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To make a filter tunable, varactor diode or PIN diode has to be incorporated in the design. Here, two varactor diodes are inserted in outer hexagonal of fractal DGS as shown in Figure 4.9. For simulation purpose in CST MICROWAVE STUDIO^® V. 2018, R-L-C components are chosen. To consider a perfect capacitor, R = 0 Ω, L = 0 H and desired values of C is selected using parametric sweep.

By using parametric sweep in simulation, various values of C (treated as varactor diode) were applied and simulation results are shown in Figures 4.10 and 4.11. As it is observed from the response, the center frequency of the band can be varied from 3.3 GHz to 3.58 GHz by changing values of C from 20 pf to 1.5 pf. As center frequency varies, variation in bandwidth is also observed from 360 MHz to 530 MHz. Tuning of center frequency is not much above 8 pf of capacitance value. For better visibility, magnified view of S₂₁ is shown in Figure 4.10(b) and magnified view of S₁₁ is shown in Figure 4.11(b). Also it is observed that insertion loss is minimized during the tuning range; it varies from 0.44 to 0.79 dB. Proposed filter is low insertion loss and a very compact filter. In S₁₁ response, return loss stays around 20 dB to 25 dB, which is expected for any filter.

Figure 4.8 Comparison of simulated and measured result (a) S₂₁ and (b) S₁₁ of hairpin bandpass filter with fractal DGS.

Table 4.2 shows comparison of center frequency, bandwidth and insertion loss. As per simulation work, it is concluded that fractal DGS helps to make filter design compact.

Figure 4.9 Hairpin bandpass filter with fractal DGS with varactor diodes.

Figure 4.10 (a) S₂₁ of tunable hairpin bandpass filter with fractal DGS (b) magnified version of Figure

Figure 4.11 (a) S₁₁ of tunable hairpin bandpass filter with fractal DGS (b) magnified version of Figure

Table 4.2 Parametric comparison of simulated work.

Filter	Center Frequency (GHz)	Bandwidth (MHz)	Insertion loss (dB)
Hairpin bandpass filter	3.48	430	0.41
Hairpin bandpass filter with fractal DGS	3.16	530	1.93
Tunable Hairpin bandpass filter with fractal DGS	3.31-3.55	360 to 530	0.44 to 0.79