06998873.pdf

7/25/2019 06998873.pdf

1/11

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 2, FEBRUARY 2015 403

Temporal Coupled-Mode Theory and the Combined

Effect of Dual Orthogonal Resonant Modes

in Microstrip Bandpass FiltersFaxin Yu, Senior Member, IEEE, Yang Wang, Zhiyu Wang, Member, IEEE,

Qin Zheng, Min Zhou, Dajie Guo, Xu Ding, Xiuqin Xu, Liping Wang, Hua Chen,Yongheng Shang, and Zhengliang Huang

AbstractWe propose a temporal coupled-mode theory for thedesign of microstrip bandpass filters with multi-resonant modesand reveals the mechanism of the filters based on multi-couplingand energy conservation theorem. As an example, the combined

effect of the two orthogonal modes in dual-mode filters is analyzed

in detail. By simply tuning the coupling efficiencies of the two res-onant modes, two K-band integrated microstrip bandpass filters

have been designed and demonstrate opposite asymmetric trans-mission responses. Both simulation and experiment results agreewell with the theoretical analysis, which provides a new approach

for filter design and optimization.

Index TermsCoupled-mode theory (CMT), dual resonantmodes, microstrip bandpass filter.

I. INTRODUCTION

I N MODERN communication systems, microstrip bandpassfilters are widely used in RF integrated circuits (RFICs) andmonolithic microwave integrated circuits (MMICs). Multi-mi-

crostrip bandpass filters consist of planar resonators, such as

split ring, miniaturized hairpin, have been proposed [1], [2]. Inrecent years, due to the rapid growth of the spectrum occupation

and the growing demand for better receiver sensitivity, many

rigorous microstrip bandpass filter designs have emerged for

specific applications to achieve compact size, low insertion

loss, extended stopband, harmonic suppression, and multi-band

operations [3][9]. Advanced filters with stepped-impedance

resonators [10][12], complementary split-ring resonators

[13][15], substrate-integrated resonators [16][18], and recon-

figurable resonators [19][21] have provided new opportunities

for designing high-performance microwave systems.

Specifically, in a compact transceiver system, where the

transmission channel and the reception channel easily interferewith each other, a pair of bandpass filters with opposite asym-

metric transmission responses is usually desired to isolate the

two channels, to let pass the signals in its own channel, and

Manuscript received July 03, 2014; revised November 03, 2014; accepted

December 03, 2014. Date of publication December 25, 2014; date of currentversion February 03, 2015. This work was supported by the National Science

Foundation of China under Grant 61401395 and by the Fundamental ResearchFunds for the Central Universities under Grant 2014QNA4033.

The authors are with the School of Aeronautics and Astronautics, ZhejiangUniversity, Hangzhou 310027, China (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMTT.2014.2381256

to block the interfering signal coupled from the other channel.

In this special case, each of these bandpass filters may only

require high selectivity on one side of the passband, and less or

none on the other side [22], [23]; thus having an asymmetric

transmission response.

To better explain all these different kinds offilter responses,

several theories are developed. Commonly, the performance ofmicrostrip bandpass filters are analyzed and explained with one

of the two theories, the equivalent circuit model [23], [24] or

the network synthesis model [25][27]. However, both theo-

ries have their limits, which may cause inconvenience in prac-

tical filter designs. The equivalent circuit model cannot pro-

vide enough accuracy for the microstrip bandpass filters with

nonstandard microstrip patterns, and cannot maintain its accu-

racy in the design at relatively high microwave band, like K-

or Ka-band. The network synthesis method, which uses a ma-

trix equation to express the relations among resonant loop cur-

rents in the filter network [26], works well in the analysis of

ideal responses offilters, but does not incorporate the effect of

ohmic losses in each resonators. The relation among resonantloop currents, which is derived based on current conservation in

equivalent circuit networks, does not directly present the funda-

mental physics of the coupling effects among input/output ter-

minals and resonators, and lacks convenience to accommodate

the practical quality factors obtained through eigenmode simu-

lations. Thus, it may slow down the speed of full-wave-simula-

tion assisted filter optimization. Although lately this method is

assisted by a box-like coupling scheme [28], [29], it is most

commonly used as an analysis tool after having a specific filter

design.

In this paper, we propose a theoretical formalism with the

temporal coupled-mode theory (CMT) [30][34] to arrive at

simple formulas for the response of microstrip bandpass fil-

ters with multi-resonant modes. These formulas provide ana-

lytic insight into the coupling behavior among input/output ter-

minals and resonators, which clearly reveals the mechanism and

provide accurate prediction of both the passband and stopband

performance of the bandpass filters. By simply tuning the pa-

rameters in the formulas, all filter responses can be accurately

obtained, which provide a new approach for guiding and ac-

celerating filter designs. The parameters of specific filters are

achieved through full-wave simulation of the filter, which ben-

efits the filter optimization. As an example, performance offil-

ters with dual orthogonal resonant modes is analyzed in detail in

0018-9480 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.

