Designing Cross-Coupled B andpass Filters with

Transmission Zeros in Lossy Microstrip

Mudrik Alaydrus, Dian Widiastuti and Teguh Yulianto Department of Electrical Engineering

Universitas Mercu Buana, Jakarta, Indonesia Email: mudrikalaydrus @yahoo.com

Abstract-Bandpass filters play a significant role in many wireless communication systems. The filters pass desired signals and reject unwanted one. In this paper, we design a four­pole bandpass filter using a rigorous computer simulation. The resonators used are square open-loop resonators. To get a sharper selectivity around the pass band, transmission zeros though cross­coupling between resonators are introduced. In simulation, we compare the results for relative permittivity 4.4 and 4.9, and for tangent loss 0.025 (lossy) and 0.0 (lossless). The simulation shows, the required specifications are fulfilled for lossless case, whereas for lossy case, an insertion loss of 8.3 dB observed. For verification, the bandpass filter is built in FR4. In this lossy microstrip, a measurement shows, we get an insertion loss of about 6.64 dB and a bandwidth of about 120 MHz.

Keywords-bandpass filter, coupling coefficient, cross-coupled resonators, square open-loop, transmission zeros

I . INTRODUCTION

The recent advanced digital cOlmnunications systems re­quire efficient use of the frequency spectrum. The use of this scarce expensive resource must be controlled strictly otherwise significant interference can occur, which can deteriorate the overall system performances . Bandpass filters are designed for this purpose. Bandpass filters pass desired signals from other unwanted signals [ 1 ] . To get sharp filtering characteristics, in traditional filter approximations, such as Butterworth and Chebychev realizations, we need many resonators, which leads to big filter dimensions . The introduction of transmission zeros enhances the selectivity near the pass band [2] .

Hong in [3] introduced a simple square open-loop resonator as based for building the filter. The filter designed around the frequency 2.46 GHz with a fractional bandwidth of 0.04 and implemented in low-loss material. Based on given coupling coefficients , the paper determined the separations between the resonators using some empirically found formulas . Lee et al [4] , based on Hong's work [3] , designed a bandpass filter for IMT-2000 around 2 GHz, they used also low-loss micros trip lines. An other resonator structure is proposed by [5] , a novel bandpass filter with sharp attenuations and wide stopband is developed through the combined use of composite resonators and stepped impedance resonators (SIRs). Parallel coupled bandpass filters are developed for several frequency regions, such as around 5 .75 GHz [6] , and around 3 .2 GHz [7] . The comparisons between simulation and measurement results , as well as with the specifications given before, are very good. In all the publications above, the microstrip used is based on expensive material like TMM1O, or RTlDuroid substrate,

which have a tangent delta smaller than 0.003 . This small value of tangent delta belongs to materials with small loss .

In this work, we develop a bandpass filter around the frequency 2.35 GHz, which is internationally allocated to amateur radio and amateur satellite use on a secondary basis. Another potential applications would be radio location, mobile and fixed communications [8] . We use the same structure as described in [3] , the square open-loop resonator. Firstly, the filter structure is simulated numerically by a commercial software package, Sonnet v 1 3 .56 [9] . In fabricating the filter, a printed circuit board (PCB) based on FR4 material is used. The relative permittivity of FR4 lies between 4.4 and 4.9 and the tangent delta of about 0.025 . The thickness of the PCB used is 1 .6 mm. Because FR4 has a tangent delta about 10 times higher that RTlDuroid or TMM 1O, in this paper we call this micros trip as lossy microstrip. In this research we observe the effects of lossy material to the coupling coefficient and to the overall filter performances. Moreover, we study the effect of the uncertain value of the relative permittivity of FR4 to the filter performances.

