*2.1.2 Utility of the hexagonal slot*

The advantages of the proposed hexagonal head DGS structure are: (1) for the equal effective area, the hexagonal shape of the slot provides increased path length for the current around the slot as compared to the square-headed slot and (2) for the equal value of resonant frequency the hexagonal slot area is 4.3% more compact than the square slot.

**Figure 1.** *Schematic diagram of the hexagonal head dumbbell type DGS.*

**Figure 2.** *S-parameter response of DGS structure.*

### *2.1.3 Parametric study of unit cell*

Various parametric studies are performed to analyze the proposed DGS structure. Based on the hexagonal-head arm length, the inductance and capacitance of the filter are calculated and listed in **Table 1**. The S-parameter responses for different arm lengths "*a*" of the hexagonal head are shown in **Figure 3**. The variation of the cutoff frequency ("*fc*") and transmission zero frequency ("*fp*") with respect to the arm length is plotted in **Figure 4**.

From **Table 1**, it is observed that the attenuation poles and attenuation zeros decrease with the increase of the arm length (a) of the hexagonal head. With the increase of the arm length, the inductance value increases significantly, and the capacitance value remains almost constant. This is due to the increment in electrical path length around the hexagonal head slot. The change in inductance and capacitance values with different slot head lengths ("*a"*) are given in **Figures 5** and **6**, respectively. Another parameter, transverse slot gap "*g*," also greatly affects the filter's S-parameter response. The S-parameter responses for different transverse slots "*g*" of the hexagonal dumbbell DGS are shown in **Figure 7**. The variation of the cutoff frequency (*fc*) and transmission zero frequency (*fp*) with respect to the transverse slot gap is plotted in **Figure 7**. With the increase of this slot, the gap capacitance changes, and correspondingly the current path along the hexagonal head also changes. As a result, the inductance of the structure also changes. This inductance and capacitance change with the structure dimension causes a change in the cutoff and pole frequency of the filter.

The change in the circuit elements are calculated and are tabulated in **Table 2**. It is clear from **Table 3** that the attenuation poles and attenuation zeros decrease with the increase of the transverse slot ("*g*") of the proposed DGS. With the increase of the transverse slot, the inductance value decreases minutely due to the small decrement


**Table 1.**

*Circuit parameters of the Hexagonal Head Dumbbell DGS for different hexagonal head lengths "*a*."*

**Figure 3.** *Equivalent circuit model of the hexagonal head dumbbell type DGS.*

*Filter Designs Based on Defected Ground Structures DOI: http://dx.doi.org/10.5772/intechopen.103065*

**Figure 4.** *Comparison of simulated and circuit model responses.*

**Figure 5.** *Variations of simulated s-parameters with hexagonal head arm length "*a."

**Figure 6.** *Variations of equivalent capacitance with hexagonal head arm length "*a."

**Figure 7.** *Variation of simulated S-parameter responses with the change in the transverse slot gap "*g."

in the current path length. The capacitance value also decreases with the increase in the transverse slot. The inductance and capacitance values change with different slot gaps ("*g*").


**Table 2.**

*Hexagonal Head Dumbbell DGS characteristics for different transverse slot gap "*g*."*


**Table 3.**

*Comparative study among the filter structures using single, double, and-triple element hexagonal head dumbbell DGS.*