See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

7/25/2019 06998873.pdf

2/11

404 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 2, FEBRUARY 2015

Fig. 1. Abstract diagram showing the multi-coupling features of the spatially

symmetric fi lter with resonant modes.

this paper. By simply tuning the two parameters that represent

the coupling efficiencies of each resonant mode, two K-band

integrated dual-mode microstrip bandpass filters with opposite

asymmetric transmission responses have been designed. Both

filters present extended upper/lower stopband. Simulations and

experiments have been conducted and have validated the theo-

retical model.

II. CMT

A. General CMT for -Mode Filters

When we couple spatially symmetric microstrip resonators

to two microstrip feed lines, shown in Fig. 1, the incoming wave

propagating along one feed line can then couple into the res-

onators or couple directly to the other feed line. Simultaneously,

the energy stored in the resonators can also couple into the two

feed lines.

For such a filter, the dynamic equations based on energy con-

servation can be written as [30]

(1)

(2)

where the amplitude vector

(3)

denotes the resonance amplitude of each mode. Here the reso-

nance amplitude is normalized such that indicates the en-

ergy stored in the th resonant mode. The matrix

(4)

denotes the resonant frequency of each mode.

All resonant modes are excited by the incoming waves

(5)

with the coupling matrix . Once excited, the resonant

modes couple with the outgoing waves

(6)

with the coupling matrix

(7)

Here, the amplitudes of the incoming/outgoing waves are nor-

malized such that and indicate the power carried

by the incoming wave and outgoing wave at terminal , respec-

tively.

and denotes the decay rates due to coupling to the ter-

minals and radiation/material loss, respectively. Given the filter

has spatial symmetry, each mode decays either symmetrically

or antisymmetrically into the two terminals. Thus, for mode ,

we have

or (8)

In addition to the resonance-assisted coupling, the wave can

also directly couple from one terminal to the other, as described

by the matrix in (2).

As a reciprocal system, the above matrices must follow the

relations [30]

(9)

(10)

Thus, letting , we have

......

. . ....

(11)

(12)

(13)

where and denote the lifetimes of mode due to the

coupling to the two feed lines and the losses, respectively, and

th th modes are both even or odd

th th modes are one even and one odd

(14)

th th modes are both even

th th modes are both odd (15)

the th mode is even

the th mode is odd. (16)

Weak direct capacitive coupling is commonly used to form a

bandpass response. Thus, the two feed lines connecting with the

two terminals are often not linked, instead, they have a gap in

between. In this case, we have

(17)

7/25/2019 06998873.pdf

3/11

YUet al.: TEMPORAL CMT AND COMBINED EFFECT OF DUAL ORTHOGONAL RESONANT MODES IN MICROSTRIP BANDPASSFILTERS 405

TABLE IRELATIONS OFRESONANT FREQUENCIES, LIFE TIMES, AND FILTERPERFORMANCES

where , , and . The equal sign is

valid when no loss in the direct coupling process is considered.

denotes the phase factor depending on the effective

length of the two feed lines, where denotes the effective

phase velocity in the microstrip feed lines, represents the 90

phase delay due to the capacitive coupling. Worth noting that,

given the small value of the capacitor for the capacitive direct

coupling between input and output feed lines, in the bandwidth

we cared about, the values of and would not have a big

change. Thus, in this paper, constant and are used as an

approximation.

After achieving all the parameters in (1) and (2) and replacing

in (1) with , we can solve the two equations and obtain

the transmission and reflection responses of thefilter in the fre-

quency domain via

(18)

B. CMT for Dual-Mode Filters

We use dual-mode filters as examples to show the derivation

of the transmission and reflection responses.For dual-mode cases, only resonators supporting two orthog-

onal modes, anodd modeand an even mode, can be used toform

bandpass filters [28]. We set in the above equations, and

let the resonant frequencies of the two orthogonal modes satisfy

. From (10)(17), we then have , and

(19)

(20)

(21)

(22)

The top signs are used when thefirstmode is odd, and the bottom

signs are used when the first mode is even.

Substitute (17)(22) into (1), (2), we can then see in a dual-

mode filter system the reflection response at terminal 1 (called

or ) and the transmission response from terminal 1 to ter-

minal 2 (called or ) in the frequency domain are deduced

as

(23)

(24)

All the parameters in (23) and (24) are clearly related to the

physical process of the multi-coupling among the resonators andthe two feed lines, which can be easily tuned to achieve the op-

timized response of the bandpass filter. Filter performances and

corresponding relations of resonant frequencies and life times of

the two modes are shown in Table I. Red curves (in online ver-

sion) represent the reflection responses and blue curves (in on-

line version) represent the transmission responses. As we men-

tioned above, the case with capacitive source/load coupling is

commonly applied.

C. Synthesis Method Assistant With Numerical Calculation

Different from the full analytic synthesis method applied only

for canonical filters like Butterworth, Chebyshevfilters, in thefilter design with our CMT method, a synthesis method assistant

with numerical calculation is applied. The flowchart is shown in

Fig. 2.

