impedance (associated with coaxial microstrip launchers)
As discussed in chapter 2, the response of a sliding termination traces out an
eclipse on the P3/P4—P5/-P4 plane of which the shape and position can be found
37
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
-0.002 h
<D -0.004
+->
1
-0.006
-0.008
10
40
70
100
130
160
phase shift (degrees)
Figure 3.11. Measured V3, V4, V5, and V6 versus electrical length of the sliding
short at 1.2 GHz.
Figure 3.12. Ellipse traced out by the sliding short on P3/P4 versus P5/P4 plane
at 1.2 GHz.
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
38
/
Wi V
-Is
1 -\
\
-li
'a
-
0.5
i
(•
i.s
-0.5'
-I.J-'
Two circles in w plane when DUT is 5dB attenuator at 1.0GHz
Two circles in w plane when DUT is 6dB attenuator at 1.1 GHz
Figure 3.13. Two circles on the w plane when DUT is a 6dB attenuator over the
frequency from 0.9GHz to 1.1GHz.
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
39
Two circles in w plane when DUT is 6dB attenuator at 1.3GHz
Figure 3.14. Two circles on the w plane when DUT is a 6dB attenuatorover the
frequency from 1.2GHz to 1.4GHz.
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
40
-11
=*«g^
-12
-13
1-14
|-15
1-16
a
-•-rreflectometer
-17
-18
-19
-»-r8720
I
— I
0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
-20
Freqnency (GHz)
-70
-80
-90
1-100
£-110
«
«
-Ireflectometer
1-120
•^8720
-130
-140 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
Frequency (GHz)
-150
!
"""
I
-Jh -L-Li1_
j_ A
XX^P-r v v WJ-1-/L/
W
*
]/
0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1-50
Frequency(GHz)
j
A
71
I 3 Lh \I
?=V ^
5
0
0.75 0.80 0-8S 0 . M
0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45
1.50
Frau*ncy(GHz)
Figure 3.15. Comparison of reflection coefficients for a 6-dB fixed attenuator measured with the prototype reflectometer and an HP8720C network analyzer.
41
8)
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
*
••
f\
-A Ul
1
^J-
c
S
\
V \ 1\ /
\L
-\
i-"'
-Freflectometer
^8720
-250.7S 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
Frequency (GHz)
150
125
100
""*y
<^
v
V
75
: so
•
Oi
s. "S^.
2 . 25
s
1 o
-Freflectometer
a.
-25
-50
,s
-F8720
s
0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
Frequency (GHz)
0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
Frequency(GHz)
i
~j
A
i
/
4 i
7
t \;
/
/
k\
./
,
A
V
l\j
i
!/
A^\J/ / Jv \ \
V
A
<•>
nn
— I — I
0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 145 1.5
Frequency (GHz)
Figure 3.16. Comparison of reflection coefficients for a 10-dB fixed attenuator
measured with the prototype reflectometer and an HP8720C network analyzer.
42
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
1
o
2T-1
2.
1-2
-Freflectometer
-F8720
-5
0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
Frequency (GHz)
150
<s,
125
100
!
50
-Freflectometer
-25
-F8720
-50
-100
0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 120 1.25 1.30 1.35 1.40 1.45 1.50
Frequency (GHz)
0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
Frequency(GHz)
0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
Frequency(GHz)
Figure 3.17. Comparison of reflection coefficients for a 0-dB fixed attenuator measured with the prototype reflectometer and an HP8720C network analyzer.
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
43
from a least-squares fit. The shape and position of the ellipse determine the sixport calibration parameters w\ and (. Figure 3.11 shows the measured voltages at
ports 3-6 at 1.2 GHz as a function of position (phase shift) of the sliding short.
Figure 3.12 shows the corresponding ellipse traced out by the sliding short on the
P3/P4—-P5/P4 plane at 1.2 GHz. Figure 3.13 and Figure 3.14 show two circles
determined by the calibration parameters w\ and ( in the w plane at different
frequencies.
To serve as a basis for comparison, a set of fixed attenuators were measured
with both the prototype six-port reflectometer and a HP8720C vector network
analyzer. The HP8720C network analyzer typically has a magnitude measurement
uncertainty of 0.01 and a phase measurement uncertainty of 2.5 degrees for a
device under test with a reflection magntitude of 0.25 in the frequency range from
0.5 to 2 GHz [2]. Figure 3.15 and Figure 3.16 show the measurement of two
fixed attenuators (6 dB and 10 dB, both open circuited at the unused port) from
0.75 to 1.5 GHz using both the six-port reflectometer (calibrated with the method
explained in chapter 2.2) and the HP 8720C vector network analyzer (calibrated
with the familiar short-open-match technique [3]). Here, A r is defined as the
distance between the two measurements on the T-plane:
Ar = |r 8 7 2 0 -r 6 _ p o r t |
(12)
with T8720 the reflection coefficient measured with the HP 8720C and r6_p0rt the
reflection coefficient measured with the prototype six-port reflectometer. In addition, A r normalized with respect to r872o is also shown in percentage. For the 6
dB and 10 dB attenuators, the difference in the measured reflection coefficient is
less than -35 dB over the operating band of the reflectometer. The normalized A r
is less than 16%.
Figure 3.17 compares measurements done with the six-port and 8720C network
analyzer on a fixed 0 dB attenuator with open circuited at the unused port. Again,
the two measurements are reasonably close and the agreement between them is
typically better than -15 dB. The normalized A r is less than 14%.
Chapter 3. A Non-Contacting Sampled-Line Refiectometer
3.4.2
44
Measurement Sensitivity to Probe Position Error
To characterize the refiectometer measurement sensitivity to vertical and horizontal positioning, the probing structure is first shifted over a coarse scale by 100
/xm, 200 /xm, and 500 pm in both vertical direction (up) and horizontal direction
(perpendicular to the interconnecting transmission line). The measured reflection coefficient is then compared with the original measured value. Figure 3.18—
3.20 show the reflection coefficient difference in magnitude and phase caused by
these coarse displacements of the probing structure when measuring low-reflection,
medium-reflection and high-reflection loads. Following the coarse displacement
measurements, the probing structure is then shifted over a fine scale by 10 /xm, 20
/xm, 30 /xm, 40 /xm, and 50 /xm in both vertical and horizontal directions. Figure
3.21-3.23 show the reflection coefficient difference in magnitude and phase caused
by these fine displacements.
It can be noticed from the plots that the errors introduced by small displacements less than 50 /xm are very similar to each other and a displacement larger
than 100 /xm causes significant error. It is also observed that the error introduced
by displacement in the vertical direction is more severe than that by the same
amount of displacement in the horizontal direction.
Apart from displacement error, other measurement error sources likely include
connector repeatability between the two measurement systems, DC voltage measurement error and the diode's deviation from square law detection. Measurement
uncertainty resulting from these sources will be discussed in chapter 4.
3.5
Conclusions
A proof-of-concept non-contacting refiectometer consisting of a probing structure
that can be accurately and precisely positioned near an open, integrated structure
for in-situ one-port scattering parameter measurements has been demonstrated.
-35 dB and -15 dB measurement accuracy has been achieved for low-mediumreflection and high-reflection loads respectively. High-reflection coefficient loads
45
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
-5
[i—'
- * - | A r 100|jm|
-10
\v ^
- * • |Ar_200|jm|
l - i
-15 >
\
S -20
I—«
- B - |Ar_500jim|
d
^
s-i
^
c
\
<. -25
7
f\[\
! >
\ /
^
\
-40
0.75 0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
jr^j
J\
p
\
"""H
^
-30
-35
r
/ \
\
*!• " - I I
—-1
1.25
1.3
^
^
1.35
1.4
1.45
1.5
Frequency(GHz)
(a)
-10
*-|ar_iooMm|
-15
* • |ar_200 Hm|
e - | A r 500 j m |
-20
r>
£0
\
S-25
(-"* \
\
-30
/
'N
-35
-40
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
»-s.
TJ
/
1.4
s,
1.45
1.5
Frequency(GHz)
(b)
Figure 3.18. Measured reflection coefficient difference resulting from shifting the
probing structure in vertical direction (a) and in horizontal direction (b) by 100/xm,
200/rni, 500^m for the 3-dB attenuator.
46
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
-5
-10
-*-|A|-_100jim|
- * - | A r 200|im|
-S- |Ar_500pm|
-15
-20
§-*
r—H
-30
-35
-40
-45
0.75 0.8 0.85 0.9 0.95
1
1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5
Frequency(GHz)
(a)
-10
_ - * - | A r 100uml
• 1 Ar_200|jm|
Ar_500|jm
-15
-20
m
S.25
-30
-35
-40
0.75 0.8 0.85 0.9 0.95
1
1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5
Frequency(GHz)
(b)
Figure 3.19. Measured reflection coefficient difference resulting from shifting the
probing structure in vertical direction (a) and in horizontal direction (b) by 100/xm,
200/xm, 500/im for the 6-dB attenuator.
47
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
o
i
•*-
-5
-10 r i .
-e-
^
-15
.-20
-25
-30
-35
,k
V
< *
I
r
.V *fiN,
V
0
V
^
'
"> \
/ *
\
;
/
/r
V Jlf
J
i
Ar_100pm
Ar_200Mm
A r 500(jm
is^
/
t
y
M V\
/
^
\ ^ \
*J
/
\
/
\
\
/
\\
>^
\
\
s
^ ,
/
7
/ /
V
r~N
•
i
f*""^
i
V
\ \
W
V'
\
-40
i
-45
0.75 0.8 0.85 0.9 0.95
1
1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5
Frequency(GHz)
(a)
-10
-20
-30
-40
-50
-•-|Ar_100|jm|
•*-|Ar_200Mm|
- B - |Ar_500Mm|
-60
]•
-70
0.75 0.8 0.85 0.9 0.95
1
1.05
1.1
1.15
1.2 1.25
1.3 1.35
1.4 1.45
1.5
Frequency(GHz)
(b)
Figure 3.20. Measured reflection coefficient difference resulting from shifting the
probing structure in vertical direction (a) and in horizontal direction (b) by 100//m,
200/xm, 500/^m for the offset short.
