a bandpass filter with adjustable bandwidth and predictable transmission zeros

A Bandpass Filter with Adjustable Bandwidth andPredictable Transmission Zeros

Li Zhu,1 Vijay Devabhaktuni,2 Chunyan Wang,1 Ming Yu3

1 ECE Department, Concordia University, Montreal, H3G 1M8, Canada2 EECS Department, MS 308, University of Toledo, Toledo, OH 436063 COM DEV Ltd., Cambridge, N1R 7H6, Canada

Received 17 June 2009; accepted 29 August 2009

ABSTRACT: In this article, a microstrip bandpass filter with an adjustable bandwidth and

predictable transmission zeros is proposed. The proposed filter is implemented by combin-

ing two hairpin edge-coupled resonators with interdigital capacitors. Compared to typical

edge-coupled filters, the proposed filter provides a wider bandwidth resulting from a higher

coupling strength between its resonators. To further increase the coupling and consequently

the bandwidth, a pair of etched slots in the ground plane is used. By adjusting the geometri-

cal parameters of the interdigital capacitors and etched slots, the bandwidth can be easily

adjusted. The filter features two transmission zeros, which are determined by means of the

semi-analytical model developed as part of this work. Furthermore, the proposed filters can

be cascaded to obtain a sharper cutoff frequency response. Frequency responses of the fil-

ters from measurements are in good agreement with those simulated using IE3D in the 5–9

GHz range. VC 2009 Wiley Periodicals, Inc. Int J RF and Microwave CAE 20: 148–157, 2010.

Keywords: bandpass filters; cascade circuits; electromagnetic coupling; interdigital capacitors;

transmission zeros

I. INTRODUCTION

In modern communication systems, e.g., satellite systems,

microwave filters exhibiting characteristics of compact

size, high selectivity, and low loss are extremely impor-

tant. Such characteristics can be realized using filters with

cross-coupling between non-adjacent resonators [1]. Typi-

cally, cross-coupled resonator filters are designed using ei-

ther waveguide cavities or dielectric resonator loaded cav-

ities because of their low loss. Planar filters, on the other

hand, are promising in terms of reduced size, weight, and

cost [2–4].

It has been reported that hairpin resonators with asym-

metric input/output feed lines tapping on the first and the

last resonators are used in the design of microstrip band-

pass filters [5, 6]. In contrast to traditional cross-coupled

filters, hairpin-resonator filters are compact, and offer

lower insertion loss, sharper cutoff frequency response,

and two transmission zeros lying on either sides of the

passband. In the design of hairpin-resonator filters, a

wider bandwidth can be achieved by improving the elec-

tromagnetic (EM) coupling between resonators, which can

be realized by reducing the gap and/or strip widths of the

resonators and increasing the number of resonators. How-

ever, such an approach can lead to a degradation in the

filtering behavior in terms of low quality factor Q and

high insertion loss. Moreover, the approach may require a

high precision in the fabrication process for accurate gap/

strip dimensions.

In this article, to achieve a wider bandwidth, we pro-

pose a new bandpass filter, which uses interdigital capaci-

tors between hairpin resonators to achieve a strong EM

coupling. Two additional slots etched in the ground plane,

can help further enhance the bandwidth. The proposed

structure exhibits two transmission zeros, one on each

side of the passband. To estimate the positions of these

transmission zeros, semi-analytical formulae are derived.

The proposed filter allows certain flexibility in the design,

i.e., ability to adjust the bandwidth by altering the geo-

metrical parameters of the interdigital capacitors and/or

the etched slots. On the basis of the proposed structures,

cascaded bandpass filters are designed, fabricated, and

tested.

Correspondence to: V. Devabhaktuni; e-mail: [email protected]

VC 2009 Wiley Periodicals, Inc.

DOI 10.1002/mmce.20412Published online 14 December 2009 in Wiley InterScience

(www.interscience.wiley.com).

148

II. PROPOSED FILTER

Figure 1 shows the layout of the proposed bandpass filter

and an illustrative comparison with a traditional edge-

coupled hairpin filter [5, 6]. As can be seen in Figure

1(b), interdigital capacitors are introduced to substitute for

the traditional gaps [see Fig. 1(a)] between microstrip

hairpin resonators. In both proposed and traditional struc-

tures, the dominant coupling is electrical coupling [7],

which is due to strong electric fringe fields near the open

ends of the folded line. As such, capacitance between two

branches becomes an important parameter to be examined.

