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A Novel Approach for Changing Bandwidth of FSS Filter Using Gradual Circumferential Variation of Loaded Elements S. M. Choudhury, M. A. Zaman, M. Gaffar, and M. A. Matin Bangladesh University of Engineering and Technology, Dhaka, Bangladesh

Abstract— A novel approach for varying bandwidth of Frequency Selective Surface (FSS) microwave filters has been discussed. The filter studied comprised of four-legged-loaded elements FSS filter. The unit cell of a conventional loaded element FSS filter contains only a single loaded element. The novel approach requires the unit cell to contain multiple loaded elements. The circumferences of the loaded elements of the unit cell are altered utilizing a factor named circumferential variability, d. The simulation results show that the bandwidth can be appreciably varied by changing the value of d. 1. INTRODUCTION

The concept of Frequency Selective Surface is to provide variable opacity for different values of the wavelength of incident radiation. FSS structures are commonly used in making reflector antenna more efficient [1], making dual band [2] or multiband [3] parabolic reflector and high directivity EBG resonator antenna [4]. FSS are commonly composed using periodic arrays to produce a resonant structure [5]. FSS geometries that possess greater than a two-fold rotational symmetry have reflection (transmission) coefficients independent of polarization at normal angle of incidence [6]. So elements for FSS are selected to maintain rotational symmetry. The loop elements are some common structures that are rotationally-symmetric and used in FSS structures. The loop element category include: three and four-legged loaded element which was issued patent in 1974 to Munk [7], square loops, hexagonal loops, and circular loops. A common property of loop elements are that they all have a fundamental resonance frequency when their circumference is approximately equals to λ, and a second resonance occurs when the circumference is approximately 2λ [5]. Munk suggested the alteration of bandwidth of such filter by reducing the distance of the transmission line spacing [7]. Callaghan et al. [8] observed change in bandwidth of such FSS filters with the introduction of dielectric layers. In this paper, a different approach for altering the bandwidth is explored. As mentioned earlier, the fundamental resonance wavelength is inversely proportional to the circumference of the filter element. The bandwidth of the filter is altered by constructing a unit cell with multiple loaded elements while gradually varying the circumference of the loaded elements within the unit cell. 2. DESIGN METHODS

The circumference of the loaded element can be determined for a particular center frequency [5]. By changing the circumference, the center frequency of the filter is changed. The novel unit cell is defined as a combination of multiple loaded elements. For continuity of pattern, 2 × 2 or 3 × 3 elements can be chosen. The circumference of these filters are changed keeping the mean center frequency same. Guo et al. [1] proposed a method of dual bandpass FSS filter using four-legged loaded elements of two different circumferences. In this paper, a design parameter Circumferential Variability, d is taken to alter circumference of the elements. For the 2 × 2 filter, there are four loaded elements, and their circumference are scaled with factors: 1 + d, 1 − d, 1 + 3d, 1 − 3d respectively. For the 3 × 3 filter, the circumferences are scaled with factors 1 − 3d, 1 + 4d, 1 − 2d, 1 − d, 1, 1 + d, 1 + 2d, 1 − 4d and 1 + 3d. The distance between the centers of the loaded elements are kept constant and chosen in such a manner so that the value of d does not cause two adjacent elements to overlap. 3. SIMULATION

Multiple layer of FSS filters were proposed by Romeu [9] to have multiband operations. In this paper, two identical layer of FSS filters is used to have same passband of both the layers. This increases the order of the filter. A cross-sectional view is show in Figure 2. For dielectric layers Duroid 5880 is used, and etched copper layers can be used to implement each layer of the FSS filter. To reduce the overall simulation time, the Babinet’s principle [10] has been applied to simulate the structure. At first the effect of changing circumference of a four-legged loaded element

Progress In Electromagnetics Research Symposium Proceedings, Cambridge, USA, July 5–8, 2010

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Figure 1: Unit cell of proposed 2 × 2 and 3 × 3 filter.

Center Frequency (GHz)

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Duroid 5880

Duroid 5880

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Figure 2: Layout of the filter structure.

