This document summarizes a research paper about the development of a ground plane aperture technique to enhance capacitive coupling in parallel-coupled microstrip lines (PCMLs) and enable the design of broadband multi-pole microstrip bandpass filters. The technique involves forming an aperture in the ground plane of the PCML. Equivalent circuit models of the PCML indicate that the aperture increases the coupling factor in a frequency-dependent manner. A novel multi-pole broadband filter topology is proposed using a single microstrip line resonator connected between two PCML sections. Predicted and measured results confirm attractive properties such as 60% bandwidth, deep stop-band rejection, and compact size.

1. Broadband and compact multi-pole microstrip
bandpassfilters using ground plane aperture
technique
L. Zhu, H. Bu and K. Wu
Abstract: A gound plane aperture technique is developed for effective enhancement of the
capacitive coupling factor in the parallel-coupled microstrip line (PCML). By applying a so-called
‘short-opencalibration’(SOC) scheme in the fullwave method of moments (MOM)algorithm, ths
PCML with two external lines is characterised by an equivalent J-inverter network with its
susceptance and two electrical line lengths. Extracted parameters indicate that the coupling factor
appears to be frequency-dependent and its maximum value rises rapidly as the aperture is widened.
With the introduction of a single microstrip line section between two identical PCMLs, a
broadband and compact multi-pole microstrip bandpass filter is proposed for the first time, and its
electrical behaviour is studied and optimised on the basis of its equivalent circuit network. The
network-based optimised results are confirmed by an EM simulation of the entire filter layout,
featuring ultra-broadband and four-pole bandpass behaviour. Further, a single capacitivelyloaded
line section is utilised to formulate a multi-pole bandpass filter, and its electrical effects are also
discussed for filter design. The predicted and measured results confirm attractive properties of the
proposed multi-pole filter with BW=60%. /SII<-16dB and 220% wide upper stop-band.
1 Introduction
The microstrip bandpass filter has been studied and
developed as an important building block in the design of
microwave circuits and systems [l]. With its easily
achievable design-specified coupling factor, the parallel-
coupled microstrip line (PCML) has widely been used in
multi-stage bandpass filtersas a capacitivecouplingelement
between two adjacent line resonators [2, 31. To realise a
multi-pole and broad bandpass filter with a deep out-of-
band rejection, the usual procedure is to reduce both its
strip and slot widths in order to acheve a tight coupling,
and a large number of line resonators are required in this
case. This may lead to a degradation of its filtering
behaviour, namely, low Q-factor and high insertion loss.
Also, it may introduce some difficulties into the design
procedure and fabrication process due to its sensitivity to
the strip/slot widths and conductor thickness/configuration.
The filter size and fabrication cost are usually not desirable
as the required number of line resonators increases.
With the rapid development of three-dimensional (3D)
microwave- and millimetre-wave integrated circuit proces-
sing techniques, much attention has been directed to the use
of a high-quality multilayer planar circuit that allowsfor an
additional degree of design freedom along the vertical
0IEE, 2002
IEE Proceedings online no. 20010145
DOE IO. 104Y/ip-map:20010145
Paper first received 3rd July 2001 and in revised form 10th December 2001
L. Zhu is with the School of Electrical & Electronic Engineering, Nanyang
Technological University, 639798, Singapore
H. Bu is with the Amplifier Design Group, Mitec Telecom Inc., Pointe Claire,
Montreal, QC, H9R 528, Canada
K. Wu is with the Department of Electrical Engineering, Ecole Polytechnique,
CP. 6079. Sum. Centre-Ville, Montreal, QC, H3C 3A7, Canada
orientation [4]. To meet the requirement of capacitive tight
coupling, an overlap-gap coupling structure has been
developed in a two-layered structure for designing a
broadband microstrip bandpass filter [5]. In [6], a high-Q
and broadband inductor was proposed by removing a
partial ground plane of the spiral circuit based on a 3D Si-
MMIC technology. By forming a backside aperture in the
ground plane, a novel parallel-coupled microstrip line
(PCML) has also been developed and characterised in [7],
to show its potential in effective enhancement of capacitive
coupling required in the design of a broadband microstrip
bandpass filter.
