The practical application of an electromagnetic bandgap (EBG) structure usually presents difficulties in accommodating its physical size, since the period of an EBG lattice has to be a half-wavelength at the stop-band center frequency. Simple increments of the EBG cells and the wave impedance difference will result in inherent problems of increasing size and pass-band degradation.1 Several authors have recently focused on achieving a compact and wide stop-band design.2-4 Although these structures are relatively small and have a wide rejection frequency bandwidth, their pass-band performances are not meeting the required performance well.


The space-filling properties of certain fractal curves, in order to obtain resonant elements that occupy a small volume and at the same time provide wideband performances, have been reported.4,5 In this article, a novel Koch-shaped EBG microstrip low pass filter is presented. The upper microstripline of the presented Koch-shaped EBG microstrip low pass filter was configured as a Koch curve of the first iteration order, inserted with novel patches. The FDTD simulation results and experimental results show that the proposed novel Koch-shaped EBG microstrip low pass filter achieved excellent pass-band and stop-band performances within a small area.

Filter Design

Figure 1 shows the 3-D and top views of the proposed Koch-shaped EBG microstrip low pass filter. As can be seen, the proposed Koch-shaped EBG microstrip low pass filter has only two EBG cells, so it is highly compact compared with the size of other EBG structures.

The patches are produced by superposing two rectangular patches, which are inserted in the microstripline with a period d. Bends of 60° and 120° are placed alternatively, according to the shape of the first iteration order Koch curve with a period d. The period d satisfies the Bragg reflection condition, which results in d = λg/2 at the center frequency.

The F4B-2 substrate has a dielectric constant εr = 2.65 and a thickness h = 0.8 mm. When the center frequency of the stop-band is set at 10 GHz, the period d of the structure can be determined as 10 mm, according to the Bragg reflection condition. The width of the microstrip line was set to be 2.2 mm, corresponding to a characteristic impedance of 50 Ω.

Two circular holes are etched in the ground plane, exactly below the microstriplines with their centers located at the mid-point between the two adjacent inserted patches. The circle radius is r = d/4. The relative location of the inserted patches and the etched circles are shown in the figure.

A Chebyshev square distribution is adopted to taper the inserted patches, and a Chebyshev linear distribution is adopted to taper the microstriplines between two adjacent patches. For more information about Chebyshev square distribution and linear distribution, please refer to Karmarkar and Mollah.6

Three- and four-Chebyshev arrays, with a major-to-minor ratio of 25 dB, are used for the proposed design, and the normalized coefficients are shown in Table 1. Based on the proposed structure and the Chebyshev coefficients shown in the table, the parameters of the proposed low pass filter can be calculated and are given in Table 2.

Numerical and Measurement Results

The performance of the proposed low pass filter was simulated with the finite-difference time-domain method (FDTD), and a prototype 20 mm wide by 25 mm long was constructed for measurements. Figure 2 shows photos of the fabricated prototype, while Figure 3 shows the simulated and measured S-parameters of the proposed Koch-shaped EBG microstrip low pass filter.

Based on these results and the structure parameters given above, comparisons can be made among the performances of the proposed structure and the structures published previously.2–4 Table 3 shows that the performance of the proposed structure is better than that of the other three structures. Although the stop-band narrows a little because of fewer EBG cells (only two cells), the Koch-shaped EBG low pass filter occupies a smaller area and achieves a better pass-band performance.

Conclusion

In this article, a novel compact wide stop-band Koch-shaped electromagnetic bandgap microstrip low pass filter is presented. The structure is highly compact with a size of 25 by 20 mm. The structure achieved a stop-band width of 8.6 GHz (S21 ≤ –20 dB) and a pass-band return loss of less than –25 dB. This structure can be easily applied to microstrip circuits and can also be used to enhance their compactness.

Acknowledgment

This research has been supported by the National High Technology Development Program of China under Grant 2003AA00 5044. The authors would also like to thank the 206th Institute of CWI Group for the fabrication and measurement supports.

References

1. I. Rumsey, M. Picket-May and P.K. Kelly, “Photonic Bandgap Structures Used as Filters in Microstrip Circuits,” IEEE Microwave and Guided Wave Letters, Vol. 8, No. 10, October 1998, pp. 336–338.

1. S.Y. Huang and Y.H. Lee, “Compact U-shaped Dual Planar EBG Microstrip Low Pass Filter,” IEEE Transactions on Microwave Theory and Techniques, Vol. 53, No. 12, December 2005, pp. 3799–3805.

1. J.Y. Kim and H.Y. Lee, “Wideband and Compact Bandstop Filter Structure Using Double-plane Superposition,” IEEE Microwave and Wireless Components Letters, Vol. 13, No. 7, July 2003, pp. 279-280.

1. W.L. Chen, G.M. Wang and Y.N. Qi, et al., “Size-reduced Fractal-shaped Dual Planar PBG Microstrip Low Pass Filter,” ISAPE2006, October 2006, Guilin, China.

1. W.L. Chen, G.M. Wang and Y.N. Qi, et al., “Fractal-shaped Stepped-impedance Transformers for Wideband Application,” Microwave and Optical Technical Letters (accepted for publication).

1. N.C. Karmakar and M.N. Mollah, “Investigations into Non-uniform Photonic-bandgap Microstripline Low Pass Filters,” IEEE Transactions on Microwave Theory and Techniques, Vol. 51, No. 2, February 2003, pp. 564–572.

Wen-Ling Chen received his BS degree in radar engineering from the Missile Institute of Air Force Engineering University, Xi’an, China, in 2004, where he is now pursuing his PhD degree. His current interests include passive microwave circuits, antennas and propagation, and the application of fractal theory in microwave engineering.





Guang-Ming Wang received his BS and MS degrees from the Missile Institute of Air Force Engineering University, Xi’an, China, in 1982 and 1990, respectively, and his PhD degree from the Electronic Science and Technology University, Chengdu, China, in 1994. In 1994, he joined the Air Force Engineering University as an associate professor and was promoted to full professor in 2000. He is now the head of the Microwave Laboratory Center, Missile Institute of Air Force Engineering University. His current interests include passive and active microwave circuits, antenna and propagation, and electromagnetic computation.




Yi-Na Qi received her BS and MS degrees in computer engineering from the Missile Institute of Air Force Engineering University, Xi’an, China, in 2004 and 2007, respectively. Her current interests include fractal theory and computer programming.