Slow-wave bandpass filters using ring or stepped-impedance hairpin resonators

Slow-Wave Bandpass Filters Using Ring or Stepped-Impedance Hairpin Resonators Lung-Hwa Hsieh,Student Member,IEEE,and Kai Chang,Fellow,IEEE

Abstract—This paper proposes a new class of slow-wave band-pass filters that uses a microstrip line periodically loaded with mi-crostrip ring or stepped-impedance hairpin resonators.The new slow-wave periodic structures utilize the parallel and series res-onance characteristics of the resonators to construct a bandpass filter.Unlike conventional slow-wave filters,the proposed bandpass filters are designed to produce a narrow passband at the funda-mental mode of the resonators.The new filters provide lower inser-tion loss than that of parallel-or cross-coupled ring and stepped-impedance hairpin bandpass filters.The calculated frequency re-sponses of the filters agree well with experiments.

Index Terms—Bandpass filter,hairpin resonator,ring resonator, slow-wave periodic structure.

I.I NTRODUCTION

M ICROSTRIP RING and stepped-impedance hairpin res-onators have many attractive features and can be used in satellites,mobile phones,and other wireless communication systems.The main advantages of the resonators are their com-pact size,easy fabrication,narrow bandwidth,and low radiation loss.Therefore,the resonators are widely used in the design of filters,oscillators,and mixers[1,Chs.2and7],[2,Ch.4]. Some of the bandpass filters that use the ring resonator utilize the dual-mode characteristic to achieve a sharp cutoff frequency response[3].However,the filters use perturbation notches or stubs that make their frequency response sensitive to fabrication uncertainties[3].In addition,bandpass filters that use parallel-or cross-coupling ring resonators to produce Chebyshev-or el-liptic-function characteristics[4],[5]suffer from high insertion loss.Recently,the ring resonator filters using high-temperature superconductor(HTS)and micromachined circuit technologies have demonstrated low insertion loss and a sharp cutoff fre-quency response,but at the expense of high fabrication costs [6].

The hairpin resonator was first introduced to reduce the size of the conventional parallel-coupled half-wavelength resonator with subsequent improvements made to reduce its size[2,Ch.4],[7].Beyond the advantage of the compact size,the spurious frequencies of the stepped-impedance hairpin resonator are shifted from the integer multiples of the fundamental resonant frequency due to the effect of the capac-itance-load coupled lines.Also,compact size bandpass filters using stepped-impedance hairpin resonators with parallel-or

Manuscript received July5,2001.

The authors are with the Department of Electrical Engineering, Texas A&M University,College Station,TX77843-3128USA(e-mail: welber@https://www.wendangku.net/doc/156338741.html,;chang@https://www.wendangku.net/doc/156338741.html,).

Publisher Item Identifier10.1109/TMTT.2002.800439.cross-coupling structures have shown high insertion loss[8], [9].

An interesting slow-wave bandpass filter has been reported [10]that uses capactively loaded parallel-and cross-coupled open-loop ring resonators.This filter also shows high insertion loss.

In this paper,slow-wave bandpass filters using a microstrip line periodically loaded by ring or stepped-impedance hairpin resonators are introduced.By using the parallel and series res-onance characteristics of the resonators,the slow-wave peri-odic structures perform as a bandpass filter.The new slow-wave bandpass filters,designed at fundamental resonant frequency of the resonators,also are different from conventional slow-wave filters,which utilize higher order modes to build up a band-pass filter with a wide passband[11]or to provide lowpass or bandstop features[12],[13].In comparison with bandpass filters that use parallel-and cross-coupled resonators with cou-pling gaps between the resonators,these new slow-wave band-pass filters show lower insertion loss at similar resonant fre-quencies[4],[5],[8],and[9].This is an important finding since the new filter structure uses more conductor than the parallel-and cross-coupled structures.This implies that the new filter topology significantly reduces the insertion loss caused in par-allel-and cross-coupled bandpass structures by eliminating cou-pling gaps between resonators.The performance of the new slow-wave filters is evaluated by experiment and calculation with good agreement.

II.A NALYSIS OF THE S LOW-W A VE P ERIODIC S TRUCTURE Fig.1(a)illustrates a conventional slow-wave periodic struc-ture.The transmission line is periodically loaded with identical open stub elements.Each unit element includes a length

of

open stub,

where

Fig.1.Slow-wave periodic structure.(a)Conventional type.(b)With loading Z

HSIEH AND CHANG:SLOW-W A VE BANDPASS FILTERS USING RING OR STEPPED-IMPEDANCE HAIRPIN RESONATORS

1797Fig. 4.Line-to-ring coupling structure.(a)Top view.(b)Side view.

(c)Equivalent circuit.

parallel and series resonances of the ring resonator

can be obtained by

setting

and

matrix of

the ring circuit

is

j for different lengths of

l

l l

1798IEEE TRANSACTIONS ON MICROWA VE THEORY AND TECHNIQUES,VOL.50,NO.7,JULY2002

Fig.7.Slow-wave bandpass filter using three ring resonators.(a)Layout.(b)Simplified equivalent circuit.

Fig.8.Measured and calculated frequency response for the slow-wave

bandpass filter using three square ring resonators.

.The dimensions of the filter are mm,

mm,mm,

mm.These parameter values are synthesized from

the design equations using numerical optimization to construct

a bandpass filter with attenuation poles centered at

,lower

,of the closed-loop ring resonator is122.

HSIEH AND CHANG:SLOW-W A VE BANDPASS FILTERS USING RING OR STEPPED-IMPEDANCE HAIRPIN RESONATORS

1799Fig.10.Slow-wave bandpass filter using six stepped-impedance hairpin resonators.(a)Layout.(b)Simplified equivalent circuit.

To improve the passband and rejection,a slow-wave bandpass

filter using three ring resonators has also been built.As seen in

Fig.7,the transmission line is loaded periodically by three ring

resonators,

where

5.5mm,which are opti-

mized by the calculation equations to obtain wider stopbands

than the filter in Fig.3.The frequency response of the filter

can be obtained

from

0.09dB.In ad-

dition,the two stop bands exhibit a rejection level larger than

50dB within 1.76–2GHz and 2.52–2.7GHz.Observing the fre-

quency response of the filters in Figs.6and 8,the differences

between the calculated and measured results are due to the use

of a lossless calculation model.

IV .S LOW -W A VE B ANDPASS F ILTERS U SING

S TEPPED -I MPEDANCE H AIRPIN R ESONATORS

The hairpin has parallel and series resonance characteris-

tics and can also be used as the loading

impedance ,the input impedance of the stepped-impedance hairpin

resonator,can be obtained from [2,Ch.4].Similar to the ring

circuit in Fig.3,the frequency response of the hairpin circuit

can also be obtained from

the

mm,

mm,mm.These parameter values are synthesized from the design equations,similar to (4),using numerical optimization to build a bandpass filter with attenuation poles centered

at

mm,which is optimized by the calculation equations for maximum rejection.Fig.11illustrates the measured and calculated results.The filter with a Chebyshev characteristic has a 3-dB fractional

bandwidth of 8.55%.A passband is from 1.84to 1.98GHz with

a return loss better than 10dB.The maximum insertion loss in

the passband is 1.82dB with a ripple

of

1800IEEE TRANSACTIONS ON MICROWA VE THEORY AND TECHNIQUES,VOL.50,NO.7,JULY2002 1.32–1.57and2.38–2.76GHz.The measured unloaded