Firstly, as we discussed above, we analytically calculate the

equations of the transmission and reflection responses of all dif-

ferent orders offilters using CMT. Then assume an initialfilter

order , maximum number of iterations, and set desired filter

specifications like central frequency, bandwidth, passband re-

turn loss and insertion loss, transmission zeros, and stopband

rejection. After that, numerically optimize all the parameters in

the th-order CMT equations to achieve the desired transmis-

sion and refl

ection responses. If the optimization cannot con-verge after reaching the maximum number of iterations, we in-

crease the filter order and redo the optimization until we obtain

all the proper parameters.

The final step is to design the filter according to the opti-

mized results through finite-element method (FEM) full-wave

simulations. The resonant frequency and the quality factor of

each mode in a concrete filter structure can be obtained through

eigenmode simulation. To achieve that, we first simulate the mi-

crowave resonators one by another. The quality factor of each

resonant mode consideringonly radiation/material losses, ,

is obtained. We then add all the resonators and the two mi-

crostrip feedlines, replace the 50- input/output terminals with

two 50- sheets, and conduct the eigenmode simulation again.

The total quality factor of each mode considering both coupling

7/25/2019 06998873.pdf

4/11


Fig. 2. Design procedure of the present CMT method.

and losses, , is obtained. Finally, the quality factor of each

resonant mode due to coupling to terminals, , is calcu-lated by

(25)

and the corresponding lifetimes in (23) and (24), and , can

be achieved through the following relations:

(26)

It is worth noting that here takes into account of

all the energy decays coupling from the resonant mode to

terminals either directly or via the other resonant modes.

D. Filter Performance Analysis of Dual-Mode Filters

We use dual-mode filters as examples to elaborate the pro-

posed filter design method in filter performance analysis.

In microstrip bandpass filters, the decay rates of each res-

onant mode due to radiation/material loss are relatively small,

often one order less comparing to the decay rates due to

coupling to the terminals, in order to achieve a high passband

transmission efficiency. Thus, are neglected in the following

analysis of reflection poles and transmission zeros for simplifi-

cation.

From (23) and (24) with top signs, and let be close to

infinity, the frequencies of the two reflection poles and the two

TABLE IIFREQUENCY DIFFERENCE TUNING FORREFLECTIONPOLES

transmission zeros are derived as follows:

(27)

(28)

From (27) and (28), we then have the central frequencies of

the reflection poles and the transmission zeros as

(29)

(30)

and the frequency differences of the two reflection poles and the

two transmission zeros as

(31)

(32)

From (29) and (30), assuming and , we can

get when is positive, will locate at

a frequency lower than, but not far from , while

will locate at a higher frequency. As reachesa relatively large positive value, both transmission zeros will

move to the upper stopband. Similarly, when is negative,

both and will shift to the opposite di-

rection, and as reaches a relatively large negative value, both

transmission zeros will move to the lower stopband.

When , then if is smaller than ,

which is a common case, then the term under the square root

in (28) is negative, and we cannot get real solutions. Thus, the

transmission response will have no zeros in both the upper and

lower stopbands.

From (31), we can get the trend of whenfine tuning

or and . The results are shown in Table II.

While, in getting the trend of whenfine tuning ,

or and from (32), specific requirements must be met in

7/25/2019 06998873.pdf

5/11


TABLE IIIFREQUENCY DIFFERENCE TUNING FORTRANSMISSION ZEROS

Fig. 3. Calculated magnitude responses, the reflection ]dashed red line (in on-line version)] and transmission[solid blueline (in online version)] of a bandpass

filter whose first mode is odd and whose , is equal to: (a) 0.1 ns, 0.2 ns,

(b) 0.15 ns, 0.15 ns, and (c) 0.2 ns, 0.1 ns.

choosing the correct branch. The results are shown in Table III,

where

(33)

As we can see from Tables II and III, when fine tuning , or

and , and will change accordingly so as the

bandwidth of the passband and the stopband. This fine tuning is

helpful to achieve a better passband and stopband performance.

In specific applications, small is designed to have a low

passband return loss, and large is designed to obtain an

extended upper or lower stopband when both transmission zeros

are on the same side of the passband.

Fig. 4. Calculated magnitude responses, the reflection [dashed red line (in on-lineversion)] and transmission [solid blueline (in online version)] of a bandpass

filter whose first mode is even and whose , is equal to: (a) 0.1 ns, 0.2 ns,(b) 0.15 ns, 0.15 ns, and (c) 0.2 ns, 0.1 ns.

The reflection and transmission responses of one example

is shown in Fig. 3, where ,

GHz, GHz, ns, ns,

equals to (0.1 ns, 0.2 ns), (0.15 ns, 0.15 ns), and (0.2 ns, 0.1 ns),

respectively. We can see from Fig. 3, by tuning the coupling

efficiencies of the two orthogonal resonant modes, the trans-

mission response can be dramatically changed. Comparing with

Fig. 3(a), an opposite transmission response, shown in Fig. 3(c),

is achieved by exchanging the values of and , which can be

easily realized by reducing the coupling efficiency between the

first, odd resonant mode and the microstrip feed lines and in-

creasing the coupling effi

ciency between the second, even res-onant mode and the microstrip feed lines.

