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Progress In Electromagnetics Research Symposium Proceedings, Taipei, March 2528, 2013 895

Design of Three-coupled Finline Bandpass Filter Using Full Wave

Analysis

V. Madhusudana Rao1 and B. Prabhakara Rao2

1Jawaharlal Nehru Technological University, Kakinada 533003, India2Electronics and Communication Engineering Department

Jawaharlal Nehru Technological University, Kakinada 533003, India

Abstract This paper presents a systematic procedure for designing a bandpass filter withwide bandwidth based on parallel coupled three finline structures. Normal mode parameters likepropagation constants, characteristic impedance and equivalent voltage eigenvector of multiplecoupled unilateral finlines are evaluated by using full wave modal analysis. A design graph forsymmetric three unilateral finline structure is presented for the design of bandpass filter. Abandpass filter of order 3 having center frequency of 10 GHz with fractional bandwidth of 20%is designed and simulated in HFSS (High Frequency Structure Simulator).

1. INTRODUCTION

THE finline is a wave guiding structure which is increasingly used as millimeter wave componentdue to various advantages such as reducing size, weight and cost. At millimeter wave frequencythe finline filter has been implemented in [13] which are mostly based on ladder/cascaded shape.Limited analysis is available on finline filter, which is based on coupled finline. This paper presentsthe design of bandpass filter using three coupled unilateral finlines. The advantage of present filteris low loss and wider bandwidth over the ladder/cascaded type filter. The unilateral coupled finlinestructures have been analyzed by many authors [48]. The full wave modal analysis for unilateralfinline coupling section and an admittance inverter circuit are derived in [9, 10].

In this paper, a Chebyshev filter of order 3 with fractional bandwidth 20% has been designed onRT-duroid 5880TM substrate using unilateral three finlines. In Section 2, the numerical procedure

based on the full wave modal analysis is formulated to compute all the frequency-dependent normalmode parameters for symmetric unilateral finlines. A bandpass filter is designed using full wavemodal analysis is presented in Section 3.

2. ANALYSIS OF THREE COUPLED UNILATERAL FINLINES

The simulated 3 dimension model of three finline filter structure is shown in Figure 1. The cross-section of the symmetric unilateral finlines structure is assumed to be uniform in z-direction isshown in Figure 2. The enclosure is ridged metal waveguide.

2.1. Normal Mode Parameters

The propagation constants are evaluated by applying the Galerkins method to the transformedGreens function matrix relating the voltage and electric fields at various boundaries of the structure

Figure 1. Model of three finline filter structure inHFSS software.

Figure 2. Cross section of three-finline structure.

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896 PIERS Proceedings, Taipei, March 2528, 2013

and solving for the roots of the determinant of the Eq. (1) in [7].

k=1

ck

n=0

pnG11Lk2nL

m2n +

k=1

dk

n=0

qnG12Lk1nL

m2n = 0

k=1

ck

n=1

pnG21Lk2nL

m1n +

k=1

dk

n=1

qnG22Lk1nL

m1n = 0

(1)

The set of basis functions used in this analysis are sinusoidal and expressed as follows:

Vz (y) =cos

2 (n 1)

(yyi)wi

1

"2(yyi)

wi

#2

, Vy (y) =sin

2n

(yyi)wi

1

"2(yyi)

wi

#2

.

where wi being the width of the ith fin, yi is the distance from origin to the center of ith fin.

2.2. Characteristics Impedances

Mode characteristics impedance of the coupled unilateral finlines lines are evaluated for all hybridmodes in a straight forward manner by calculating the power associated with a given finline for a

given mode and the corresponding finline voltage as shown in [7]. The finline mode impedance isgiven by

Zlm =(Vlm)

2

Plm(2)

where Vlm is the modal voltage of the lth slot given by the integral of the electric field across theslot and Plm is the partial modal power associated with the same slot when the mth normal modeis excited.

