Study of Different Shape Electromagnetic Band Gap (EBG) Structures for Single and Dual band Applications

In this paper, single and dual band EBG structures for wider bandwidth are proposed. In each of the discussed EBGs, a metallic patch of regular geometry is chosen for the unit element. The patch is further modified by cutting slots to get extra inductance and capacitance which results into lower cut-off frequency and larger bandwidth. The proposed EBG structures are compared with the standard mushroom type EBG with respect to surface wave attenuation. The -20 dB cut-off frequencies and bandwidths of the various EBGs are compared. The effect of unit element size, gap between unit elements and via diameter on the transmission response is presented. Among the discussed EBGs, the swastika type structure is compact, single band and has wider bandwidth. The square patch with a single disconnected loop type slot EBG and the Fractal EBG are dual band. While square patch is more compact, the fractal EBG has wider bandwidth. All the EBGs can be useful in the design of antenna and other microwave circuits. Index Terms – Microstrip line, Electromagnetic band gap, fractal structure, surface wave and dual band.

The above discussed problems in microwave circuits can be minimized or overcome by the application of Electromagnetic Band Gap (EBG) structures. Electromagnetic band gap structures consist of periodic metal patches on a dielectric substrate. EBG structures can also be made by combination of dielectric only. EBG structures have properties such that, in a particular frequency band they stop the propagation of surface waves and also reflect back any incoming wave with no phase change. The above properties of EBG structures can be used to get improved characteristics of an antenna [1][2][3]. The gain of an antenna can be improved by using EBG structure in two different ways; EBG structure as a superstrate [3][4] and EBG structure as a ground plane [5][6]. EBG is also use to improve the isolation and diversity gain in MIMO systems [8][9][10]. EBG is also used to get notched characteristic in ultra wideband antenna [11]. EBGs are also used to suppress the noise and reduction of EMI in high speed circuits [12][13][14][15]. Some of the theoretical analyses and models for the EBG structures are available in references [16][17][18]. Many techniques are presented for design of dual band and multiband EBG structures in the open literature but most of them are having narrow or small bandwidth [19][20][21][22]. In [19], double U type slot is made in the patch to generate multiple band, [20] uses a fractal structure to generate the dual band characteristic, while [21] uses a spiral type structure to generate multiband characteristic.
In this paper, single band and dual band EBG structures having wide bandwidth have been

A. Mushroom Type EBG
Mushroom type EBG is a conventional three dimensional EBG consisting of a solid patch with a cylindrical via. The transmission response of mushroom type EBG depends upon the size of the patch, diameter of via and the gap between the unit elements. The transmission characteristic also depends upon the thickness of the substrate and the substrate material used. Fig. 1 shows a mushroom type EBG and its equivalent circuit model. Fig. 2 shows the variation of the transmission response of the mushroom type EBG with different unit element (patch) sizes. The gap between the unit elements is taken as 1 mm, the via diameter 0.6 mm and the substrate thickness is 0.8 mm. It can be seen from figure that as the patch size increases, the stop band shifts towards the lower frequency side and this is due to an increase in the capacitance value. For a mushroom type EBG, the value of capacitance 'C', inductance 'L' and resonance frequency are given by (1), (2) and (3) respectively [2].
Here 'W' is the side length of the patch, 'g' is the gap between the unit elements, 'h' is the thickness of the substrate, 'r' is the radius of the via, is the permittivity of free space and is the relative permittivity.

C. Swastika type EBG
The swastika type EBG is made by introducing a discontinuity in the cross hair type EBG. The discontinuity in the cross hair type introduces capacitance; hence better resonance is obtained than cross hair. Fig. (6a) shows a unit element of the swastika type EBG along with the fabricated prototype while Fig. (6b) shows the equivalent circuit. The inductor L is due to the via and capacitor C is due to the dielectric between the centre patch and the ground. The inductor L 2 is due to microstrip lines connected with the centre patch and the capacitance C 2 is due to the dielectric between the microstrip line and ground. The capacitor C 1 is due to the gap between the two outer microstrip lines.
The swastika type EBG is made on the same substrate (FR-4) as used for the standard mushroom type EBG. The diameter of via is again taken as 0.6 mm. Fig. 7 shows the measured and simulated transmission response of the swastika type EBG. The measured band of the swastika type EBG is seen shifted towards the higher frequency side; it is due to the fabrication constraint which keeps a little air gap between the EBG and the 50 ohm line and this air gap shifts the band towards the higher side.The swastika type EBG has better transmission response and larger bandwidth than the above two EBGs (Mushroom and Cross hair).  Fig. 8 shows the effect of variation of the strip width g 1 on the transmission response. It can be seen from the figure that as g 1 increases, the resonance frequency shifts towards the higher frequency side due to decrease in the capacitance value. It is also observed that as gap g 1 increases, the bandwidth increases (if -15dB bandwidth is considered). Fig. 9 shows the effect of via diameter variation on the transmission response of swastika type EBG. It can seen from the figure that as the via diameter increases, the stop band shifts towards the higher frequency side this is due to a decrease in the via inductance.    Fig. 11 shows a comparison of the simulated transmission responses of the above discussed three EBGs. It can be seen from the figure that the swastika type EBG has the lowest frequency of operation and highest bandwidth. The Cross Hair type EBG has advantage of lower frequency of operation when compared to the mushroom type EBG. Fig. 11

