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Novel corrugated coupled-line stage with ideal frequency response and its application to bandpass filter design with multi-harinonic suppression

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Novel

Corrugated Coupled-Line Stage with Ideal

Frequency Response

and Its Application

to

Bandpass

Filter Design with Multi-Harmonic Suppression

Jen-Tsai Kuo, U-Hou Lok and Meng-Huan Wu

Department

of Communication Engineering, National Chiao

Tung

University

1001 Tahsueh

Rd., Hsinchu 300 TAIWAN

Abstract - Coupled-linestages aredesigned withcorrugated

periods to accurately allocate inherent transmission zeros at three leading even harmonics of design frequency, fO. The corrugation pattern is finely trimmed sothatphase velocities of the two eigenmodes can be simultaneously equalized at these frequencies. Bydecreasingnumberofcoupledperiodsin a stage, frequencies of the zeros can be arbitrarily scaled up to a certain extent. Inthis way,aparallel-coupled line bandpass filter with a cascade of several such stages can be synthesized to be free of spurious harmonics up to at least

10f,,

with aid of tapped input/output coupling scheme. The measured data of the fabricated bandpass filter show arejectionlevelof better than 30 dB in theupper stopband up to18f0.

IndexTerms-Bandpassfilter, corrugation, coupled-linestage,

spurious suppression, stopband.

I.INTRODUCTION

Parallel-coupled line bandpasss filters (BPFs) have been widely used in theRFfront end of microwave and millimeter-wavecommunication systems for several decades. It is easyto design, reliable and suitable for mass repetition. The development of design method for such filters has been matureand well documented inopen literature and microwave engineering textbooks, e.g. [1]. The circuit response, however, suffers fromspurious peakat every harmonic of thepassband

frequency

(f0)

[2-10]. The first spurious at 2fo is of the most concern since itnot only degradesthepassbandsymmetry but also greatly deteriorates the circuitperformances in theupper

stopband.This spuriousarises duetothateven- and odd-mode phase constants of the stage, /3e and

,6,

are unequal. Thus, many effective approachesforequalizing/3eand

,6

[2-5] have beenproposedtotackle thisproblem.

Twoimportant points about this issue are worth mentioning. First, such circuits on a substrate with higher permittivity will exhibit more difference in

3,6

and

8,

and make the spurious

problem more seriously. The second point is that spurious responses may occur at each harmonic of the passband frequency. Although the methods in [2-5] eliminate the

spurious peakat

2f0,

there are also unwanted passbands at

4f0,

6f0,

etc. This isagain causedbytheunequal

8,

and

/,3

atthese frequencies. Itwill be demonstratedmathematically later that

the success ofspurious suppression critically depends on the equality of/3eand /3 atthese frequencies. Furthermore, there

are also undesired peaks at odd harmonics due to the distributednatureof thecoupledstages.

Recently,manyconvincible approaches have been proposed

to suppressmulti-order harmonics. Thewiggly-linein [6] isa

significant extension of [2]. Bymodulating the linewidths of the coupled-stages following a sinusoidal law with different periods, multiple spurious passbands can be significantly rejected.In [7],the undesiredresponses atboth 2fo and

3f,

are

eliminatedby imposing capacitive terminationstothecoupled

stages. In [8-9], spurious peaks are suppressed by choosing constitutive resonators having identical fundamental frequency but staggered higher orderresonances. Inthis way,

spurious peaks ofone resonator canberejected by stopband of the other. The dual behavior resonator filter in [10] achieves themulti-spurious suppression by integrating alow-pass filter

in the design. In [11], the multi-spurious elimination is achieved by periodic stepped-impedance resonators. In [12], coupled-line stagesofk/4, k/6, andk/8are tunedtoaccurately place transmission zeros at

2f0,

3f,

and

4f,

respectively, so that the spurious at these frequencies can be effectively eliminated. Thetapped input/outputscheme is also feasible for generationtwo zerosfortackling undesired peaks [13].

This paper enhances the design of corrugated coupled stages in [5] to allocate at least three leading inherent transmissionzeros at

2f,

4f,

and

6f/

accurately. Thegeometric

parameters of such stages on a substrate with

e,

= 10.2 are presented. Then the approach in [12] is employed to design the corrugated stages to create transmission zeros at other harmonics of the design frequency. Finally, the tapped input/output is adopted to generate transmission zeros for

suppression of unwanted responses. As a result, a successive spectrum of attenuation polescanbe established upto atleast ten times the passband frequency. In the following, Sec. II discusses the spurious property ofa cascade oftwo

coupled-linestages, Sec. IIIdescribes thecorrugationand transmission characteristic of a coupled stage, Sec. IV demonstrates simulation and measured results ofanexperimental BPF, and Sec. V draws the conclusion.