The analysis based on (23) and (24) with bottom signs is a

little bit complex due to the existence of imaginary terms. Here

we only show the results obtained through numerical calcula-

tions. O ne e xample i s given i n Fig. 4 , where GHz

and GHz, other parameters are the same as those

in Fig. 3. Comparing with the results in Fig. 3, a useful filter

response appears when is close to zero, shown in Fig. 4(b).

In this case, on both sides of the passband, there exists a single

transmission zero.

E. Method Comparison

The present CMT method is based on the energy conserva-

tion in the multi-resonatorfilter system, while the conventional

7/25/2019 06998873.pdf

6/11


network-based filter synthesis method is based on the current

conservation in the equivalent circuit network. For practical mi-

crostrip filter design, both methods need the assistance of the

full-wave simulation.

Comparing with the conventional network-based filter syn-

thesis method, our CMT method directly provides the decay

rates of each resonant mode, which is more convenient to link

with the quality factors obtained directly through eigenmode

simulations via (26). When we start from the optimized theo-

retical results to approach the concrete microstrip filter, which

consists of multi-resonators or a resonator with multi-resonant

modes through eigenmode simulations, our method is more di-

rect and will save time in comparing the quality factors of the

designed microstrip filter and the optimized theoretical values.

Also, our method conveniently includes the dissipations via ,

while most of the published approaches have not taken the ef-

fect of loss into account; thus our approach may save time infine

tuning the microstrip filter. The method comparison is shown in

Table IV.

III. SIMULATION RESULT ANDDISCUSSION

To validate the CMT described above, we perform analytic

calculations and numerical simulations to two kinds of dual-

mode microstrip bandpassfilters, which provide opposite asym-

metric transmission responses. One of the two transmission re-

sponses has an extended upper stopband, and the other one has

an extended lower stopband. Both numerical simulations are

conducted with the commercial finite-element simulation soft-

ware HFSS.

Direct coupling between input/output terminals are intro-

duced in the two bandpass fi

lter designs. Thus, as shown inTable I, one more transmission zero is obtained on one side of

the passband. As a result, the conventional narrow stopband

on this side is extended to a much wider range. Based on our

theoretical analysis, to achieve the first kind with extended

upper stopband, the lifetime of the first, odd resonant mode due

to coupling to the terminals must be smaller than the second,

even resonant mode, which means having a larger coupling

efficiency. Conversely, for an extended lower stopband, the

odd resonant mode should have a smaller coupling efficiency.

As specific examples, a K-band integrated microstrip band-

pass filter A with a dual-mode resonator is carried out as a proto-

type of the first kind, and another K-band integrated microstrip

bandpass filter B with two single-mode resonators is carried out

as a prototype of the second kind. Both of the two microstrip

bandpass filters have spatial symmetry, and the two supported

resonant modes of eachfilter are orthogonal, with one odd mode

and one even mode. In both cases, the frequency of the odd

mode is designed to be lower than the frequency of the even

mode, which corresponds to (23) and (24) with top signs.

A. Filter A With Extended Upper Stopband

The presented filter A is shown in Fig. 5, whose topological

pattern is borrowed from [22]. Fig. 5(a) shows the schematic

diagram illustrating different layers of the integrated microstrip

bandpass filter. There are four layers in total. The top layer is

a 4.8- m-thick gold layer, which contains the pattern of the

TABLE IVMETHODCOMPARISON

Fig. 5. (a) Schematic diagram of the integrated microstrip bandpass filter A

with a four-layer structure. (b) Dimensions of the filter. (c) Brief illustration of

the direct coupling path (solid black line) and the odd [long dashed red line (inonline version)] and even [short dashed blue line (in online version)] resonant

modes in the filter. (d) Simulated magnitude distribution of the electric field onthe top surface of the GaAs substrate within the odd and even resonant modes.

TABLE VDIMENSIONS OFFILTERA

present bandpass filter. At the bottom, another gold layer forms

the ground plane. Between them, there are two dielectric layers:

a 0.1-mm-thick GaAs substrate, with relative dielectric constant

12.9, and above it an optional thin SiN passivation layer to pro-

tect the electric properties of the GaAs layer.

Forfilter A, the odd and even modes are introduced within

one microstrip resonator. The effective length of the microstrip

along the current path in the resonator is about the half wave-

length at the resonant frequency of each mode. The dimensions

of the filter are shown in Fig. 5(b) and Table V.

7/25/2019 06998873.pdf

7/11


Fig. 6. (a) Magnitude responses and (b) phase responses of bandpass fi lter Afrom the analytic calculations of the reflection [dashed orange line (in online

version)] and transmission [solid green line (in online version)], and from the

finite-element simulations of the reflection [dotted red line (in online version)]and transmission [dasheddotted blue line (in online version)].

The dual orthogonal modes excited in this filter are illustrated

in Fig. 5(c). The solid black line indicates the path of direct cou-

pling, the long dashed red line (in online version) indicates the

odd resonant mode, and the short dashed blue line (in online

version) indicates the even resonant mode. The simulated mag-

nitude distributions of the electric field within the odd and even

resonant modes on the top surface of the GaAs substrate areshown in Fig. 5(d). The simulated surface current on the gold

pattern has the same symmetry as the illustration in Fig. 5(c).

