Advanced Microwave Circuits and Systems Part 1

I

Advanced Microwave
Circuits and Systems



Advanced Microwave
Circuits and Systems

Edited by

Vitaliy Zhurbenko

In-Tech

intechweb.org


Published by In-Teh
In-Teh
Olajnica 19/2, 32000 Vukovar, Croatia
Abstracting and non-profit use of the material is permitted with credit to the source. Statements and
opinions expressed in the chapters are these of the individual contributors and not necessarily those of
the editors or publisher. No responsibility is accepted for the accuracy of information contained in the
published articles. Publisher assumes no responsibility liability for any damage or injury to persons or
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publication of which they are an author or editor, and the make other personal use of the work.
© 2010 In-teh
www.intechweb.org

Additional copies can be obtained from:

First published April 2010
Printed in India
Technical Editor: Sonja Mujacic
Cover designed by Dino Smrekar
Advanced Microwave Circuits and Systems,
Edited by Vitaliy Zhurbenko

p. cm.
ISBN 978-953-307-087-2


V

Preface
This book is based on recent research work conducted by the authors dealing with the design
and development of active and passive microwave components, integrated circuits and
systems. It is divided into seven parts. In the first part comprising the first two chapters,
alternative concepts and equations for multiport network analysis and characterization are
provided. A thru-only de-embedding technique for accurate on-wafer characterization is
introduced.
The second part of the book corresponds to the analysis and design of ultra-wideband lownoise amplifiers (LNA). The LNA is the most critical component in a receiving system. Its
performance determines the overall system sensitivity because it is the first block to amplify
the received signal from the antenna. Hence, for the achievement of high receiver performance,
the LNA is required to have a low noise figure with good input matching as well as sufficient
gain in a wide frequency range of operation, which is very difficult to achieve. Most circuits
demonstrated are not stable across the frequency band, which makes these amplifiers prone
to self-oscillations and therefore limit their applicability. The trade-off between noise figure,
gain, linearity, bandwidth, and power consumption, which generally accompanies the LNA

design process, is discussed in this part.
The requirement from an amplifier design differs for different applications. A power amplifier
is a type of amplifier which drives the antenna of a transmitter. Unlike LNA, a power amplifier
is usually optimized to have high output power, high efficiency, optimum heat dissipation
and high gain. The third part of this book presents power amplifier designs through a series
of design examples. Designs undertaken include a switching mode power amplifier, Doherty
power amplifier, and flexible power amplifier architectures. In addition, distortion analysis
and power combining techniques are considered.
Another key element in most microwave systems is a signal generator. It forms the heart of all
kinds of communication and radar systems. The fourth part of this book is dedicated to signal
generators such as voltage-controlled oscillators and electron devices for millimeter wave and
submillimeter wave applications. This part also covers studies of integrated buffer circuits.
Passive components are indispensable elements of any electronic system. The increasing
demands to miniaturization and cost effectiveness push currently available technologies to the
limits. Some considerations to meet the growing requirements are provided in the fifth part
of this book. The following part deals with circuits based on LTCC and MEMS technologies.


VI

The book concludes with chapters considering application of microwaves in measurement
and sensing systems. This includes topics related to six-port reflectometers, remote network
analysis, inverse scattering for microwave imaging systems, spectroscopy for medical
applications and interaction with transponders in medical sensors.
Editor

Vitaliy Zhurbenko


VII

Contents
Preface
1. Mixed-mode S-parameters and Conversion Techniques

V
001

Allan Huynh, Magnus Karlsson and Shaofang Gong

2. A thru-only de-embedding method for on-wafer
characterization of multiport networks

013

Shuhei Amakawa, Noboru Ishihara and Kazuya Masu

3. Current reuse topology in UWB CMOS LNA

033

TARIS Thierry

4. Multi-Block CMOS LNA Design for UWBWLAN Transform-Domain
Receiver Loss of Orthogonality

059

Mohamed Zebdi, Daniel Massicotte and Christian Jesus B. Fayomi

5. Flexible Power Amplifier Architectures for Spectrum
Efficient Wireless Applications

073

Alessandro Cidronali, Iacopo Magrini and Gianfranco Manes

6. The Doherty Power Amplifier

107

Paolo Colantonio, Franco Giannini, Rocco Giofrè and Luca Piazzon

7. Distortion in RF Power Amplifiers and Adaptive Digital Base-Band Predistortion

133

Mazen Abi Hussein, YideWang and Bruno Feuvrie

8. Spatial power combining techniques for semiconductor power amplifiers

159

Zenon R. Szczepaniak

9. Field Plate Devices for RF Power Applications

177

Alessandro Chini

10. Implementation of Low Phase Noise Wide-Band VCO with
Digital Switching Capacitors

199

Meng-Ting Hsu, Chien-Ta Chiu and Shiao-Hui Chen

11. Intercavity Stimulated Scattering in Planar FEM as a Base
for Two-Stage Generation of Submillimeter Radiation
Andrey Arzhannikov

213


VIII

12. Complementary high-speed SiGe and CMOS buffers

227

Esa Tiiliharju

13. Integrated Passives for High-Frequency Applications

249

Xiaoyu Mi and Satoshi Ueda

14. Modeling of Spiral Inductors

291

Kenichi Okada and Kazuya Masu

15. Mixed-Domain Fast Simulation of RF and Microwave MEMS-based
Complex Networks within Standard IC Development Frameworks