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
-10
-15
48
I J^
A
-20
-25
_ -30
CO
£-35
-•-|Ar_10Mm|
• * • |Ar_20Mm|
|Ar_30nm|
|ar_40|jm|
- * - |Ar_50|jm|
-40
-45
-50
^
\S
S.
HNfc*
$c
s>
\ l
|
-55
-60
0.75
0.8
0.85
0.9
0.95
1
:
\
1.05
1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5
Frequency(GHz)
(a)
-10
-15
II
^ _
-+-L if 10(jm
•m-t kr_20pm
-20
••**•• AI~_40Mm
- * - A r 50 ••"
-25
L > -
Sf
*-30
Y\
<_
-35
T
-40
-45
-50
0.75
1 fo*\
vJS^j
\ >
^
0.8 0.85 0.9 0.95
1
1
1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5
Frequency(GHz)
(b)
Figure 3.21. Measured reflection coefficient difference resulting from shifting the
probing structure in vertical direction (a) and in horizontal direction (b) by 10/xm,
20/xm, 30/xm, 40^m, 50^m for the 3-dB attenuator.
49
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
-50 4
1
1
1
1
0.75 0.8 0.85 0.9 0.95
1
1
1
1
1
1
1
1
1
1
1
1
1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5
Frequency(GHz)
(b)
Figure 3.22. Measured reflection coefficient difference resulting from shifting the
probing structure in vertical direction (a) and in horizontal direction (b) by 10/zm,
20/xm, 30/xm, AOfira, 50yum for the 6-dB attenuator.
50
Chapter 3. A Non-Contacting Sampled-Line Reflectometer
-10
ar_i0|jm|
&r 20(jm|
-15
iar_30pm|
-20
-25 tk
-30
i
—
—-
\ \
&r_40|jm| ar_50jjm|
7
I
5^-35
/1
-40
\
v 7/T ^
\
-45
\
-50
>W
/"7\\
V V
i
-55
-60
0.75 0.8 0.85 0.9 0.95
1
1.05 1.1
1.15 1.2 1.25 1.3 1.35 1.4 1.45
1.5
Frequency(GHz)
(a)
-10
-20
-30
"*>J
r~*
£\
<
^
h—-j
ifV^".'
-40
|Ar_10pm|
-m-|Ar_20|jm|
|Ar_30|jm|
|Ar_40|jm|
|Ar_50Mtn
-50
V*s
-60
!
-70
0.75 0.8 0.85 0.9 0.95
1
1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45
1.5
Frequency(GHz)
(b)
Figure 3.23. Measured reflection coefficient difference resulting from shifting the
probing structure in vertical direction (a) and in horizontal direction (b) by 10/xm,
20^m, 30/xm, 40/zm, 50/xm for the offset short.
Chapter 3. A Non- Contacting Sampled-Line Reflectometer
51
present relatively high measurement inaccuracy. However, when normalized to
the magnitude of the reflection coefficient, the accuracy for high-reflection loads
become comparable to that for low-medium reflection loads. It should be noted that
the larger error associated with the measurement of high-reflection loads may be
due primarily to the five-port architecture of the instrument. It has been noted by
others and discussed in the beginning of Chapter 2 that the five-port reflectometer
exacerbates measurement error when applied to high-reflection loads. [4]
Bibliography
[1] J. Stenarson, K. Yhland, C. Wingqvist,
"An in-circuit noncontacting mea-
surement method for s-parameters and power in planar circuits," IEEE Trans.
Microwave Theory Tech., vol. 49, no. 12, pp. 2567-2572, Dec. 2001.
[2] "HP8719C/8720C Network Analyzer Service Manual," Agilent Technologies,
Inc., P.O. Box 50637, Palo Alto, CA 94303-9511; website: www.agilent.com.
[3] Application Note 8510-5B, "Specifying Calibration Standards for the Agilent
8510 Network Analyzer," Agilent Technologies, Inc., P.O. Box 50637, Palo
Alto, CA 94303-9511; website: www.agilent.com.
[4] G.F. Engen, "The six-port reflectometer: an alternative network analyzer,"
IEEE Trans. Microwave Theory Tech., vol. 25, no. 12, pp. 1075-1080, Dec.
1977.
52
Chapter 4
Calibration of Six-Port
Reflectometers Using Null Double
Injection
4.1
Introduction
Of the many algorithms that have been developed for calibrating six-port reflectometers, the six-port-to-four-port reduction technique given by Engen is among
the most widely used [1]. This technique, described in chapter 2, typically employs
a sliding termination that traces out a circle in the reflection-coefficient (r) plane,
constraining the power readings taken at the six-port measurement ports to lie on
a quadratic surface (paraboloid) in three-dimensional "P"-space (or power-space).
The six-port-to-four-port reduction coefficients can be found from a least-squares
fit to this paraboloid and results in a virtual four-port equivalent reflectometer
with error coefficients that can be determined by one of the numerous standard
methods for calibrating four-port network analyzers.
The popularity of Engen's technique derives from its inherent advantages: the
calibration process is divided into two well-defined steps, no apriori known standards are required for the six-port-to-four-port reduction, the procedure is compatible with automation, and the redundancy present in the power measurements
53
Chapter 4. Calibration of Six-Port Reflectometers Using Null Double Injection 54
can be exploited to improve estimation of the six-port-to-four-port reduction parameters and enhance the accuracy of measurements made with the instrument.
The success of the technique has spawned numerous variations and refinements
— most designed to assist in determination of the network coefficients [2], avoid
singularities [3], compensate for ill-conditioned reflectometer configurations [4] [5],
enhance bandwidth [6], adapt to different propagation media [7], or facilitate automation and convenience. Most often, these methods utilize some combination
(usually five or more) of sliding terminations, offsets, or other standard loads.
In this chapter, we propose and demonstrate an alternative technique for the
six-port-to-four-port reduction algorithm that requires no terminations and can be
implemented and automated using only a few widely-available microwave components. The technique is based on "null double injection," a concept that has found
important application as an analytical tool in circuit theory [8] and consists of
driving a network with independent sources at two excitation points to produce a
null at a given measurement point.
4.2
Background and Theory
The fundamental operation and theory of the six-port reflectometer has been described in detail in chapter 2 and here we will only summarize the basic relations
pertinent to developing the null double injection method. Figure 4.1 illustrates the
general architecture of the six-port reflectometer in which port 1 is the excitation
port, the device under test (DUT) is placed at port 2, and ports 3-6 represent
the power measurement ports. Because the six-port network is assumed linear and
all ports properly terminated, the wave amplitude emerging at any port (&,) can
be expressed as a linear combination of two independent inputs to the network
(for instance, ai and a 2 ). It is convenient to follow Engen's development [1] in
which the wave amplitudes emerging at ports 5 and 6 are written in terms of those
emerging at ports 3 and 4:
65 = Kb3 + L64
(1)
Chapter 4. Calibration of Six-Port Reflectometers Using Null Double Injection 55
1
*b3 J ft
&
Linear Six-Port
Network
^
DUT
ra
Microwave
Synthesizer
i
Power Detector
Figure 4.1. Diagram of a general six-port reflectometer, the six-port network is
assumed to be linear.
66 = M63 + Nb4
(2)
where the complex coefficients K, L, M, and TV are constants of the network.
These relations are readily manipulated into the well-known form,
N2 =
,|2
(3)
\lV — Wi\2 = £
(4)
be 2
\W-W2\
where w = b3/h,
Wl
= -L/K,
(5)
=/0
w2 = -N/M,
( = 1/\K\2, and p = 1/\M\2.
Equations (3-5) describe a set of three circles in the w-plane (Figure 4.2), the
intersection of which determines the complex ratio 63/64. Once this ratio has been
determined, the six-port reflectometer has effectively been reduced to an equivalent
four-port that is calibrated by one of several standard techniques [9].
Transformation of the six-port to an equivalent four-port reflectometer is achieved
once the three scalar parameters, p, (, and wi, and one complex parameter, W2,
Chapter 4. Calibration of Six-Port Reflectometers Using Null Double Injection 56
I Im(W)
Figure 4.2. Illustration of the circles in the w-plane denned by equations (3)-(5).
have been determined through a calibration procedure. Engen's six-port-to-fourport reduction method consists of observing the power detected at the four measurement ports for different positions of a sliding termination. As mentioned previously, the constraint imposed by the sliding load produces a quadratic surface
in "P-space." A two-dimensional section of this surface is an ellipse and its coefficients can be determined through a least-squares fitting. An inconvenience of the
method is that the coefficients of the quadratic are indirectly related to the desired
six-port parameters (p, £, w\ and u^), requiring a series of algebraic manipulations
to complete the six-port-to-four-port reduction. Furthermore, several sign ambiguities are encountered in this process and they must be resolved by either additional
measurements or detailed prior knowledge of the six-port network architecture [1].
In contrast to calibration methods that rely on observing the response of the
reflectometer resulting from various loads placed at the DUT port (port 2), the
null double injection technique is based on simultaneously driving the source and
DUT ports (ports 1 and 2) with a pair of phase-locked sources. In this respect,
Chapter 4. Calibration of Six-Port Reflectometers Using Null Double Injection 57
the null double injection method bears some similarity to the procedure described
by Hoer and Roe [10]. Their technique, however, relies on maintaining a constant
signal at port 1 (with internal leveling and an isolator) and using a phase-shifter,
attenuator, and two-position insertion device to vary the signal at port 2. Detected
power readings are taken for both values of the two-position insertion device for
different settings of the attenuator and phase-shifter.
This results in a set of
equations that are solved to determine the network parameters.