Corresponding to the dimensions of the microstrip bandpass

filter A, we have , , ns,

GHz, GHz, ns,

ns, ns, and ns. The reflection and

transmission of thefilter obtained from both the analytic calcu-

lations and the finite-element simulations are shown in Fig. 6.

We can see the numerical simulation results match well with

the present CMT. The minor differences between the theoretical

results and the numerical results on both ends of the curves are

caused by the effect of the other resonances far away from thepassband, which are considered in the simulations, but not in

the theoretical model.

We can tune the filter bandwidth, in-band return-loss level,

and the transmission zeros by changing the dimensions of the

resonator and the inner end of the two microstrip feed lines. The

analysis of thefilter performance tuning is shown in Table VI.

B. Filter B With Extended Lower Stopband

In order to achieve the other kind of microstrip bandpass filter

with extended lower stopband, and clearly reveal the relation

between the transmission response and the two coupling effi-

ciencies of the two orthogonal resonant modes, we designed

the K-band integrated microstrip bandpass filter B with two

TABLE VIPERFORMANCE TUNING OFFILTERA

Fig. 7. (a) Schematic diagram of the integrated microstrip bandpass filter Bwith a four-layer structure. (b) Dimensions of the filter. (c) Brief illustration of

the direct coupling path (solid black line) and the odd [long dashed red line (inonline version)] and even [short dashed blue line (in online version)] resonant

modes in the filter. (d) Simulated magnitude distribution of the electric field on

the top surface of the GaAs substrate within the odd and even resonant modes.

single-mode resonators, shown in Fig. 7. Fig. 7(a) shows the

schematic diagram illustrating different layers of the integrated

microstrip bandpass filter. The definitions of different layers are

the same as Fig. 5(a).

Based on the presented theory, we know that, in order to

obtain an opposite transmission response offilter A, the only

necessary treatment is to change the coupling efficiencies of

the two orthogonal modes, and , from to

. To commit that in filter B, we can simply increase the dis-

tance between the feed lines and the odd-mode resonator, which

is located on the top side of the feed lines, and correspond-

ingly increasethe coupling length between thefeed lines and the

even-mode resonator, which is located on the bottom side of the

feed lines. After optimization, filter B with an extended lower

7/25/2019 06998873.pdf

8/11


TABLE VIIDIMENSIONS OFFILTERB

Fig. 8. (a) Magnitude responses and (b) phase responses of bandpassfi lter Bfrom the analytic calculations of the reflection ]dashed orange line (in online

version)] and transmission [solid green line (in online version)], and from thefinite-element simulations of the reflection [dotted red line (in online version)]

and transmission [dasheddotted blue line (in online version)]. Inset shows thesimulated magnitude distributions of the electric field within the third resonant

mode.

stopband is achieved. The dimensions of the filter are shown in

Fig. 7(b) and Table VII.

The dual orthogonal modes excited in this filter are illustrated

in Fig. 7(c). The simulated magnitude distributions of the elec-

tric field within the odd and even resonant modes are shown in

Fig. 7(d). We can see that the distance between the odd-mode

resonator (the split-ring resonator) and the feeding lines is tuned

to be relatively large so as to achieve a lower coupling efficiency

comparing with the one of the even-mode resonator.Corresponding to the dimensions of the microstrip bandpass

filter B, we have , , ns,

GHz, GHz, ns,

ns, ns, and ns. The reflec-

tion and transmission of the filter obtained from both the an-

alytic calculations and the finite-element simulations are shown

in Fig. 8. The analysis of the filter performance tuning is shown

in Table VIII.

Again, the numerical simulation results match well with the

present CMT. The additional resonant peak appeared in the

lower stopband is induced by a third resonant mode supported

by the lower resonator shown in Fig. 7(b). The third resonant

mode is a weak odd mode, which resonates at 18.3 GHz. The

simulated magnitude distribution of the electric field within

TABLE VIIIPERFORMANCE TUNING OFFILTERB

Fig. 9. (a) Photograph of the microstrip bandpass filter A under optical mi-

croscopy. (b) Magnitude responses and (c) phase responses offilter A from theanalytic calculations of the reflection [dashed orange line (in online version)]

and transmission [solid green line (in online version)], and from the experi-mental measurements of the reflection [dotted red line (in online version)] and

transmission [dasheddotted blue line (in online version)].

this mode is shown in the inset of Fig. 8(a). This mode has

relatively low coupling efficiency and is far away from the

passband, and thus is not considered in our theoretical analysis.

IV. EXPERIMENTAL MEASUREMENT

To further validate the present CMT, the microstrip bandpass

filter A and B are fabricated and measured using a vector net-

work analyzer (Rohde & Schwarz, ZVA 40) and a microwave

probe station (Cascade Microtech, Summit 11000M). The pho-

tographs of the two filters under optical microscopy are shown

in Figs. 9(a) and 10(a). The experimental results of the two fil-

ters are shown in Figs. 9(b) and (c) and 10(b) and (c), respec-

tively.

