The Design of Bandpass Filter that uses Disk Resonator and Parallel Coupled Lines

Tharoeun Thap Dept. of Electrical and Communication System

Engineering Soonchunhyang University

Asan, Chungnam, Republic of KOREA, 336-745

thap _tharoeun@yahoo.com

JongsikLim Dept. of Electrical and Communication System

Engineering Soonchunhyang University

Asan, Chungnam, Republic of KOREA, 336-745 j slim@sch.ac.kr

Abstract-In this paper, the bandpass filter design that uses a

disk resonator and parallel coupled lines is proposed. The

purpose of design is to apply the disk resonator's equivalent

circuit which has been introduced in our previous paper [I].

The filter design method is based on the general J-inverter­

based equivalent circuit of 2-pole bandpass filter. The design

relative equations have been derived and to verify the accuracy

and practicality of the design method, the 2-pole bandpass

filter having a center frequency of 2.2GHz and bandwidth of

20MHz has been designed. As results, the simulated

performances of Circuit and EM-simulation show an excellent

agreement with each other.

Keywords-Disk Resonator; Bandpass Filter (BPF); Parallel

Coupled Line; Disk Resonator's equivalent circuit.

I. INTRODUCTION

Disk resonators are of interest for the design of filters, in order to increase the power handling capability. An associated advantage of disk resonators is their lower conductor losses as compared with narrow microstrip line resonators. Although disk resonators tend to have a stronger radiation, they are normally enclosed in metal housing for filter applications so that the radiation loss can be minimized. Disk resonators usually have a larger size; however, this would not be a problem for the application in which the power handling or low loss has a higher priority. The size may not be an issue at all for the filters operating at very high frequencies [10]. It is very rare to find the circuit design with disk resonators in any other articles because of the difficulty in fmding the equivalent circuit for itself. As the equivalent circuit has been introduced [1], it gives an account for this paper to extend the application of disk resonator to design a bandpass filter which the equivalent circuit of itself is being used.

Sang-Min Han Dept. of Information and Communication Engineering

Soonchunhyang University Asan, Chungnam, Republic of KOREA, 336-745

smhan@sch.ac.kr

Dal Ahn Dept. of Electrical and Communication System

Engineering Soonchunhyang University

Asan, Chungnam, Republic of KOREA, 336-745 dahnkr@sch.ac.kr

II. DERrv A TION OF DESIGN FORMULAS

Fig. 1 illustrates the disk resonator and its equivalent circuit which will be used to design bandpass filter with the connection of parallel coupled lines as shown in Fig. 2. The

electrical length of coupled line is ¢, and the even- and odd­

mode characteristic impedance are ZOe and Zoo, respectively. A single parallel coupled line can approximately model by the J-inverter-based equivalent circuit as shown in Fig. 3 and the relative equations can be expressed as follow:

(a)

Figure I. Disk Resonator and its Equivalent Circuit.

I"

o---1L __ ---' ZOe, Zoo

� ZOe, ZOo ZOe. Zoo III

'-----_-----"f-o ZOe, Zoo

Figure 2. A structure of bandpass filter and its equivalent circuit.

978-1-4673-5537-7/13/$31.00 ©2013 IEEE

z = Zosin'¢+JZgsin¢+J'Zgsin'¢ 0, sin'¢-J'Z�cos'¢

(I)

(2)

Also, the equivalent circuit of disk resonator can be formed into a n-type equivalent circuit as illustrated in Fig. 4. Where

Y = i [Y (tan�+ tan 8, J __ l_] = iB p 2 2 OJI P

Y, = -iY (csc8, + csc82) = iB,

(3)

(4)

Then the structure of bandpass filter in Fig. 2 can be reconstructed as shown in Fig. 5.

The general J-inverter-based equivalent circuit of 2-pole bandpass filter is illustrated in Fig. 6. And our goal is to synthesize the structure of Fig. 5 to be equivalent with the structure in Fig. 6. So that, the bandpass filter can be design.

¢ �-¢-� ��� o--1�l. :::::::�. �

0

Zo C}-I.;l-D ZO

Z�,Z�

0 c}-�-D o

o

Figure 3 Parallel coupled line and its J-inverter-based equivalent circuit.

Figure 4. 1!-type equivalent circuit of Disk Resonator.

Figure 5. The reconstructed structure of Fig. 2.

----0

Figure 6. J-inverter-based equivalent circuit of 2-pole bandpass filter.

Figure 7. The J-inverter-based equivalent circuit of Fig. 5.