313

Jacopo Iannacci

16. Ultra Wideband Microwave Multi-Port Reflectometer in Microstrip-Slot Technology:
Operation, Design and Applications
339
Marek E. Bialkowski and Norhudah Seman

17. Broadband Complex Permittivity Determination for Biomedical Applications

365

Radim Zajíˇcek and Jan Vrba

18. Microwave Dielectric Behavior of Ayurvedic Medicines

387

S.R.Chaudhari ,R.D.Chaudhari and J.B.Shinde

19. Analysis of Power Absorption by Human Tissue in Deeply Implantable

Medical Sensor Transponders

407

Andreas Hennig, Gerd vom Bögel

20. UHF Power Transmission for Passive Sensor Transponders

421

Tobias Feldengut, Stephan Kolnsberg and Rainer Kokozinski

21. Remote Characterization of Microwave Networks - Principles and Applications

437

Somnath Mukherjee

22. Solving Inverse Scattering Problems Using Truncated Cosine
Fourier Series Expansion Method

455

Abbas Semnani and Manoochehr Kamyab

23. Electromagnetic Solutions for the Agricultural Problems
Hadi Aliakbarian, Amin Enayati, Maryam Ashayer Soltani,
Hossein Ameri Mahabadi and Mahmoud Moghavvemi

471

Mixed-mode S-parameters and Conversion Techniques

1

x1
Mixed-mode S-parameters
and Conversion Techniques
Allan Huynh, Magnus Karlsson and Shaofang Gong

Linköping University
Sweden

1. Introduction
Differential signaling in analog circuits is an old technique that has been utilized for more
than 50 years. During the last decades, it has also been becoming popular in digital circuit
design, when low voltage differential signaling (LVDS) became common in high-speed
digital systems. Today LVDS is widely used in advanced electronics such as laptop
computers, test and measurement instrument, medical equipment and automotive. The
reason is that with increased clock frequencies and short edge rise/fall times, crosstalk and
electromagnetic interferences (EMI) appear to be critical problems in high-speed digital
systems. Differential signaling is aimed to reduce EMI and noise issues in order to improve
the signal quality. However, in traditional microwave theory, electric current and voltage
are treated as single-ended and the S-parameters are used to describe single-ended
signaling. This makes advanced microwave and RF circuit design and analysis difficult,
when differential signaling is utilized in modern communication circuits and systems. This
chapter introduces the technique to deal with differential signaling in microwave and
millimeter wave circuits.

2. Differential Signal
Differential signaling is a signal transmission method where the transmitting signal is sent
in pairs with the same amplitude but with mutual opposite phases. The main advantage
with the differential signaling is that any introduced noise equally affects both the
differential transmission lines if the two lines are tightly coupled together. Since only the
difference between the lines is considered, the introduced common-mode noise can be
rejected at the receiver device. However, due to manufacturing imperfections, signal
unbalance will occur resulting in that the energy will convert from differential-mode to
common-mode and vice versa, which is known as cross-mode conversion. To damp the
common-mode currents, a common-mode choke can be used (without any noticeable effect
on the differential currents) to prevent radiated emissions from the differential lines. To
produce the electrical field strength from microamperes of common-mode current,
milliamperes of differential current are needed (Clayton, 2006). Moreover, the generated
electric and magnetic fields from a differential line pair are more localized compared to


2

Advanced Microwave Circuits and Systems

those from single-ended lines. Owing to the ability of noise rejection, the signal swing can be
decreased compared to a single-ended design and thereby the power can be saved.
When the signal on one line is independent of the signal on the adjacent line, i.e., an
uncoupled differential pair, the structure does not utilize the full potential of a differential
design. To fully utilize the differential design, it is beneficial to start by minimizing the
spacing between two lines to create the coupling as strong as possible. Thereafter, the
conductors width is adjusted to obtain the desired differential impedance. By doing this, the
coupling between the differential line pair is maximized to give a better common-mode
rejection.
S-parameters are very commonly used when designing and verifying linear RF and

microwave designs for impedance matching to optimize gain and minimize noise.
Although, traditional S-parameter representation is a very powerful tool in circuit analysis
and measurement, it is limited to single-ended RF and microwave designs. In 1995,
Bockelman and Einsenstadt introduced the mixed-mode S-parameters to extend the theory
to include differential circuits. However, owing to the coupling effects between the coupled
differential transmission lines, the odd- and even-mode impedances are not equal to the
unique characteristic impedance. This leads to the fact that a modified mixed-mode Sparameters representation is needed. In this chapter, by starting with the familiar concepts
of coupling, crosstalk and terminations, mixed-mode S-parameters will be introduced.
Furthermore, conversion techniques between different modes of S-parameters will be
described.
2.1 Coupling and Crosstalk
Like in single-ended signaling, differential transmission lines need to be correctly
terminated, otherwise reflections arise and distortions are introduced into the system. In a
system where parallel transmission lines exist, either in differential signaling or in parallel
single-ended lines, line-to-line coupling arises and it will cause characteristic impedance
variations. The coupling between the parallel single-ended lines is also known as crosstalk
and it is related to the mutual inductance (Lm) and capacitance (Cm) existing between the
lines. The induced crosstalk or noise can be described with a simple approximation as
following
ܸ௡௢௜௦௘ ൌ ୫

‫ܫ‬௡௢௜௦௘ ൌ ‫ܥ‬௠

ୢ୍ౚ౨౟౬౛౨

(1)

ௗ௏೏ೝ೔ೡ೐ೝ

(2)