3. FILTER DESIGN

Figure 2 shows the port convention and connections of a resonator used to realize the band passfilter structure. The resonator consists of three parallel-coupled unilateral finlines approximatelyquarter wavelength long. In this paper, multi resonators are cascaded to achieve high rejections.

The six port impedance matrix parameters for a section of three coupled finlines of length l arefound from mode characteristic impedances, phase velocities and voltage ratios [711].

This three-coupled finline structure supports three dominant modes as OE, EE, and OO, whichcorrespond to 1, 2 and 3, respectively [711]. Each mode has its own modal phase constant,eigenvoltage vector and characteristic impedance. The eigenvoltage matrix for symmetrical threeline which have equal fin-width and spacing are given by

[M v] =

1 1 1

m1 0 m31 1 1

Each vector of [Mv] is the eigenvoltage vector of the matrix product [L] [C]. The matrix [Mv]can be used to derive the relation between port voltages and port currents.

VAVB

=

ZA ZBZB ZA

IAIB

where

[VA] = [V1, V2, V3]T, [VB] = [V4, V5, V6]

T,

[IA] = [I1, I2, I3]T, [IB] = [I4, I5, I6]

T

And the impedance matrix [ZA] and [ZB] can be derived as

[ZA] = [MV]diag[jZmi cot i][MV]T

[ZB] = [MV ]diag[jZmi csc i][MV]T

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Now i = il with i is the phase constant of the ith mode, l the length of the coupled section, andZmi given by

Zmi =Zoi

m2i + 2(3)

where Zoi is the characteristic impedance of ith mode. In Eq. (3), m2 = 0. Comparing the twoport Z-parameters of the circuit in Figure 3(b) with Figure 3(c), we obtain Eqs. (4), (5), (6).

m1Zm1 m3Zm3 = J ZAZB (4)

m21Zm1 m23Zm3 = ZA(J

2ZAZB + 1) (5)

Zm1 + Zm3 = ZB(J2ZAZB + 1) (6)

According to [9] boundary conditions shown in Figure 3(a)

m1Zm1

2 + 2

2

(Z0/2) (J

2Z20 + J Z0 + 1) (7)

Zm3

2 + 2

2

(Z0/2) (J

2Z20 J Z0 + 1) (8)

where

=

2

2 (Zee Zoo)2 Zoe (Zoe Zee Zoo) ZeeZoo

2Zee Zoe Zoo

The value ofJZO for each admittance inverter can be determined from the values of lumped circuitelements of the low pass prototype.

J1 =1

Z0

2g1(9)

Jn =1

Z0

2gn1gn, for n = 2, 3, . . . , N , (10)

JN+1 =1

Z0

2gNgN+1(11)

where = 210

.

For N = 3, the values of g1 to gN+1 are given below using [12].

g1 = 1.5963, g2 = 1.0967, g3 = 1.5963, g4 = 1.0000.

Once JZO is known the values of m1Zm1 and m3Zm3 for each coupled section can be known. Thevalues ofm1Zm1 and m3Zm3 for Section 1 are 82.02 and 64.69 respectively and for the Section 2are 37.65 and 40.94 respectively. The designed data from the above is calculated and finallythe filter is optimized. Both the data are shown in Table 1.

The design graph in Figure 4 for r = 2.2 is used to determine the line width and line spacing ofthree coupled unilateral finlines at 10 GHz. Due to symmetry of filter only the width, spacing and

Table 1.

Dimensions Designed Data Optimized Data

Section 1 Section 2 Section 1 Section 2

W 0.650 0.680 0.750 0.750

S 1.320 2.370 1.400 2.400

L 9.592 10.164 12.970 13.413

G 1.975 2.033 1.076 1.633

All the dimensions are in mm.

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898 PIERS Proceedings, Taipei, March 2528, 2013

(a)

(b) (c)

Figure 3. Reduction of a coupled three-finline sec-tion to a two-port network. (a) Coupled three-linesection as a six-port network. (b) Equivalent ad-mittance inverter. (c) Further approximated admit-tance inverter.

