99
Analysis and Design of Novel Structures of Artificial
Transmission Lines for MMIC/MHMIC Technology
Yansheng Xu and Renato G. Bosisio
Abstract— In this paper, some new types of artificial transmission
lines, compatible with monolithic-microwave integrated-circuit/miniature
hybrid-microwave integrated-circuit technology are presented. In the new
designs, short subsections of different lines are connected together to
achieve the needed performance of various transmission-line functions
such as impedance transformation, power coupling, etc. Theoretical calculations are given and some typical design data are provided, including
models of extremely low impedance lines, which are very practical in the
design of microwave power amplifiers and oscillators using heterojunction bipolar transistors or high electron-mobility transistors. Calculation
results are validated by simulations and experiments. The proposed
structures are very flexible and can easily provide transmission lines with
widely varying characteristics.
Index Terms—Coplanar waveguides, microstrip, microwave integrated
circuits, MMIC’s, transmission lines.
I. INTRODUCTION
Transmission lines are the basic elements used in the design of
microwave components, circuits, and subsystems. Numerous types of
microwave transmission lines have been proposed and successfully
used. However, transmission lines capable of achieving very high and
very low impedances with large operating bandwidths and compatible with monolithic-microwave integrated-circuit (MMIC)/miniature
hybrid-microwave integrated-circuit (MHMIC) technology are still
an important topic of study due to applications in wireless and
satellite communications. Ultra-low impedance transmission lines
find applications in matching networks wherever low-impedance
devices such as power FET’s [heterojunction bipolar transistors
(HBT’s), high electron-mobility transistors (HEMT’s), pseudomorphic HEMT’s (pHEMT’s)] are used. Recently, low-loss coplanar
waveguide (CPW) and thin-film microstrip transmission line (TFMS)
with ultra-low characteristic impedance on multilayer MMIC’s were
realized [1]–[5]. The fabrication of such transmission lines is complex
and the required multilayer technology is very costly and is not always
available in certain MMIC foundries. This paper provides numerical
calculations and designs of structures composed of numerous connected short subsections containing different types of transmission
lines, as shown in Fig. 1. This arrangement makes the design more
flexible, and such structures can be easily realized using strip lines,
microstrip lines, CPW, or other standard transmission lines. This
concept in designing transmission lines is especially effective in
the construction of ultra-low characteristic impedance wide-band
transmission lines as used in MMIC/MHMIC technology. The proposed approach uses only metal–insulator–metal (MIM) capacitors
and air bridges, in addition to standard transmission lines available
in every MMIC or MHMIC foundry. Numerous new transmission
lines and components can be developed using this concept, as is
further illustrated in this paper.
Manuscript received November 4, 1997; revised September 21, 1998. This
work was supported by the National Science and Engineering Research
Council of Canada (NSERC).
The authors are with the Centre de Recherches Avancées en Microondes
et en Electronique Spatiale (Poly-Grames), Département de Génie Electrique
et de Génie Informatique, Ecole Polytechnique de Montréal, Montréal, P.Q.,
Canada H3C 3A7.
Publisher Item Identifier S 0018-9480(99)00391-9.
Fig. 1. Illustration of a single transmission line composed of
This transmission line is matched to impedance Z0 .
n unit cells.
II. THEORETICAL ANALYSIS
The calculated transmission lines consist of n unit cells, as shown
in Fig. 1.
A. Analysis of Single Transmission Lines
At first, a unit cell of the transmission line composed of m
subsections, shown in Fig. 1, is calculated and then we will study the
cascade connection of these unit cells into the whole transmission
line [see Fig. 1].