7/25/2019 06998873.pdf

9/11


Fig. 10. (a) Photograph of the microstrip bandpass filter B under optical mi-

croscopy. (b) Magnitude responses and (c) phase responses offilter B from the

analytic calculations of the refl

ection [dashed orange line (in online version)]and transmission [solid green line (in online version)], and from the experi-mental measurements of the reflection [dotted red line (in online version)] and

transmission [dasheddotted blue line (in online version)].

Well matched results are again obtained. The minor differ-

ences are caused by the same reason as the ones discussed above

between the simulation and the calculation results, and also the

limited accuracy of the integrated circuit (IC) fabrication.

V. CONCLUSION

In this paper, we have developed a CMT of microstrip band-

passfi

lters comprising multi-resonant modes. As an example,the combined effect of the two modes in dual-mode filters has

been analyzed in detail through our theory. Different reflection

and transmission responses can be accurately obtained by tuning

few parameters in the formulism of our theory, which paves the

way of fast filter designs. All the parameters in the formulism

have clear physical meanings and can be easily extracted from

the concrete filter model through numerical optimization and

full-wave simulations. To validate the present CMT, we have

performed both full-wave simulations and experimental mea-

surements of two specific K-band integrated microstrip band-

pass filters, which have opposite asymmetric transmission re-

sponses. The results match well with our theory. The present

CMT provides accurate analysis and would be helpful in accel-

erating filter design and optimization in practical applications.

ACKNOWLEDGMENT

Author Z. Wang thanks Prof. L. Ran and Prof. Z. Xu, both

with Zhejiang University, for their valuable discussions and re-

vision suggestions for this paper.

REFERENCES

[1] G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters,Impedance-Matching Networks, and Coup ling Structures. Norwood,MA, USA: Artech House, 1980.

[2] J.-S. Hong, Microstrip Filters for RF/Microwave Applications, 2nded. Hoboken, NJ, USA: Wiley, 2011.

[3] I. Wolff, Microstrip bandpass fi lter using degenerate modes of a mi-crostrip ring resonator,Electron. Lett., vol. 8, pp. 2930, 1972.

[4] J.-S. Hong, H. Shaman, and Y. H. Chun, Dual-mode microstrip open-loop resonators and filters, IEEE Trans. Microw. Theory Techn., vol.55, no. 8, pp. 17641770, Aug. 2007.

[5] W. Shen, X.-W. Sun, and W.-Y. Yin, A novel microstripfilter usingthree-mode stepped impedance resonator (TSIR), IEEE Microw.Wireless Compon. Lett., vol. 19, no. 12, pp. 774776, Dec. 2009.

[6] C.-L. Wei, B.-F. Jia, Z.-J. Zhu, and M.-C. Tang, Design of differentselectivity dual-mode filters with E-shaped resonator,Progr. Electro-magn. Res., vol. 116, pp. 517532, 2011.

[7] L. Wang and B.-R. Guan, A novel high selectivity dual-band band-pass filter with inductive sourceload coupling, J. Electromagn.Waves Appl., vol. 26, pp. 17341740, 2012.

[8] J. Xu, W. Wu, and C. Miao, Compact and sharp skirts microstripdual-mode dual-band bandpass filter using a single quadruple-moderesonator (QMR),IEEE Trans. Microw. Theory Techn., vol. 61, no. 3,

pp. 11041113, Mar. 2013.[9] S.-J. Sun, T. Su, K. Deng, B. Wu, and C.-H. Liang, Shorted-ended

stepped-impedance dual-resonance resonator and its application tobandpass fi lters, IEEE Trans. Microw. Theory Techn., vol. 61, no. 9,pp. 32093215, Sep. 2013.

[10] M. Makimoto and S. Yamashita, Bandpassfi lters using parallel cou-pled stripline stepped impedance resonators, IEEE Trans. Microw.Theory Techn., vol. MTT-28, no. 12, pp. 14131417, Dec. 1980.

[11] X. Lai, C. H. Liang, H. Di, and B. Wu, Design of tri-bandfilter basedon stub loaded resonator and DGS resonator,IEEE Microw. WirelessCompon. Lett., vol. 20, no. 5, pp. 265267, May 2010.

[12] W. Y. Chen, M. H. Weng, and S. J. Chang, A new tri-band bandpassfilter based on stub-loaded step-impedance resonator,IEEE Microw.Wireless Compon. Lett., vol. 22, no. 4, pp. 179181, Apr. 2012.

[13] M. Gil, J. Bonache, J. Garcia-Garcia, J. Martel, and F. Martin, Com-posite right/left-hand ed metamaterial transmission lines based on com -plementary split-rings resonators and their applications to very wide-band and c ompact filter design,IEEE Trans. Microw. Theory Techn. ,vol. 55, no. 6, pp. 12961304, Jun. 2007.

[14] X. Luo, H. Qian, J.-G. Ma, and E. Li, Wideband bandpass filter withexcellent selectivity using new CSRR-based resonator,Electron. Lett.,vol. 46, pp. 13901391, 2010.