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port 2

Wu

u

1U

port1 l

Fig. 1. A uniformmicrostrip coupled stage as a two-port network.

0 -10 ^-20 c -30 -40 -50L 1 2 3 4 5 6 7 8 9 Frequency(GHz)

Fig. 2. Frequency response of a typical uniform coupled stage. f=1 GHz, W4 =0.8 mm,Su=0.5mm.

II. TRANSMISSION ZEROS OF A FIRST-ORDER BPF For aparallel-coupled line filter on a substrate with higher

£, the spurious peak levels will be much higher than those with lower

e,.

Forinstance, the

IS211

peak at 2fo for a substrate of

e,

- 10 can be close to 0 dB [3-6]. It is the purpose of this

work to demonstrate the effectiveness of coupled-line coffugation on simultaneous elimination of multiple unwanted harmonics, a substrate with Sr 10.2and thickness= 1.27 mm

is adopted herein.

Fig. 1 shows the layout ofa uniform coupled-line stage.

Given fractional bandwidth Aofa BPF, the linewidth WU, and

gap sizeS, of eachstage canbe determined after theeven-and odd-mode characteristic impedances, Zo and ZO, are

calculatedby the synthesis formulas [1]. Considerafirst-order

BPF with a cascade of two such stages. The forward

transmission coefficient can be obtained by directly multiplying two identicalABCDmatrices converted from the Z-matrixparameters of the stage. Based onthefact that all Z-parameters consist of csc or cot functions so that their magnitudes aremuch larger than ZO (the system impedance)

near

2nf,

(n=integer),wehave

1S21

-2

1+ z

oez00

J

X(1+COSSecos00)

L Z° (Zoesin O-

ZOO

sinSe

)2

j

J=

Zoesin0O cos0e+ZOO

sin0,

cosSO (2)

where 0e and 00 denote the electric lengths for theeven- and odd-modes ofa coupled stage, respectively. Notethat

O,e

00

0,

d d2

atf0.

+-P--~ --~d +-- port2

Tf

tS port1 -- d

~-Fig. 3. A corrugated coupled-line stage. 0 -10 - - - stage A ---stage B ttqgeC

~-20

W-30 \

/

\

-40/ -50 1.9 2 2.1 3.9 4 4.1 6 6.1 Frequency (GHz)

Fig. 4. Corrugation tuning ofacoupled stagefor obtaining zeros at

2f,

4fo and 6fo

(f,

= 1 GHz). Stage A: W= 0.3, S=0.5, T= 0.95,d=

1.35; stage B: W=0.3, S= 0.5, T= 1.02,d= 1.35; stage C: W= 0.3,

S=0.5,T=0.99,d= 1.2,allin mm.

Thetransmission zeros of

JS211

can be obtained by enforcing

Z sinSO-ZoosinOe=0 (3)

One possible set of solution to (3) is 0e =

0,

= ni. Not only

will there be no spurious peak near

2nf,

but also will the

response present a dip at

2nf,

because the zero of the denominator in (1) has one order higher than that of the numerator.When it isnotthe case,however, the

IS21

response will exhibit alarge peak, since when 0-0O e- nr butthey are

unequalat 2nf (de> 00 for coupled microstrips),

j

in(2)will

have a zero, and

IS211

may become as high as 0 dB. Thus, it

canbe concluded that the conditions

0,e

=

0o

=narerequired

toavoid thespurious peaksnear

2nfo.

III.CORRUGATED COUPLEDSTAGE

Fig. 2 shows frequencyresponse ofatypical coupled stage in Fig. 1. Its length is finely tuned to allocate the maximal coupling atf= 1 GHz. Due to the dispersion of coupled microstrips, nevertheless, the inherent transmission zeros

deviate away from

2nf0,

n = 1, 2, 3... Also, the effective

rejection levels at these zeros are degrading as frequency is increased. Based onthe discussion in Sec. II, spurious peaks will occur. This motivates us to develop the corrugated coupled stage shown in Fig. 3. The geometric parameters

includeS=S, W=WU,-T2,periodP,andlengthTand width

d ofthecorrugation "teeth."NotethatWU, and S,inFig. 1 have been definedby the conventional synthesis formulas [1], thus therearethreedegrees of freedom for tuning theresponse.

554

I N,

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0 -10 --20 W-30 -40L -50 t 0 1 2 3 4 5 6 7 8 9 Frequency(GHz) Fig. 5. Frequency response of stage C inFig.4.

1.6 1.4 E 1.2 0.8 0.2 0.4 0.6 0.8 1 1.2 W(mm)

Fig. 6. Corrugationparameters ofcoupledstages for

JS211

responses with transmissionzeros at2f0,4f0, and 6fo.