In recent years, ultra-wideband technologies have
stimulated interest in communication and radar applica-
tions [8]. Nevertheless, it is difficult to design broadband
activeand passive circuitswith a bandwidth >20%0.In fact,
the filter design procedure available to date was essentially
establishedwith (quasi-)lumpedelementsas described in [11,
and its design formulas were developed over a narrow
frequency range around the centre frequency. It therefore
seems difficult to apply this procedure in the design of
bandpass filters with BW>20%. This is because all the
basic elements such as the line resonator and coupling
section are strongly frequency dependent in this case. In
other words, their electricalcharacteristicsare too frequency
dependent over a wide frequency range.
In ths work, a ground plane aperture technique is
proposed and developed for effective enhancement of a
tight coupling over the frequency range of interest, and
realisation of periodic frequency-dependent coupling char-
acteristics over a wide frequency range. This is achieved by
forming a wide aperture on the ground plane of the PCML.
With the use of a so-called ‘short-open calibration’ (SOC)
scheme [9],that is self-contained in our fullwave method of
moments (MOM)algorithm [lo], the two-port PCML with
external lines is generally characterised as an equivalent J-
IEE Proc.-Microw. Antennu Propug., Vol. l49>No. I , February 2002 71

2. inverter network. Consequently, a novel multi-pole and
broadband microstrip bandpass filter with a single line
resonator is originated for the first time by attaching a
uniform line section between the two PCML sectionswith a
backside aperture. A closed-form equation is established to
demonstrate the operating mechanism of the proposed
filter.It is shown that the multi-pole bandpass behaviour is
generated by the first-/second-orderresonant modes of the
line resonator and the J-inverter susceptance with the same
value as the characteristicadmittance of the microstrip line
in the PCML. To further realise design specificationssuch
as low return loss, adjustable broad bandwidth and wide
out-of-band rejection, a pair of capacitive open-ended stubs
is introduced into the central location of the line resonator
that is used to shift downward its second-order resonant
frequency [II]. Two filter layouts are optimally designed
and the optimised electrical performances are verified by
our predicted results through field simulations of the entire
layout and our experiments.
2
aperture
Fig. la shows a 3D geometry of the PCML, in which a wide
aperture is formed over its ground plane. A tight coupling
of this PCML can be readily acheved by reducing its
ground-to-strip coupling with such a backside aperture. To
investigate its coupling behaviour, this PCML with two
external lines is initially modelled by using our 3D
admittance-type MOMalgorithm, as detailed in [lo]. Fig. lb
shows a scheme arranged for its MOM characterisation, in
whch a pair of impressed electrical fields (E, and E2) is
introduced to formulate a deterministicMOMat two ports
(PI and P2) far away from the referenceplanes (Rl and R2).
To accurately de-embed circuit parameters of this PCML
from the MOM calculation, the SOC procedure [9] is
deployed to remove error terms involved in the algorithm
that allows extracting an equivalent circuit model at the
reference planes (R1 and R2). Fig. IC gives a circuit
description of Fig. 16, where the entire layout is partitioned
into two identical error terms [X, ] and an equivalent J-
inverter network.
As detailed in [9], these error terms stand for the
approximation of sourceexcitation and inconsistencyof 2D
and 3D MOM-based impedance definitions. They can
effectively be evaluated and removed with the help of two
numerical calibration standards, namely, short and open
elements. As such, the circuit network of the PCML can be
explicitly extracted as a general-purpose two-port admit-
tance matrix that accounts for all of its discontinuityeffects.
The equivalenceof two networks allows the transforming of
ths admittance matrix into a J-inverter network that
consists of a susceptance (4and two equivalent electrical
line lengths (8/2), as shown in Fig. IC. For a symmetric two-
port network, the relationship can be simplified from (2) in
[12] as follows:
- tan(e/2) +Bll
J = - ( l a )
Unifield circuit model of PCML with backside
B12 tan(e/2)
in which J = J/Yo, B11 = Bl,/Yo = B22/Yo, = B I ~ / Y o
= Bzl/Yo, and Yo is the characteristic admittance of the
microstrip line.