ୢ୲

ௗ௧

where Vnoise and Inoise are the induced voltage and current noises on the adjacent line and
Vdriver and Idriver are the driving voltage and current on the active line. Since both the voltage
and current noises are induced by the rate of current and voltage changes, extra care is
needed for high-speed applications.
The coupling between the parallel lines depends firstly on the spacing between the lines and
secondly on the signal pattern sent on the parallel lines. Two signal modes are defined, i.e.,
odd- and even-modes. The odd-mode is defined such that the driven signals in the two
adjacent lines have the same amplitude but a 180 degree of relative phase, which can be
related to differential signal. The even-mode is defined such that the driven signals in the
two adjacent lines have the same amplitude and phase, which can be related to common-


Mixed-mode S-parameters and Conversion Techniques

3

mode noise for a differential pair of signal. Fig. 1 shows the electric and magnetic field lines
in the odd- and even-mode transmissions on the two parallel microstrips. Fig. 1a shows that
the odd-mode signaling causes coupling due to the electric field between the microstrips,
while in the even-mode shown in Fig 1b, there is no direct electric coupling between the
lines. Fig. 1c shows that the magnetic field in the odd-mode has no coupling between the
two lines while, as shown in Fig. 1d, in the even-mode the magnetic field is coupled
between the two lines.

Current into the page

Current out of the page

a. electric field in odd-mode

b. electric field in even-mode

c. magnetic field in odd-mode
d. magnetic field in even-mode
Fig. 1. Odd- and even-mode electric and magnetic fields for two parallel microstrips.
2.2 Odd-mode
The induced crosstalk or voltage noise in a pair of parallel transmission lines can be
approximated with Equation 1. For the case of two parallel transmission lines the equation
can be rewritten as following
ௗூ
ௗூ
(3)
ܸଵ ൌ ‫ܮ‬଴ ௗ௧భ ൅ ‫ܮ‬௠ ௗ௧మ
ܸଶ ൌ ‫ܮ‬଴

ௗூమ
ௗ௧

൅ ‫ܮ‬௠

ௗூభ
ௗ௧

(4)

where L0 is the equivalent lumped-self-inductance in the transmission line and Lm is the
mutual inductance arisen due to the coupling between the lines. Signal propagation in the
odd-mode results in I1 = -I2, since the current is always driven with equal magnitude but in
opposite directions. Substituting it into Equations 3 and 4 yeilds
ௗூ

ܸଵ ൌ ሺ‫ܮ‬଴ െ ‫ܮ‬௠ ሻ ௗ௧భ

(5)


4

Advanced Microwave Circuits and Systems
��

(6)

�� � ��� � �� � �
��

This shows that, due to the crosstalk, the total inductance in the transmission lines reduces
with the mutual inductance (Lm).
Similarly, the current noise in the parallel transmission lines can be estimated with Equation
2. For two parallel transmission lines the equation can be rewritten as following
�� � ��

�� � ��

���

��

���
��

� ��

� ��

���� ��� �

(7)

���� ��� �

(8)

��

��

where C0 is the equivalent lumped-capacitance between the line and ground, and Cm is the
mutual capacitance between the transmission lines arisen due to the coupling between the
lines. Signal propagation in odd-mode results in V1 = -V2. Substituting it into Equations 7
and 8 yields
��
�� � ��� � ��� � �
(9)
��

���

�� � ��� � ��� �

(10)

��

Equations 9 and 10 show that, in opposite to the inductance, the total capacitance increases
with the mutual capacitance.
The addition of mutual inductance and capacitance shows that the characteristic impedance
as well as the phase velocity is directly dependant of the mutual coupling, as shown with
the following equations
�����

������ �� �

��� � ������ � ������� ����� �
��� �

�

√��

�

�

�

�

���� ��� ���� ���� �

(11)
(12)

where Zoo and vpo are the odd-mode impedance and phase velocity, respectively.
Consequently, the total characteristic impedance in the odd-mode reduces due to the
coupling or crosstalk between the parallel transmission lines and the phase velocity changes
as well.
2.3 Even-mode
In the case of even-mode where the signals are driven with equal magnitude and phase, V1
= V2 and I1 = I2, Equations 3, 4, 7 and 8 can be rewritten to the following:
��

(13)

��

(14)

�� � ��� � �� � ���

�� � ��� � �� � ���


Mixed-mode S-parameters and Conversion Techniques

�� � ��

�� � ��

5

���

(15)

���

(16)

��

��

Consequently, in opposite to the odd-mode case, the even-mode wave propagation changes
the even-mode impedance (Zoe) and phase velocity (vpe) as shown below:
�����

��� � ������ � �
��� �

�

√��

�

������� ��� �

(17)

������

�

(18)

���� ��� ���� �

2.4 Terminations
As shown in the previous section, the impedance varies due to the odd- and even-mode
transmissions and the coupling between the transmission lines. Fig. 2 shows a graph of the
odd- and even-mode impedance change as a function of the spacing between two specific
parallel-microstrips. If the loads connected to the parallel lines have a simple termination as
commonly used in the single-ended case, reflections will occur due to Zoo ≠ Zoe ≠ Z0. Fig. 3
shows two termination configurations, i.e., Pi- and T-terminations, which can terminate both
the odd- and even-mode signals in coupled parallel transmission lines.

Fig. 2. Variation of the odd- and even-mode impedances as a function of the spacing
between two parallel microstrips.