The corrugation tuning starts with

WU,

= 0.8 mm and Su,

0.5mm asused inFig. 2.Based on [5], stage A with d= 1.35

mm andT= 0.95mm is obtainedtoallocate the first inherent

zero at 2fo precisely. Its second and third zeros, however, are at

4.05f0

and 6.

If.

They are more than 1% away from the

target frequencies, as shown in Fig. 4. According to our

experience, the spurious will be lower than 25 dB if the deviation is less than 0.5%. Itcanbe deduced that

Oe

> 00>

2);

and hence /e >

/3,

provided Zoe > Zoo at

4f,.

Here, the subscripts e and orespectively stand for the c and rmodes, and

/3e

and

/3o

are their respective phase constants. First, the teethlengthTis extendedto 1.02mm(stage B)toincrease

/3o.

The three zeros shift to frequencies with about the same

distances to their respective target positions. Then d is decreased to 1.2 mm, along with finely tuned T= 0.99 mm,

and finallystage Cis obtained with the three inherentzeros at

2fo, 4fo

and

6fo.

Fig. 5 plots the

frequency

response of the corrugated stage

(stage C)upto9 GHz. The transmission characteristics of the

stageare closeto that ofaTEM

(dispersionless)

stage.

Fig.

6

plots the corrugation parameters of coupled stages for simultaneously allocatingzeros at

2fo, 4fo

and

6fo

whenS=0.4,

0.8 and 1.2 and d= 0.4, 0.5 and 0.6, all inmm. When S is

increased or d isdecreased, the required T is increased. This is

because that increasing S or decreasing d will decrease the coupling between thetwoconductors and hence theodd-mode wave cantravel faster. The "teeth"length is then increasedto compensate orslow down itsphase velocity[5].

IV. APPLICATIONTOBPFDESIGN AND EXPERIMENT A fifth-order BPF in Fig. 7(a) is synthesized and fabricated for demonstration of multi-spurious suppression using the developedcorrugatedstages. It hasf = 1 GHz, A= 8% and a 0.1-dB ripple. There are fourcoupled stages in the circuit in addition to the tapped input/ouput stages designed to place zeros at 5f. An impedance transformer is required for compensating the altered external Q value due to the change of the tappoint[13]. The two end stages are tuned to suppress the spurious at

2f0, 4f0,

6fo and8f. The second stage usesonly a coupling length of k/6 to eliminate the spurious at

3f,

6fo and

9f,

[12]. The third stage has seven corrugation periods, and four of them are used forinterstage coupling. Its leading three transmission zerosare thenat

3.5f0,

7f0and l0f,

since its coupling length is

(417)xQ(X4)

=2/7. Thegap sizes of the

k/6-and k/7-stages have to be decreased for providing necessary coupling levels specifiedby the synthesis procedure [12].

(a) 0 -10 -20 - -30 1-;i -40 - 50 -60 -70 SO(""0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Frequency(GHz) (b)

Fig. 7. Layout and performances of the fabricated fifth-order corrugated BPF. (a) Circuit layout. (b) Simulation and measured results. Geometricparameters: W1 =0.26,SI =0.79, Ti = 1.12,

d,

=

1.4, W2=0.33, S2=1.03, T2=1.13, d2= 1.4, W3=0.33, S3=1.05, T3

=1.09,d3 =1.4, allin mm.

555 9

(4)

0

-601

'v

-60

2 4 6 8 10 12 14 16 18

Frequency(GHz)

Fig. 8. Frequency responses of the coupled stages in Fig. 7(a).

Fig. 9. Photo of the fabricated circuit.

Fig. 7(b) plots the simulation and measuredresponses of the synthesized circuit. The measured in-band insertion loss is 2.6 dB, and the return loss is 15 dB. Theexperimentresults show that the upper stopband covers the full measured band up to 18fo with

rejection

levels of better than 30 dB. Toinvestigate why the BPF has such good

rejections

beyond

l0/,

Fig. 8 plots the

IS211

responses of all thestages inFig. 7(a). Whenf<

l0f0,

totally eleven transmission zeros can be observed. Besides, there are stopbands from 9 GHz to 14 GHz created

by stages 1, 2and4, and aband withhigh

rejections

covering

from 11 GHz to 16 GHz by stage 3. These are the essential

electromagnetic property of the periodic corrugated stages.

Corrugated BPFsdesigned with suchabandgap property will be reported in other fashion. Fig. 9 shows the photo of the fabricated circuit.