II . CHEB YCHEV ApPROXIMATION WITH TRANSMISSION ZEROS AND CALCULATING THE COUPLING C OEFFICIENTS

In this paper, we try to design a bandpass filter, whose spesifications should somewhat conform with a filter produced by AMTI, the C0423501 [ 10] . The filter should work at the interval 2 .3 GHz and 2.4 GHz, with maximal insertion loss of 1 .5 dB . The voltage standing wave ratio is 2 .0 : 1 , the ripple and flatness in the pass band are smaller than 1 dB , and the rejection at 2.2 GHz and 2.5 GHz is minimal 20 dB . We do not consider another additional specifications like temperature compatibility and the dimensions of the filter. With the interval given above, the midband frequency becomes fo = \12.3 . 2 .4G H z = 2 . 3495G H z , and the fractional band­width F BW = BW / fo = 0 .04256 . In designing the filter, the filter order is set to n=4 (four resonators), so that the dimension of the filter can be kept small. The VSWR of 2.0 : 1 leads to a reflection factor of -9.54 dB , which generally can be achieved by any filter configuration. To fulfill the requirement of the band rejection at 2.2 GHz and 2.5 GHz, we introduce a pair of transmission zeros at about 2.26 GHz and 2.44 GHz, so that we have Sla = (2 .44/2 . 3495 - 2 . 3495/2 .44) /0 .04256 = 1 . 78.

Cameron [ 1 1 ] gives an efficient algorithm to synthesis a generalized Chebychev filter by introducing a coupling matrix. However, in this paper we follow the procedure described in [ 1 ] . In [ 1 ] we can find component values for n =4 and RL = -20 dB . We choose the value Sla = 1 . 8 , so we have in page

978-1-4799-0425-9/13/$31.00 ©2013 IEEE

264 in [ 1 ] the following component values g1 = 0 . 95974, g2 = 1 .42 1 92 J1 = - 0 . 2 1 083 and J2 = 1 . 1 1 769.

With these values, the coupling coefficient Mi,H1 and the external quality factors Qe can be calculated

Qe ,i

FBW M3 4 = -- = 0 .03643 ,

y'g1g2 FBW · J2 ------=. = 0 .03346

g2 F BW . J1 = -0.00935

g1 g1

Qe o = -- = 22 .55 , FBW

III . REALIZATION THE COUPLING IN MICROSTRIP RESONATORS

( 1 )

(2)

(3)

(4)

The feeding line is defined to have the standard wave impedance of 50 fl, leads to strip width of about 3 mm (for relative permittivity of 4.9) , and for the resonator is chosen to the wave impedance of 60 fl leading to resonator line width of about 2 mm. The line width of 2 mm gives an effective relative permittivity of Cr, ej j = 3 . 366, and the guided half wavelength inside the microstrip line at the mid frequency 2.35 GHz becomes about 35 mm.

We use the similar resonator as in [3 ] , the square open­loop resonator with the total physical length of 35 .5 mm, a gap length of 1 . 3 mm, and line width of 2 mm.

o 81 1 [dB]

-0 . 1

-0 . 2

-0 . 3

-0 .4 2 2 . 1

r "\ r

wid! 1 mm 't. d!h 2 mn

2.2 2 . 3 2 .4 Frequency (GHz)

2 . 5 2 . 6

Fig. 1 . resonant frequency for different line width of the resonator total physical length 35 .5 mm.

Fig. 1 shows comparison the posItIOn of the resonance between different line width of the resonators . In designing we base on the line width of 2 mm, the figure gives the position of the resonance at about 2 .36 GHz. A smaller line width of 1 mm gives smaller effective relative permittivity. The reason is as follows. The total physical length of the resonator used here, 35 .5 mm, leads to higher guided wave length. The resonance happens consequently at a lower frequency, at about 2. 1 3 GHz.

According to the coupling coefficients obtained in the previous section, we propose to use the schematic given in fig. 2. The couplings between resonator 1 and 2 and between 3 and 4 are realized as mixed coupling (combination electric and

magnetic couplings), whereas the coupling between resonator 2 and 3 is magnetically and between 1 and 4 is electrically (negative coupling value) . The couplings between resonators 1 and 2, 2 and 3 and 3 and 4 are the direct couplings, whereas the coupling between resonators 1 and 4 is the cross coupling, which realizes the transmission zeros .

In the next section, we will vary the separation between resonator 1 and 2, 8 1 , to gain the coupling coefficient M1 ,2 = 0 .03643, also for other coupling coefficients.

port 1

Fig. 2. Schematic for realizing the couplings

IV. RESULTS

port 2

A. Coupling Coefficients k as Function of Separation 8

From the physical consideration, that small distances will cause strong coupling and large distances lead to weak cou­pling, we begin the observation with very small distance (8 1=0. 1 mm) and very large distance (8 1=3 mm). At resonance, the transmission factor (52 1 ) of a resonator will have an optimum value, and if two resonators are coupled mutually, there are two resonant points, the lower frequency h and the higher h . From these resonant frequencies, the coupling coefficient can be calculated to

k Ii - if fi + If (5)

Fig. 3 gives the transmission factor from port 1 to port 2 for two different distances mentioned above for lossy and lossless case. In simulating the lossy case, the tangent delta is set to 0.025, whereas for lossless case, the value is set to 0.0. For the strong coupling case, the resonant frequencies are located far away from each other, which gives big coupling coefficient value. For the lossless case we see the two peaks very well, and for the lossy case we can still recognize the maximal value of 521 . For weak coupling case, the resonant frequencies get closer, and for lossy case they degenerate to each other, we cannot resolve them, and there is no possibility to calculate the coupling coefficient.