V1
R3
V2
a. Pi-termination

R1

R2

+
-

Differential
reciever


6

Advanced Microwave Circuits and Systems

R1

V1

R3
R2

+
-

V2

Single-ended
recievers

+

b. T-termination
Fig. 3. Termination configurations for coupled transmission lines.
Fig. 3a shows the Pi-termination configuration. In the odd-mode transmission, i.e., V1 = -V2 a
virtual ground can be imaginarily seen in the middle of R3 and this forces R3/2 in parallel
with R1 or R2 equal to Zoo. Since no current flows between the two transmission lines in the
even-mode, i.e., V1 = V2, R1 and R2 must thus be equal to Zoe. For a matched differential
system with optimized gain and noise, the following expressions need to be fulfilled for a
Pi-termination configuration.
(19)

ܴଵ ൌ ܴଶ ൌ ܼ௢௘
௓ ௓

(20)

ܴଷ ൌ ʹ ௓ ೚೐ି௓೚೚
೚೐

೚೚

Fig. 3b shows the T-termination configuration. In the odd-mode transmission, i.e., V1 = -V2,
a virtual ground can be seen between R1 and R2 and this makes R1 and R2 equal to Zoo. In the
even-mode transmission, i.e., V1 = V2 no current flows between the two transmission lines.
This makes R3 to be seen as two 2R3 in parallel, as illustrated in Fig. 4. This leads to the
conclusion that Zoe must be equal to R1 or R2 in serial with 2R3. Equations 21 and 22 show the
required values of the termination resistors needed for the T-termination configuration in
order to get a perfect matched system (Hall et al., 2000).
V1

R1

R2

V2

2R3
2R3

Fig. 4. Equivalent network for T-network termination in even-mode.
ܴଵ ൌ ܴଶ ൌ ܼ௢௢
ଵ

3. S-parameters

ܴଷ ൌ ଶ ሺܼ௢௘ െ ܼ௢௢ ሻ

(21)
(22)

Scattering parameters or S-parameters are commonly used to describe an n-port network
operating at high frequencies like RF and microwave frequencies. Other well-known
parameters often used for describing an n-port network are Z (impedance), Y (admittance), h
(hybrid) and ABCD parameters. The main difference between the S-parameters and other


Mixed-mode S-parameters and Conversion Techniques

7

parameter representations lies in the fact that S-parameters describe the normalized power
waves when the input and output ports are properly terminated, while other parameters

describe voltage and current with open or short ports. S-parameters can also be used to
express other electrical properties like gain, insertion loss, return loss, voltage standing
wave ratio, reflection coefficient and amplifier stability.
3.1 Single-ended
The travelling waves used in the transmission line theory are defined with incident
normalized power wave an and reflected normalized power wave bn.
ଵ

ܽ௡ ൌ

ଶඥ௓బ
ଵ

ܾ௡ ൌ

ଶඥ௓బ

(23)

ሺܸ௡ ൅ ܼ଴ ‫ܫ‬௡ ሻ

(24)

ሺܸ௡ െ ܼ଴ ‫ܫ‬௡ ሻ

where index n refers to a port number and Z0 is the characteristic impedance at that specific
port. The normalized power waves are used for the definition of single-ended S-parameters.
Fig. 5 shows a sketch of a two-port network with the normalized power wave definitions
(Kurokawa, 1965).

a1

a2

S

b1

b2

Fig. 5. S-parameters with normalized power wave definition of a two-port network.
The two-port S-parameters are defined as follows.
௕

ܵଵଵ ൌ ௔భ ቚ
భ

௕

ܵଵଶ ൌ ௔భ ቚ
మ

௕

ܵଶଵ ൌ ௔మ ቚ
భ

௕

௔భ ୀ଴

௔మ ୀ଴

ܵଶଶ ൌ ௔మ ቚ
మ

and in matrix form

௔మ ୀ଴

‫ͳݐݎ݋݌ݐܽ݊݋݅ݐ݈݂ܿ݁݁ݎ ؠ‬

‫݊݅ܽ݃݁݃ܽݐ݈݋ݒ݁ݏݎ݁ݒ݁ݎ ؠ‬

‫݊݅ܽ݃݁݃ܽݐ݈݋ݒ݀ݎܽݓݎ݋݂ ؠ‬

௔భ ୀ଴

‫ʹݐݎ݋݌ݐܽ݊݋݅ݐ݈݂ܿ݁݁ݎ ؠ‬

ܵ
ܾ
൜ ଵ ൠ ൌ ൤ ଵଵ
ܵଶଵ
ܾଶ

ܵଵଶ ܽଵ
൨ቄ ቅ
ܵଶଶ ܽଶ

(25)
(26)
(27)
(28)

(29)

When measuring S-parameters, it is important not to have any power wave reflected at port
1 or 2, i.e., a1 = 0 or a2 = 0, as shown in Equations 25-28. Otherwise errors are included in the


8

Advanced Microwave Circuits and Systems

results. For an n-port network, Equation 29 can be extended to the following expression
(Ludwig & Bretchko, 2000):
ܾଵ
ܵଵଵ
ܵଶଵ
ܾଶ
൮ ൲ൌ൦
‫ڭ‬
‫ڭ‬
ܵ௡ଵ
ܾ௡

ܵଵଶ
ܵଶଶ
‫ڭ‬

ܵ௡ଶ

‫ڮ‬
‫ڮ‬
‫ڰ‬
‫ڮ‬

ܵଵ௡ ܽଵ
ܵଶ௡ ܽଶ
൪൮ ‫ ڭ‬൲
‫ڭ‬
ܵ௡௡ ܽ௡

(30)

