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A hairpin filter is a popular bandpass filter in microstrip filter theory. The hairpin bandpass structure is compact in size. They can be derived by folding the resonators (λ/2 length) of parallel coupled lines, into a “U” shape. This folded resonator is named as a hairpin resonator [25]. A 3^rd order bandpass filter centred at 3.5 GHz with 430 MHz Bandwidth (FBW=12.28%) has been selected. Substrate is chosen as RO3010 (ɛ_r=10.2) with thickness 1.27 mm. Design formula for hairpin filter can be used from [25, 26]. Also, design parameters can be extracted from facility available in CST MICROWAVE STUDIO^® V. 2018 by providing requirements of the filter. The design parameters for the hairpin bandpass filter are as shown in Table 4.1. We have chosen to have a 3^rd order filter to have less complexity and reduction in size. Designed filter with specific dimensions is shown in Figure 4.2.

The simulated results of S₂₁ and S₁₁ of the designed hairpin bandpass filters are shown in Figure 4.3. The graph is plotted between gain (in dB) versus frequency (in GHz). S₂₁ shows the passband of the filter and it is observed that the passband of the filters has center frequency 3.48 GHz and 430 MHz 3-dB bandwidth. Filter response also shows good out of band rejection. S₁₁ shows the return loss of the filter. The filter is resonating exactly at 3.5 GHz frequency and has return loss of 28 dB, which is quite good.

Table 4.1 Design specification of proposed hairpin bandpass filter.

Design specifications
Band Pass Centre Frequency	3.5 GHz
Substrate (Ɛr)	10.2
Substrate Thickness	1.27 mm
Bandwidth	430 MHz
Insertion loss	<1 dB
Return loss	< -20 dB

Figure 4.2 Layout of the hairpin bandpass filter.