The null double injection technique represents a simplification of the method
of Hoer and Roe in that the relative amplitude and phase of the excitations at
ports 1 and 2 are adjusted to produce a null at one of the measurement ports
and the detected power is read at the remaining measurement ports. There is
no requirement for a two-state insertion device and no need to isolate the signals
incident at ports 1 and 2. With the excitations at ports 1 and 2 adjusted to produce
a null at port 3 (63 = 0), equations (1) and (2) give the following:
PA
63=0
Pi
63=0
= \L?
(6)
= \N\*
(7)
where Pi = |6j| 2 . If instead the inputs are adjusted to null the output at port 4,
equations (1) and (2) lead to
Pp_5
P3
64 =0
p6
p3
64=0
= \K\"
11
(8)
"c
= \M\2 = -
(9)
p
nulling port 5 yields,
L
K
^3
Pe
PA b5=0
P4
65=0
=
1M I2
N
~M
*-w
L
K
2
(10)
1^1 -- ™ 2 I
2
p
(11)
Nulling port 6 yields no new information, but does provide some redundancy that
can be exploited to improve estimation of the six-port network parameters.
Chapter 4. Calibration of Six-Port Refiectometers Using Null Double Injection 58
The relations (6)—(11) underscore the primary advantage of the null double injection method — simple ratios of the powers measured at the those ports that are
not nulled provide the six-port calibration parameters directly. As with many other
six-port calibration techniques (for example, those based on sliding terminations)
no known standards are required. Moreover, knowledge of the relative phase and
amplitude of the waves at the two driving points is not needed — it suffices that
they can be adjusted appropriately to produce nulls at the measurement ports.
A basic implementation of the double null injection calibration setup is shown in
Figure 4.3. The two excitations are derived from a common source using a broadband power splitter. Adjustable attenuators are placed in both signal paths and a
tunable phase-shifter is included in one path to permit the relative amplitude and
phase of the excitations at ports 1 and 2 to be adjusted. In principle each of these
components can be programmable, permitting full automation of the calibration
process.
4.3
Implementation
The prototype non-contacting reflectometer described in Chapter 3 was used to investigate calibration using the null double injection method. The calibration setup
for implementing null double injection is based upon the diagram in Figure 4.3.
The output of a microwave synthesizer (Systron-Donner model 1626) is connected
to a 6 dB resistive power divider (Pasternack PE2065) to provide phase-coherent
excitations at the input and DUT ports of the reflectometer. A variable attenuator
(model HP 8494B, 1-dB step) is placed in one arm of the measurement setup and a
tunable phase shifter (Weinschel model 1584) is placed in the other. A fixed 3-dB
attenuator (Narda 4780-3) is placed between the phase shifter and the DUT port of
the reflectometer. This attenuator is also present during the four-port calibration
and serves to reduce the standing wave ratio on the microstrip line as mentioned in
Chapter 3 and [11]. Due to the presence of the 3-dB attenuator and the relatively
uniform coupling to the probes, it was found that only one variable attenuator
placed at the source port was necessary for implementing the null double injection
Chapter 4. Calibration of Six-Port Refiectometers Using Null Double Injection 59
Computer
IOTech
DAQ/55
mv
Diode Detectors
(PE-8013)
Six-Port
Reflectometer
Variable Attenuators
(model # HP-8494B)
htm-nm
Resistive Power
Divider (PE-2065)
Q
Tunable Phase Shifter
(Weinschel#1584)
Systron-Donner 1626
Frequency Synthesizer
Figure 4.3. An experimental setup for implementing the null double injection calibration technique. The manufacturer part labels provided in the figure correspond
to those components used to implement the method in this work.
Chapter 4. Calibration of Six-Port Reflectometers Using Null Double Injection 60
method (instead of one in each arm, as indicated in Figure 4.3).
4.4
Measurement and Analysis
The six-port reflectometer described above was calibrated using the null double
injection technique and the resulting virtual four-port network was subsequently
calibrated using an open, short, and matched termination from a Hewlett-Packard
85052D calibration kit. To evaluate the calibration method as well as operation
of the reflectometer, a set of sample loads with various magnitude and phase responses were measured, including a variety of fixed attenuators and offset shorts.
Measurements of the same loads were performed with a Hewlett-Packard 8720C
Automatic Network Analyzer to serve as a reference for comparison.
4.4.1
Measurements
Figure 4.4(a) shows the measured response of the diode detectors (in mV) as the
phase shift between the source and DUT ports is varied. For this measurement, the
frequency (1.15 GHz) and the stepped attenuator settings are fixed as the phase
shifter is tuned to minimize each detector output in turn. The figure illustrates the
degree of uniformity of the coupling to the sampling probes as well as the variation
of the detected voltages as a null is neared. For the actual calibration, both the
attenuator and phase-shifter are adjusted to produce detector outputs that are
as close to a null as can be determined with the measurement apparatus. With
the IOTech DAQ/55 data acquisition module, this minimum detectable voltage is
approximately 7 fj,V. Figure 4.4(b) shows the response of the system near a null
in greater detail and illustrates the measurement uncertainty associated with the
position of the null for the given experimental setup.
Figure 4.5 shows the magnitude of the six-port network parameters {\K\, \L\,
\M\, and \N\) as a function of frequency. These parameters are found by adjusting
the attenuator and phase-shifter to produce nulls, in turn at ports 3, 4 and 5,
and then applying equations (6)-(9). Because the minimum detectable voltage is
Chapter 4. Calibration of Six-Port Refiectometers Using Null Double Injection 61
4 --
V
4
/ *
1
1
1
1
1
v3
%
|
60
a
*5
+->
->c
2 -
e$r
Jr
j /
igr
\
is£ -
O
U
Q
'Hs^-ui^rn
| h h++4^-Pt+
&W^*tf^
60
120
180
240
Phase Shift (degrees)
300
360
(a)
10
M o.i
o
<D
0.01
4)
Q
0.001
160
161
162
163 164
165
Phase Shift (Degrees)
166
167
168
(b)
Figure 4.4. (a) Measured detector outputs as a function of relative phase-shift
between input signals at the source and DUT ports. The attenuation for each
arm of the calibration setup is fixed for this measurement. Subscripts refer to
the detector port, (b) Detail showing the variation of the sampled voltages in the
vicinity of a null.
Chapter 4. Calibration of Six-Port Reflectometers Using Null Double Injection 62
1.6
1.4
1.2
1.0
°' 8 1
1.1
1.2
1.3
frequency (GHz)
1.4
1.5
(a)
2.5
i
T
r
2
1.5
1
0.5
0
1
1.1
1.2
1.3
frequency (GHz)
1.4
1.5
(b)
Figure 4.5. Measured magnitude of the six-port network coefficients (K, L, M,
and N) as a function of frequency.
Chapter 4. Calibration of Six-Port Reflectometers Using Null Double Injection 63
approximately 7 fiV, there is some uncertainty in the exact position of each null.
However, the values of the nulls do not enter into the calculations and, provided
the voltages detected at the measurement ports do not vary rapidly as the null is
approached, the network parameters can be determined with reasonable accuracy.
Prom Figure 4.4(b), it is noted that the phase shift producing a null can be determined to within a few degrees and that the detected voltages at the remaining
ports do no vary rapidly over that range. Consequently, with a typical uncertainty
in the null position of ~2-3° the error in the measured detector response is on the
order of a few percent. A more detailed discussion of the uncertainties in the estimated reflection coefficient with the present six-port implementation is presented
in a following subsection.
To serve as a basis for comparison, a set of offset shorts and fixed attenuators
were measured with both the prototype six-port reflectometer and a HP8720C
vector network analyzer. Fig. 4.6(a) and Fig. 4.7(a) shows the measurement of
two fixed attenuators (6 dB and 10 dB) from 1 to 1.5 GHz using both the six-port
reflectometer (calibrated using the null double injection method) and HP 8720C
vector network analyzer (calibrated with the familiar short-open-match technique
[10]). Because the two sets of data overlap closely on the Smith Chart plots, the
measured difference in the s-parameters (AT) is shown in Fig. 4.6(b) and Fig.
4.7(b). Here, A r is defined as the distance between the two measurements on the
T-plane:
Ar = |r 8 7 2 0 -r 6 _ p o r t |
(12)
with T8720 the reflection coefficient measured with the HP 8720C and r6_p0rt the
reflection coefficient measured with the prototype six-port reflectometer. In addition, A r normalized with respect to |r872o| is shown in percentage in Fig. 4.6(c)
and Fig. 4.7(c). For the 6 dB and 10 dB attenuators, the difference in the measured
reflection coefficient is less than -35 dB over the operating band of the reflectometer. The minimum reflection coefficient magnitude that can be measured with the
prototype system is approximately —30 dB and is limited by the dynamic range
of the diode detectors used for this demonstration. Employing higher-quality de-
Chapter 4. Calibration of Six-Port Refiectometers Using Null Double Injection 64
• HP 8720C
O Six-Port Reflectometer
ST
<
-60 1.05
1.1
1.15
1.2
1.25
1.3
Frequency (GHz)
1.35
1.4
1.45
1.5
(b)
(%)lF
i\
/ \
1
UilOU
/
3
T
\
^1NN^
N/
/
\
\
j
\
1.2
1.25
1.3
Frequency(GHz)
1.35
/
/
r-^
kN
'
c
1.4
1.45
0 ^
1.05
1.1
1.15
1.5
(c)
Figure 4.6. (a)Comparison of reflection coefficients for 6 dB fixed attenuators measured with the prototype reflectometer (circle) and an HP8720C network analyzer
(square). (b)(c) Difference between the measured reflection coefficients (Ar) as a
function of frequency.