3.2 Mixed-mode
A two-port single-ended network can be described by a 2x2 S-parameter matrix as shown by
Equation 29. However, to describe a two-port differential-network a 4x4 S-parameter matrix
is needed, since there exists a signal pair at each differential port. Fig. 6 shows a sketch of
the power wave definitions of a two-port differential-network, i.e., a four-port network.
a1
b1

a3
P1

P3

b3

DUT
a2
b2

a4
P2

P4

b4

Fig. 6. Power wave definition of a differential two-port network.
Since a real-world differential-signal is composed of both differential- and common-mode
signals in general, the single-ended four-port S-parameter matrix does not provide much
insight information about the differential- and common-mode matching and transmission.
Therefore, the mixed-mode S-parameters must be used. The differential two-port and
mixed-mode S-parameters are defined by Equation 31 (Bockelman & Eisenstadt, 1995).
ܾௗଵ
ܵ
൤ ௗௗଵଵ
ܾௗଶ
ܵௗௗଶଵ
൦ ൪ൌ൦
ܵ
ܾ௖ଵ
൤ ௖ௗଵଵ
ܵ௖ௗଶଵ
ܾ௖ଶ

ܵௗௗଵଶ

൨
ܵௗௗଶଶ
ܵ௖ௗଵଶ
൨
ܵ௖ௗଶଶ

ܵௗ௖ଵଵ
ܵௗ௖ଶଵ
ܵ
൤ ௖௖ଵଵ
ܵ௖௖ଶଵ

൤

ܵௗ௖ଵଶ ܽௗଵ
൨
ܵௗ௖ଶଶ ܽௗଶ
൪ ൦ܽ ൪
ܵ௖௖ଵଶ
௖ଵ
൨ ܽ
ܵ௖௖ଶଶ
௖ଶ

(31)

where adn, acn, bdn and bcn are normalized differential-mode incident-power, common-mode
incident-power, differential-mode reflected-power, and common-mode reflected-power at
port n. The mixed-mode S matrix is divided into 4 sub-matrixes, where each of the submatrixes provides information for different transmission modes.






Sdd sub-matrix: differential-mode S-parameters
Sdc sub-matrix: mode conversion of common- to differential-mode waves
Scd sub-matrix: mode conversion of differential- to common-mode waves
Scc sub-matrix: common-mode S-parameters


Mixed-mode S-parameters and Conversion Techniques

9

With mixed-mode S-parameters, characteristics about the differential- and common-mode
transmissions and conversions between differential- and common-modes can be found
(Bockelman & Eisenstadt, 1995).
3.3 Single-Ended to Mixed-Mode conversion
The best way to measure the mixed-mode S-parameters is to use a four-port mixed-mode
vector network analyzer (VNA). In the case where the mixed-mode S-parameters cannot
directly be simulated or measured, the single-ended results can first be obtained and then
converted into mixed-mode S-parameters by a mathematical conversion. This section shows
how it is done for a differential two-port network shown in Fig. 6.
The differential- and common-mode voltages, currents and impedances can be expressed as
below, where n is the port number,
ܸௗ௡ ൌ ܸଶ௡ିଵ െ ܸଶ௡ ܸ௖௡ ൌ
‫ܫ‬ௗ௡ ൌ

ூమ೙షభ ିூమ೙

ܼௗ ൌ

௏೏
ூ೏

ଶ

௏మ೙షభ ା௏మ೙
ଶ

‫ܫ‬௖௡ ൌ ‫ܫ‬ଶ௡ିଵ ൅ ‫ܫ‬ଶ௡

ൌ ʹܼ௢௢ ܼ௖ ൌ

௏೎
ூ೎

ൌ

௓೚೐
ଶ

(32)
(33)
(34)

Similar to the single-ended incident- and reflected-powers, the differential- and commonmode incident- and reflected-powers are defined as follows
ܽௗ௡ ൌ

ܽ௖௡ ൌ

ܾௗ௡ ൌ

ܾ௖௡ ൌ

ଵ

ଶඥ௓೏೙
ଵ

ଶඥ௓೎೙
ଵ

ଶඥ௓೏೙
ଵ

ଶඥ௓೎೙

ሺܸௗ௡ ൅ ܼௗ௡ ‫ܫ‬ௗ௡ ሻ

(35)

ሺܸௗ௡ െ ܼௗ௡ ‫ܫ‬ௗ௡ ሻ

(37)

ሺܸ௖௡ ൅ ܼ௖௡ ‫ܫ‬௖௡ ሻ

(36)

ሺܸ௖௡ െ ܼ௖௡ ‫ܫ‬௖௡ ሻ

(38)

ሺܽ௡ ൅ ܾ௡ ሻ

(40)

where adn, acn, bdn and bcn are normalized differential-mode incident-power, common-mode
incident-power, differential-mode reflected-power, and common-mode reflected-power at
port n, respectively. The voltage and current at port n can be expressed by rewriting
Equations 35-38 to as follow
(39)
ܸ௡ ൌ ඥܼ଴ ሺܽ௡ ൅ ܾ௡ ሻ
‫ܫ‬௡ ൌ

ଵ

ඥ௓బ

Inserting Equations 32-34 and Equations 39-40 into Equations 35-38 and assuming that Zoo =
Zoe = Z0, yields the following results


10

Advanced Microwave Circuits and Systems

��� �

��� �

����� ����
√�

����� ����
√�

������������� �
������������� �

����� ����

(41)

