IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 4, APRIL 2005 1221
Guided-Wave Characteristics of Periodically
Nonuniform Coupled Microstrip
Lines—Even and Odd Modes
Sheng Sun, Student Member, IEEE, and Lei Zhu, Senior Member, IEEE
Abstract—Even- and odd-mode guided-wave characteristics of
periodically nonuniform coupled microstrip lines (PNCML) are
thoroughly investigated in terms of the two sets of per-unit-length
transmission parameters, i.e., characteristic impedance and phase
constant. By executing the short-open calibration (SOC) procedure
in the method-of-moments platform, the two-port
ma-
trices of the PNCML with finite unit cells are numerically deem-
bedded via two sets of SOC standards so as to explicitly derive
the effective per-unit-length parameters. After our investigation
on the behaviors of numerical convergence, extensive results are
derived to demonstrate the frequency- and periodicity-dependent
per-unit-length parameters of the three types of PNCML against
those of the uniform coupled microstrip line. In final, the
-pa-
rameters of a PNCML circuit are directly simulated via extracted
per-unit-length parameters and they are validated in magnitude
and phase by those from the Momentum simulator.
Index Terms—Even mode, method of moments (MoM), odd
mode, periodically nonuniform coupled microstrip line (PNCML),
per-unit-length transmission parameters, short-open calibration
(SOC).
I. INTRODUCTION
C
OUPLED microstrip lines (CMLs) with two strip conduc-
tors placed parallel in close proximity with each other, as
illustrated in Fig. 1(a), have been extensively studied and uti-
lized as basic circuit elements for directional couplers, bandpass
filters, etc. [1]. Due to the inhomogeneous dielectric medium,
the two dominant modes, i.e., even and odd modes, exist in
this CML with different velocities of propagation. This non-
synchronous feature deteriorates the performances of microstrip
circuits using the uniform CML, such as low directivity in direc-
tional coupler [2] and spurious harmonic passband in a bandpass
filter [3]. Extensive research has been done thus far toward the
equalization of propagating velocities for these two modes at
certain frequencies by forming periodically varied coupled-slot
configurations, e.g., wiggly line [2], [4], zigzag line [5], corru-
gated line [3], [6]. On the other hand, these periodic structures
are strongly expected to miniaturize the overall size of various
microwave circuits by using their slow-wave behavior at the cost
of extra transmission loss with a lowered
factor.
In order to investigate in depth these periodically nonuni-
form coupled microstrip lines (PNCML) for circuit design, it is
Manuscript received May 11, 2004; revised July 15, 2004 and August 5, 2004.
The authors are with the School of Electrical and Electronic
Engineering, Nanyang Technological University, Singapore 639798 (e-mail:
ezhul@ntu.edu.sg).
Digital Object Identifier 10.1109/TMTT.2005.845709
Fig. 1. Geometry of the uniform and various PNCMLs to be considered.
(a) Uniform CML. (b) PNCML (A). (c) PNCML (B). (d) PNCML (C).
commonly recognized as the most critical issue to characterize
the fundamental per-unit-length transmission parameters of the
even and odd modes, i.e., phase constants and characteristic
impedances. Under the static assumption that each periodic
unit is extremely shorter than the wavelength, propagating ve-
locities and characteristic impedances of the coupled striplines
were approximately obtained via cascaded lumped capaci-
tances and inductances [4]. According to Floquet’s theorem,
the two-dimensional (2-D) spectral-domain method of mo-
ments (MoM) was developed without including complicated
0018-9480/$20.00 © 2005 IEEE
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