## 2 Design and Analysis
### The Proposed DGS Unit Cell and Final Structure  
The proposed DGS structure is of a 2-D multiperiod EBG geometry [27]. The analysis of the final structure begins with a 1-D pair of lattices etched in the metallic ground plane parallel to the feed line. This pair of EBGs can be thought of as a dumbbell-shaped DGS where the gap is removed. From Figure 8a, it is found that increasing the etched area of both the lattices results in a lower cutoff frequency which means that the series inductance increases due to the increase in the areas. Now unlike the conventional dumbbell-shaped DGS unit, the change in attenuation location is too small as shown in Figure 8b. This is because removing the gap from the dumbbell-shaped DGS causes it to separate into two rectangular EBG units. Each EBG unit can be thought of as a parallel LC resonator where the size of the etched area controls the inductance, and the distance between the edges controls the capacitance of the resonator. Increasing the etched area increases the series inductance, but the shunt capacitance decreases due to the increment of the distance between the edges. So, in this case, the resonance depends on the product of the two reciprocal terms (L and C) which slightly changes the location of the attenuation pole. In the present case, the product increases for the decrease in the etched area resulting in a lower passband frequency. On the other hand, if the etched area is kept constant and the gap width of the conventional dumbbell-shaped DGS is varied, the series inductance remains almost constant, and the shunt capacitance varies. For the proposed design, there is no such gap distance and hence, varying the distance between the two EBG units while the etched area is kept constant results in no change in the inductance value as well as no change in the shunt capacitance value. That's why the location of the attenuation pole does not change as shown in Figure 9b. There is a slight change, however, in the cutoff frequency which is due to the inductance value introduced as a result of the narrow strip of copper between the two units (Figure 9a). So, for the EBG structure consisting of one pair of unit cells, the equivalent circuit can be imagined as two parallel LC resonators connected with an inductor as shown in Figure 10a. This circuit can be simplified to a single LC resonator as given in Figure 10b which is the equivalent to the circuit of the conventional dumbbell-shaped DGS structure. Figure 7: The effect of the gap width on the S-parameters of the parallel dumbbell-shaped DGS unit cell with a constant lattice size of g1 = 11.91 mm and g3 = 10.09 mm. (**a**) S11; (**b**) S21. Parameter Extraction  
In order to apply the proposed pair of EBG unit cells, the equivalent circuit parameters need to be extracted. To extract the parameters of the EBG configuration, the values of some dimensions such as g1, g3, and g5 need to be fixed. The effects of these parameters on the frequency characteristics have been discussed earlier. The dimensions of these parameters have been chosen as the dimensions of the final fabricated prototype parameters which are, g1 = 11.91 mm, g3 = 10.09 mm, and g5 = 1 mm. The linewidth of the microstrip line has been chosen to be the characteristic impedance of 50 ohms for the simulation. To describe the cutoff and attenuation pole characteristic simultaneously, the circuit should give performances of low-pass and band-stop filter at the same time. So, the simulation result  
Figure 8: The effect of the lattice size on the S-parameters of the parallel 1-D EBG unit cell with a constant gap width of 1 mm. (**a**) S11; (**b**) S21. Figure 10: (**a**) The equivalent circuit of the proposed pair of EBG unit cells; (**b**) A simplified circuit. Figure 9: The effect of the gap width on the S-parameters with a constant lattice size of g1 = 11.91 mm, g3 = 10.09 mm. (**a**) S11; (**b**) S21. can be matched to the one-pole Butterworth-type low-pass response which has a 3 dB cutoff frequency at 6.424 GHz and an attenuation pole near 10.176 GHz.