Develop Procedure for Designing Fourth Order Microstrip Dual-Mode Bandpass Filters

Abdulla. A. Rabeea, Member, IEEE, Fred Barlow, Member, IEEE, and Aicha Elshabini, IEEE Fellow & IMAPS Fellow Electrical & Electronics Department Electrical and Computer Department University of Bahrain University of Idaho Isa Tow, Kingdom of Bahrain Moscow, Idaho, USA arabeea@eng.uob.bh fbarlow@uidaho.edu elshabini@uidaho.edu

Abstract– This paper presents a straightforward procedure for designing four order microstrip dual-mode bandpass filters using full-wave electromagnetic (EM) simulation tools. This can be utilized by beginner designer in a microwave filter field, especially for complex distributed microstrip planar structure. The designed methodology was demonstrated by fabricated and measured of several experimental samples of fourth order microstrip dual-mode bandpass filters. The simulated and practical results are obtained.

Index Terms-Design methodology, fourth order, microstrip, dual-mode, microwave bandpass filters, full-wave electromagnetic simulation.

I. INTRODUCTION

ow, microwave filters are designed by complex computer-aided packages based on the insertion loss

method. Currently, most of the filter-designed methods depend on the design of early methods finding that accuracy and efficiency of these methods were unmatched. The dual-mode filters have been studied widely by a number of researches [1-5] investigating their characteristics in terms of bandwidth, size, and selectivity. These studies did not describe a clear procedure for designing fourth order microstrip dual mode bandpass filters. They emphasized on the filter performance not on the construction of physical dimensions of planar microstrip filters. This paper consternates on utilizing computer aided design (CAD) tools such as a full-wave electromagnetic (EM) simulation and fabrication to expand a design methodology for determining the sizes of planar structure of four order microstrip dual-mode filters. The developed procedure is easy to follow and to be implemented by beginner designer for designing fourth order microstrip dual mode bandpass filters with less tuned processes and in less time.

The filters are composed of two or number of simple building blocks and each block represents a resonator. These blocks of resonators constructed from lumped element for low frequency applications or from distributed elements for high frequency applications. The well known procedure for designing a microwave filter is the insertion loss method. It applies for both lumped and distributed filter components. First, it starts by determining the low-pass prototype parameters for specified type of response such as Chebyshev

or Maximally flat filter. Then, the reactance of low pass design converted to a desired bandpass, high pass, or stop band application. Finally, Richard’s transformation and Kuroda’s identities are implemented to convert lumped elements to distributed transmission line elements [6,7].

Basically, system synthesis methods of filter design begin with a desired complex transfer function. Then, the input impedance, the poles, the zeros, and the prototype lumped elements are computed from this transfer function. These factors will define the exact response of lumped element filter, while it will be approximated for microwave filters. Therefore, a tuning process is often used for designing microwave filters [8].

The equations in [9] are the core for designing a microwave filter; for example, the design of microwave filter by using the insertion loss method started with the equations of low pass prototype filter that are normalized in terms of frequency and impedance. Then, these prototype designs are converted to the specified frequency range and impedance value. The low pass prototype elements may be classified as lumped or distributed elements from which the actual filters can be designed. This can be transformed to high-pass, band-pass, or band-stop characteristic response. Therefore, the low pass prototype is the main aspect in designing any type of microwave filters, and it is applicable to derive the model of distributed element filters.

II. DEVELOPED PROCEDURE

The procedure for designing the fourth order microstrip dual-mode filter is mainly based on generating graphical data for extracting the quality factor, the coupling coefficient of each single dual mode resonator and the coupling between two adjacent resonators.

In designing of any microwave filter, the desired filter electrical specifications should be defined first, as following:

a) Filter response type such as Chebyshev response b) Center frequency, f0 c) Order of filter, N d) Bandwidth, BW e) Band pass Ripple, LAr f) Substrate material such as microstrip

The design procedure for designing fourth order microstrip dual-mode filter is presented as flowchart in Fig. 2.