Fig. 2 shows the SOC-calibrated normalised J-inverter
susceptance (J)and equivalent electrical length (e/2) of a
apertureY .
h - 7
ground
a
c
Fig. 1
microstrip line (PCML) with u ground plune uperture
u Geometrical layout
b Full-wave MOMmodelling
c Equivalent circuit network
Topologicalview and characterisation of parallel-coupled
PCML with different aperture widths W over a wide
frequency range. It indicatesthat the parameter J varies in a
periodical manner with frequency for all three cases, thus
exhibiting a frequency dispersion behaviour. It can be
interpreted that the coupling between the two strip
conductors depends strongly on the electrical length of this
PCML section, e.g. Lly0. The peak coupling essentially
appears around the frequency of 4L/,,-, =(2n- 1) and the
null J is close to that of 4L/@=2n, where n = 1 or 2 in ths
case. The peak value of J increases significantlyfrom 0.6 to
1.2 as W is widened from 1.4 to 3.0", showing an
effective enhancement of its coupling factor by a backside
aperture. Fig. 2b illustrates that the electrical length (8/2)
increases from 15" to 260" in an approximately linear
manner as the frequency increases from 1.0 to 16.0GHz.
From Figs. 2a and b, we can further elicit that the peak J
occurs in the proximity of the frequency at which 0/2 =90"
or 270",while the null J is around a frequency correspond-
ing to Q/2= 180".
On the other hand, this frequency dependent periodicity
of 1,as shown in Fig. 2a, provides us with a hint for
constructing an alternative bandpass filter, whose bandpass
behaviour can be formulated by a tight coupling factor, e.g.
J M .l. Interestingly, the frequency of I=1 strictly
corresponds to the pole location over the bandpass range.
Looking into the J-inverter network as in Fig. IC,the return
loss ISI I can analyticallybe reduced to (2) in a closed form
of J . Fig. 3 gives predicted return/insertion losses of the
PCML with W= 2.2" and 3.0" based on the obtained
J-inverter parameters in Fig. 2a. It shows the bandpass
behaviour of one pole and two poles, respectively. This
initial result demonstrates that the frequency-dependent J-
inverter susceptance itself can generate its own pass-band
around its maximum value. In the following, our main
interests are focused on the proposal and investigation of a
new class of miniaturised, multi-pole and broadband
IEE Proc -Microw Antenrius Propay, Vol 149, No 1, February 200212

3. 1.2
1.o
t"
,; 0.8
U
ul._
3 0.6
0.4
5
,2
0.2
0
2 4 6 8 10 12 14 16
frequency t GHz
a
300
J
2 4 6 8 10 12 14 16
frequency f, GHz
b
Fig.2
with dijfevent uperture widths W
a Normalised J-inverter susceptance (J/Yo)
b Equivalent electrical line length (0/2)
SOC-calibratedJ-inverter network parameters of PCML
microstrip bandpass filter. This is acheved by utilising the
PCML's J-inverter susceptance as well as the first- and
second-order resonant modes in a microstrip line resonator.
3
verification
Prototypebandpass filter: concept and
Fig. 4a shows the schematic layout of a prototype micro-
strip bandpass filter proposed for achieving ultra-broad-
band and multi-pole bandpass behaviour. A microstrip
line is used to link two identical PCML sections with a
backside aperture. Fig. 46 presents its complete equivalent
circuit topology, arranged for gaining insight into its
operating mechanism that also allows an efficient optimisa-
tion. The PCML section is characterised as a J-inverter
susceptance (J) and two electrical lengths (Oj2) that
represent its series capacitive coupling and equivalent phase
shifts, respectively. On the other hand, the central uniform
0
-5
-1 0
-15
-20
-
-
z -25
4
-
- -30
-35
-40
-45
-50
2 4 6 8 10 12 14 16
frequency f, GHz
Predictedfrequency response of PCML with W=2.2 andFig. 3
3.0mm us shown in Fig.2
Fig. 4
pole bandpassfilter with single unfijrm line resonator
a Schematic layout
b Equivalent circuit network model
Topview und equivalent circuit topology of proposed multi-
line can be perceived as an additional phase factor 4, so
that the total electrical length di should be made up of
three separate parts, i.e. @ =6/2+ +Qj2.This equivalent
line resonator is formulated to generate two additional
bandpass poles from its first- and second-order resonant
modes.