V. CONCLUSION

Coupled-line stages with finely trimmed corrugation are shown to have a nearly ideal frequency response, which has transmission zeros at

2f,

4f/

and

6f/

precisely. Position accuracy of thezeros is shown critical forpreventingtheBPF fromspuriouspeaks. TheBPFdesign isveryflexible since 2/3 of suchak/4-stage can be usedto allocate the inherent zeros at

3f,

6f/

and

9fo,

and 4/7 of this k/4-stage can eliminate the unwanted passbands at

7f/

and

l0/,

even on a substrate ofa relatively high

e,.

The measured

JS211

responseof the fabricated circuit validates these ideas. Theapproachis suitable for BPFs

designed at relatively low frequencies since the periodic corrugationmaycauseserious radiationathigh frequencies.

ACKNOWLEDGEMENT

This work was supported by the MoE ATU program and by the National ScienceCouncil, Taiwan, under Grants NSC 95-2221-E-009-037-MY2 and NSC 95-2752-E-009-003-PAE.

REFERENCES

[1] D. M. Pozar, Microwave Engineering, 3rd ed. New York: Wiley, 2005.

[2] T. Lopetegi, M. A. G. Laso, J. Hernandez, M. Bacaicoa, D. Benito, M. J. Garde, M. Sorolla and M. Guglielmi, "New microstrip "wiggly-Line" filters with spurious passband suppression,"IEEE Trans. Microwave Theory Tech.,vol. 49, no.9, pp.1593- 1598, Sept. 2001.

[3] J.-T. Kuo, S.-P. Chen and M. Jiang, "Parallel-coupled microstrip filters with over-coupled endstagesfor suppression ofspurious responses," IEEEMicrowave Wireless Compon. Lett.,vol. 13, no. 10, pp.440-442, Oct. 2003.

[4] S. Sun and L. Zhu, "Periodically nonuniform coupled microstrip-line filters with harmonic suppression using transmission zero reallocation," IEEE Trans. Microwave Theory Tech., vol.53, no.5, pp. 1817-1822, May 2005. [5] J.-T. Kuo, W.-H. Hsu and W.-T. Huang, "Parallel coupled

microstrip filters with suppression of harmonic response," IEEE Microwave Wireless Compon. Lett., vol. 12, no. 10, pp.383-385,Oct. 2002.

[6] T. Lopetegi, M.A.G.Laso, F.Falcone, F.Martin,J. Bonache, J. Garcia, L. Perez-Cuevas, M. Sorolla and M. Guglielmi, "Microstrip "wiggly-line" bandpass filters with multispurious rejection,"IEEEMicrowave Wireless Compon. Lett., vol. 14, no. 11, pp.53 1-533,Nov. 2004.

[7] P. Cheong, S.-W. Fok andK.-W.Tam,"Miniaturizedparallel coupled-line bandpass filter with spurious-response suppression,"IEEE Trans. Microwave Theory Tech., vol. 53, no.5, pp. 1810-1816,May 2005.

[8] C.-F. Chen,T.-Y.Huang andR.-B.Wu, "Design of microstrip bandpass filters with multiorder spurious-mode suppression," IEEE Trans. Microwave Theory Tech., vol. 53, no.12, pp. 3788-3793,Dec.2005.

[9] S.-C.Lin,P.-H.Deng,Y.-S.Lin, C.-H. Wang andC. H.Chen, "Wide-stopband microstrip bandpass filters using dissimilar quarter-wavelength stepped-impedance resonators," IEEE Trans. MicrowaveTheory Tech., vol. 54, no.3,pp. 1011-1018, Mar.2006.

[10] A. Manchec, C. Quendo, E. Rius, C. Person and J.-F. Favennec,"Synthesis of dual behaviorresonator(DBR) filters with integrated low-pass structures for spurious responses suppression,"IEEEMicrowave Wireless Compon. Lett., vol. 16,no. 1,pp.4-6,Jan.2006.

[11] Y.-C. Chiou, M.-H. Wu and J.-T. Kuo, "Periodic stepped-impedance resonator (PSIR) bandpass filters with multispurious suppression," 2006 IEEE MTT-S Int. MicrowaveSymp. Dig.,pp.349-352,June2006.

[12] M. Jiang, M.-H. Wu and J.-T. Kuo, "Parallel-coupled microstrip filters with over-coupled stages for multispurious suppression"2005 IEEE MTT-S Int. Microwave Symp. Dig., pp.687-690,June2005.

[13] J.-T. Kuo and E. Shih, "Microstrip stepped impedance resonator bandpass filter with an extended optimal rejection bandwidth," IEEE Trans. Microwave Theory Tech., vol. 51, no.5,pp. 1554-1559, May2003.

數據

Fig. 1. A uniform microstrip coupled stage as a two-port network.
Fig. 7. Layout and performances of the fabricated fifth-order corrugated BPF. (a) Circuit layout
Fig. 8. Frequency responses of the coupled stages in Fig. 7(a).

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