[15] A. Ebrahimi, W. Withayachumnankul, S. F. Al-Sarawi, and D. Abbott,Compact dual-mode wideband filter based on complementary split-ring resonator, IEEE Microw. Wireless Compon. Lett., vol. 24, no. 3,

pp. 152154, Mar. 2014.[16] B. Potelon, J. Favennec, and C. Quendo, Design of a substrate in-

tegrated waveguide (SIW) fi lter using a novel topology of coupling,

IEEE Microw. Wireless Compon. Lett., vol. 18,no. 9,pp. 596598, Sep.2009.

[17] B. Potelon et al., Design of bandpass filter based on hybrid planarwaveguide resonator, IEEE Trans. Microw. Theory Techn., vol. 58,no. 2, pp. 635644, Feb. 2010.

[18] Y. Wanget al., Half mode substrate integrated waveguide (HMSIW)bandpass filter,IEEE Microw. Wireless Compon. Lett., vol. 17, no. 4,pp. 265267, Apr. 2007.

[19] S. W. Wong and L. Zhu, Implementation of compact UWB bandpassfilter with a notch-band, IEEE Microw. Wireless Compon. Lett., vol.18, no. 1, pp. 1012, Jan. 2008.

[20] Y.-H. Chun, H. Shaman, and J.-S. Hong, Switchable embedded bandnotch structure for UWB bandpass filter, IEEE Microw. WirelessCompon. Lett., vol. 18, no. 9, pp. 590592, Sep. 2008.

[21] K. Rabbi and D. Budimir, Highly selective reconfigurable filter forUWB systems,IEEE Microw. Wireless Compon. Lett., vol. 24, no. 3,

pp. 146148, Mar. 2014.

[22] X.-C. Zhang, Z.-Y. Yu, and J. Xu, Design of microstrip dual-mode fil-ters based on sourceload coupling, IEEE Microw. Wireless Compon.

Lett., vol. 18, no. 10, pp. 677679, Oct. 2008.

7/25/2019 06998873.pdf

10/11


[23] C. Hua, C. Chen, C. Miao, and W. Wu, Microstrip bandpass filtersusing dual-mode resonators with internal coupled lines,Progr. Elec-tromagn. Res. C, vol. 21, pp. 99111, 2011.

[24] J.-R. Lee, J.-H. Cho, and S.-W. Yun, New compact bandpass filterusing microstrip resonators with open stub inverter, IEEE Mi-crow. Guided Wave Lett., vol. 10, no. 12, pp. 526527, Dec. 2000.

[25] A. Atia and A. Williams, New type of waveguide bandpass filters forsatellite transponders,COMSAT Tech. Rev., vol. 1, pp. 2143, 1971.

[26] S. Amari, U. Rosenberg, and J. Bornemann, Adaptive synthesis and

design of resonatorfilters with source/load-multiresonator coupling,IEEE Trans. Microw. Theory Techn., vol. 50, no. 8, pp. 19691978,Aug. 2002.

[27] R. J. Cameron, Advanced coupling matrix synthesis techniques formicrowave filters,IEEE Trans. Microw. Theory Techn., vol. 51, no. 1,

pp. 110, Jan. 2003.[28] U. Rosenberg and S. Amari, Novel coupling schemes for microwave

resonatorfilters,IEEE Trans. Microw. Theory Techn., vol. 50, no. 12,pp. 28962902, Dec. 2002.

[29] C.-K. Liao, P.-L. Chi, and C.-Y. Chang, Microstrip realization ofgeneralized Chebyshev filters with box-like coupling schemes,IEEETrans. Microw. Theory Techn., vol. 55, no. 1, pp. 147153, Jan. 2007.

[30] W. Suh, Z. Wang, and S. Fan, Temporal coupled-mode theory andthe presence of non-orthogonal modes in lossless multimode cavities,

IEEE J. Qua ntum Electron., vol. 40, no. 10, pp. 15111518, Oct. 2004.[31] J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade,

Photonic C rystal: M olding t he Flow of Light, 2nd ed. Princeton, NJ,

USA: Princeton Univ. Press, 2008.[32] R. E. Hamam, A. Karalis, J. D. Joannopoulos, and M. Soljacic, Cou-

pled-mode theor y for gener al free-space res onant scattering of waves,Phys. Rev. A, Gen . Ph ys., vol. 75, 2007, Art. ID 053801.

[33] K. X. Wang, Z. Yu, S. Sandhu, and S. Fan, Fundamental bounds ondecay rates in asymmetric single-mode optical resonators, Opt. Lett.,vol. 38, pp. 100102, 2013.

[34] L. Zhu, S. Sandhu, C. Otey, S. Fan, M. B. Sinclair, and T. S. Luk,Temporal coupled mode theory for thermal emission from a singlethermal emitter supporting either a single mode or an orthogonal set ofmodes, Appl. Phys. Lett., vol. 102, 2013, Art. ID 103104.