D. Hexagonal patch type EBG
A hexagonal patch has been selected instead of the rectangular patch used in case of mushroom type EBG. The hexagonal patch has a side length of 4 mm and the diameter of via used is 1.0 mm. FR-4 is used for the substrate having thickness of 1.53 mm. Fig. 10 (a) shows the fabricated prototype of the hexagonal patch EBG. Figure. Table 1 shows the comparison of the -20 dB cut-off frequencies and bandwidths of single band EBGs. The variation with unit element size for mushroom type EBG and cross hair EBG is also given.
From the comparison, it can be concluded that the Swastika type EBG has better performance in terms of bandwidth and compactness.  Fig. 11. Two different sizes for the mushroom type EBG (8 mm x 8mm and 6 mm x 6mm) are taken for the purpose. The substrate has thickness 1.53 mm, via diameter is 1 mm and the gap between the unit elements is 1 mm. It can be seen from the figure that there is very less attenuation of surface waves in case of solid ground in comparison to the EBGs. It can also be seen from the figure that as the size of the EBG increases, the bands shift towards the lower frequency side due to increase in the capacitance. A. Hexagonal patch with Double C Type Slot EBG Fig. 12 (a) shows the 'C' type slot EBG and Fig. 12(b) shows the transmission responses for different slot widths. It can be seen by comparing Fig. 10(b) and Fig. 12 (b) that by cutting 'C' type slot in the hexagonal patch, the stop band shifts towards the lower frequency side. Also, an additional stop band appears below 10 GHz. This is due to introduction of extra inductance caused by cutting the slot. It can be seen from Fig. 12(b) that as the slot width increases the band shifts towards the lower frequency side due to further increase in inductance.  Cutting a slot in the patch introduces extra inductance and hence it shifts the bands towards the lower frequency side. Fig. 13(b) shows the measured and simulated transmission response of the EBG. Fig.   14 shows the effect of slot width on the transmission response of the EBG. It can be seen from Fig. 14 that as the slot width increases, the lower band shifts towards the lower frequency side.

C. Fractal type EBG
A fractal type EBG having unit element dimensions 6 mm x 6 mm is designed. Fig. 16 shows the unit element of the fractal type EBG and the comparison of the transmission response of fractal type EBG with conventional mushroom type EBG having equal unit element size. It can be seen from the figure that the fractal type EBG has better stop band characteristic than conventional EBG. The optimized dimensions for the fractal EBG are x = 2 mm, y = 1.4 mm, a = b = 0.6 mm, g = 0.8 mm.
The via diameter is 1.2 mm. Fig. 17 shows the effect of variation of slot width 'y' on the transmission response of the EBG. It can be seen from Fig. 17 that as the patch width decreases, the higher frequency band shifts towards the higher side and after a particular value of slot width the band splits.
The optimum value of slot width is found to be 1.4 mm. There is no effect of slot width variation on the lower frequency band. Fig. 18 shows the effect of gap between unit elements. It can be seen from Fig. 18 that as the gap increases, the band shifts towards the higher frequency side due to decrease in the capacitance. It is noticed that the bandwidth of the higher band depends also on 'g'. The optimum value of 'g' is found to be 0.8 mm.   and via diameter on the transmission response of the EBGs are studied. As the unit size increases, the stop bands shift towards the lower frequency side due to an increase in the capacitance. Increase in the gap between the unit elements shifts the stop bands towards higher frequency side due to decrease in the capacitance. Increase in the via diameter shifts the stop bands towards higher frequency side due to decrease in inductance. Among the single band EBGs, the swastika type EBG is seen to offer better performance in terms of both compactness (lower resonance frequency) and bandwidth. Among the dual band EBGs, the square patch with a single disconnected loop type slot EBG offers better performance in terms of compactness while the fractal type EBG offers better performance in terms of bandwidth. The proposed EBGs will have applications such as enhancement of antenna gain and bandwidth, signal integrity enhancement and noise reduction for filters, reduction of mutual coupling for antenna arrays and suppression of noise in high speed switching circuits.

V. ACKNOWLEDGEMENT
The author likes to acknowledge vice chancellor DIAT (DU), for financial support. Author also likes to acknowledge R. V. S. Rama Krishna for his technical suggestions.