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 theupperstopband.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
and8,
and make the spuriousproblem 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 at4f0,
6f0,
etc. This isagain causedbytheunequal8,
and/,3
atthese frequencies. Itwill be demonstratedmathematically later thatthe 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,
areeliminatedby 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,
and4f,
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,
and6f/
accurately. Thegeometricparameters 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 forsuppression 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.
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, theIS211
peak at 2fo for a substrate ofe,
- 10 can be close to 0 dB [3-6]. It is the purpose of thiswork 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),wehave1S21
-2
1+ z
oez00
J
X(1+COSSecos00)L Z° (Zoesin O-
ZOO
sinSe)2
jJ=
Zoesin0O cos0e+ZOOsin0,
cosSO (2)where 0e and 00 denote the electric lengths for theeven- and odd-modes ofa coupled stage, respectively. Notethat
O,e
000,
d d2
atf0.
+-P--~ --~d +-- port2Tf
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 enforcingZ sinSO-ZoosinOe=0 (3)
One possible set of solution to (3) is 0e =
0,
= ni. Not onlywill there be no spurious peak near
2nf,
but also will theresponse 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, theIS21
response will exhibit alarge peak, since when 0-0O e- nr butthey areunequalat 2nf (de> 00 for coupled microstrips),
j
in(2)willhave a zero, and
IS211
may become as high as 0 dB. Thus, itcanbe concluded that the conditions
0,e
=0o
=narerequiredtoavoid 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 effectiverejection 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,
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 thetarget 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 at4f,.
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 samedistances 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
and6fo.
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.
6plots the corrugation parameters of coupled stages for simultaneously allocatingzeros at
2fo, 4fo
and6fo
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 at3f,
6fo and9f,
[12]. The third stage has seven corrugation periods, and four of them are used forinterstage coupling. Its leading three transmission zerosare thenat3.5f0,
7f0and l0f,
since its coupling length is(417)xQ(X4)
=2/7. Thegap sizes of thek/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
0
-601
'v-60
2 4 6 8 10 12 14 16 18Frequency(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 goodrejections
beyondl0/,
Fig. 8 plots theIS211
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 createdby stages 1, 2and4, and aband withhigh
rejections
coveringfrom 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/
and6f/
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 at3f,
6f/
and9fo,
and 4/7 of this k/4-stage can eliminate the unwanted passbands at7f/
andl0/,
even on a substrate ofa relatively highe,.
The measuredJS211
responseof the fabricated circuit validates these ideas. Theapproachis suitable for BPFsdesigned 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.
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