Faxin Yu (SM'10) received the B.S., M.S., and

Ph.D. degrees from the School of Electronics and

Information Engineering, Harbin Institute of Tech-

nology, Harbin, China, in 1997, 1999 and 2002,

respectively.From 2002 to 2005, he was a System Architect

with UTStarcom. In 2006, he joined the School of

Aeronautics and Astronautics, Zhejiang University,

Hangzhou, China, as a Postdoctoral Researcher, be-

came an Associate Professor in 2007, and a Professor

in 2011. His research interests include monolithic mi-

crowave integrated circuit (MMIC design) and encrypt cognitive radio tech-

nology.

Yang Wang received the B.S. degree in electronic

information engineering from The PLA Information

Engineering University, Zhengzhou, China, in

2010, the M.S. degree in circuits and systems from

Hangzhou Dianzi University, Hangzhou, China, in

2013, and is currently working toward the Ph.D.degree at Zhejiang University, Hangzhou, China.

His research interests include the design and

analysis of monolithic microwave integrated circuits

(MMICs).

Zhiyu Wang(M'13) received the B.S. and Ph.D. de-

grees in information and electronic engineering fromZhejiang University, Hangzhou, China, in 2007 and

2013, respectively.

From 2011 to 2013, he was a Visiting Student withthe Massachusetts Institute of Technology (MIT),

Cambridge, MA, USA, and Harvard University,Cambridge, MA, USA. In 2013, he joined the

School of Aeronautics and Astronautics, ZhejiangUniversity, as a Lecturer. His research interests

include active metamaterial design and application,

antenna design, multipactor discharge suppression, and monolithic microwaveintegrated circuit (MMIC) design.

Qin Zhengreceived the B.S. degree in communica-

tions engineering from Ningbo University, Ningbo,

China, in 2012, the M.S. degree from the School of

Aeronautics and Astronautics, Zhejiang University,Hangzhou, China, in 2014, and is currently workingtoward the Ph.D. degree at the School of Aeronautics

and Astronautics, Zhejiang University.His research interests include RF and microwave

circuit modeling and design.

Min Zhou received the Ph.D. degree in information

technology of aeronauticsand astronautics from Zhe-

jiang University, Hangzho u, C hina i n 201 4.

In September 2014, he joined the Institute of As-

tronautics Electronic Engineering, Zhejiang Univer-

sity, as a Researcher. His current research interests

include microwave and millimeter-wave circuits and

components.

Dajie Guo received the B.S. degree from theSchool of Electrical Engineering, Beijing Jiaotong

University, Beijing, China, in 2013, and is currentlyworking toward the M.S. degree at the School of

Aeronautics and Astronautics, Zhejiang University,Hangzhou, China.

His research interests include the design and

analysis of monolithic microwave integrated circuits(MMICs).

Xu Ding received the B.S. degree from the School

of Electrical Engineering, Zhejiang University,Hangzhou, China, in 2008, and is currently working

toward the M.S. degree at the School of Aeronautics

and Astronautics, Zhejiang University.His research interests include the design and

analysis of monolithic microwave integrated circuits(MMICs) and the development of automatic testing

systems of MMICs.

Xiuqin Xureceived the B.S. degree from the School

of Mechanical and Automotive Engineering, South

China University Of Technology, Guangzhou, China,

in 2012, and is currently working toward the Ph.D.

degree at theSchoolof Aeronauticsand Astronautics,

Zhejiang University, Hangzhou, China.

Her researchinterests includemechanical structure

designand thermal design of monolithic microwave

integrated circuits (MMICs).

7/25/2019 06998873.pdf

11/11


Liping Wang received the B.S. degree from theSchool of Software Engineering, Sichuan University,

Chengdu, China, in 2012, and is currently working

toward the M.S. degree at the School of Aeronauticsand Astronautics, Zhejiang University, Hangzhou,

China.His research interests include monolithic mi-

crowave integrated circuits (MMIC) design and testsystem development.

Hua Chenreceived the B.S. degree from the School

of Biomedical Engineering and Instrument Scienceand Ph.D. degree from the School of Aeronautics and

Astronautics, Zhejiang University,Hangzhou, China,

in 2008 and 2013, respectively.In 2013, he joined the School of Aeronautics and

Astronautics, Zhejiang University, as a Postdoctoral

Researcher. His research interests include active

low-power integrated circuits, data converters,

power management circuits, and RF circu its.

Yongheng Shang received the B.S. and Ph.D. de-grees in information and electronic engineering from

the University of Surrey, Guildford, U.K., in 2005

and 2011, respectively.In 2011, he joined the School of Aeronautics

and Astronautics, Zhejiang University, Hangzhou,China, as a Post-Doctoral Researcher, and in 2013,

became a Lecturer. His research interests includephased-array radar-system design and signal pro-

cessing, monolithic microwave integrated circuits(MMIC) design, and test and reliability studies.

Zhengliang Huang received the Bachelors degreein microelectronics and solid-state electronics

Doctorate degree in information technology of aero-nautics and astronautics from Zhejiang University,

Hangzhou, China, in 2004 and 2010, respectively.He is currently involved in the microwave area

with the Institute of Astronautics Electronics Engi-

neering, Zhejiang University. His research interestsinclude microwave and RF circuits, especially

monolithic microwave integrated circuit (MMIC)power amplifiers (PAs) and low-noise amplifiers

(LNAs).

06998873.pdf

Documents