In both proposed and traditional structures of Figure 1,

the mutual electrical coupling can be represented by a

coefficient KE, which is identical to the ratio of the

coupled electric energy to the stored electric energy of an

uncoupled single resonator, given by

KE ¼ f 2r2 � f 2r1f 2r2 þ f 2r1

¼ Cm

C: (1)

In eq. (1), C represents the self-capacitance, Cm the

mutual capacitance, and fr1 and fr2 the lower and higher

resonant frequencies, respectively. The larger the Cm, the

higher the KE, which implies a stronger coupling or

smaller external quality factor QE of the resonator [7].

The 3 dB bandwidth of the filter can be expressed as

Df3dB ¼ f0ðQE=2Þ ; (2)

where f0 represents the center frequency. Hence, a higher

Cm or KE results in a relatively wider bandwidth.

As mentioned earlier, a traditional edge-coupled hair-

pin filter is shown in Figure 1(a). The substrate thickness

is 0.635 mm and dielectric constant (er) is 10.2. The width

of the microstrip hairpin is 1 mm, and the gap is set to

0.13 mm (5 mil), which is the closest/smallest distance

allowed by the fabrication process used. Using Zeland

IE3D, the EM simulation results of Figure 1(a), illustrated

in Figure 1(c), exhibit an f0 ¼ 6.5 GHz, a 3 dB bandwidth

¼ 375 MHz, an insertion loss of 0.83 dB at 6.49 GHz, a

maximum return loss of �11 dB at 6.5 GHz, and two

transmission zeros, one at 5.45 GHz with �66.34 dB

rejection and the other at 8.3 GHz with �36.6 dB rejec-

tion. The relatively high loss and narrow bandwidth could

not be improved due to gap limitation imposed by the fab-

rication process.

As shown in Figure 1(b), the proposed structure uses

two interdigital capacitors, each with four fingers, between

the hairpin resonators. The length and width of the fingers

are 0.3 mm and 0.2 mm, respectively, and gap between ad-

jacent fingers is 0.2 mm. EM simulation results of Figure

1(b) are shown in Figure 1(c). Because of a stronger cou-

pling effect, the proposed filter exhibits a wider 3 dB band-

width than traditional filter (602 MHz vs. 375 MHz), while

its f0 and locations of transmission zeros remain unchanged.

The size of the proposed filter (with a 9.6% bandwidth at

6.25 GHz) is �5 � 7 mm2. To be able to design the filter

using the traditional structure of Figure 1(a) with the same

bandwidth, at least one more resonator needs to be added.

As such, the traditional approach leads to a 40% increase in

size as compared to the proposed filter.

Further, the proposed filter provides an insertion loss

of 0.41 dB at 6.49 GHz and a return loss below �20 dB

in the 6.34–6.61 GHz range, both of which are lower than

those of the traditional hairpin filter. In conclusion, the

increased mutual capacitance provided by interdigital

capacitors helps to obtain a relatively stronger EM cou-

pling and hence a relatively wider bandwidth compared to

edge-coupled hairpin filters.

III. SALIENT FEATURES OF THE PROPOSED FILTER

A. Bandwidth ModulationBandwidth-efficient modulation techniques can enhance

bandwidth efficiency while retaining reasonable power

efficiency and implementation complexity/simplicity,

thereby maximizing the use of available frequency spec-

trum of terrestrial and space-based communication sys-

tems. The interdigital capacitor is a multi-finger periodic

structure, which uses the capacitance that occurs across a

narrow gap between thin conductors. The capacitance Cint

of an interdigital capacitor of length lc can be expressed

as [8],

Cint ¼ ðer þ 1Þlc½ðN � 3ÞA1 þ A2�; (3)

Figure 1 (a) Layout of a traditional edge-coupled bandpass fil-

ter, (b) Layout of the proposed bandpass filter, and (c) Compari-

son of IE3D simulations of the proposed and traditional filters.

[Color figure can be viewed in the online issue, which is avail-

able at www.interscience.wiley.com.]