To investigateits electrical behaviour, let us start with the
characterisation of its equivalent cascaded circuit topology
as shown in Fig. 4b. On the basis of a transmission line
theorem, the normalised input admittance (T2,,= Kn/y0) at
one termination (# l), looking into its opposite termination
(# l'), can be easily deduced and expressedas a closed-form
function of 7 and di such that
Accordingly, its reflection coefficient (SI1)at # 1 can be
further simplified as follows to provide a better under-
1 3IEE Proc-Microw. Antennas Propug., Vol. 149, No. I , February 2002

4. standing of its fundamental filtering performance:
Considering the fact that the pole is usually defined as a
frequency point where IS11I =0 or ISl]I achieves a
minimum value, it is understood from (4) that there exist
multiple poles of frequency where @ = 180", @ = 360" and
J = 1. The former two poles correspond to the first- and
second-order resonant frequencies, and we can find in the
followingthat the frequency spacing between them basically
forms a desired ultra-broad bandwidth of the filter. The
latter one or two poles are contributed by a highly enhanced
J-inverter susceptance ( J = l), and they are arranged
around the central operating frequency through a suitable
choice of the line length L in Fig. 4a.
Figs. 5a and b show our predicted frequency responsesof
the filter with L =4.9" over the frequency range (1.0 to
10.0GHz)obtained from (4) via three groups of J-inverter
network parameters in Fig. 2. In the case of a narrow
aperture width (W=1.4mm), only two poles can be
observed, and they appear at the half- and full-wavelength
0
- :; -.---------; I: I
-10
a, W = 2.2mm
...........
-35
-40 I
1 2 3 4 5 6 7
frequency f, GHz
a
-60
I 2 3 4 5 6 7 8 9 1 0
frequency f, GHz
b
Fig. 5
Fig. 4 with di$erent aperture widths W
u Insertion loss IS2,I
b Return loss 1SI1I
14
Predictedfrequency response of$lter luyout us described in
18 9 10
resonant frequencies, marked by Fol and Fo2, which
correspond to those of @ = 180"and @ =360", respectively.
The maximum J in this case is about 0.8, from Fig. 2a,
indicating a relatively weak coupling. Ths leads to a worse
bandpass behaviour with a return loss of ISII 1 = -6dB
between two resonant frequencies (FOIand F02) in the
absence of any additional pole from the condition J z 1.
As W is enlarged to 2.2mm, 1SI I rapidly decreases in
such a way that its entire pattern is separated into two parts
by an additional pole (minimum value) around the central
location, while IS2,1 gradually increases to close to its 0dB
level between FOland Fo2. With reference to Fig. 2 4 ths
additional pole is physically generated by the maximum
value of its normalised J-inverter susceptance where J = 1.
As W increases further to 0.3mm, it can be observed from
Fig. 5b that one pole is split into two poles at its two sides
withn the pass band. Due to the maximum J> 1 in this
case, the two frequency points where J = 1 can be found
from Fig. 2a, and they lead to the emergence of these two
additional poles via (4).Unfortunately, the return loss ISI I
shifts up slightly in the central location, which degrades its
whole bandpass behaviour due to its extremely enhanced
coupling degree, e.g.J >> 1.Nevertheless, thls problem can
be solved by suitably adjusting the backside aperture width
of PCML to meet the requirement of its J-inverter
susceptance in the optimisation procedure.
So far, the operating mechanism of the proposed multi-
pole bandpass filter with a single line resonator has been
explained on the basis of equivalentJ-invertercircuit theory,
and its filtering behaviour has been characterised by a
closed-form equation. Next, our interest is to optimally
designits frequency response in order to obtain a low return
loss over the passband. Fig. 6a gives the optimised results of
the filter with the same dimension as in Fig. 4a, except for a
different aperture width (W=2.5"). In this case, we find
that J = 1.05(maximum)effectively reduces the return loss
IS11I to -17dB from about -9.0dB as illustrated in Fig. 5b
for the case of W=3.0". Similarly, the four poles also
appear withn the pass band, allowing the design of ultra-
broad and flat bandpass with an insertion loss of
Over a wide frequency range (1.0 to 16.0GHz),a parasitic
harmonic pass-band begins to emerge aroundf= 11.8GHz,
close to the pass-band of interest.This leads to an unwanted
degradation of its pass-band performance and a very
narrow upper stop-band. To verify our predicted results
from its equivalent circuit model, the commercial software
HP Momentum is used to carry out an independent
simulation of the entire filter layout. Fig. 6b illustrates the
simulated results showing a very similar filtering behaviour
to Fig. 6a, including the parasitic effects. In the following,
we shall look into the possibility of suppressingthe spurious
harmonic band by attaching a capacitive stub into the line
resonator.