Fig. 4 shows the comparison of calculated mixed coupling coefficient for lossless case (solid line) and lossy case (circle) . Due to the similarity of the results , for smaller coupling we

o ,----------------------------------------, S2 1 [dBI - 1 0

-20

-30

-40

-50

-60

-70

-BO

-90 L-______________________________________ � 2 2.2 2 .4 2 .6 2 .B 3

Frequency (GHz)

Fig. 3. Strong and weak coupling in mixed coupling between two resonators in lossless (solid lines) and lossy case (dashed lines).

prefer to use the lossless case for better resolution, which consequently leads to more accurate results in computing the coupling coefficient. In this figure, we learn to calculate the coupling coefficient, it is enough to consider the lossless ver­sion of the problem. From fig. 4, we can determine the distance 8 1 , which yield the coupling coefficient M1 ,2=O.03643, namely 8 1 = 1 . 9mm. In a similar fashion, we calculate the distances 82=2.5 Illin and 83=2.9 mm.

0.2

0. 1 B

0. 1 6

0 . 1 4 .

0. 1 2 u � x 0 . 1 E

.>:

O.OB

0.06

0.04

0.02

00 5 1 [mm)

Fig. 4 . Coupling coefficient for mixed coupling.

The distance from the feed point to the symmetry line of the resonator 84 will determine the external quality factor of the resonator. For the calculation of the external quality factor we use just a resonator, and calculate again the transmission factor 821 . At the resonance, again the transmission factor have a maximum, so that we get the resonant frequency of the system. By getting the frequency interval of the 3-dB line, we get the bandwidth of the resonator circuit. It is clear, that a system having large bandwidth will have small quality factor, and narrow bandwidth is the effect of a system with higher quality factor. So, by dividing the resonant frequency and bandwidth to each other we get the external quality factor of the resonator fed by this microstrip line. The iterative calculation gives the

value 84 = 2.65 mm.

The complete schematic of the bandpass filter designed is depicted in fig. 5 on the left side.

Fig. 5. left: Schematic (all dimensions in mm), right: the prototype

B. Simulation and Measurement

The schematic in fig. 5 on the left side is the structure under consideration. A full-wave computation with the software Sonnet gives a very good simulation result. Fig . 6 shows the transmission factor in the frequency interval of 2 GHz and 3 GHz. The loss less FR4 with the relative permittivity of 4 .9 gives an insertion loss smaller than 1 .5 dB in the intervall 2 .32 GHz and 2.4 15 GHz. The pass band is located at around 2 .36 GHz. A rejection of more than 28 dB at 2.2 GHz and about 1 9 .7 dB at 2 .5 GHz. The reflection factor for this case is smaller than - 1 0 dB in the same frequency interval (fig. 7) .

S 21 [dB] 0

I -5 I - 1 0 ,'" ; f I

- 1 5 t f Er = 4.9 -20

-25

-30 I -35

-40 t t -45

2 2 . 1 2 . 2 2 . 3 2 . 4 2 . 5 2 . 6 2 . 7 2 . 8 2 . 9 3

Frequency (GHz)

Fig. 6. Transmission factor for lossless (solid) and lossy (dashed) FR4 with different relative permittivity.

Furthermore, we see transmission zeros at about 2.27 GHz and at 2.45 GHz. All requirements given are fulfilled very well .

The condition is rather different for lossy case (dashed curves). A minimal insertion loss of about 8 . 3 dB is observed. However, other specifications are still fulfilled.

In other occasion, we consider, what will happen, if our designed filter is not embedded in an FR4 of relative per­mittivity of 4.9 but rather 4.4 . In this case is certainly our filter is electrically smaller, the consequence is, the pass band

will be shifted in higher frequencies . A simple calculation gives us a prediction of a new mid frequency, 2 .36 GHz . J4 .9/4.4 = 2 .4905 GHz. A computer simulation based on the software Sonnet verifies this result, as depicted in fig. 6, the pass region is now around 2.49 GHz, as predicted before.

