**5.2 Two-stage BPF with diamond-shaped CSRR**

The two-stage filter is proposed to improve the passband and stopband performance of the filter, as shown in **Figure 13**. The length of the two-stage SIW filter is taken as LSIW<sup>0</sup> = 18 mm with horizontal distance between centers of rings, L = 8 mm. Other dimensions remain the same as in the single-stage SIW bandpass filter. Hence, the total filter size of the two-stage is 1.2 λ<sup>0</sup> � 0.28 λ0, where λ<sup>0</sup> is the free space wavelength of the center frequency of passband. **Figure 14a** and **b** show the current distribution of the proposed filter in the passband and stopband, respectively.

**Figure 15** shows the simulated frequency response of two-stage SIW BPF. The response clearly shows that one passband is formed with two poles and transmission zero. The passband has a center frequency of 8.86 GHz with 3-dB bandwidth of 0.74 GHz and an in-band insertion loss of 0.48 dB. The maximum return loss is �29.4 dB. Further, the stopband rejection is more than 60 dB, which is relatively better than a single-stage filter. In the second stage of transmission, zero is in proximity to poles leading to a high roll-off rate of 72.5 dB/GHz and 40.5 dB/GHz at the upper and lower edge, respectively.