Chapter 4. Calibration of Six-Port Reflectometers Using Null Double Injection 65
• HP 8720C
O Six-Port Reflectometer
(a)
V
\
-fid 1
/ \
/
>
\
1
1.05
1.1
\
\ r-—^
1.15
, y
N/
1.2
1.25
1.3
Frequency(GHz)
1.35
1.4
1.45
1.5
(b)
1.05
1.1
1.15
1.2
1.25
1.3
Frequency(GHz)
1.35
1.4
1.45
1.5
(c)
Figure 4.7. Comparison of reflection coefficients for 10 dB fixed attenuators measured with the prototype reflectometer (circle) and an HP8720C network analyzer
(square). (b)(c) Difference between the measured reflection coefficients (Ar) as a
function of frequency.
Chapter 4. Calibration of Six-Port Reflectometers Using Null Double Injection 66
30 GHz
1.20 GHz
.1.40 GHz
1.10 GHz
1.50 GHz
1.00 GHz
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
1.45
1.5
Frequency(GHz)
(b)
i
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
1.45
1.5
Frequancy(GHz)
(C)
Figure 4.8. (a) Measurement of the return loss for a 66.67 mm offset short with the
prototype refiectometer (circle) and the 8720C network analyzer (square). (b)(c)
Difference between the measured reflection coefficients (Ar) as a function of frequency.
Chapter 4. Calibration of Six-Port Reflectometers Using Null Double Injection 67
tectors with greater sensitivity would permit the dynamic range of the instrument
and measurement accuracy to be improved substantially.
Figure 4.8 compares measurements done with the six-port and 8720C network
analyzer on a short-circuit with fixed offset length of 6.667 cm. Again, the two
measurements are reasonably close and the agreement between them is typically
better than -28 dB. It should be noted that discrepancies between the measurements may arise from a number of sources, including connector repeatability between the two measurement systems and non-systematic errors associated with the
non-contacting architecture of the six-port. These sources of error, however, are
difficult to quantify with precision and are generally small for carefully constructed
instruments.
4.4.2
Measurement Uncertainty
The precision with which the detected voltages can be determined is a primary
contributor to measurement error and, thus, a quantity of considerable interest.
The rms noise voltage in the present implementation of the reflectometer is approximately 7 //V and this limits the precision with which voltage nulls can be
ascertained as well as the uncertainty in the estimation of the six-port network
coefficients. Deviation from square law detection may also play a role in measurement error, but this can be mitigated to some extent through power calibration
and leveling techniques [12] [13]. In the present reflectometer, the source power was
monitored to ensure the detectors operated well within their square-law region.
Measurement uncertainty for the given six-port was determined experimentally
by taking one-hundred sample measurements for each null point. The mean square
error or variance (AV^2) for V3, V4, and V5 was estimated by averaging the residuals
of these measurements [14],
^^E^-^)2
( 13 )
i—l
where {vj} are the sampled voltages at port j , vi is their mean, and N — 100.
Subsequently, a simple error propagation model is employed in which these de-
Chapter 4. Calibration of Six-Port Refiectometers Using Null Double Injection 68
Im{w}
|
w-plane
Figure 4.9. Annuli in the w-pl&ne corresponding to measurements done on a 6
dB attenuator at 1.25 GHz. The region of overlap (detailed in the inset) provides
a measure of the precision with which w is known. Mapping of this region to
the T-plane allows the error in phase (A(f>) and magnitude (Ap) of the reflection
coefficient to be estimated.
Chapter 4. Calibration of Six-Port Reflectometers Using Null Double Injection 69
0.30
0.28
r
T
l
1
1
1
six port reflectometer
:
0.26 + 0«0<t»»
0.24
0.22
HP 8720C
0.20
0.18
1.0
1.1
1.2
1.3
frequency (GHz)
1.4
1.5
(a)
-60
-70
-80
i
si
OH
HP 8720C
-90
-100
six-port reflectometer
-110
-120
1.1
J
L
1.2
1.3
frequency (GHz)
1.4
1.5
(b)
Figure 4.10. Measured reflection coefficient (a) magnitude and (b) phase of a 6
dB attenuator. The error bars show the standard deviation in the measurement,
corresponding to a confidence interval of 70%.
Chapter 4. Calibration of Six-Port Reflectometers Using Null Double Injection 70
tected voltages are assumed to be statistically independent. Because the network
parameters (for example, |w|2 and () are found from simple ratios of the detected
voltages (equations 8 and 10), the fractional error squared of these quantities is
the sum of the fractional error squared of the measured voltages comprising their
ratios [15], that is:
s
V j=3>5
Since the DUT's w is the intersection point of two circles centered at the origin
and at w\ (the mean value of wi) in the lower half of the w-plane. The true value
of w is bounded between four circles: two circles centered at the origin with radii
of r — Ar and r + Ar, and two circles centered at uJj" with radii of r\ — Ari and
r^+Ari. Ar and Ari are the errors propagated into the radii of the circles from the
DC voltage measurements. Thus errors in the measured detector voltages result
in annuli in the u;-plane, centered at the origin and at W[ (the mean value of w\)
respectively. The circles corresponding to these annuli are shown in Figure 4.9 for
the measurements performed on the 6 dB attenuator at 1.25 GHz. The region of
overlap between the annuli provides a measure on the precision with which w is
known. The four-port calibration, in turn, provides the coefficients for the bilinear
transform that maps this region to the T-plane. The resulting region in the Tplane is still in the shape of annuli because bilinear transformations map circles
into circles. This allows the uncertainties in both the magnitude and phase of the
reflection coefficient to be estimated (shown in Figure 4.9). Figure 4.10 shows the
magnitude and phase response of the 6-dB attenuator measured with the six-port
reflectometer and includes error bars, based on the analysis described above, that
specify a confidence interval of 70% [14]. The reflection coefficient measured by
an HP 8720C network analyzer is also shown in the figure and is clearly within
the range of error bars. It should be noted that, in this simple error analysis, the
bilinear transformation is assumed to be error free. However, in real measurements,
its coefficients are derived from six-port DC measurements too and subsequently
suffer from the noise in the DC measurements. Thus the noise analysis results
presented here might give an underestimated error.
Chapter 4. Calibration of Six-Port Reflectometers Using Null Double Injection 71
4.5
Discussion
In this work, we have introduced a new method for calibrating six-port reflectometers t h a t requires no terminations and can be implemented using only a few
widely-available microwave components. The technique permits the six-port-tofour-port reduction coefficients to be determined directly from simple power ratios
and eliminates the tedious (and rather unintuitive) algebra associated with the
sliding load method. By incorporating programmable phase-shifters and attenuators in the system, the null double injection calibration can be automated. In
addition, the technique eliminates mechanically tuning backshorts and any need
to physically exchange terminations during the calibration process.
It should be pointed out that in the implementation and analysis described
above, only two of the three six-port circles (or annuli) in the w-plane are utilized.
The intersection of these circles provide two possible solutions and determine w to
within the sign of its imaginary part. A cursory examination of equations (9-10)
shows t h a t the network constant w2 is also determined only to within the sign
of S{t<;2}. The null double injection technique does not, as a result, resolve this
final sign ambiguity (also encountered in the sliding load method) that appears
to be inherent to six-port reflectometers as a consequence of their capacity to
measure only magnitudes. Determining the sign of $s{w} is possible from specific
apriori knowledge of the six-port network architecture or through measurement of
additional phase standard.
As discussed by Engen [16], the additional information provided by the third
measurement center (w2) can be used to enhance accuracy of the reflectometer by
providing a better estimate for w, regardless of the sign ambiguity in its imaginary
part. Significant improvement in measurement accuracy, however, is predicated
on the six-port measurement centers being oriented at approximately 120° relative
to one-another [17], a condition that is not met by the sampled-line architecture
used in this demonstration [11]. Actually, the three measurement centers (in the
u;-plane) for this sampled-line reflectometer lie on a straight line (more specifically,
the real axis). Nevertheless, the fundamental technique of null double injection
Chapter 4. Calibration of Six-Port Refiectometers Using Null Double Injection 72
is applicable to any six-port and is not restricted to the particular architecture
employed in this work.
Bibliography
[1] G.F. Engen, "Calibrating the six-port reflectometer by means of sliding terminations," IEEE Trans. Microwave Theory Tech., vol. 26, no. 12, pp. 951—957,
Dec. 1978.
[2] F. Wiedmann, B. Huyart, E. Bergeault, and L. Jallet, "A new robust method
for six-port reflectometer calibration," IEEE Trans. Instrum. and Meas., vol.
48, no. 5, pp. 927-931, Oct. 1999.
[3] H.F. Ebbeson and G.F. Engen, "Singularities in the calibration of six-port
network analyzers," International Microwave Symposium Digest, June 1989,
pp. 149-150.
[4] U. Stumper, "Finding initial estimates needed for the Engen method of calibrating single six-port reflectometers," IEEE Trans. Microwave Theory Tech.,
vol. 38, no. 7, pp. 946-949, July 1990.
[5] B. Neumeyer, "A new analytical method for complete six-port reflectometer
calibration," IEEE Trans. Instrum. and Meas., vol. 39, no. , pp. 376-379, Apr.
1990.
[6] J. Hesselbarth, F. Wiedmann, and B. Huyart, "Two new six-port reflectometers
covering very large bandwidths," IEEE Trans. Instrum. and Meas., vol. 46, no.
4, pp. 966-969, Aug. 1997.
[7] G. Hjipieris, R.J. Collier, and E.J. Griffin,
"A millimeter-wave six-port re-
flectometer using dielectric waveguide," IEEE Trans. Microwave Theory and
Tech., vol. 38, no. 1, pp. 54-61, Jan. 1990.
73
Bibliography
74
[8] R.D. Middlebrook, "Null double injection and the extra element theorem,",
IEEE Trans, on Education, vol. 32, no. 3, pp. 167-180, Aug. 1989.
[9] Application Note 8510-5B, "Specifying Calibration Standards for the Agilent
8510 Network Analyzer," Agilent Technologies, Inc., P.O. Box 50637, Palo
Alto, CA 94303-9511; website: www.agilent.com.