N

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Develop graphical data for coupling coefficient versus size length of stub from simulation results

Develop graphical data for coupling coefficient versus size length of stub from measured results

Simulate 4th order dual-mode filter separated by stub with different size to obtain k23

Fabricate fourth order microstrip dual-mode filter

Determine k & Qe for fourth order filter from low pass prototype filter equations

Determine physical structure (design)

Simulate dual-mode filter using full-wave EM simulation

Compare with filter specifications

Fabricate and measure four order microstrip dual-mode filters

Does it meet filter specifications?

Methodology applied successfully

Tuning

No

Ye

Yes

No

Define filter specifications (fc, BW, εr, Order of Filter, shape, etc.)

Obtain for few samples the k12 & Qe using EM full-wave

Develop graphical data for k12 & Qe from simulated results

Fabricate and measured the above samples

Develop graphical data for k12 & Qe from measured results

Determine resonator length (D) and width (W1 and W2)

3

5

4

1

2

Fig. 2. The developed

methodology for fourth order dual-mode microstrip filter Part A: Design Second Order Microstrip Dual-mode Filter

This part consecrates on designing second order microstrip dual-mode filter by considering the effect of physical dimensions such as width of feed lines (W1) and resonator (W2), side length of the square ring resonator (D),

coupling gap between resonator and feed lines (g), and the perturbation size patch (P) as described in [10 ]. Step (1): Determine the feed line width of microstrip (W1) and microstrip resonator width (W2) shown in Fig. 3 either by using classical formulas provided in [6], or by using the estimator tool available in some EM software packages, or by using simulation data plotted of width versus the characteristic impedance. The wavelength size for square-ring resonator will be the physical mean length of the resonator structure. This can be determined either using the formula in equation (1), or using the estimator tool available in Ansoft Designer package, or using square resonator length (D). This dimension can be determined from the obtained EM simulation data, which represents the relationship between the resonator size and the center frequency.

effg

fncε

λ0

= (1)

Fig. 3. Structure of second order microstrip dual-mode filter Step (2): Using commercial packages [11] to obtain simulation results for number samples of second order microstrip dual-mode resonators by considering the effect of the quality factor (Qext.) generated by the coupling gap of feed lines and the coupling coefficient (k12= k43) generated by the effect of the perturbation patch. Step (3): Compute the quality factor in step (2) using equations provided in [6] and create a graphical plot based on the simulated data that represent the relationship between quality factor and the size of feed lines coupling gap. Compute the coupling factor in step (2) using equation (2) and create a graphical plot based on the simulated obtained data that represents the relationship between the coupling coefficient (k12) and the perturbation patch size.

237

21

22

21

22

12 ffff

k+−

= (2)

Step (4) and (5): Fabricate samples for step (2) using the desire dielectric substrate. Measure the quality factor (Qext.) and the coupling coefficient (k12) from the s-parameters. Then, create a graphical plot based on measured data, which represent the relationship between the quality factors (Qext.) and coupling coefficient (k12). Part B: Design Fourth Order Microstrip Dual-mode Filter

In the case of designing fourth order two single second order microstrip dual-mode filter coupled by a designed stub with length (L). Therefore, this part mainly depends on the design of second order microstrip dual-mode filter stated in part A. Step (6): Obtain simulation results for a number of samples of fourth order dual-mode filters by considering the effect of the coupling coefficient (k23) generated by the stub length as shown Fig. 4 (a) and (b). This is done by changing the length of the stub.

(a)

(b) Fig. 4. Illustration of existence modes in fourth order dual-mode filter (a) and (b) Step (7): Compute the coupling coefficient in step (6) using equation (18) and create a graphical plot data that represents

the relationship between the simulated coupling coefficient (k23) and the length of stub. Step (8) and (9): Fabricate samples for step (7) using the desire dielectric material. Next, measure the coupling coefficient (k23) from the s-parameters. Then, create a graphical plot based on the measured data that represent the relationship of the coupling coefficient (k23) in terms of stub length, and the measured data is compared with simulated results to verify the agreement between them. Step (10): Compute the quality factor (Qext.) and coupling coefficient (k23) for fourth order filter from classical equations of low pass prototype filter. Step (11): Refer to data obtained from simulation and measurement (steps (4) and (5)), to build fourth order microstrip dual-mode filters by determining the length of stub at the specified coupling coefficient (k23) obtained from low pass prototype filter equations for given filter specifications (step (10)). Step (12): Simulate the fourth order microstrip dual-mode filter by using the EM full-wave simulation tools [11] and the simulated data is compared with the filter specifications. Step (13): Fabricate and measure the simulated fourth order microstrip dual-mode filter in step (12). Step (14): Compare the measured data of the fourth order designed microstrip dual-mode filter with the desired filter specifications to verify the validity of the developed methodology for the fourth order microstrip dual-mode filter. If the measured satisfy desired data of the fourth order microstrip dual-mode filter, then the developed methodology has been applied successfully to the fourth order microstrip dual-mode filter, other wise the filter needs to be tuned.