-30

-35 + t .. ..

-40 L-_____________________ ---' 2 2 . 1 2 . 2 2 . 3 2 .4 2 . 5 2 . 6 2 . 7 2 . 8 2 . 9 3

Frequency (GHz)

Fig. 7. Reflexion factor for lossless (solid) and lossy (dashed) FR4 with different relative permittivity.

In order to verify the simulation with measurements, a prototype is built (fig. 5 on the right side). The measurement is performed with a vector network analyzer ZVL 1 3 . The trans­mission factor and reflection factor is depicted in fig. 8. The mid frequency is located at about 2.45 GHz with insertion loss of about 6 .64 dB . 3 dB below this value is the region between the frequency 2.4 1 GHz and 2.53 GHz, or the filter has the bandwidth of about 120 MHz. Transmission zeros around the pass band are not observed. The shift of the frequency response of the filter compared to the simulation result is probably due to, we simulate and measure with different values of relative permittivity. Probably, the FR4 used has a relative permittivity of about 4.4, so that the measurement results conforms with the simulation results with this relative permittivity value. A smaller insertion loss obtained by measurements could have the reason, that we in simulation used higher tangent delta, than we have in reality. From the comparison between simulation and measurement, we have the opportunity to measure the relative permittivity and the tangent delta of FR4.

V. C ONCLUSION

Designing a bandpass filter around the frequency 2.35 GHz with a pair of transmission zeros was verified by a simulation with a computer. All specifications are fulfilled, if we use lossless FR4. The simulation of lossy FR4 shows a degradation of the insertion loss to the value of 8 .3 dB . A measurement of the filter revealed, that the frequency characteristics of the filter was shifted to higher region. A possible reason is we have in reality an FR4 with the relative permittivity of about 4.4 . The insertion loss obtained by measurement is about 6 .64 dB . In this research, we learnt two things, firstly, to calculate the coupling coefficient is it enough to simulate the lossless microstrip, secondly, through comparison between simulation

reflection and transmission factor in dB

Fig. 8. Measurement Results

and measurement, we can measure the relative permittivity of the material.

REFERENCES

[1] Hong, Jia-Seng, Microstrip Filters for RFIMicrowave Applications, Sec­ond Edition. New Jersey : John Wiley & Sons, 201 l .

[2] RJ.Wenzel, Understanding Transmission Zero Movement In Cross­Coupled Filters, Microwave Symposium Digest, 2003 IEEE MIT-S In­ternational, pp. 1459 - 1462.

[3] J.S. Hong, and MJ. Lancaster, Couplings of Microstrip Square Open­Loop Resonators for Cross-Coupled Planar Microwave Filters, TEEE Trans. Microwave Theory Tech. , Vol. 44, No 12, Dec. 1996, pp. 2099-2 109.

[4] Y.H.Lee, W.H. Kwon, B .H. Koo, C .S . Lee, A study on a RF filter of IMT-2000 terminal using coupled rectangular microstrip loop resonators, Asia-pacific Microwave Coriference 1999, pp.295-298 .

[5 ] H. Miki, Z. Ma, and Y. Kobayashi, A Novel bandpass filter with sharp attenuations and wide stopband developed through the combined use of composite resonators and stepped impedance resonators, Asia-pacific Microwave Conference 2006, pp. 1683-1686.

[6] O.A.R. Ibrahim, I.M. Selamat, M. Samingan, M. Aziz, A. Halim, 5.75 GHz microstrip bandpass filter for ISM band, Applied Electromagnetics, 2007 Asia-Pacific Con! on, Dec. 2007, pp. 1 -5 .

[7 ] M. Alaydrus, Designing Microstrip Bandpass Filter at 3 .2 GHz, Inter­national fournal on Electrical Engineering and Iriformatics, Volume 2, Number 2, 20 10, pp.7 1 -83 .

[8 ] Federal Communications Commission, www.fcc.gov (verified on July 14, 20 13)

[9 ] www.sonnetsoftware.com (verified on June 15 , 20 13) [ 10] www.diplexer.com (verified on June 15 , 201 3) [ 1 1 ] R. J. Cameron, General coupling matrix synthesis methods for cheby­

shev filtering functions, TEEE Trans. Microwave Theory Tech. , vol. 47, no . 4, pp. 433442, Apr. 1 999.