[10] C.A. Hoer and K.C. Roe, "Using an arbitrary six-port junction to measure
complex voltage ratios," IEEE Trans. Microwave Theory and Tech., vol. 23,
no. 12, pp. 978-984, Dec. 1975.
[11] W.L. Williams, Computer Aided Measurements of Microwave Circuits, Ph.D.
Dissertation, California Institute of Technology, Pasadena, CA 1989.
[12] P.I. Somlo and J.D. Hunter, "A six-port reflectometer and its complete characterization by convenient calibration procedures," IEEE Trans. Microwave
Theory and Tech., vol. 30, no. 2, pp. 186-192, Feb. 1982.
[13] P.I. Somlo, J.D. Hunter, and D.C. Arthur, "Accurate six-port operation with
uncalibrated nonlinear diodes," IEEE Trans. Microwave Theory and Tech., vol.
33, no. 3, pp. 281-282, March 1985.
[14] J. Mandel The Statistical Analysis of Experimental Data, Dover Publications,
Inc., New York, 1964.
[15] J.R Taylor An Introduction to Error Analysis, second ed., pp. 57-61, University Scientific Books, Sausalito, CA, 1997.
[16] G.F. Engen, "The six-port reflectometer: an alternative network analyzer,"
IEEE Trans. Microwave Theory Tech., vol. 25, no. 12, pp. 1075-1080, Dec.
1977.
[17] G.F. Engen, "An improved circuit for implementing the six-port technique of
microwave measurements," IEEE Trans. Microwave Theory Tech., vol. 25, no.
12, pp. 1080-1083, Dec. 1977.
Chapter 5
A Non-Contacting Reflectometer
W i t h a Compact Coupling
Probing Structure
5.1
Introduction
A proof-of-concept non-contacting reflectometer has been described in the previous chapters. For most microwave integrated circuits, the transmission lines
that interconnect the microwave components are short in electrical length. The
non-contacting reflectometer structure that was described in the previous chapters
required a minimum of three probes occupying an interconnecting transmission
line with extent that is at least a quarter wavelength. This limits the practical
applications of this structure for in-situ measurements.
In this chapter, the aforementioned issue is addressed and several new approaches are described that are suitable for true in-situ measurements . The approaches include a compact probing structure design, the introduction of a modified
sampled-line reflectometer and on-wafer calibration techniques.
75
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
76
Port 3 Port 4
Figure 5.1. Basic configuration of the proposed compact probing structure.
5.2
Compact Coupling Probing Structure
The functionality of a probing structure for a non-contacting reflectometer to be
investigated in this chapter is to sample two independent linear combinations of the
forward-travelling and reverse-travelling waves on an interconnecting transmission
line. To occupy a relatively short length of interconnecting transmission line, a
compact planar probing structure shown in Figure 5.1 is investigated. The probing
structure is essentially a directional coupler: when port 1 is excited, port 2 is the
direct port, port 3 is the coupled port and port 4 is the isolation port. Thus,
ideally, its port 3 samples the forward-travelling wave and port 4 the reversetravelling wave when port 2 is terminated with a DUT. It should be noted that the
compact probing structure is a versatile one in that it can be used in a variety of
non-contacting reflectometer architectures. This point will be illustrated in next
section.
The interconnecting microstrip line is a 50 0 line on quartz substrate (er = 3.8,
thickness = 10 mil). The probing structure is also on a quartz substrate (er — 3.8,
thickness = 10 mil) and its total length along the direction of the interconnecting
microstrip line is 32 mil, which is only approximately Aff/24 at the center design
frequency of 9 GHz. The probing structure has been simulated using HFSS over
the frequency range from 6 GHz to 12 GHz. Simulation results for the structure
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
77
8
9
10
12
Frequency (GHz)
Figure 5.2. HFSS simulation results of the compact probing structure.
Port4
PortL
Port3
ort2
Figure 5.3. Dimension of testing compact probing structure.
are shown in Figure 5.2. These simulation results show that the magnitudes of Sll,
S33 (input matching), S21 (insertion loss), S31 (coupling), and S41 (isolation) are
better than -35 dB, -16 dB, -0.03 dB, -27 dB, and -41 dB respectively over the
frequency range from 6 GHz to 12 GHz.
To verify the concept that the proposed compact structure indeed works as a
directional coupler, another probing structure that is much larger that the abovedescribed one (which is too small to test directly with convenience) is fabricated
on Roger's RT/Duroid 5880 substrate (er = 2.2, thickness of the substrate = 15
mil) and tested. Its dimensions are shown in Fig. 5.3. Its s-parameters are shown
in Fig. 5.4 where the property of a directional coupler can be easily seen.
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
78
X^
—5
/
1.0
1.2
1.4
1 .8
1.6
2.0
2.2
2.4
2.6
2.8
3.0
Frequency{GHz)
pbf V*\K
MlArt
\
V
Vvpft
I
•>
1 t L
\
if
\
I
V
Ail
(J
w
V
1.0
1.2
1.4
1.E
1.8
2.0
2.2
2.4
2.6
2.8
3.0
Fraqiwncy(GHz)
-35
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
Frequency(GHz)
Figure 5.4. Measured S-parameters of the testing compact probing structure.
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
79
Compact probing structure
y\
Source
Load'
Figure 5.5. A possible configuration of a non-contacting reflectometer with a vector
voltmeter.
5.3
Modified Sampled-Line Reflectometer
To process the sampled signals from a probing structure, a microwave vector voltmeter can be used that gives the complex ratio of the sampled signals. The microwave vector voltmeter can be realized by using mixers that frequency downconvert the sampled signals to a low frequency (e.g. 10 MHz) where an analog
vector voltmeter can be used to process the complex ratio. This approach was
adopted in Stenarson's work where a commercially available microwave vector voltmeter was used [1]. Fig. 5.5 presents a possible non-contacting reflectometer that
integrates the compact probing structure with a vector voltmeter. This kind of
vector voltmeters tend to be expensive and complicated to implement due to the
use of an external frequency-tunable local oscillator as well as mixers and analog
vector voltmeters.
Another way to implement a microwave vector voltmeter is to use a powerdetector-based six-port architecture such as the one shown in Fig. 5.6 [2]. Its
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
80
D—Power Divider
Q—Quadrature Hybrid
Figure 5.6. An optimized six-port vector voltmeter.
principle is based on the fact that the complex ratio of the incident waves into the
six-port network (ai and a-i in Fig. 5.6 can be derived from the measurements of
the power detectors (P3, P4, P5, and P% in Fig. 5.6). Fig. 5.7 presents a possible
non-contacting reflectometer that integrates the compact probing structure with
the six-port vector voltmeter. Compared to the microwave vector voltmeters base
on the principle of frequency down conversion and analog processing, the six-port
vector voltmeters have less complexity and tend to be less expensive. However,
it still requires significant amount of passive devices such as power dividers and
quadrature hybrids.
A modified sampled-line reflectometer (shown generically in Fig. 5.7) is utilized
in this work to explore the simplicity offered by a sampled line and the compactness
by the compact probing structure presented in the previous section. The sampled
signals incident on both ends of a meandered section of transmission line and three
power detectors are placed along the transmission line to tap a small amount of
power from it. It is different from a sampled-line reflectometer in that neither end
of the transmission line is terminated with a definitive load and a signal loop is
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
81
DC Voltages
Six-port Vector Voltmeter
I Bonding
trt s
Positioner
Load'y"\
Source
Figure 5.7. A modified sampled line reflectometer.
V4
V3'
low pass filter
low pass filter L/VWW\V5
1
/Sh
w\i
t
U-Shaped probe component
Source
^^\
Loa<T
Figure 5.8. Sampled-line reflectometer with the proposed compact probing structure.
Chapter 5. A Non- Contacting Reflectometer With a Compact Coupling Probing
Structure
82
formed by the transmission line and the compact probing structure. This prompts
the need to verify carefully if the modified sampled-line reflectometer can still be
calibrated as a sampled-line one. Its design and simulation will be discussed in the
next section.
5.4
Design and Simulation of t h e Modified SampledLine Reflectometer
A more detailed implementation of the reflectometer shown in Fig. 5.8 is presented
in Fig. 5.9 (dimensions are not shown in proportion). A Wilkinson power divider
is incorporated to attenuate the sampled reflected wave from the DUT and thus
reduce the problem of deep voltage nulls discussed in Chapter 2. The low pass
filters following the diodes, which are implemented in 3-section hi-Z-low-Z filters,
present a short circuit to the diodes at RF frequencies and let DC voltages through.
A quarter-wavelength high-impedance line terminated with two radial stubs is
used to provide the DC-return-to-ground path while presenting a close-to-opencircuit impedance to the signal line. The radius of the radial stubs is chosen to be
approximately quater-wavelength long such that their center (point A in Fig. 5.8)
is approximately an RF short. This RF short transforms to an open circuit by the
quarter-wavelength high-impedance line. A wire is bonded to point A to set to DC
ground.
The modified sampled-line reflectometer has been simulated using Agilent's
Advanced Design System (ADS). Fig. 5.10 shows the ADS simulation bench for
the reflectometer where the HFSS-yielded s-parameters of the compact probing
structure are incorporated as a four-port device. The intrinsic diodes excluding
parasitic capacitances are treated as ports with an impedance equal to that of the
small-signal resistance of the diodes (at zero bias voltage) which is the inverse of
the slope of the diode's current-voltage curve (I-V curve). In Fig. 5.10, port 1 is
the signal source port, port 2 the DUT port and port 3, 4 and 5 intrinsic diode
ports. The DC output voltages from the diodes are proportional to the RF powers
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
83
Figure 5.9. A more detailed implementation of sampled-line reflectometer with the
compact probing structure.
delivered to the diodes,i.e. the powers delivered to the ports 3, 4 and 5 in Fig.