A Bandpass Filter with Adjustable Bandwidth 149

International Journal of RF and Microwave Computer-Aided Engineering DOI 10.1002/mmce

where

A1 ¼ 4:409 tan h½0:55ðh=wcÞ0:45� � 10�6 (4)

and

A2 ¼ 9:92 tan h½0:52ðh=wcÞ0:5� � 10�6: (5)

In eqs. (3–5), er is the dielectric constant, h is the

thickness of the substrate, and N and wc represent the

number and width of the fingers of an interdigital capaci-

tor respectively. By adjusting N or other parameters of an

interdigital capacitor, Cint can be changed. Accordingly,

the bandwidths of the filter can be effectively adjusted by

the interdigital capacitors. IE3D simulations of the pro-

posed filter with different values of N are illustrated in

Figure 2. The bandwidths of these filters can be increased

by increasing N, while keeping f0 fixed by slightly

decreasing the lengths of the hairpin resonators. A sum-

mary of the simulation results is presented in Table I. It

can be observed that the bandwidth increases with N,while f0 and locations of transmission zeros remain more

or less unchanged. Increasing N from 0 (traditional gap)

to 8 leads to an increase in 3 dB fractional bandwidth

(FBW) from 5.8% to 15.5%, and a change in QE from

34.7 to 12.9. However, it could be difficult to design a fil-

ter with an FBW > 20% using the proposed structure,

since all the elements (e.g., line resonators, coupling ele-

ments, etc.) are highly dependent on frequency.

Recently, a ground plane aperture technique has been

proposed [9] for effective enhancement of EM coupling

over a wider frequency range. On the basis of this tech-

nique, we propose to etch two rectangular slots in the

ground plane below the two 4-finger interdigital capacitors

as shown in Figure 3(a) to further improve the bandwidth.

Simulation results in Figure 3(b) show that, increasing the

width (T) of the ground plane apertures from 1.9 mm to

3.3 mm while keeping all other parameters unchanged,

results in an increase in 3 dB FBW from 17.4% to 22.3%,

and a change in QE from 11.5 to 8.8. It is to be noted that

increasing T also results in a slight decrease in the lower

cutoff frequency, an increase in the upper cutoff fre-

quency, and a corresponding shift in the locations of the

transmission zeros. The shift, i.e., an increase in f0, can be

countered by slightly increasing N alone [10]. In essence,

the proposed filters with etched slots offer flexibility in

terms of broadband filter design. Although our focus is on

bandwidth, it may be noted that relatively more flat S21responses can be achieved by tuning the interdigital fin-

gers and slot shapes [9].

B. Transmission ZerosFilters exhibiting transmission zeros can effectively reject

undesired signals, and are hence used in high-selectivity

systems. Here, we present a consolidated formulation,

which helps the estimation of transmission zeros of the

proposed filter of Figure 1(b). The filter uses two hairpin

resonators with asymmetric feed lines tapping the resona-

tors. The input and the output feed lines divide the resona-

tors into two sections of lengths l1 and l2, respectively.The coupling between the two resonators is expressed by

Cint (the interdigital capacitance). The entire circuit of

Figure 1(b) can be treated as a shunt circuit consisting of

upper and lower sections. Each section is made up of l1,Cint, and l2. The ABCD matrices of the upper and the

lower sections of the lossless shunt circuit can be

expressed as

Mupper ¼ A BC D

� �upper

¼ M1M2M3; (6)

and

Mlower ¼ A BC D

� �lower

¼ M3M2M1 (7)

where

Figure 2 S-parameter (S21) of the proposed bandpass filter

structures with different values of N.

TABLE I Summary of IE3D Simulations for Different Values of N

Number of Fingers 0 4 6 8

3 dB Bandwidth 375 MHz 602 MHz 841 MHz 1005 MHz

3 dB FBW 5.8% 9.3% 12.9% 15.5%

QE 34.7 21.6 15.5 12.9

Dimension 5.3 � 6.0 mm2 4.9 � 6.4 mm2 4.1 � 7.2 mm2 3.45 � 8.0 mm2

Transmission Zeros 5.43 GHz 5.44 GHz 5.45 GHz 5.45 GHz

8.19 GHz 8.25 GHz 8.31 GHz 8.25 GHz

International Journal of RF and Microwave Computer-Aided Engineering/Vol. 20, No. 2, March 2010

150 Zhu et al.

M1 ¼ cos bðl1 þ DlÞ jz0 sinbl1ð11 þ DlÞjy0 sin bðl1 þ DlÞ cos bl1ðl1 þ DlÞ

� �; (8)

M2 ¼ 1 zc0 1

� �; (9)

and

M3 ¼ cos bðl2 þ DlÞ jz0 sin bðl2 þ DlÞjy0 sinbðl2 þ DlÞ cos bl2ðl2 þ DlÞ

� �: (10)

In eqs. (8) through (10), b is the propagation constant,

z0 ¼ 1/y0 is the characteristic impedance of each resona-

tor, Dl accounts for the additional length of the microstrip

in the interdigital capacitors, and zc¼ 1/jx Cint is the im-

pedance of Cint.