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Figure 3: Center frequency vs. scaling factor of a four-legged loaded element FSS filter.

is simulated. For this simulation, the distance between the centers of two adjacent unit cells are kept constant, and all dimensions of each loaded element is scaled using a constant value. Afterwards, the circumferential variability is swept using parametric sweep and the effect of changing circumferential variability on bandwidth is studied. 4. RESULTS

In Figure 3, the Center Frequency vs Scaling factor curve of a single four-legged loaded element FSS filter has been shown. The center frequency gradually decreases with the scaling factor of the loaded element. This is concept which is utilized in increasing bandwidth of the filter. For this purpose, parametric analysis of the proposed filter structures is performed. For the 2 × 2 filter, the 5 dB bandwidth can be varied from 2.75 to 4.5 GHz, by changing the circumferential variance from 0.015 to 0.04. Further increasing circumferential variance causes the bandwidth to decrease. Cubic interpolating function fits the datapoints within the range. The interpolating function can be written as BW = p1 d3 + p2 d2 + p3 d + p4 where the coefficients are p1 = −1.2136e + 005, p2 = 11140, p3 = −243.27, p4 = 4.2228. The Norm of residuals is 0.019317. For the 3 × 3 filter, the 5 dB bandwidth vs. circumferential variance characteristics is irregular in shape. By varying the circumferential variance, the bandwidth can be varied from 1.886 to 3.705 GHz. So the 3 × 3 filter cannot give wider bandwidth compared to the 2 × 2 filter, but it can give narrower bandwidth compared to the original filter. 5 dB bandwidth vs. circumferential variance is shown on figure. The bandwidth can be appreciably varied in for the values of circumferential variance in the range 0.011 to 0.023. Two quadratic

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3x3 Filter

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5db Bandwidth of filter GHz

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Figure 4: Bandwidth vs. circumferential variance of 2 × 2 filter.

0

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Figure 5: Bandwidth vs. circumferential variance of 3 × 3 filter.

functions can appreciably fit the data points, the function being BW = p1 d2 + p2 d + p3 For the range of values of d from 0.011 to 0.015, the coefficients are p1 = −16457, p2 = 697.87, p3 = −3.813. Norm of residuals is 0.053674. For the range of values of d from 0.015 to 0.02, the coefficients are p1 = 7196, p2 = −176.45, p3 = 3.9647. Norm of residuals is 0.025662. 5. CONCLUSIONS

In this paper, a design procedure for FSS filters to vary bandwidth is illustrated. This novel technique of creating filters with wider bandwidth gives designers the flexibility to choose a particular bandwidth, specific to the application of the microwave filter. ACKNOWLEDGMENT

The authors would like to express their sincere gratitude towards Bangladesh University of Engineering and Technology (BUET), for supporting the research work of the paper. REFERENCES

1. Guo, C., H. Sun, and X. Lu, “A novel dual dualband frequency selective surface with periodic cell perturbation,” Progress In Electromagnetics Research B, Vol. 9, 137–149, 2008 2. Mittra, R., C. H. Chan, and T. Cwik, “Techniques for analyzing frequency selective surfaces-a review,” Proceedings of the IEEE, 1988. 3. Wu, T. K., “Four-band frequency selective surface with double-square-lop patch elements,” IEEE Trans. Antennas Propagat., Vol. 42, No. 12, 1994. 4. Lee, Y. J., J. Yeo, R. Mittra, and W. S. Park, “Design of a high-directivity electromagnetic band gap (EBG) resonator antenna using a frequency-selective surface (FSS) superstrate,” Microwave and Optical Technology Letters, Vol. 43, No. 6, 2004. 5. Volakis, J. L., Antenna Engineering Handbook, 4th Edition, McGraw-Hill, 2007. 6. Mackay, A., “Proof of polarization independence and non-existence of crosspolar terms for targets presenting n-fold (n > 2) rotational symmetry with special reference to frequency selective surfaces,” Electronics Letters, Vol. 25, No. 24, 1624–1625, 1989. 7. Munk, B. A., Frequency Selective Surfaces, Wiley, New York, 2000. 8. Callaghan, P., E. A. Parker, and R. J. Langley, “Influence of supporting dielectric layers on the transmission properties of frequency selective surfaces,” IEE Proceedings, Vol. 138, No. 5, 448–454, 1991. 9. Romeu, J., “Fractal FSS: A novel dual-band frequency selective surface,” IEEE Trans. Antennas Propagat., Vol. 48, No. 7, 2000. 10. Kraus D. K. and R. J. Marhefka, Antennas for All Applications, McGraw-Hill, 2003.