According to the n-type equivalent circuit of J-inverter, the structure in Fig. 5 can be finally reconstructed as illustrated

in Fig. 7. Where J12 = IBsl. The admittance Yl2 seen looking from Jl2 is

Yl2 = Y, + jYo tan fJ

= i( Bp + B, +Yo tanfJ) = jB"

And the admittance YOl seen looking from JOl is

(B +B )+YotanfJ Yo, = iYo Y �(B' + B )tanfJ iBo, o p s

The basic formula of J12 of bandpass filter is

J = Bl2 (OJ,) Bl2 (OJ,) _ B" (OJ,) 12 (OJ;g,)(OJ;g,) - Jg,g, Thus,

(5)

(6)

(7)

(8)

The relationship of susceptance at the passband edge frequencies is

(9)

Assume that fc is the physical length of coupled line and fJ, f2 are the physical length of transmission line having electrical length OJ, O2, respectively. And fy is the physical length of 50n line, therefore

(10)

Substituting (10) into (3) and (4), then into (5), thus (9) can be rewrite as

(OJ) (OJ) I (OJ' (e, + e ) J Ycot ---Le, +Ycot ---Le, +L-Yotan r

up up OJ, up

(11)

(12)

Now we got two equations (11) and (12), but only one variable le is involved. The concept is, in order to make these two equations correlate with each other we need one more variable which has been considered on the product of glg2' It simply means, fust of all calculate le from (11) then substitute into (12) to find the value of g,g2'

As long as the product of g,g2 is found, thus we can calculate the ripple level Lar as

Lw = 17.37coth-1 e '18;8,-' [ 4,;nh-' rI:J

The basic formula of Jo, of bandpass filter is

rosol «(VJ gl

(13)

(15)

Therefore the even- and odd-mode impedance of coupled line ZOe and Zoo can be obtained as indicated in (1) and (2).

To avoid the coupling effect between coupled line and disk resonator, we will provide some distance, lm, of 50n line to keep them apart as shown in Fig. 8. This length will be taken from le that has been calculated above. Which mean instead of le we will calculate ZOe and Zoo by lem = le -lm. Thus,

(J2 Z2sin (Vo' e"" -J Z +sin (Vo' ecm Jz sin (Vo' ecm 01 0 01 0 0

Z = up up up

00 sin2 (Vo '(m _ J2 Z2 cos2 (Vo' ecm

01 0 up up

{O + {O • where (Vo = _I _2 ; IS passband center frequency. 2

(16)

(17)

e "" = f c -f m ;e m is a distance provided by designer to avoid

the coupling between coupled line and disk resonator.

... . e e e : i cm= c- m �

e m

Figure 8. Providing 50n line length lm to avoid coupling effect.

III. SIMULATIONS

To verify the accuracy and practicality of design formulas which just has been derived above, we will design a bandpass filter at center frequency 2.2GHz and bandwidth of 20MHz on a substrate having a relative dielectric constant of 2.2 and thickness ofO.7874mm.

The process of design is; fust of all, find the values of every element of disk resonator's equivalent circuit, referred to reference [1]. And then apply (1 )-(17) to obtain the even­and odd-mode impedances of coupled line.

15.1 Z=12.!ll33dm F<Q5.4575mTj5.1

Figure 9. Circuit simulation of bandpass filter.

0.00 -,--------,---."...,.,...-------,-----,

-20.00

-40.00

;: -60.00

-80.00

-100.00 1.70 1.90 2.10 2.70

F[GHz] 0.3645 -----=�

Figure 10. Circuit simulated perfonnance of Fig. 9.

Figure 11. Structure of bandpass filter in EM-simulation.

0.00

-20.00

-40.00 +

;: -60.00 t- +

-80.00 +

-100.00 1.70

;:

-60.00

-80.00

1.90 2.10 2.30 2.50

Figure 12. EM simulated frequency response of Fig. 11.

OJrve hfo

-e- dB(S(F\::Irtl,A::Irtl)) UnearFrequency

..s;;- dB(S(F\::Irt2,A::Irtl)) UnearFrequency

- d6(S(l,llLEM �orted

� dB(S(2,1)LEM hllorted

2.70

-100.00 +-���"""'r---"'��-+-.����.-......,--,!f--,---r-.-.�-r-I 1.70 1.90 2.10 2'3�i 2.50 2.70 Freq [GHz] "'2n,.06"' 04;oL--- 0.3645

2.4249

Figure 13. The comparison of Circuit and EM simulation responses.

The filter was designed using simulation tool of ANSYS Designer ver. 7.0 and HFSS ver. 14.0, software packages for the circuit and electromagnetic (EM) simulations.

Fig. 13 plots the frequency responses of filter obtained by Circuit- and EM-simulation. The performance is seen to be in good agreement with the design objective.

IV. CONCLUSION

We have proposed a method to design a bandpass filter with attenuation poles occurring around the upper and lower passband edge frequencies by using a disk resonator and parallel coupled lines. The design formulas have been derived with the verifying validity through simulation tools.

Nevertheless, the research still has limit because of the filter design is impossible to select the specific ripple level. The ripple level is obtained by the calculation of (13). However the ripple level is related to angle a and bandwidth, so one can adjust a or consider on the bandwidth in order to get the desired ripple level.

REFERENCES

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