Calculation of a Unit Cell: Referring to Fig. 1, the impedances
and electrical lengths of the different subsections of the unit cell are
equal to Z1 ; Z2 ; Z3 ; 1 1 1 ; Zm and 1 ; 2 ; 1 1 1 ; m , respectively. The
transfer matrices of this unit cell takes the following form:
A = A1 A2 A3 ;
1 1 1 ; A
(1)
i
= (j=Zcossin
i )
i
jZi sin i
cos i
(2)
1
1
m
with
Ai
for i = 1; 2; 3; 1 1 1 ; m. Here Zi , i are the impedance and electrical length of the ith subsection, respectively. The reflection and
transmission coefficients for this unit cell take the following form:
A + B=Z0
A + B=Z0
0=
0 CZ0 0 D
+ CZ0 + D
(3)
and
T
=
2
(A + B=Z0 + CZ0 + D)
(4)
where A, B , C , D are the elements of the transfer matrices of the
unit cell and Z0 is the characteristic impedance of the terminating
input and output lines. In the design of a practical transmission line,
it is essential to use a symmetrical structure. The components A and
D of the transfer matrix A are then equal and, hence, the matching
condition at each end of the unit cell simplifies to
0=
B=Z0
0 CZ0
2A + B=Z0 + CZ0
=0
(5)
and Z0 = B=C .
For both the symmetrical and asymmetrical cases, under the
condition that the electrical lengths of all the subsections are small
and neglecting all the higher order terms of i , the reflection and
transmission coefficients for this unit cell take the following form:
0 =:
m
i=1
0i = j
m
i=1
(Zi i =2Z0 0 Z0 i =2Zi )
(6)
and
T
0018–9480/99$10.00  1999 IEEE
=: 1 0 j
m
i=1
(Zi i =2Z0 + Z0 i =2Zi ):
(7)
100
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 47, NO. 1, JANUARY 1999
each connection point and takes the following form:
0t =: 0r1 +
n
i=2
0ri ej 2
(9)
where 0t is the total reflection of the whole line, 0ri stands for the
reflection of the ith unit cell, and ri is the total phase shift from
the input plane of the transmission line to the input plane of the ith
unit cell. It is common to use identical unit cells to build a piece
of transmission line. In this case, the calculation is simplified to the
well-known results as follows:
j0t j =: j0r j sin(n + 1)r = sin r = j0r jUn (cos r ):
Fig. 2. Dependence of impedance ratio Z1 =Z2 with electric length ratio
1 =2 of the inhomogeneous transmission line with Z02 =Z1 Z2 as the parameter.
The matching condition requires that the reflection coefficient
vanishes and, from (6), we have
Z0
=
(
(
)
:
)
m
i=1 Zi i
m
i=1 i =Zi
0
(8)
In the case where m = 2, we can solve for the length ratio 1 =2 =
(1 0 Z02 =Z22 )=(Z1 =Z2 )(Z02=Z12 0 1) or Z1 =Z2 = (SK 0 1)=(K 0 S )
where K = 1 =2 and S = Z02 =Z1 Z2 . The dependence of the electric
length ratio K with impedance ratio Z1 =Z2 for different S values is
shown in Fig. 2. The horizontal line S = 1 extends to the vertical
axis Z1 =Z2 at point (1,1) and then may take any value along this
axis for 1 =2 = 1. The above equations and Fig. 2 are also valid
for the symmetrical case m = 3 with Z1 = Z3 , 1 = 3 if the
substitution 1 ! 21 is made. It should be mentioned that the choice
of subsection 1 and 2 is arbitrary and, hence, we need only to plot
the curves of Fig. 2 for K 1.
When the above matching condition is satisfied, the residual
reflection coefficient of a single cell 0r due to higher order terms of i
can be obtained from the second-order term of the small values i in
m
m
(3) and takes the form of
j =i+1
i=1 (Zj =Zi 0 Zi =Zj )i j =2.
However, for the symmetrical cases, these second-order terms of
i cancel each other and only the third and higher order terms
are left in the expressions of 0r . Hence, it is preferable to use
symmetrical structures in practical designs, such as to reduce the
reflection coefficient of the designed transmission line, especially
when i is not very small.