The ABCD parameters are transformed into Y-parame-

ters. The Y-parameters of the upper and lower sections are

given by

Y11 Y12Y21 Y22

� �i

¼ Di=Bi ðBiCi � AiDiÞ=Bi

�1=Bi Ai=Bi

� �; (11)

where i is either upper or lower accordingly. The Y-parameters of the entire shunt circuit/structure can be

obtained by adding those of the upper and the lower sec-

tions, i.e.,

Y11 Y12Y21 Y22

� �¼ Y11 Y12

Y21 Y22

� �upper

þ Y11 Y12Y21 Y22

� �lower

:

(12)

From the above Y-parameters, S21 of the filter circuit

can be derived. The numerator of S21 is given by

S21ðnumeratorÞ ¼ �j4

(z0 sin½bðl1 þ DlÞ þ bðl2 þ DlÞ�

� cos bðl1 þ DlÞ cos bðl2 þ DlÞxCint

): ð13Þ

Transmission zeros of the proposed filter can then be

estimated by setting S21 ¼ 0 resulting in

z0 sin½bðl1 þ DlÞ þ bðl2 þ DlÞ�

� cos bðl1 þ DlÞ cos bðl2 þ DlÞxCint

¼ 0:(14)

In addition, we assume Cint to be small, therefore,

leading to

cos bðl1 þ DlÞ cos bðl2 þ DlÞ � 0; (15)

which relates the transmission zeros to the tapping posi-

tions. Substituting b ¼ 2pfffiffiffiffiffiffiffieeff

p=c in eq. (15) yields esti-

mated locations of the transmission zeros, i.e.,

f1 ¼ c

4ðl1 þ DlÞ ffiffiffiffiffiffiffieeff

p (16)

and

f2 ¼ c

4ðl2 þ DlÞ ffiffiffiffiffiffiffieeff

p ; (17)

where f represents the frequency, eeff the effective dielectric

constant, c the speed of light in free space, and f1 and f2represent the frequencies of transmission zeros correspond-

ing to the tapping positions determined by l1and l2. We

eliminate Dl by introducing coefficients {P1, P2} (0, 1), i.e.,

f1 ¼ P1c

4l1ffiffiffiffiffiffiffieeff

p (18)

and

f2 ¼ P2c

4l2ffiffiffiffiffiffiffieeff

p (19)

At these transmission zeros, maximum rejection is

observed.

Figure 3 (a) Layout of the proposed filter with etched ground

plane apertures and (b) its simulated S21 for different values of T.[Color figure can be viewed in the online issue, which is avail-

able at www.interscience.wiley.com.]



To determine the numerical values of f1 and f2 for the

proposed filters of Figure 1(b), we performed EM simula-

tions in Zeland IE3D to first determine P1 and P2 for dif-

ferent N. As can be seen in eq. (3), the capacitance Cint

varies proportionally with N.As such, the branch lengths of the hairpin resonators

need to be slightly adjusted for keeping the center fre-

quency f0 fixed at 6.5 GHz. On the basis of the simula-

tions, we report a set of empirical values for P1 and P2 in

Table II, applicable to the interdigital capacitor of Figure

1(b). It can be seen from Figure 4 that both P1 and P2

decrease with increasing N. This is expected since as the

number of fingers increases, the extra microstrip length Dlincreases, leading to smaller values of P1 and P2. In

essence, eqs. (18) and (19) are based on linear coeffi-

cients, which offer reasonably accurate estimations of the

transmission zeros with relative errors below 6.5%. To

illustrate this, several 4-finger bandpass filters are virtually

designed with f0 ¼ 6.5 GHz and with different positions

of the transmission zeros. Two approaches, i.e., IE3D sim-

ulations and the proposed semi-analytical formulae (18)

and (19) are used. A comparison of the results is pre-

sented in Table III. For N ¼ 4, the maximum relative

error is 3.8%.