5.10. Since only the DC voltage ratios are concerned in a six-port calibration and
measurement, the |£3i| 2 , IS41I2 and |-S'si|2 yielded from s-parameter simulation of
the ADS simulation bench can be used to represent the DC voltages from the
diodes.
During the simulation, it is found that the electrical lengths of the interconnecting transmission lines for the modified sampled-line reflectometer are important in
determining the operating bandwidth as well as the order in which the voltage
ratios are taken to satisfy 7771(63/64} < 0 (this is the main assumption for the
sampled-line reflectometer as discussed in Chapter 2). Fig. 5.11 shows the phases
Chapter 5. A Non-Contacting Refiectometer With a Compact Coupling Probing
Structure
84
diode port
1
1
TL35
Subtt^"MSub1W=W1 mil
L-LFmrl
1 ?,;;. hi
nn_36
1 1 Sub»t="HSub1"
||TL34
1 1 Sub»l="MSub1'
Uw=Wlmi!
pln_a3
1 ISutwfWSubl'
compact probing
structure
Figure 5.10. ADS simulation bench for the sampled-line refiectometer.
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
85
180
150
120
-*-phase(S(1,3))
90
- » - Phase(S(1,4))
Phase(SM.5tt
60
30
0
-30
-60
1
-90
-120
-150
-180
6.0
7.0
8.0
10.0
9.0
11.0
12.0
Frequency(GHz)
-20
-25
-•-dB(S(1,3))
HHdB(S(1,4))
dB(S(1,5))
m •30
JM*I
Jf
\
•o
c
is -35
2
-40
,
u***
^r
-45
6.0
7.0
8.0
9.0
Frequency(GHz)
10.0
11.0
12.0
Figure 5.11. ADS simulation results for the sampled-line reflectometer.
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
86
°0
1
2
P3/P4
3
4
Figure 5.12. Simulated eclipse traced out by a sliding short on the P3/P4—P5/P4
plane.
and magnitudes of 531, ^41 and S51 versus frequency after setting those electrical
lengths to appropriate values. The operation frequency range is chosen to be between 6 GHz and 12 GHz where the advance-lag relationship between the phases
is kept with good margin and the magnitudes are relatively flat with respect to
frequency.
Fig. 5.12 shows the simulated eclipse traced out by a sliding short on the
P3/P4—P^/Pi plane at the center frequency of 9 GHz. The six-port-to-four-port
reduction can be performed based on the sliding short measurements as proposed
by Engen [2]. For the four port calibration, an open circuit, an open circuit with
60° offset and an open circuit with 120° offset (all at the center frequency) are
used as the three standards. A variety of DUT's are "measured" in simulation and
their s-parameters derived from the "simulated" readings of the diode detectors
are compared to their true s-parameters. Table 5.1 show the simulation results
using Engen's method. The simulated reflection coefficients agree well with the
true ones with the reflection-coefficient difference (Ar) less than 0.2%, where A r
Chapter 5. A Non-Contacting Refiectometer With a Compact Coupling Probing
Structure
87
DUT
]•!•
\simulated
in
1
I
{true
"simulatedy
)
"true\
open with 15° offset
1
1
-30.009
-30
Z=150fi
0.5
0.5
-0.014
0
Z=100Q
0.333
0.333
0.0003
0
Z=53^
0.029
0.029
-0.129
0
)
Table 5.1. Simulated and true T for different DUTs
is defined as the distance between the two measurements on the T-plane:
Ar
|p
'-* 1 — I 1 simulated
_ T
1
I
true|
It should be noted that the above simulations were also performed selectively at
other frequencies between 6 GHz and 12 GHz with yielding similar results.
Fig. 5.13 shows a photograph of the fabricated reflectomter. The supporting
metal (bronze) piece (which also serves as an RF ground) is cut into the shape
with a narrow bottom to facilitate its positioning in the probe station for measurement. The main refiectometer (excluding the compact probing structure) has
to be fabricated from two pieces that are assembled together using boding wires.
This is shown in the right-upper inset of Fig. 5.13. The compact probing structure
(shown in the right-lower inset of Fig. 5.13) is fabricated separately and bonded
to the main circuit using bonding wires. Metelics zero-bias beamlead diodes are
soldered onto the circuit.
5.5
Measurements of t h e Modified Sampled-Line
Refiectometer
In order to calibrate the modified sampled-line refiectometer and verify its performance on wafer, a set of on-wafer reflection standards are needed. Those standards
can be obtained by first performing an on-wafer TRL calibration with an HP8510C
network analyzer and then measuring a set of reflection standards with it afterwards.
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
88
diode detectors
Low Pass Filters
•Wilkinson
power divider
U-shape probe
Figure 5.13. A photograph of the fabricated reflectomter.
GSG probe
Figure 5.14. TRL calibration standards for the HP8510C network analyzer.
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
89
calibration
coaxial cable
II
VNA
^—4
coaxial cable
3
C
*1
VNA
5—S.
|port-2
| port-1
coaxial cable
coaxial cable
^
Si
VNA
H
U
VNA
port-2
| port-1
coaxial cable
coaxial cable
h.
t-^B.
Si
VNA
port-1
VNA
port-2
measurement
coaxial cable
If
coaxial cable
±L
r
VNA
port-1
coaxial!
load
Figure 5.15. connection for TRL calibration.
coaxial cable
£E
sweep
oscillator
coaxial cable
r
Jl
coaxial
load
DUT, 6-port
Figure 5.16. Sampled-line refiectomer placed on top of the THRU line.
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
90
Agilent signal
generator E8257D
Sampled-line refletometer
with U-shaped probe
Calibration circuit
Figure 5.17. A photograph of the measurement setup.
Fig. 5.14 shows the calibration standards used in the TRL calibration for the
HP8510C network analyzer. The semi-circles in the figure facilitate broadband
transition from GSG coaxial probes to microtrip lines [4]. Fig. 5.15 illustrates
the connection between the network analyzer and the TRL standards during the
TRL calibration using the THRU standard as an example. After TRL calibration,
the GSG probes are put back onto the THRU standard with the port-2 of the
network analyzer disconnected. The Sn of the set of coaxial reflection standards
are measured using the TRL calibrated network analyzer with the setup shown in
Fig. 5.15 where the measurement reference plane is at the middle of the THRU
standard. These measured standards include three four-port calibration standards
for the modified sampled-line reflectometer and those for its verification purpose.
The verification standards are obtained by connection coaxial attenuators with
their unused port open-circuited.
After all this done, the network analyzer is
disconnected completely.
The modified sampled-line reflectomer is then placed on top of the THRU
line as shown in Fig. 5.16. Fig. 5.17 shows a photograph of the measurement
setup. A multi-channel Keithley multimeter is used to measured the DC voltages
and an Agilent 8257D signal generator serves as the R F source. Both of them are
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
91
-2
•a - 3 •
I:
^rreflectometer
c
s
If
'
.
-»~r8510
-6
Fraquency(GHz)
-•-rreflectometer
-•~r8510
Fraquency(GHz)
A
"*\
A , A \l \ f\
v\
/
v
f
V
V
\
\
v/
'
nFr«qu«ncy(GHz)
Figure 5.18. Comparison of reflection coefficients for a 0-dB fixed attenuator measured with the prototype reflectometer and a HP8510 network analyzer.
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
92
I
ft
i
U
i
-Freflectometer
^8510
•I
8.5
9
9.5
Frequency(GHz)
8.5
9
-Freflectometer
-F8510
9.5
Frequency(GHz)
v A/
\J
8.5
9
Frequ*ncy(GHz)
9.5
10
1
A
\
/
f G
/\
f\
/
\
r-. /
/ \
J \ J>J
/
\
\
1
\
V
/
\ / \ /
0
3.8
9
9.2
Fraqu«flcy(GHz)
9.4
Figure 5.19. Comparison of reflection coefficients for a 4-dB fixed attenuator measured with the prototype reflectometer and a HP8510 network analyzer.
Chapter 5. A Non-Contacting Refiectometer With a Compact Coupling Probing
Structure
93
fjjj
-Freflectometer
^8510
Fr»quancy(GHz)
-Freflectometer
-r8510
Frtquwicy(GHz)
8
8.2
8.4
Figure 5.20. Comparison of reflection coefficients for a 6-dB fixed attenuator measured with the prototype refiectometer and a HP8510 network analyzer.
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
94
A
A
i
/
V
f\ A
M
rA
AA
AA
1r
•r»
A
r
\
/
Jreflectometer
-r85l0
-in
Frequsncy(GHz)
220 -I
A
i A
1 ?0
iI
i M PA
i /V
/I
ft '
I y
V v y Vu
Jreflectometer
v \
V
-180 -
-T8510
Frequency(GHz)
.6
9.8
10
\
/ \
_10
&
o
o
S
y-
\
/
f
n
/
/
\
1
<-,
/
v
\
0
8.2
8.4
i.S
9
9.2
\
\
J
V
8
1
V
9.4
Froquency(GHz)
Figure 5.21. Comparison of reflection coefficients for a 9-dB fixed attenuator measured with the prototype reflectometer and a HP8510 network analyzer.
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
95
Figure 5.22. Photograph of the matching circuit.
8
8.5
9
9.5
10
Frequency(GHz)
Figure 5.23. Comparison of reflection coefficients for a matching circuit measured
with the prototype reflectometer and a HP8510 network analyzer.
automated with a laptop computer with GPIB cables connected to them. A coaxial
sliding short is first measured to perform six-port to four-port reduction. Three
coaxial standards (open, short and load) that have been already measured with
the HP8510C network analyzer are then measured to perform four-port calibration
for the modified sampled-line reflectometer.