Cascade Connection of n Unit Cells: It should be pointed out that
the above analysis is valid when the total length of the unit cell
is small. Hence, we can connect numerous unit cells in cascade
to construct a piece of transmission line with the needed length.
Generally speaking, these unit cells may be different from each
other. However, all unit cells should be matched to the same
terminating impedance Z0 to keep this transmission line matched
at all interconnecting points of different cells. The phase change
and losses of the whole transmission line is equal to the sum of
the phase change and losses of the unit cells, respectively. The total
reflection coefficient of a piece of transmission with n unit cells
should be calculated by superposition of the individual reflections at
(10)
Generally speaking, it is recommended to choose the electrical
length of each unit cell to be less than 1/40 of a wavelength. This
is equivalent to the use of more than ten unit cells in constructing
a =4 coupled line to design a quadrature coupler, as suggested in
[6]. This rule is not critical, since the resultant j0t j also depends on
many other factors, such as the impedance ratio Zi =Zj and so forth.
In the case where the total length of the transmission line is shorter
than =4, no maximum value of j0t j will appear and, hence, larger
values of r are acceptable.
III. IMPLEMENTATION OF SOME NEW STRUCTURES
OF TRANSMISSION LINES
In this section, we will study the implementation of some new
structures of the CPW and microstrip line. However, the same principle of implementation may be applied to other types of transmission
lines without difficulty.
1) Miniaturized Microstrip Line (MMSL): From the analysis
given in the previous section, an MMSL can be designed and
fabricated using air bridges, support posts, and the ground plane,
as shown in Fig. 3(a) (cross section) and Fig. 3(b) (side view),
respectively. The effects of the MIM capacitors formed by the
support posts and ground plane can be handled by using (3)–(8).
The characteristic impedance of MMSL can be increased or reduced
by changing the width of the strip or the lengths of the support
posts. The advantages of MMSL are: 1) achievement of ultra-low
impedances by using wide strips and large dimensions of the support
posts; 2) the strip is suspended for the most part in air and, hence,
the dispersion can be expected to be small; and 3) MMSL needs
no substrate and, hence, it can be used conveniently as transmission
lines in low-cost SiGe MMIC circuits [7].
2) Ultra-Low-Impedance CPW and Microstrip Line: The ultralow-impedance CPW is achieved by adding MIM capacitors to the
conventional CPW line. These MIM capacitors are connected to the
ground plane by air bridges or via holes, as shown in Fig. 3(c) (cross
section).
3) Miniaturized Twin-Conductor Line (MTCL) The construction of the MTCL is the same as the MMSL with the difference that
the width of the ground plane is reduced to form the lower line of
the MTCL. A cross section of the MTCL is shown in Fig. 3(d).
4) Broadside Tightly Coupled CPW Line: A broadside tightly
coupled CPW line can also be made, as shown in Fig. 3(e). Its
advantage lies in that very tight coupling can easily be achieved by
using this type of transmission line.
In an actual MMIC fabrication processes, a thin dielectric layer
(100–200-nm thickness) is deposited on the main metal layer to
form MIM capacitors. This dielectric layer is omitted in Fig. 3 for
simplicity.
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 47, NO. 1, JANUARY 1999
101
(b)
(a)
(d)
(c)
(e)
Fig. 3. The proposed MMSL and ultra-low-impedance CPW and microstrip. (a) Cross section of MMSL. (b) Side view 1: air bridge, 2: support post, 3:
ground plane, 4: substrate. (c) Cross section of a ultra-low-impedance CPW. 1: air bridge, 2: center conductor of CPW, 3: support post or via hole, 4:
substrate, 5: ground plane, 6: support post. (d) Cross section of an MTCL. 1: air bridge, 2: support post, 3: lower conductor, 4: substrate. (e) Cross section
of a broadside tightly coupled CPW line. 1: air bridge, 2: support post, 3: lower conductor, 4: substrate, 5: ground.