As can be seen in Figure 5, the shorter the distance

from the center of the hairpins to the input/output ports,

the closer the two transmission zeros are to the passband,

consequently providing a high selectivity. However, it has

to be noted that the tapping positions also affect the cou-

pling between the resonators. The closer the tapping posi-

tions are to the center of the hairpins, the larger the QE

[11]. A large QE puts the filter into an over-coupled situa-

tion [12, 13], i.e.,

K >1

Qu

þ 1

QE

; (20)

where K is the coupling coefficient and Qu is the unloaded

quality factor of either of the two resonators. For instance,

the case of l1 ¼ 2.8 mm and l2 ¼ 3.6 mm in Figure 5

reflects an over-coupled situation causing a hump within

the passband. The coupling condition of the filter can be

identified by using either measured or simulated values of

K, Qu, and QE [14–16]. While K and QE can be calculated

using eqs. (1) and (2), an expression for Qu is available in

[16]. In the case of the proposed filter of Figure 1(b) with

N ¼ 4, K ¼ 0.03 < 1/Qu þ 1/QE ¼ 1/78.9 þ 1/25,

thereby satisfying the under-coupled condition, and the fil-

ter response does not show a hump in the passband. The

coupling gap Sint between the interdigital capacitors also

affects the EM coupling between two resonators [14]. In

the case of the proposed filter of Figure 1(b), Sint ¼ 0.2

TABLE II Proposed Empirical Values of P1 and P2 forInterdigital Capacitors

Number of Fingers P1 P2 Relative Error

2 0.7754 0.8232 <6.4%

3 0.7531 0.7947 <5.0%

4 0.7243 0.7566 <3.8%

5 0.6862 0.7055 <3.2%

6 0.6455 0.6520 <4.2%

7 0.6134 0.6104 <5.1%

8 0.5853 0.5740 <3.9%

9 0.5633 0.5469 <5.7%

Figure 4 Empirical values of linear coefficients P1 and P2 for

the proposed bandpass filters with different N.

TABLE III Simulated and Estimated Transmission Zerosfor Bandpass Filters with N 5 4 and with DifferentTapping Positions

Locations

Zeland IE3DSimulation

Proposed

Approximation

Relative

Error

l1 ¼ 2.4 mm f1 ¼ 8.25 GHz f1 ¼ 8.49 GHz E1 ¼ 2.9%

l2 ¼ 4.0 mm f2 ¼ 5.45 GHz f2 ¼ 5.32 GHz E2 ¼ 2.4%

l1 ¼ 2.6 mm f1 ¼ 7.85 GHz f1 ¼ 7.84 GHz E1 ¼ 0.1%

l2 ¼ 3.8 mm f2 ¼ 5.58 GHz f2 ¼ 5.60 GHz E2 ¼ 0.4%

l1 ¼ 2.8 mm f1 ¼ 7.49 GHz f1 ¼ 7.28 GHz E1 ¼ 2.8%

l2 ¼ 3.6 mm f2 ¼ 5.77 GHz f2 ¼ 5.91 GHz E2 ¼ 3.8%

l1 ¼ 3.2 mm No passband f1 ¼ 6.37 GHz NAl2 ¼ 3.2 mm f2 ¼ 6.65 GHz

Figure 5 Simulated S-parameters (S21) of the proposed filters

with N ¼ 4 and with different tapping positions.


152 Zhu et al.

mm, set by the trial-and-error simulations for the optimal

frequency response. In essence, both the tapping positions

and the gap size must be carefully chosen to avoid over-

coupling.

C. Cascaded StructuresIn general, cascaded structures are used in a bandpass fil-

ter for achieving relatively sharper frequency response

and relatively more flat passband response. Consider being

given user-specifications of a filter that require the maxi-

mum passband attenuation ¼ 2 dB, minimum stopband

attenuation ¼ 30 dB, maximum return loss ¼ �15 dB, f0¼ 6.5 GHz, and 3 dB bandwidth � 650 MHz. Such speci-

fications are difficult to achieve by a single unit, and

therefore, cascading becomes necessary.

On the basis of the center frequency and bandwidth

specifications, two proposed filter units both with N ¼ 4

Figure 6 (a) Layout, (b) photograph of a cascaded coupling

bandpass filter based on the proposed structure, and (c) its simu-

lated and measured S-parameters. [Color figure can be viewed in

the online issue, which is available at www.interscience.wiley.com.]

