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IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 14, NO. 5, MAY 2004 231

New Formulas for Synthesizing Microstrip Bandpass

Filters With Relatively Wide Bandwidths

Kuo-Sheng Chin, Liu-Yang Lin, and Jen-Tsai Kuo, Senior Member, IEEE

Abstract—New formulas are proposed for designing wideband parallel-coupled microstrip bandpass filters with improved predic-tion of bandwidth. When a fracpredic-tional bandwidth1 is required, a correction = ( 2)(1 1 2) is incorporated into the formu-lation for determining the dimensions of each coupled stage. Two filters with1 = 50% are designed and fabricated to show the im-provement. The measurement shows a very good agreement with the simulation.

Index Terms—Parallel-coupled filter, wide bandwidth.

I. INTRODUCTION

T

HE ULTRA-wideband (UWB) technologies for commer-cial communication applications have created a need of a transmitter with bandwidths of up to or more than several gi-gahertz [1]. Microwave passive devices with such a wide band-width have been investigated recently [2]–[4]. Lumped elements are incorporated into the circuit design for a directional cou-pler with an octave-band [2]. The three-line structures in [3] and ground plane aperture compensation techniques in [4] are suit-able for implementing filters of a wide bandwidth.

Consisting of a cascade of coupled stages, parallel-coupled line configuration is attractive for realizing microstrip bandpass fil-ters in microwave frequencies [3]–[7]. Approximate design and synthesis formulas have been well documented for determining the dimensions of each stage for an all-pole bandpass filter [6], [7]. In deriving these formulas, one of the key steps is to estab-lish the equivalence of a coupled stage to a two-port network of two quarter-wave transmission line sections with an admittance inverter in between. The approximation has a good accuracy when the filter has a relatively small bandwidth. This is because the fre-quency response of a coupled stage has a zero derivative at center frequency , and thus is relatively insensitive to variation of fre-quency. When the designed bandwidth becomes larger, however, the coupling of the coupled stage is no longer a constant, and it apparently rolls off as the frequency moves away from . Thus, a modification is required for the formulas when the microstrip filters are designed to have a wide bandwidth.

The distribution method in [8] can provide correct solu-tions for filters with narrow- and wide-bandwidths. The entire

Manuscript received May 19, 2003; revised November 21, 2003. This work was supported in part by the National Science Council of Taiwan, R.O.C., under Grants NSC 91-2213-E-009-126, and in part by the joint program of the Ministry of Education and the National Science Council under Contract: 89-E-F-A06-2-4. The review of this letter was arranged by Associate Editor A. Sharma.

The authors are with the Department of Communication Engineering, National Chiao Tung University, Hsinchu, Taiwan 300, R.O.C. (e-mail: jtkuo@cc.nctu.edu.tw).

Digital Object Identifier 10.1109/LMWC.2004.827865

procedure for finding the -distribution includes choosing the number of sections, creating the composite matrix for a cascade of transmission line sections and coupled stages, and then solving for individual admittance values of the resonators. For direct-coupled microwave filters of to ele-ments having to 43% and VSWR ripple levels from 1.01 to 1.50, the theory in [9] can give good agreement with computed response characteristics.

In this paper, simple formulas are proposed for improving prediction of the bandwidth of parallel-coupled microstrip filters. Two experimental Chebyshev filters are measured to demonstrate the significant improvement.

II. DESIGNFORMULASWITHIMPROVEDACCURACY

From the perspective of circuit synthesis, accurate dimen-sions of the coupled stage are the most important in imple-menting the filter. The coupled stage in Fig. 1(a) has an electrical length , and even and odd mode characteristic impedances and . The matrix for the coupled-line stage can be derived as

(1) Here, the even and odd modes are assumed to have identical phase velocities. The matrix for the inverter circuit in Fig. 1(b) can be derived as [7]

(2)

Equating the right hand sides of (1) and (2), one can express and in terms of the circuit parameters of the admittance inverter as follows:

(3a)

(3b)

(2)

232 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 14, NO. 5, MAY 2004

Fig. 1. (a) Coupled-line stage. (b) Equivalent circuit of (a). TABLE I

EVEN ANDODDMODECHARACTERISTICIMPEDANCES FOR THEn COUPLED

STAGES OF ANN -ORDERCHEBYSHEVFILTEROBTAINED BY THEIMPROVED ANDCLASSICALFORMULAS.Ripple level = 0:1 dBAND1 = 50%

It is difficult to implement a coupled microstrip stage having a frequency-dependent behavior as described in (3). In fact, con-stant values for and have to be used to determine the dimensions of each stage from the characteristic impedance de-sign graphs. Note that if is used, (3a) and (3b) reduce to those given in [7]. Since the approximation is accu-rate only in the vicinity of the center frequency, this may lead to an error in estimating the filter bandwidth. Thus, when the required fractional bandwidth is

(4) can be used to calculate the and for each coupled stage. Obviously, an exact equivalence between the circuits in Fig. 1(a) and Fig. 1(b) is assured at the passband edges. This will make the prediction of filter bandwidths more accurate, which will be demonstrated later.