����� ����

(42)

√�

√�

As shown by Equations 41 and 42 the differential incident and reflected waves can be
described by the single-ended waves. Inserting Equations 41 and 42 into Equation 31, the
following expression is obtained.
�� �� � � �����������

�����
�

�������� �� � � � ����
�����
�����

���
���
��� � �
���
���

���
���
���
���

���
���
���
���

�����
�����
�����
�����

�����
�����
�����
�����

���
1
1 0
���
� �������� �
�
���
√2 1
���
0

(43)
�����
�����
��
�����
�����

�1 0
0 1
1 0
0 1

0
0
�
�1
1

As shown by Equation 43, single-ended S-parameters can be converted into mixed-mode Sparameters with the [M]-matrix (Bockelman & Eisenstadt, 1995).

Note that the conversion method assumes that Zoo = Zoe = Z0. This assumption is only true if
the coupling between the differential signals does not exist. Figure 2 clearly shows that if
there is a coupling between the transmission lines then Z0 ≠ Zoo ≠ Zoe. Although this
conversion method is widely used today, the weakness of the conversion method has been
noticed by people working in the area (Vaz & Caggiano, 2004).
Based on this observation, two new parameters koo and koe depending on the coupling
between the transmission lines are introduced (Huynh et al., 2007). By this extension, the
effect of differential- and common-mode impedances are included in the conversion.
Inserting Zoo = kooZ0 and Zoe = koeZ0 into Equations 35-38, the following equations can be
obtained
��� �
��� �

��� �
��� �

������ ������� ���� �������� ������� ���� �

(44)

������ ������� ���� �������� ������� ���� �

(45)

������ ������� ���� �������� ������� ���� �

(46)

������ ������� ���� �������� ������� ���� �

(47)

������

������

������

������

Inserting Equations 44-47 into Equations 31 results in the following equation
�� �� � � ���� ���� � ��� ������ � � ��� �������

(48)


Mixed-mode S-parameters and Conversion Techniques

� � ���
�
�2�2���
�
� 0
��������� � � �
� � � ���
�2�2���
�
� 0
�
� � ���

�
�2�2���
�
� 0
������� � � �
� � � ���
�2�2���
�
� 0
�

�

� � ���

2�2���
0

� � ���

2�2���
0

�

� � ���

2�2���
0

� � ���

2�2���
0

11

0

� � ���

2�2���
0

� � ���

2�2���
0

� � ���

2�2���
0

� � ���

2�2���

�
�

� � ��� �
�
�
2�2���
�
�
0
�
� � ��� �
�
2�2��� �
0

�
�
� � ��� �
�
�
2�2���
�
�
0
�
� � ��� �
�
2�2��� �
0

As shown by Equation 48, the single-ended S-parameter representation can be converted to
mixed-mode S-parameters with the [M1] and [M2] matrixes for coupled transmission lines.

4. Conclusions
Owing to the existence of coupling between two parallel transmission lines, the
characteristic impedance of the transmission line will change depending on the line spacing
and the signal pattern transmitting on the adjacent lines. The defined odd- and even-mode
signals can be related to differential- and common-mode signals in the differential
transmission technique. Consequently, this leads to the fact that working with highly
coupled differential transmission lines one must take the odd- and even-mode impedance
variations into account. Otherwise, mismatching will occur and distortions will be
introduced into the system.
Furthermore, mixed-mode S-parameters were introduced and how to convert single-ended
to mixed-mode S-parameters was also presented. The impedance changes due to the oddand even-mode signal pattern are included to give a high accuracy when using mixed-mode
S-parameters.
What is not included in this chapter is how to find the odd- and even mode impedances in
practice. However, one can do it by using a differential time domain reflectormeter (TDR) to
find the odd- and even-mode impedances. In fact, companies providing vector network
analyzers can provide TDR as an embedded module, so only one vector network analyzer is
needed for real measurements.
Moreover, complex odd- and even-mode impedance have not been taken into consideration
in this chapter. Further studies can be done for verification of the theory.


12

Advanced Microwave Circuits and Systems

5. References
Bockelman D. E. and Eisenstadt W. R., Combined Differential and Common-Mode
Scattering Parameters: Theory and Simulation. IEEE transactions on microwave theory
and techniques, Vol. 43, No. 7, pp.1530-1539, July 1995.

Clayton P.R. Introduction to Elecctromagnetic Compatibility, John Wiley & Sons, Inc., ISBN13:978-0-471-75500-5, Hoboken, New Jersey, United States of America, 2006.
Hall S. H.; Hall G. W. and McCall J.A. High-Speed digital System Design, John Wiley & Sons,
Inc., ISBN 0-471-36090-2, USA, 2000.
Huynh A.; Håkansson P. and Gong S., “Mixed-mode S-parameter conversion for networks
with coupled differential signals” European Microwave Conference, pp. 238-241,
July 2007.
Ludwig R. & Bretchko P. RF Circuit Design Theory and Applications, Prectice Hall, ISBN 0-13095323-7, New Jersey, USA, 2000.
Kurokawa K. Power Waves and the Scattering Matrix, IEEE Transactions of Microwave Theory
and Techniques, Vol., 13, Marsh 1965, pp. 194-202.
Pozar D.M. Microwave Engineering Third Edition, John Wiley & Sons Inc., ISBN 0-471-48878-8,
USA, 2005.
Vaz K. & Caggiano M. Measurement Technique for the Extraction of Differential SParameters from Single-ended S-Parameters. IEEE 27th International Spring Seminar
on Electronics Technology, Vol. 2, pp. 313-317, May 2004.