IS21 I >-0.2dB.
4
experiment
Harmonic resonant frequencies of a uniform line resonator
are approximately two or three times its fundamental
resonant frequency [l]. To enable the change of resonant
frequency spectrum, the non-uniform line resonator was
found to be a powerful candidate decades ago [131.In [111, a
specific non-uniform line resonator, called a 'stepped
impedance resonator' (SIR), was presented for the design
of a parallel-coupled stripline bandpass filter with good
harmonic suppression. Ths line resonator is made up of
Improved bandpassfilter: design and
IEE Proc-Microw Antennus Propay., Vol. 149, No. I. February 2002

5. 0
-10
%!
rz"
7
-6
-20-
.-
- -30
-40
-50
2 4 6 8 10 12 14
frequency f, GHz
a
0
-1 0
m
-" -20
rz"
F
5
U
-
7 -30
-40
-50 I
2 4 6 8 10 12 14
frequency f, GHz
b
Fig. 6 Optimisedand predicted jiequency responses for $Iter
layout in Fig. 4
u Equivalent circuit model
b Fullwave EM simulation
cascaded line sections with different characteristic impe-
dance to shift up its first-orderharmonic resonant frequency
in terms of its impedance ratio. As pointed out in [l13, this
SIR allows the realisation of a broad rejection-band
between its fundamental and spurious harmonic pass-bands
in the filter.
Following the above description, the first harmonic
passband in our filter is attributed to the third-order
resonant frequency. Therefore, it is critical to build up a
non-uniform line resonator with a large difference between
its second- and third-order resonant frequencies. Fig. 7a
shows the schematic layout of an improved bandpass filter
with a non-uniform line resonator. This resonator is
constructed by attaching a pair of open-ended stubs at its
central location. Fig. 76 is its equivalent circuit topology, in
which such a pair of stubs can be perceived as an equivalent
frequency-dependent capacitance C,(a).In this case, the
central location represents perfect short- and open-circuit
terminals for the first/thrd-order resonant modes and for
the second/fourth-order resonant modes, respectively. The
attachment of such stubs is expected to lower the second/
fourth-order resonant frequencies, whde the first-/third-
order resonant frequenciesremain almost unchanged.
,
HI2 912 dl2 012
~~~ C*(4
#1 #2 #2 #I
b
Fig. 7
posed bundpassjlter with single cupacitive-loadedline resonator
a Geometrical descnption with added stub tuner
b Equivalent circuit model
Schematiclayout and equivalent circuit topology of pro-
Figs. 8a and b show the predicted frequency response of
the filter layout with a fixed aperture, as shown in Fig. 7 4
for three different stub lengths. They are obtained on the
basis of an equivalent circuit topology as in Fig. 7b for a
relatively weak coupling, arranged to demonstrate the
complete frequency spectrum of the first four resonant
modes for the non-uniform line resonator. We observe that
the first and third (odd) resonant frequencies remain
stationary, even though the stub length is extended to a
great extent.It is valid in theory because the central location
corresponds to a perfect short circuit with an extremely
large admittance. The second and fourth (even) resonant
frequencies are found to simultaneously decrease towards
the first- and third-order counterparts as the stub length
increases. As a result, the rejection band of interest can be
successfully tuned from 4.2GHz to 7.0GHz while the
fundamental pass bandwidth drops down significantly from
3.2GHz to 0.8GHz. Thus, the attachment of such stubs
raises the possibilityof realisinga broad bandpass filterwith
a good harmonic suppression, as well as an easy-to-tune
broad frequency bandwidth ranging from 15% to 70%
estimated from Fig. 8. Further, we can predict from its low
return loss characteristic ISI1I <-20dB in a weakly
coupling case of S= 4.8" that the capacitive shunt stubs
may allow one to greatly alleviate the strict requirement of
an extremelytight coupling. It provides us with a possibility
for the development of a broad bandpass filter in the
complete absence of the backside aperture with relatively
weak coupling.