IV. SIMULATED
AND
EXPERIMENTAL RESULTS
A simulation of the MMSL, which was described in the previous
section and shown in Fig. 3(a) and (b), is made. The height of the
air bridge is equal to 1.6 m, its width equals 20 m, the length
of the air-bridge post is also 20 m, and the length of the air
bridge is equal to 80 m. An MMSL with 12 unit cells (n = 12,
m = 2) is designed with the above data, its total length equals
12 2 (20 + 80) = 1200 m. The impedances and propagation
constants of these two different subsections (subsection 1 stands for
the air-bridge part and subsection 2 stands for the air-bridge post part)
are obtained by simulation on HFSS1; the coefficient K = 1 =2
is calculated to be 1.677 and the characteristic impedances are
Z1 = 24:21 , Z2 = 1:29 . This MMSL is matched to 7.01
impedance. Simulation on MOMENTUM1 is performed and the
reflection coefficient is 045.5 dB at 2 GHz and increases to 023.5 dB
at 20 GHz. Simulation of the same line with symmetrical unit cells
(m = 3 and 1 ! 21 = 23 ) is also made and the obtained
reflection coefficient is the same as the asymmetrical case at 2
GHz, increases more slowly, and reaches 030 dB at 20 GHz. A
similar design of MMSL matched to 50-
impedance is also made.
In this case, the width of the air bridge is 5 m, the dimension
of the air bridge post is 4 2 4 m, and distances between the
posts are equal to 40 m. Altogether, 17 air-bridge posts are used.
Individual unit cells are designed using HFSS and the whole MMSL is
simulated using MOMENTUM. This MMSL was fabricated together
with two MMSL to 50-
CPW transitions, as shown in the MMIC
layout in Fig. 4. The simulated and test results are shown in the
same figure and agreement between these data are obtained. The
measured loss of this MMSL is around 0.3 dB, including the MMSL
to CPW transitions.
V. CONCLUSION
Novel structures of different artificial transmission lines are proposed. Simulation and experimental results show that the nonuniform
1 HFSS
is a trademark of Hewlett-Packard Company.
Fig. 4. Reflection coefficient of a typical MMSL, ——: simulation using
MOMENTUM, xxxxx: measured.
lines can provide similar performance to ordinary homogeneous
lines, with the added advantages of providing design flexibility, as
shown by the demonstration of some new types of transmission
lines such as MMSL, ultra-low impedance CPW, and so forth.
Theoretical analysis and design formulas are provided. It is noted
that the symmetrical structure has important advantages over the
asymmetrical one. Simulation and experimental results are in agreement with theoretical analysis values. In the new transmission-line
designs, only standard MIM capacitors and air bridges are used. Such
circuit fabrication technology is quite common and it is available
in every MMIC/MHMIC foundry, whereas other low-impedance
transmission lines such as TFMS can be realized only using multilayer
MMIC techniques.
102
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 47, NO. 1, JANUARY 1999
ACKNOWLEDGMENT
The authors wish to thank Y. Coulibaly for measurement of the
MMSL. The fabrication of the MMSL was made by the MMIC
foundry of Nortel through Canadian Microelectronics Corporation
(CMC).
REFERENCES
[1] T. Hiraoka, T. Tokumitsu, and M. Aikawa, “Very small wide-band
MMIC magic-T’s using microstrip lines on a thin dielectric film,” IEEE
Trans. Microwave Theory Tech., vol. 37, pp. 1569–1575, Oct. 1989.
[2] M. Gillick and I. D. Robertson, “Ultra low impedance CPW transmission
lines for multilayer MMIC’s,” in IEEE MTT-S Int. Microwave Symp.
Dig., 1993, pp. 145–148.
[3] M. Gillick and I. D. Robertson, “An X -band monolithic power amplifier
using low characteristic impedance thin-film microstrip transformers,”
IEEE Microwave Guided Wave Lett., vol. 2, pp. 328–330, Aug. 1992.