Figure 4. The bandpass filter design graph for asymmetric three unilateral finline structure. [Sub-strate dielectric constant r = 2.2, substrate thick-ness (D) = 0.8 mm, frequency = 10 GHz].

I II

Figure 5. PCB layout of the three finline filter oforder 3.

-60

-50

-40

-30

-20

-10

0

10

8 8.5 9 9.5 10 10.5 11 11.5 12

S11_simS21_sim

Sparameters[dB]

Frequency [GHz]

Figure 6. The simulated S-parameters response ofthree finline filter.

length of two sections has been mentioned here. Simulated model of three finline filter structure inHFSS Software is shown in Figure 4. The pattern of the designed filter has been shown in Figure 5.

The designed filter dimension has been simulated in HFSS. The return loss S11 and insertionloss S21 over a frequency band have been given in Figure 6. The insertion loss in passband is 0.5 dBand return loss is less than 10 dB and stop band attenuation is 20 dB at 11.5 GHz frequency. Ifdesired a tradeoff between the bandwidth and return losses can be achieved by further optimizationof the filter dimensions. The above simulated results are not been compared with fabricated resultsdue to lack of fabrication facilities in university.

4. CONCLUSION

The most important advantage of three finline filter presented here is that it can be widely used inmicrowave and millimeter wave applications. Another advantage of this three coupled finline filter

design is that the tight line spacing for designing wideband bandpass filter can be greatly relaxed.The design presented here, provides a relatively compact ultra wideband filter using coupled finlinestructure.

REFERENCES

1. Vahldieck, R. and W. J. R. Hoefer, Finline and metal insert filters with improved passbandseparation and increased stopband attenuation, IEEE Trans. Microwave Theory & Tech.,Vol. 33, No. 12, 13331339, Dec. 1985.

2. Vahldieck, R., Quasi planar filters for millimeter-wave applications, IEEE Trans. MicrowaveTheory & Tech., Vol. 37, No. 2, 324334, Feb. 1989.

3. Bhat, B. and S. K. Koul, Analysis, Design and Application of Finlines, Artech House, 1987.4. Meier, P. J., Integrated finline millimeter components, IEEE Trans. Microwave Theory &

Tech., Vol. 22, No. 12, 12091216, Dec. 1974.

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5. Syahkal, D. M. and J. B. Davies, An accurate, unified solution to various finline structures,of phase constant, characteristic impedance and attenuation, IEEE Trans. Microwave Theory& Tech., Vol. 30, No. 11, 18541861, Nov. 1982.

6. Schmidt, L. P., C. Chang, and T. Itoh, Spectral domain analysis of dominant and higherorder modes in finlines, IEEE Trans. Microwave Theory & Tech., Vol. 28, No. 9, 981985,Sep. 1980.

7. Luo, S., A. Biswas, and V. K. Tripathi, Finline mutiport couplers, IEEE Trans. Microwave

Theory & Tech., Vol. 42, No. 12, 22082215, Dec. 1994.8. Biswas, A. and V. K. Tripathi, Analysis and design of symmetric and multiple coupled finline

couplers and filters, IEEE MTT-S Int. Microwave Symp. Dig., 403406, 1990.9. Kuo, J.-T. and E. Shih, Wideband band-pass filter design with three line microstrip struc-

tures, IEEE MTT-S Int. Microwave Symposium Digest, 15931596, 2001.10. Awasthi, S., A. Biswas, and K. V. Srivastava, Realization of broadband band-pass filter

structure in suspended substrate using multi-conductor lines, Asia Pacific Microwave Con-ference04, New Delhi, Dec. 2004.

11. Srivastava, K. V., S. Awasthi, and A. Biswas, Effect of anisotropy on effective dielectricconstant and characteristic impedance of multi-port finlines, 36th European Microwave Con-

ference, 107110, Manchester, UK, Sep. 2006.12. Pozar, D. M., Microwave Engineering, John Wiley & Sons, Inc., 2011.

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