The verification standards are measured with the sampled-line reflectometer
and the results are compared to those obtained by the HP8510C network analyzer
over the frequency range from 8 GHz to 10 GHz. The comparisons are shown
in Fig. 5.18—Fig.5.21 where the magnitude, phase, error vector magnitude and
error vector magnitude in percentage are all shown. The overall relectometer mea-
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
96
Radiation Interference Measuremnet
Reflectometer Measurement
Frequency
detector1
detector2
detector3
detector 1 detector2
detector3
(GHz)
(mV)
(mV)
(mV)
(mV)
(mV)
(mV)
8
0.0886
0.0681
0.137
0.083
0.038
0.439
8.5
0.144
0.0798
0.153
0.21
0.015
1.286
9
0.193
0.239
0.228
0.025
0.046
0.832
9.5
0.111
0.0688
0.236
0.0029
0.036
0.647
10
0.138
0.089
0.112
0.666
0.014
2.031
Table 5.2. Maximum DC voltages detected from radiation of the matching circuit
when input RF power is 16dBm
surements agree well with those by an HP8510C network analyzer. However, its
operation bandwidth is narrower than that predicted by simulation.
The reflectometer is not placed in an electromagnetic shielding structure. The
proceeding measurements using the reflectometer are made in a lab that is relatively free from electromagnetic interference such as radiation from cell phones
or wireless area network transmitters. This prevents such interference signals being picked up by the reflectometer circuit and subsequently converted by detector
diodes to DC voltages that will degrade the six-port DC response. In addition, the
proceeding measurements are all performed with shielded DUTs. This eliminates
the possibility of interference from direct radiation of a DUT itself.
To investigate the measurement degradation caused by direct radiation from
a DUT itself, a microstrip matching circuit that is not shielded (a photograph is
shown in Fig. 5.22) is fabricated and tested with the reflectometer. Its reflection
magnitude is shown in Fig.5.23 where the HP8510C measured results are also
given for comparison purpose. The two measured results differ noticeably from
each other.
To verify the error associated with radiation from the matching circuit, we
performed a measurement of the signal directly detected by the six-port through
radiation from the microstrip circuit. The microstrip circuit is directly driven with
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
97
Frequency
RF Power
Maximum
Maximum
Maximum
(GHz)
(dBm)
Voltage at
Voltage at
Voltage at
Detector 1
Detector2
Detector3
(mV)
(mV)
(mV)
8
0
0.0497
0.0478
0.0506
8
5
0.0521
0.0542
0.0547
8
10
0.062
0.0594
0.074
8
16
0.0886
0.0681
0.137
8.5
0
0.0532
0.0519
0.0497
8.5
5
0.067
0.544
0.0595
8.5
10
0.0958
0.0692
0.0794
8.5
16
0.144
0.0798
0.153
9
0
0.0509
0.0505
0.0518
9
5
0.0656
0.0623
0.0624
9
10
0.0692
0.109
0.0928
9
16
0.193
0.239
0.228
9.5
0
0.0563
0.056
0.0861
9.5
5
0.0789
0.059
0.096
9.5
10
0.879
0.0634
0.142
9.5
16
0.111
0.0688
0.236
10
0
0.0549
0.0606
0.0585
10
5
0.0661
0.068
0.0869
10
10
0.086
0.073
0.094
10
16
0.138
0.089
0.112
Table 5.3. Maximum DC voltages detected from radiation of the matching circuit
as input RF power changes
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
98
a signal generator and the dc response of the detectors in the six-port reflectometer
is measured. A coaxial cable connects the RF signal generator (instrument type)
directly to the matching circuit. Because the coaxial transmission line is shielded,
the reflectometer only receives the power radiated directly from the microstrip
circuit. The available power (nominally 16 dBm) from the RF signal generator
and the distance from the signal source to the reflectometer (nominally at 15
cm) are kept the same as in the case of the reflectometer measurement. At a
given frequency, the orientation and position of the matching circuit are varied
slightly and the maximum DC output voltage for each detector diode is recorded.
These maximum voltages represent the worst-case scenario of the radiation from
the matching circuit and they are shown in Table 5.2. For comparison purpose,
this table also shows the DC voltages obtained when measuring the reflection
coefficient of the DUT using the reflectometer. It is observed that the voltages
introduced by radiation are comparable to or even larger than those obtained in
reflectometer measurement. Next, the available power from the RF signal generator
is changed to a lower level and the same procedure as above is carried out to
obtain maximum DC output voltages introduced by radiation (shown in Table
5.3). This table demonstrates the correlation between the radiation power and its
introduced detector DC output voltages: an increased radiation power corresponds
to an increased detector DC output voltage.
To illustrate quantitatively how much error in the reflection coefficient the radiation causes, the voltages resulting from radiation interference in Table 5.2 are
used to perturb the voltages obtained in reflectometer measurement. It is worthwhile to note that the six-port calibration are performed with shielded circuits and
radiation only affect the DC output voltages for the matching circuit measurement. The errors in the DC output voltages corresponding to the matching circuit
measurement propagate into w and subsequently into T. This results in error bars
shown in Fig.5.24.(the details of the error analysis are presented in the following
section.) Notice that the HP8510C measured results are close to or within the
error bars, demonstrating that the radiation from the matching circuit is likely a
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
99
^<3rsJ -3*<A
\^
^
i:
r\ J*\S /^>
L
r~H
mr
M1
xy
^
\
-359
9.5
Frequency(GHz)
I ^non-contacting reflectometer — HP 851 PC |
Figure 5.24. Measured reflection coefficients for a matching circuit. The error bar
shows the perturbation from the radiation of the matching circuit.
significant source the major cause of the discrepancy between the six-port reflectometer measurement and HP8510C measurement. It is thus very important to
design electromagnetic shielding structures for the reflectometer circuit for future
work.
5.6
Preliminary Error Analysis
To estimate the error due to the noise of the DC voltage measurements, error
analysis is carried out with the assumptions that the noise voltages for different DC
measurement channels (with a certain DUT) are independent and noise voltages
for different DUTs (at a certain channel) are independent. It is further assumed in
this analysis that W\ and ( are perfectly estimated by a least square fit. Because of
these assumptions, the error analysis is preliminary. However, the error analysis is
meaningful in that the order of magnitude of error introduced by the DC voltage
measurements can be estimated.
The reduction from the six-port to a virtual four-port is achieved by mapping
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
100
measured DC voltages P3, P4 and P5 to a complex ratio w — / ( P 3 , P4, P5):
Re{w} =
(5.1a)
2\wi\
5"A - (JfeM)3
7m{tt;} =
(5.16)
where it; is a bilinear transformation of the true reflection coefficient V:
w =
AT + B
(5.2)
cr + i
The following analysis is based on the above two equations. The noise voltages
(£P's) introduce noises (5w}s) in the IO'S for the four-port calibration standards
(namely, open, short and load):
df_
df_
8wk = - E r ? r | f c • <5P3ife + -^-\k
dP4
dP3
• SPiik
df_
dP5
(5.3)
+ ^ r r l f c • ^s.fc
where k = 1(= open),2(— short), 3(= load).
(5.3) can be rewritten in a more convenient matrix form:
=
5u>2
M-8P
(5.4)
\ ^3 y
where
/ _a^i
_an
_an
0
0
0
0
0
0
aPal 1
M=
V
9P4 11
WV1
a/ I
dP312
a/ I
ap412
a/ I
ap 5 12
0
0
0
0
ALL
13
ap 3
ALL3
9P41
ALL3 1
aPs I
/
6P = (<5P3,1, ^ 4 , 1 , W5.1, <JP3,2, <^4,2, <$P5,2, W 3 ,3, ^ 4 , 3 , SP5<3)T
The calibration coefficients A, B, and C can be derived from the measurements of
to's of the four-port calibration standards:
(A\
( r
r
B
\
C
=
)
1
-WX
r
- i open
open
*
J- short
-L
— ^ 2 • Ts/iort
y r;oad
1
- ^ 3 • Tfoad
\1 - 1
^2
J
V^3/
(5.5)
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
101
In other words, A, B, and C are explicit functions of w\ (open), w2 (short),
and w3 (load):
A = gi(w1,w2,w3)
(5.6a)
B = g2(w1,w2,w3)
(5.66)
C = 9s{wi, w2, w3)
(5.6c)
Thus the noises in A, B, and C can be derived from the noises in w\ (open),
w2 (short), and W3 (load):
( SA \
8Wl\
I
SB
(5.7)
5w2
= Q-
\ Sw3 J
\SCJ
where
I
Q =
\
dgi_
dgi_
dgi_ \
dw\
dw2
dw3
9g2
dwi
9g2
dw-2
dgt
dwi
dg3
dw\
dg3
9ui2
dgs
dws
.
J
For the measurement of a device under test (DUT), its noise in w can be easily
found from the noises in its F3, P4 and P5:
\
( 5P3dut
X,„ ,
owdut-
— (
dj_\
df_ I
df I
A
Mdut • SPdut
SPi,dut
y Qp-\dut -gpiUut ap-\dut J
(5.8)
\ SP^dut J
And finally the noises in wdut and A, B, C propagate into Tdut through the inverse
of the equation (5.2):
r<iut —
Wdut ~ B
(5.9)
A - CWdut
The noise in Tdut can be expressed as:
(
ST J *=(&£.
dut
V aA
1L ML dr A
B 9C dwdut J
d
SA
^
SB
(
= V-
SA
\
SB
SC
SC
\ SWdut J
\ Swdut j
(5.10)
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
102
Thus the mean square error (of.) in 8Tdut (alternatively variance or squared
standard deviation) is
(
4 = E [STdut • ST^\
SA
=V-E
8A
\ (
5B
5B
6C
6C
5w,
Vdut
\"
VH
(5.11)
5wdut
J
where E is ensemble average operator and H is Hermitian transpose operator. On
the other hand, because of the independency assumptions made at the beginning
of the analysis, the ensemble average of the product of 8P's for different channels
or DUT measurements is zero.