III. SIMULATED EXAMPLE OF A FOURTH ORDER MICROSTRIP DUAL-MODE FILTER

The fourth order dual-mode microstrip filter was simulated to verify the developed methodology of the fourth order with a center frequency at 4.9 GHz, and 0.3 GHz bandwidth. The fourth order microstrip dual-mode filter was designed on a commercial substrate (RT/duroid 5880) with a relative dielectric constant 2.2 and a thickness of 0.508 mm. The physical parameters of the fourth order dual-mode microstrip filter had been determined based on the methodology procedure provided in section II for the given specified external quality factor and the coupling coefficient which are determined from the filter specifications. The physical structure dimension of the fourth order dual-mode microstrip filter is shown in Fig. 5. The size of this filter is approximately 50% of a conventional fourth order filter. The EM simulated response is shown in Fig. 6 with a passband insertion loss of 2.51 dB, and the return loss is greater than 16 dB. The center frequency agrees with the desired specified value.

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Fig. 5 Physical dimensions of fourth order dual-mode microstrip filter (All dimensions in mm)

Fig. 6. EM simulated response of fourth order dual-mode microstrip filter

IV. FABRICATION AND MEASUREMENT OF SOME EXAMPLES OF FOURTH ORDER MICROSTRIP DUAL-MODE

FILTER

The fourth order dual-mode filter is constructed from the two single second order dual-mode filters separated by a short transmission line. This transmission stub will govern the coupling coefficient between the two single second order dual-mode filters. In designing the fourth order dual-mode filter for a given electrical parameters and specified substrate material, the physical length of the transmission stub and the dimensions of second order dual-mode filter needed to be determined. Therefore, the methodology was applied to design the fourth order microstrip dual-mode filter.

Four samples of the fourth order dual-mode filters with different transmission stub length were fabricated on RT/duroid 5880 substrate with a relative dielectric constant of 2.2, a thickness of 0.508 mm, and a loss tangent of 0.0009 at 10 GHz. This is done in order to extract the coupling coefficient versus the stub length. The coupling coefficient was computed using equation (2) from the amplitude response of transmitted S-parameters. Fig. 7 shows the photograph

layout and Fig. 8 shows the measured and simulated amplitude response of the S-parameters and there is a good agreement in the insertion loss with a small shift in the center frequency as expected and this due to mismatch and fabrication errors. There was a good agreement in the simulated and measured data for the coupling coefficient (k23) between two single dual-mode filters with a different separated stub size between them as shown in Table 1.

Fig. 7. The photograph layout for fourth order microstrip dual-mode filter

Fig. 8. Measured and simulated amplitude response of the transmitted S-parameters

Coupling Coefficient, k23

Stub Length Size #1 (FD4)

5.25 mm

Stub Length Size #2 (FD5)

5.5 mm

Stub Length Size #3 (FD3)

5.6 mm

Stub Length Size #4 (FD2)

5.8 mm

Simulated 0.0543 0.0536 0.0535 0.0531

Measured 0.0548 0.0542 0.0540 0.0539

Difference % 0.81 1.19 0.90 1.46

Table 1. Simulated and the measured data of coupling coefficient

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V. CONCLUSION

The validation of the developed design methodology was tested by considering a number of experimental design examples of the fourth order. In these examples, the results of center frequency, quality factor and coupling coefficients were in good agreement with the design values, in spite of the errors in fabrication process and measurements. The designed methodology optimized the performance of microstrip dual mode filters in time and effort. Therefore, the developed procedure in this paper is simple methodology and adaptable mechanisms to design fourth order microstrip dual-mode filters. This will be a useful tool, especially for the beginner designer in microwave filters.

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