Now let us turn to the design of a four-pole bandpass
filter with a single stub-loaded resonator through the
equivalent circuit, as in Fig. 7b. Fig. 9a presents its
optimised frequency response over a wide frequency range
(1.O to 1S.OGHz), showingan excellent bandpass behaviour
with bandwidth about 60% and return loss 1SII 1 <-30dB.
Also, the four-poleswith a minimum value of IS,I I can be
observed from Fig. 90. A spurious harmonic band appears
at f= 14.0GHz, exhibiting a much wider upper stop-band
BW= 220% with reference to its central operating
frequencyfo=6.OGHz. To verify such attractive features,
the HP Momentum softwareis further used to simulate the
entirefilter layout through slightadjustment of line/aperture
dimensions (L, Wand S),and a bandpass filter sample is
15IEE Proc.-Microw. Antennas Propug., Vol. 149. No. I , February 2002

6. 0
-1 0
8
-x
9
-- -20-
U
m
= -30
-40
-50
O r
' ..-,. ' . i
-I0tg -20 1
I W =1.4 mm I
/ ~ = 4 . 9 m m1
-60-50 tl 6 8 10 12 142 4
frequency f, GHz
a
2 4 6 8 10 12 14 16
frequencyf, GHz
a
0
-10
-20
m
* -30
-40
--N
u)
-c -50
._4-
$ -60
._
-70
-80
-90
2 4 6 8 10 12 14 16
frequencyf, GHz
b
Fig.8
dijj7erent stub length S
a Retum loss ISI I
b Insertion loss IS,, 1
Optimisedfrequency response ofjlter layout in Fig. 7 with
0
-Y-1 0
8-- -20
-x-
U
-30
5
g-40
-50
2 4 6 8 10 12 14
frequency f, GHz
b
Fig.9
Fig. 7
a Equivalent circuit model
b Simulations and experiments
Predictedand measured frequency responses of filter in
behaviour with two poles in the case of J L 1. Subse-
quently, a uniform line section is brought between the two
PCML sections to construct a prototype layout of the
proposed bandpass filter. The operating mechanism of this
filter has been explained and its frequency response
optimally designed to exhibit its multi-pole and broad
filtering property. The multiple poles are conceptually
contributed by the first- and second-order resonant modes
of the line resonator as well as a tight coupling of the two
PCMLs,
e.g. J = 1. Our results show a ultra-broadband and
4-pole bandpass behaviour with BW>70% and
ISI I<-15dB. Furthermore, a pair of open-stubs is
attached at the central location of this line resonator to
effectively tune resonant frequencies of the second- and
fourth-order harmonics. An improved version of the
bandpass filterwith a single capacitive-loaded line resonator
has been designedto show its attractive features such as low
return loss (<-30dB), wide upper stop-band (>220%)
and broad bandwidth (60%). Our measured results are in
an excellent agreement with our predicted results over a
wide frequency range (1.0 to 15.OGHz), and the fabricated
filter shows IS1 1 <-16dB and IS,, I>-0.6dB within the
pass-band BW= 60%.
,
IEE Proc.-Microw. Antennas Propug.. Vol. 149, No. I , February 2002
then fabricated and measured. Fig. 9b describes simulated
and measured frequency responses that are almost identical
over the whole frequency range. Fig. 9b shows that both
insertion losses IS,, I can be made with -0.6dB withn the
pass band, wlule the simulated return loss ISI I is lower
than -20dB against the measured ISllI lower than -16dB.
On the other hand, the total length of this stub-loaded
bandpass filter (D+L+D= 13.36") is about 0.7, at
fo=6.lGHz against 1.25,,,, for a conventional 4-pole
parallel-coupled microstrip hne bandpass filter as in [1-31,
demonstrating its attractive miniaturisation and low cost of
fabrication.
5 Conclusions
In ths work, a ground plane aperture technique has been
originated in the PCML for effective enhancement of a tight
frequency-dependent coupling, and further applied for
innovative design of a new class of miniaturised, multi-pole
and broadband microstrip bandpass filter. With our SOC
de-embedding (calibration) procedure, the PCML can
generally be characterised as an equivalent J-inverter
network, allowing one to gain a better understanding of
its couplingbehaviour. The PCML itself exhibits its filtering
16

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