Figure 7 (a) Layout, (b) photograph of a cascaded coupling

bandpass filter based on the proposed structure, and (c) its simu-

lated and measured S-parameters. [Color figure can be viewed in

the online issue, which is available at www.interscience.wiley.com.]



are selected to design a cascaded filter as shown in Figure

6(a). The tapping positions are l1 ¼ 2.4 mm and l2 ¼ 4.0

mm for the first and the last resonators. By simulation and

optimization, we choose D ¼ 2.68 mm for asymmetric

feed between the two cascaded units, to obtain lower

return loss and sharper cutoff frequency response. The

horizontal coupling gap between the units is designed to

be S ¼ 0.522 mm. The locations of the transmission zeros

of the cascaded filter are estimated to be around 5.5 GHz

and 8.3 GHz using eqs. (18) and (19), which are compara-

ble to simulation results. On the basis of eqs. (1) and (2),

the external quality factor QE is calculated to be 19.1 and

the coupling matrix M is found to be

M ¼0 �0:038 0 0

�0:038 0 0:029 0

0 0:029 0 �0:0430 0 �0:043 0

2664

3775: (21)

Negative and the positive values in M represent elec-

tric and magnetic couplings, respectively [7].

An alternative cascaded structure is shown in Figure 7(a).

In this case, a double stub microstrip is used to adjust the

impendence matching between the two cascaded units.

Because of the added microstrip, the transmission zeros of

the cascaded filter are expected to differ from the estimated

values. As can be seen from the IE3D simulations in Figure

Figure 8 (a) Photograph of an 8-finger bandpass filter, (b) its simulated and measured S-parameters, (c) its simulated and measured

group delay, (d) photographs of top view and bottom view of a 4-finger bandpass filter with etched ground planes, and (e) its simulated

and measured S-parameters. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]


154 Zhu et al.

7(c), the transmission zeros occur at f1 ¼ 5.6 GHz and f2 ¼7.6 GHz. The external quality factor QE is calculated to be

22.1 and the coupling matrix M is found to be

M ¼0 �0:042 0 0

�0:042 0 0:820 0

0 0:820 0 �0:0480 0 �0:048 0

2664

3775: (22)

Compared to the cascaded filter structure of Figure 6,

the filter of Figure 7 exhibits a larger QE, a lower inser-

tion loss, and a sharper cutoff frequency response. As

such, the filter of Figure 7 has better frequency selectivity,

although it is relatively bulky.

IV. FABRICATION AND MEASUREMENTS

The proposed bandpass filters are fabricated on a 0.635

mm thick RT/duroid 6010.2 substrate with er ¼ 10.2.

Measurements are performed using Anritsu 37369D vector

network analyzer.

Figure 8(b) shows the measured S-parameters of the

fabricated 8-finger bandpass filter of Figure 8(a). The filter

shows a center frequency of 6.5 GHz and a 3 dB band-

width of 1018 MHz, both of which agree well with the

IE3D simulations. The filter has a return loss below �15

dB over the passband ranging from 6.48 GHz to 6.91

GHz and an insertion loss less than 1.5 dB within the

6.3–6.88 GHz range. Maximum group delay variation

within the passband is 0.23 ns [see Fig. 8(c)]. Figure 8(e)

shows the measured S-parameters of the fabricated filters

with etched ground plane for the case of T ¼ 3.3 mm [see

Fig. 8(d)]. The filter shows a 3 dB FBW of 24.2%. The

filter has a return loss below �15 dB over a passband

range of 6.81–7.82 GHz and an insertion loss less than

1.5 dB within the 6.51–7.85 GHz range.

Both the simulations and experimental measurements

of cascaded structures are shown in Figure 6(c) and Figure

7(c), respectively. Regardless of some small deviation in

the higher frequency, satisfactory agreement between the

simulation and the measured responses is achieved. Figure

9 shows a group of 4-finger bandpass filters designed and

fabricated with different tapping positions. These filters

exhibit different transmission zeros as expected.

Discrepancies between measurements and simulations

can be attributed to fabrication tolerances considering the

high sensitivity of ring resonators with respect to dielec-

tric constant and thickness of the substrate [17] and to

some extent to calibration errors. In addition, the undesir-

able effects of radiation from discontinuities (fingers in

particular) in the proposed filters tend to be also the cause

for the minor deterioration of the insertion loss [18].

