A dumbbell-shaped slot metamaterial along with varactor diode is used to change center frequency from 9.1 GHz to 11 GHz. Another way to reduce the size of the filter is to use Defected Ground Structure (DGS) with fractal geometry. Research activity has increased to use DGS in planar filters as it offers better performance and compactness. If a higher iteration level of fractal DGS is utilized, the bandpass filter becomes more compact [24].
The next section proposes a tunable bandpass filter utilizing hairpin structure along with fractal DGS for size reduction. Tuning is proposed by varactor diodes used in the geometry of fractal DGS.
4.3 Proposed Work
Here, initial design of hairpin bandpass filter having a center frequency of 3.5 GHz with bandwidth 430 MHz is proposed. Fractal DGS (3rd iteration of hexagonal shape) is introduced into it, so that its dimension can be reduced. After fractal DGS, varactor diode (variable capacitor) is inserted and thus, by changing the capacitance the center frequency of the band can be changed.
4.3.1 Design of Hairpin Bandpass Filter
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 3rd order bandpass filter centred at 3.5 GHz with 430 MHz Bandwidth (FBW=12.28%) has been selected. Substrate is chosen as RO3010 (ɛr=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 3rd 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.
4.3.2 Design of Hairpin Bandpass Filter with Fractal DGS
As discussed in an earlier section, fractal DGS has become popular to reduce size and to improve the return loss. After designing hairpin bandpass filter, fractal DGS geometry is added in the ground plane to reduce the size of the filter. Two fractal hexagonal shapes connected with vertical rode as shown in Figure 4.4 are etched in the ground plane. Here, 3rd iteration hexagonal fractal shape is used for better results.
Simulated result of the hairpin bandpass filter with fractal DGS is shown in Figure 4.5. Figure 4.5 (a) shows that center frequency is shifted towards lower side to 3.16 GHz. Response shifting in the lower frequency range indicates size reduction. Insertion loss in the case of fractal DGS filter is 1.93 dB, which is more compared to filter without fractal DGS (0.41 dB). The 3-dB bandwidth of the filter is 530 MHz. Similarly, as per Figure 4.5 (b) the resonance frequency is shifted towards the left side and return loss in fractal DGS filter is 39 dB, which is improved compared to hairpin bandpass filter without fractal DGS. Figures 4.6 (a) and (b) show a comparison of S21 and S11 of hairpin bandpass filter and hairpin bandpass filter with fractal DGS, respectively. Comparing the result, it is observed that shifting of the center/resonant frequency to lower side and return loss improvement for a filter with fractal DGS.
Figure 4.3 (a) S21 and (b) S11 of hairpin bandpass filter.
Fabricated hairpin bandpass filter with fractal DGS is tested with Anritsu MS2307C Vector Network Analyzer (VNA). Before testing, SOLT calibration was performed for the VNA. Figure 4.7 shows hairpin filter with Fractal DGS under test. The measurement results are shown for S21 and S11 of hairpin filter with the fractal DGS in Figure 4.8 (a) and Figure 4.8 (b).
Figure 4.4 Fractal DGS (Back/GND) portion of hairpin bandpass filter.
Figure 4.5 Simulated return loss characteristics (a) S21 and (b) S11 of haripin bandpass filter with fractal DGS.
Figure 4.6 Comparison of simulated response