A thru-only de-embedding method for on-wafer characterization of multiport networks

13

2
0
A thru-only de-embedding method for
on-wafer characterization of
multiport networks
Shuhei Amakawa, Noboru Ishihara, and Kazuya Masu
Tokyo Institute of Technology
Japan

1. Overview
De-embedding is the process of deducing the characteristics of a device under test (DUT) from

measurements made at a distance ((Bauer & Penfield, 1974)), often via additional measurements of one or more dummy devices. This article reviews a simple thru-only de-embedding
method suitable for on-wafer characterization of 2-port, 4-port, and 2n-port networks having
a certain symmetry property. While most conventional de-embedding methods require two
or more dummy patterns, the thru-only method requires only one THRU pattern.
If the device under measurement is a 2-port and the corresponding THRU pattern has the
left/right reflection symmetry, the THRU can be mathematically split into symmetric halves
and the scattering matrix for each of them can be determined (Ito & Masu, 2008; Laney, 2003;
Nan et al., 2007; Song et al., 2001; Tretiakov et al., 2004a). Once those scattering matrices are
available, the effects of pads and leads can be canceled and the characteristics of the device obtained. The method was applied up to 110GHz for characterization of an on-chip transmission
line (TL) (Ito & Masu, 2008).
In the case of 4-port devices such as differential transmission lines, 4-port THRU patterns with
ground-signal-ground-signal-ground (GSGSG) pads or GSSG pads can often be designed to
have the even/odd symmetry in addition to the left/right reflection symmetry. In that case,
the scattering matrix for a THRU can be transformed into a block-diagonal form representing two independent 2-ports by an even/odd transformation. Then, the 2-port thru-only deembedding method can be applied to the resultant two 2-ports. This 4-port thru-only method
was applied to de-embedding of a pair of coupled transmission lines up to 50 GHz (Amakawa
et al., 2008). The result was found to be approximately consistent with that from the standard open-short method (Koolen et al., 1991), which requires two dummy patterns: OPEN and
SHORT .
In the above case (Amakawa et al., 2008), the transformation matrix was known a priori because of the nominal symmetry of the THRU. However, if the 4-port THRU does not have the
even/odd symmetry or if the device under measurement is a 2n-port with n ≥ 3, the above
method cannot be applied. Even if so, the thru-only method can actually be extended to
4-ports without even/odd symmetry or 2n-ports by using the recently proposed S-parameterbased modal decomposition of multiconductor transmission lines (MTLs) (Amakawa et al.,
2009). A 2n-port THRU can be regarded as nonuniform multiconductor transmission lines,


14

Advanced Microwave Circuits and Systems

PAD left

DUT

PAD right

TL

Tdut

TR

Tmeas
(a) A test pattern with pads and a DUT.

PAD left

PAD right

TL

TR

Z/2
Y

Z/2
Y

Tthru
(b) Model of THRU.

Fig. 1. DUT embedded in parasitic networks.
and its scattering matrix can be transformed into a block-diagonal form with 2 × 2 diagonal
blocks, representing n uncoupled 2-ports. The validity of the procedure was confirmed by applying it to de-embedding of four coupled transmission lines, which is an 8-port (Amakawa
et al., 2009).
The thru-only de-embedding method could greatly facilitate accurate microwave and
millimeter-wave characterization of on-chip multiport networks. It also has the advantage
of not requiring a large area of expensive silicon real estate.

2. Introduction
Demand for accurate high-frequency characterization of on-chip devices has been escalating
concurrently with the accelerated development of high-speed digital signaling systems and
radio-frequency (RF) circuits. Millimeter-wave CMOS circuits have also been becoming a hot
research topic.
To characterize on-chip devices and circuits, on-wafer scattering parameter (S-parameter)
measurements with a vector network analyzer (VNA) have to be made. A great challenge
there is how to deal with parasitics. Since an on-wafer device under test (DUT) is inevitably
“embedded” in such intervening structures as probe pads and leads as schematically shown
in Fig. 1(a), and they leave definite traces in the S-parameters measured by a VNA, the characteristics of the DUT have to be “de-embedded” (Bauer & Penfield, 1974) in some way from
the as-measured data.
While there have been a number of de-embedding methods proposed for 2-port networks,
very few have been proposed for 4-port networks in spite of the fact that many important
devices, such as differential transmission lines, are represented as 4-ports. In this article, we
present a simple 4-port de-embedding method that requires only a THRU pattern (Amakawa


A thru-only de-embedding method for on-wafer characterization of multiport networks

G

G

S

S

150µm

PAD left PAD right

S

S
pad

pad
G

G
G

G

15

Zthru (Ythru)

Fig. 2. Micrograph and schematic representation of THRU (Ito & Masu, 2008).
et al., 2008). This method is an extension of a thru-only method for 2-ports. In addition, we
also present its extension to 2n-ports (Amakawa et al., 2009).
The rest of this article starts with a brief description of the thru-only de-embedding method for

2-ports in Section 3. It forms the basis for the multiport method. In Section 4, we explain the
mode transformation theory used in the multiport de-embedding method. Section 5 presents
an example of performing de-embedding by the thru-only method when the DUT is a 4-port
having the even/odd symmetry. Section 6 explains how the mode transformation matrix can
be found when the DUT does not have such symmetry or when the DUT is a 2n-port with
n ≥ 3. Section 7 shows examples of applying the general method. Finally, Section 8 concludes
the article.