V. CONCLUSIONS

In this article, a class of new microstrip bandpass filters

has been proposed. The proposed filters use interdigital

capacitors combined with ring resonators, and exhibit

wider bandwidths compared to traditional edge-coupled

filters. The bandwidths of the filters can be easily adjusted

by changing the geometrical parameters of the interdigital

capacitors and/or the ground plane apertures. The filters

can be used in both narrowband (FBW < 20%) and wide-

band (FBW > 20%) applications. Semi-analytical equa-

tions derived in this work help designers quickly yet accu-

rately estimate the locations of transmission zeros.

Further, cascaded filters based on the proposed structure

exhibit a very sharp cutoff frequency and low loss. Com-

parison of IE3D simulations and experimental measure-

ments has been shown for several of these filters.

ACKNOWLEDGMENT

The Duriod microstrip substrate materials are provided by

the Rogers Corporation. The authors acknowledge the help

of Mr. J. Gauthier of the Ecole Polytechnique de Montreal,

Quebec, in fabricating the filters.

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Figure 9 (a) Photograph of a group of bandpass filters with N¼ 4 and with different tapping positions and (b) their measured

S-parameters. [Color figure can be viewed in the online issue,

which is available at www.interscience.wiley.com.]



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BIOGRAPHIES

Li Zhu received the B. Eng. degree

in electrical engineering from the

University of Science and Technol-

ogy of China, Hefei, China, in 2004,

and the M. Sc. degree in electrical

and computer engineering from Con-

cordia University, Montreal, Canada,

in 2008. In October 2009, he will be

joining COMDEV as an RF Engineer. His research inter-

ests are modeling and design of microwave passive com-

ponents, computer aided design of VLSI circuits, and de-

velopment of iPhone accessories.

Vijay Devabhaktuni received the B.

Eng. degree in EEE and the M. Sc.

degree in physics both from BITS,

Pilani, India, in 1996, and the Ph.D.

degree in electronics from Carleton

University, Ottawa, Canada, in 2003.

He held the prestigious 2005–2008

Canada Research Chair in Computer-

Aided High-Frequency Modeling and Design in the

Department of ECE at Concordia University, Montreal,

Canada. Currently, he is an Associate Professor in the

EECS Department at the University of Toledo, Toledo,

OH. His research interests include applied electromag-

netics, computer aided design, neural networks, optimiza-

tion, RF/microwave devices, and biomedical applications

of wireless sensor networks. In these areas, Dr. Devabhak-

tuni secured funding of about $2M from government and

industry, authored 60 peer-reviewed articles, and is super-

vising a dozen or so M.S. and Ph.D. students. Dr. Devab-

haktuni is a Senior Member of the IEEE.

Chunyan Wang received the B.

Eng. degree in electronics from Jiao-

Tong University, Shanghai, China,

and the M. Eng. and Ph.D. degrees

from Universite Paris Sud, Paris,

France. She joined Concordia Uni-

versity, Montreal, QC, Canada, in

1997, as an Assistant Professor,

where she is presently an Associate Professor of Electrical

and Computer Engineering. Her current research areas are

low-power analog-mixed VLSI design, CMOS sensor inte-

gration, and VLSI implementation of digital signal proc-

essing systems. Dr. Wang is a Senior Member of the

IEEE.

Ming Yu received the Ph.D. degree

in electrical engineering from the

University of Victoria, Victoria, Can-

ada, in 1995. In 1993, while working

on his doctoral dissertation part-time,

he joined COMDEV, Cambridge,

Canada, as a Member of Technical

Staff. Currently, he is the Chief Sci-

entist and Director of R&D. He is responsible for


156 Zhu et al.

overseeing the development of the company’s R&D road-

map and next-generation products and technologies,

including high-frequency and high-power engineering,

electromagnetic CAD, and tuning for complex and large

problems. He has authored or co-authored over 90 publi-

cations. He holds eight patents with six more pending. Dr.

Yu is the Vice-Chair of MTT-8 and served as Chair of

TPC-11. He is a member of editorial boards of several

IEEE and IET publications. He was the recipient of the

1995 and 2006 COMDEV Achievement Award for the de-

velopment of computer-aided tuning algorithms and sys-

tems for microwave filters and multiplexers. Dr. Yu is a

Fellow of the IEEE. He is an IEEE Distinguished Micro-

wave Lecturer from 2010 to 2012.



a bandpass filter with adjustable bandwidth and predictable transmission zeros

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