[4] T. Tokumitsu, T. Hiraoka, H. Nakamoto, and T. Takenaka, “Multilayer
MMIC using a 3 m 3 layer dielectric film structure,” in IEEE MTT-S
Int. Microwave Symp. Dig., 1990, pp. 831–834.
[5] D. Willems and I. Bahl, “An MMIC-compatible tightly coupled line
structure using embedded microstrip,” IEEE Trans. Microwave Theory
Tech., vol. 41, pp. 2303–2310, Dec. 1993.
[6] Y. Xu and R. G. Bosisio, “A novel structure of tightly coupled lines for
MMIC/MHMIC couplers and phase shifters,” IEEE Trans. Microwave
Theory Tech., vol. 45, pp. 1594–1599, Sept. 1997.
[7] M. Case, “SiGe MMIC’s and flip-chip MIC’s for low cost microwave
systems,” Microwave J., vol. 40, pp. 264–276, May 1997.
(a)
2
Accuracy Estimation of Mixed-Mode
Scattering Parameter Measurements
(b)
David E. Bockelman, William R. Eisenstadt, and Robert Stengel
Fig. 1. Simplified block diagrams of typical (a) PMVNA and (b) FPVNA.
Abstract—The pure-mode vector network analyzer (PMVNA) provides
direct measurement of differential circuits. Residual error models are
derived for the PMVNA and a traditional four-port vector network
analyzer (FPVNA). The residual error models are used to calculate
the maximum and root-mean-square uncertainties in measurements of
mixed-mode scattering parameters of a typical differential amplifier. The
uncertainties produced by the PMVNA are compared to the transformed
mixed-mode s-parameters of the FPVNA. The PMVNA is shown to have
lower uncertainty when measuring differential devices.
conversion. Recently, a new specialized vector network analyzer
(VNA) system has been developed for the measurement of differential
circuits [2]. This new analyzer, called a pure-mode VNA (PMVNA),
directly measures mixed-mode s-parameters by stimulating and measuring the DUT with differential-mode and common-mode signals.
The calibration of the PMVNA has been described in [3], and shown
to have good accuracy with respect to measurements of two-port verification standards. However, these reported results do not establish
the relative accuracy of the PMVNA with respect to a traditional
four-port VNA. This paper will assess the relative accuracy of the
two analyzers, showing that the PMVNA has significant accuracy
advantages for the measurement of mixed-mode s-parameters of
differential devices.
As developed in [1], the mixed-mode s-parameters of a two-port
differential circuit are
Index Terms—Calibration, measurement standards, networks.
I. INTRODUCTION
Differential circuits are becoming increasingly important in RF
and microwave applications, particularly in integrated circuits due
to crosstalk immunity and increased dynamic range over ground
referenced circuits. This increase has lead to the development of
mixed-mode scattering parameters (s-parameters) [1] where a differential device-under-test (DUT) is characterized by its response
to both differential and common-mode signals, including any mode
Manuscript received January 14, 1998; revised June 10, 1998.
D. E. Bockelman and R. Stengel are with Motorola Radio Products Applied
Research, Plantation, FL 33322 USA (e-mail: d.bockelman@ieee.org).
W. R. Eisenstadt is with the University of Florida, Gainesville, FL 32611
USA.
Publisher Item Identifier S 0018-9480(99)00392-0.
S
S
mm
=
S
S
dd
cd
S
S
dc
cc
(1)
S
where dd are the differential s-parameters, cc the common-mode
s-parameters, and dc and cd the mode-conversion s-parameters.
The PMVNA directly measures these mixed-mode s-parameters, as
illustrated in Fig. 1(a). Standard four-port s-parameters and mixedmode s-parameters are related by the similarity transformation [2]
0018–9480/99$10.00  1999 IEEE
S
S
S
mm
= MSstd M01
(2)