3. Thru-only de-embedding for 2-ports
Commonly used de-embedding methods usually employ OPEN and SHORT on-chip standards
(dummy patterns) (Wartenberg, 2002). De-embedding procedures are becoming increasingly
complex and tend to require several dummy patterns (Kolding, 2000b; Vandamme et al., 2001;
Wei et al., 2007). The high cost associated with the large area required for dummy patterns is
a drawback of advanced de-embedding methods.
Thru-only methods, in contrast, require only one THRU and gaining popularity (Daniel et
al., 2004; Goto et al., 2008; Ito & Masu, 2008; Laney, 2003; Nan et al., 2007; Song et al., 2001;
Tretiakov et al., 2004a).
In (Ito & Masu, 2008; Laney, 2003; Nan et al., 2007; Song et al., 2001; Tretiakov et al., 2004a), the
THRU is modeled by a Π-type equivalent circuit shown in Fig. 1(b). The method of (Goto et al.,
2008), on the other hand, was derived from (Mangan et al., 2006), which is related to (Rautio,
1991). It is applicable if the series parasitic impedance Z in Fig. 1(b) is negligible (Goto et al.,
2008; Ito & Masu, 2008; Rautio, 1991). In what follows, we will focus on the method of (Ito &
Masu, 2008; Laney, 2003; Nan et al., 2007; Song et al., 2001; Tretiakov et al., 2004a).
The THRU pattern used in (Ito & Masu, 2008) is shown in Fig. 2. The 150 µm-pitch groundsignal-ground (GSG) pads are connected with each other via short leads. It turned out that
the THRU can be adequately represented by the frequency-independent model shown in Fig. 3.
Fig. 4 shows good agreement between the measurement data and the model up to 100 GHz.
The procedure of the thru-only de-embedding method ((Ito & Masu, 2008; Laney, 2003; Nan
et al., 2007; Song et al., 2001; Tretiakov et al., 2004a)) is as follows. The 2-port containing the
DUT and the THRU a are assumed to be representable by Fig. 1(a) and Fig. 1(b), respectively.

16

Advanced Microwave Circuits and Systems

0.55Ω

16 pH 16 pH

0.55Ω

41 fF
1.0 Ω

76 fF

41 fF
1.0 Ω

76 fF

0
S 21

−10
−20
−30

Model
Measurement

−1

S11

−3

−2

−40
−4
0.01 0.1 1
10 100
Frequency [GHz]

Phase [deg.]

0

Magnitude [dB]

Magnitude [dB]

PAD left PAD right
Fig. 3. Lumped-element Π-model of THRU (Ito & Masu, 2008).

0

S 21

60

S11

120
180
0.01 0.1 1
10 100
Frequency [GHz]

Fig. 4. Measured and modeled (Fig. 3) S-parameters of the THRU pattern. (Ito & Masu, 2008).
In terms of transfer matrices (Mavaddat, 1996), this means that
Tmeas = TL Tdut TR ,

(1)

Tthru = TL TR .

(2)

The S-matrix and T-matrix of a 2-port are related to each other through
S=
T=

S11
S21

S12
S22
T12

T22

T11
T21

=
=

1
T11

1
S21

det T
− T12

T21
1
1
S11

−S22
− det S

Suppose now that the Y-matrix of the THRU is given by
Ythru =

y11
y12

y12
y11

.

,

(3)
.

(4)

(5)

Note that in (5), reciprocity (y21 = y12 ) and reflection symmetry (y22 = y11 ) are assumed. (5)
can be found by converting the measured S-matrix of the THRU into a Y-matrix through (18).
If the THRU is split into symmetric halves according to the Π-equivalent in Fig. 1(b),
YL =

Y + 2Z −1
−2Z −1

−2Z −1
2Z −1

(6)


A thru-only de-embedding method for on-wafer characterization of multiport networks

17

Magnitude [dB]

0.15
0.10

S 21

0.05
0
−0.05

S 12

−0.10
−0.15
0

S11, S22

20

40
60
80
Frequency [GHz]

100

Phase [deg.]

1.0
S 21
0
S 12
−1.0

0

20

40
60
80
Frequency [GHz]

100

Fig. 5. De-embedded results of the THRU pattern. The thru-only de-embedding method is
applied. The maximum magnitude of S11 is −33.7 dB (Ito & Masu, 2008).
and
YR =

2Z −1
−2Z −1

−2Z −1
Y + 2Z −1

,

(7)

respectively. The parameters in Fig. 1(b) are then given by
Y = y11 + y12 ,

(8)

Z = −1/y12 .

(9)

The characteristics of the DUT can be de-embedded as
−1
.
Tdut = TL−1 Tmeas TR

(10)

For the procedure to be valid, it is necessary, at least, that the de-embedded THRU that does
nothing. That is, S11 and S22 should be at the center of the Smith chart, and S12 and S21 are
at (1,0). Fig. 5 shows that those do hold approximately. Published papers indicate reasonable
success of the thru-only de-embedding method for 2-ports (Ito & Masu, 2008; Laney, 2003;
Nan et al., 2007; Song et al., 2001; Tretiakov et al., 2004a).

4. Theory of mode transformation
4.1 General theory

In this section, we explain the theory of S-matrix mode transformation (Amakawa et al., 2008)
in preparation for developing thru-only de-embedding for multiports based on the 2-port
method explained in the preceding section.