III. RESULTS

To show the significant improvement in predicting the filter bandwidth provided by (3) and (4), we first examine the changes of and of coupled microstrip stages due to the deviation of from . Table I lists their values for the coupled stage in a third- and a fifth-order Chebyshev filters with 0.1-dB ripple level and 50% fractional bandwidth. It is noted that for an -order Chebyshev filter, the coupled stage is identical to the one. The numbers in Table I indicate that the end stages have the largest change in , which is increased by no more than 6% for all cases shown here. On the other hand,

Fig. 2. Bandwidth decrement versus designed bandwidth from simulation responses of a third- and fifth-order Chebyshev filters with 0.1-dB ripple level.

Fig. 3. Comparison of responses for third-order filters designed by the improved and classical formulas. The designed bandwidth is 50% and ripple level is 0.1 dB. The substrate has" = 10:2 and thickness h = 1:27 mm.

the value of exhibits a significant change; for example, is increased by more than 20 for the end stages.

Next, we proceed to synthesize the parallel-coupled mi-crostrip wideband filters. All the filters are designed on an RT/duroid 6010 substrate with and thickness . Fig. 2 plots the bandwidth decrement against the designed specification. The test vehicle includes a third-, a fifth- and a seventh-order Chebyshev filters of ripple level 0.1 dB. In simulation by the full-wave simulator IE3D [10], the responses are obtained by discretizing the circuits with 20 and 40 cells per wavelength, and they are found indistinguishable. In Fig. 2, the curves denoted by “classical” are of filters obtained by (3) with , and those by “improved” are of filters synthesized by (3) and (4). When the filter order and the designed bandwidth is less than 25%, the bandwidth decrement is insignificant. If is increased to 35%, however, the classical formulas produce a fractional bandwidth with 5% less than the specification. The bandwidth decrement deteriorates as the filter order or the designed is increased. Upon the requirement of , in the classical design, the

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CHIN et al.: NEW FORMULAS FOR SYNTHESIZING MICROSTRIP BANDPASS FILTERS 233

Fig. 4. Comparison of responses for fifth-order filters designed by the improved and classical formulas. The designed bandwidth is 50% and ripple level is 0.1 dB. The substrate has" = 10:2 and thickness h = 1:27 mm.

bandwidth decrements are close to 19% and 25% for

and , respectively, while in our proposed equations, the decrements are only about 5% and 12.5%.

Finally, we examine the quality of the passband responses for filters designed with (3) and (4). Fig. 3 plots the simulation and measured responses for a third-order Chebyshev filter, and they show a very good agreement. Detailed data show that the simulated and measured results have fractional bandwidths of 48.4% and 48.2%, respectively, which are close to the designed bandwidth 50%. The measured results of a filter designed by classical formulas are also plotted for comparison. Its fractional bandwidth is only 41%.

Fig. 4 plots the results for a fifth-order filter. Again, the simu-lation and measured responses have a good agreement, and frac-tional bandwidths of 44.4% and 44%, respectively. For the filter

based on the classical design, the measured response shows .

IV. CONCLUSION

Formulas for determining and of coupled stages are derived for synthesizing relatively wideband parallel-coupled microstrip filters with improved accuracy. A third- and a fifth-order Chebyshev filters with 50% designed bandwidth are fab-ricated and measured. The measurements show that the pro-posed formulas not only provide a significant improvement in predicting the filter bandwidth, but also preserve the quality of passband responses.

REFERENCES

[1] Y. C. Yoon and R. Kohno, “Optimum multi-user detection in ultra-wide-band (UWB) multiple-access communication systems,” in Proc. IEEE

Int. Conf. Communications, 2002, pp. 812–816.

[2] D. P. Andrews and C. S. Aitchison, “Wide-band lumped-element quadra-ture 3-dB couplers in microstrip,” IEEE Trans. Microwave Theory Tech., vol. 48, pp. 2424–2431, Dec. 2000.

[3] J.-T. Kuo and E. Shih, “Wideband bandpass filter design with three line microstrip structures,” Proc. Inst. Elect. Eng., vol. 149, no. 5, pp. 243–247, Oct. 2002.

[4] L. Zhu, H. Bu, and K. Wu, “Broadband and compact multi-pole mi-crostrip bandpass filters using ground plane aperture technique,” Proc.

Inst. Elect. Eng., pp. 71–77, Feb. 2002.

[5] C.-Y. Chang and T. Itoh, “A modified parallel-coupled filter structure that improves the upper stopband rejection and response symmetry,”

IEEE Trans. Microwave Theory Tech., vol. 39, pp. 310–314, Feb. 1991.

[6] G. L. Matthaei, L. Young, and E. M. T. Johns, Microwave Filters,

Impedance Matching Networks, and Coupling Structures. Norwood, MA: Artech, 1980.

[7] D. M. Pozar, Microwave Engineering, 2nd ed. New York: Wiley, 1998. [8] J. M. Drozd and W. T. Joines, “Maximally flat quarter-wavelength-cou-pled transmission-line filters usingQ distribution,” IEEE Trans.

Mi-crowave Theory Tech., vol. 45, pp. 2100–2113, Dec. 1997.

[9] R. Levy, “Theory of direct coupled cavity filters,” IEEE Trans.

Microwave Theory Tech., vol. 15, pp. 340–348, June 1967.

數據

Fig. 2. Bandwidth decrement versus designed bandwidth from simulation responses of a third- and fifth-order Chebyshev filters with 0.1-dB ripple level.
Fig. 4. Comparison of responses for fifth-order filters designed by the improved and classical formulas

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