E[6PX • 5Py] = 0
(12)
Utilizing (12) and plugging (8), (7) and (4) subsequently into (11) yields:
4 = V-(
Tl
\n
T2
T4
| -VH
(5.13)
J
where T<i and T3 are a zero-padded 3x1 and 1x3 matrices respectively.
T1 = Q-M-CQ-MH
-QH
T4 — Mdut • Cdut • Mdut
where CQ is a diagonal 9x9 matrix (CQ = E[5P • SPH]) and Cdut is a diagonal 3x3
matrix {Cdut = E[SPdut • 5P»ut}).
Since Tdut is a complex number, the physical meaning of the (a^) is illustrated
in Fig. 5.25. It means that there is a 68% chance that the true value of Tdut lies
within the error circle drawn in the figure.
The error analysis method is applied to the measurements of OdB fixed attenuator. The resulting a r ' s are added and subtracted from the measured |r|'s
by six-port measurement to form error bars (Fig. 5.26). |r|'s measured by an
HP8510C network analyzer is also superposed on the plot for comparison. It can
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
103
Im(r)
1 six-port
R=(Tr
Re(T)
Figure 5.25. Illustration of <rr on T plane.
1
0.9
0.8
0.7
0.6
AA
*,
/
\
'y
;o.5
-•-ir dut
-*-ir hpi
V. A r> sj A
*Y\J
V
ry V
/, K
/5v
)k
/< \
\ /
\ /
T]
0.4
0.3
0.2
0.1
0
8.2
8.4
8.6
8.8
9
9.2
9.4
9.6
9.8
10
Frequency(GHz)
Figure 5.26. Measured reflection coefficient in magnitude of a 0 dB attenuator.
The error bars show the standard deviation in the measurement.
Chapter 5. A Non-Contacting Reflectometer With a Compact Coupling Probing
Structure
104
be noticed from the plot that, at some frequency points, the HP8510C measurements are not within the error bars. This might be due to the underestimation of
the noise because of the assumptions adopted for the error analysis. It might also
be caused by the systematic errors (not random error) that are not accounted for
during the error analysis.
5.7
Conclusion
A relatively simple reflectometer integrated with a novel compact probing structure has been demonstrated. The reflectometer architecture is modified from that
of a sampled-line one. Its operation principle, design, measurements and error
analysis have been presented. It requires only a short section of interconnecting
transmission line to make the non-contact measurement possible and hence it is
attractive for practical in-situ circuit measurement. It is also expected that the
novel compact probing structure will be useful for other reflectometer architecture
too.
Bibliography
[1] Cletus A. Hoer, and Keith C. Roe, "Using an Arbitrary Six-Port Junction to
Measure Complex Voltage Ratios," IEEE Trans. Microwave Theory Tech., vol.
23, pp. 978-982, Dec. 1975.
[2] G.F. Engen, "Calibrating the six-port reflectometer by means of sliding terminations," IEEE Trans. Microwave Theory Tech., vol. 26, no. 12, pp. 951—957,
Dec. 1978.
[3] Chen Gao, Bo Hu, I Takeuchi, Kao-Shuo Chang, Xiao-Dong Xiang, and Gang
Wang, "Quantitative Scanning Evanescent Microwave Microscopy and Its Applications In Characterization of Functional Materials Libraries," Measurement
Science and Technology., vol. 16, pp. 248—260, 2005.
[4] Aga R S, Brookman J, Dizon J, and Wu J Z, "Development of a dual channel
scanning microwave optical microprobe," Applied Physics Letters., vol. 84, pp.
1979-1981, 2004.
[5] EMP-2003, Intematix Corporation, 351 Rheem Blvd, Moraga, CA.
105
Chapter 6
Summary and Future Work
6.1
Summary
Non-contacting in-situ measurements allow the characterization of a device under
test (DUT) in the same environment where it is designed to operate, with no need
of precision connectors nor test fixtures. Applying the six-port reflectometer architecture to non-contacting in-situ measurements is the main contribution of the
research work presented in this dissertation. Furthermore, non-contacting planar
probing structures have been utilized to sample the travelling waves in the DUTs
in this work. Compared to coaxial probe techniques, planar probing structures significantly reduce positioning error thus enhancing the measurement repeatability.
In addition, the planar structure is suitable for monolithic integration using microfabrication technology and facilitate the integration of the probing structures with
other microwave processing circuitry.
The non-contacting measurement systems investigated in this work are standalone instruments that can be potentially monolithic integrated and hence benefits
from low-cost compared to other non-contacting in-situ measurement systems.
A prototype non-contacting measurement system combining a sampled-line reflectometer with a capacitive-coupling planar probing structure has been implemented to demonstrate the proposed approach for non-contacting measurement.
The measurement results are generally within 15% of those performed with a com-
106
Chapter 6. Summary and Future Work
107
mercial network analyzer (HP8720).
In addition, a new calibration method based on null double injection technique
has been described and demonstrated as an alternative six-port calibration method
that does not require sliding terminations. This technique can be implemented and
potentially automated using only a few widely-available microwave components,
resulting in a more convenient and frequency-scalable system solution.
The prototype system required a minimum of three probes occupying an interconnecting transmission line with extent that is at least a quarter wavelength.
This limits the practical applications of this structure for in-situ measurements. A
novel compact probing structure that functions essentially as a directional coupler
is proposed to address this issue. Furthermore, a modified sampled-line reflectometer is proposed. Finally, a non-contacting measurement system combining
the modified sampled-line reflectometer with the compact probing structure has
been demonstrated. The measurement results of this implementation generally
agree with those of commercial instruments to with 20%.
6.2
Discussions and Suggestions for Future Work
The overall effort in this work has been focused on the investigation of new techniques that will potentially improve the state of the art for non-contacting in-situ
measurements. The measurement results have demonstrated the potential of those
techniques. To fully take advantage of those techniques, several discussions and
suggestions for future work are at hand.
The circuitry for the non-contacting measurement systems implemented in this
work occupies relatively large area. More specifically, the distributed implementation of low pass filters takes majority of the circuit area consumption. Circuits
with large area are cumbersome and present some difficulties in their fabrication
and assembling. Low pass filters that are either of compact distributed form or
consisting of lumped elements may be implemented in future work to reduce the
circuit area.
It has been demonstrated in Chapter 5 that the radiation interference can cause
Chapter 6. Summary and Future Work
108
significant measurement error. The radiation signal that is picked up by the noncontacting measurement circuit is random in nature. This makes it difficult to
calibrate out the resulting error systematically. It is therefore very important to
design an electromagnetic shielding structure the non-contacting measurement circuit to prevent any interference RF signal from traveling into the power detectors.
In addition, it will be a good practice to keep the lab free from unintentional radiation from devices such as a cell phone or a wireless local area network transmitter.
Off-the-shelf commercial zero-biased diode detectors have been used in this
work for power detection. Their junction resistance is sensitive to temperature
and thus the DC output voltage is also sensitive to temperature [1]. Therefore, it
will enhance measurement accuracy if the diodes temperature can be stabilized for
future work. In addition, the smaller the junction resistance is, the less sensitive
it is sensitive to temperature [1]. This presents a trade-off with the need for
maximum DC output voltage for a given available RF power. It will therefore be
beneficial in the future to explore this trade-off from a more integrated fabrication
process such as diode-based quartz MMIC technology developed at the University
of Virginia [2]. With this level of integration, the diode parameters can be tailored
by a designer [2].
The operating frequencies of the non-contacting measurement systems implemented in this work are designed to be below 10 GHz. It will be of great interest
to extend the operation frequencies into the millimeter wave bands and above.
As the frequency scales up, circuit performance becomes more sensitive to circuit
variations introduced by diode mounting and wire-bonding. It is therefore of benefit to use the above-mentioned more integrated process for circuit fabrication [2].
Another issue is that the available power from an RF source has a general trend
to decrease with increased frequency. This requires more sensitive power detection
schemes.
Compared to other elements such as thermistors and thermocouple used in a
power meter, power detection based on diodes gives the best sensitivity and thus
makes it more suitable than others for non-contacting measurement where low
Chapter 6. Summary and Future Work
109
power detection is required. However, the Flicker noise associated with the diode's
square-law detection limits the sensitivity to about -70 dBm, which is worse than
that of an heterodyne mixer (typically -110 dBm) [1]. One technique to solve
the issue is to apply modulation to the signal source and use lock-in amplifiers
at the detector outputs [3]. Another way to improve sensitivity is to use a mixer
that down-converts the RF signal. The down-converted signal is then amplified
and detected by a low-frequency power detector. It is of interest to explore the
advantages offered by the above-mentioned power detection schemes in the future
work.
Throughout the research in this work, the sampled-line reflectometer or its variant has been used for its simplicity. The sampled-line reflectometer only represents
a special class of six-port reflectometers. There are also other classes of six-port reflectometers that are also suitable for non-contacting measurement with potential
improvement on measurement accuracy. As illustrated in Fig. 5.7 in last chapter, a six-port reflectometer may be combined with the compact probing structure
proposed in the work to yield a measurement system with better accuracy and
bandwidth. The six-port reflectometer may be realized using multiple hybrids as
shown in Fig. 5.6.
Bibliography
[1] G.H. Bryant, "Principles of Microwave Measurements," Revised Edition., Peter
Peregrinus Ltd., The Institution of Electrical Engineers, 1993.
[2] S.M. Marazita, "Integrated Planar GaAs Schottky Mixers for Submillimeter
Wavelength Receivers," Dissertation., University of Virginia, Electrical Engineering, May 1999.
[3] S.A Chahine, el "A six-port reflectometer calibration using Schottky diodes
operating in AC detection mode," IEEE Trans, on Instrumentation and Measurement, vol. 42, issue 2 , pp. 281-282, April 1993.
110
Документ
Категория
Без категории
Просмотров
0
Размер файла
1 485 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа