**2.2 Bandstop filters using circular split-ring type defected ground structure**

A compact bandstop filter using circular split-ring type DGS is designed. First, a unit cell circular ring type DGS with a split at the lower portion underneath a microstrip transmission line is analyzed. The microstrip line is placed on the top plane and the DGS on the ground plane, as illustrated in **Figure 16**. The different dimensions of the DGS unit are: - the outer radius of the ring, r2 = 3.3 mm, the inner radius of the ring, r1 = 2.9 mm, the width of the ring, g1 = 0.4 mm, the width of the gap, g2 = 0.2 mm, a width of the 50 Ohm microstrip line, W = 1.92 mm.

### *2.2.1 Simulated result*

The simulated response shows a one-pole bandstop type response. The attenuation zero frequency is obtained at 4.14 GHz, and attenuation pole frequency is obtained at

**Figure 16.** *Schematic diagram of the circular split-ring type DGS.*

4.5 GHz with attenuation of 31.5 dB, as shown in **Figure 17**. The sharpness factor at the lower passband edge is 79.17 dB/GHz. Maximum passband insertion loss is –0.07 dB with a return loss greater than 18 dB.

#### *2.2.2 Parametric study*

The stopband of the proposed bandstop filter can be tuned by simply changing the inner radius (r1), keeping the slot width (g1) and split gap (g2) of the ring DGS fixed, as shown in **Figure 18**. The ratios of cutoff frequencies and pole frequencies (fc/f0) for different values of the ratios of inner radii and the 50-Ohm line width (r1/W) are plotted in **Figure 19**. The slot width (g1) of the split ring DGS also determines the cutoff and the pole frequency, keeping the outer radius (r2) and split gap (g2) at constant values as given in **Figure 20**. It is clear from **Figure 21** that changes in the ratios of the slot width to 50-ohm line width (g1/W) cause variation in the ratios of

**Figure 17.** *S-parameters of the circular split-ring type DGS.*

**Figure 18.** *Tuning of S-parameter responses with the inner radius (r1).*

**Figure 19.** *Tuning of cutoff and pole Frequencies- with the slot width (g1).*

**Figure 20.** *Tuning of S-parameter responses with the slot width (g1).*

**Figure 21.** *Variation of the ratios of cutoff and pole frequencies with slot width (g1).*

cutoff frequencies and pole frequencies (fc/f0). Again when studying the effect of the parameter g2 on the frequency response, it is obvious from **Figure 22** that g2 causes change in the values of cutoff and pole frequencies. The ratios of split gaps and the 50 ohm line widths (g2/W) are plotted with the ratios of cutoff frequencies and pole frequencies (fc/f0), as shown in **Figure 23**.
