Compact Bandpass Filters With Low Loss and TZs Based on 1/<inline-formula> <tex-math notation="LaTeX">$n$</tex-math> </inline-formula> Mode Circle-SIW in Through Silicon Vias (TSVs) Technology

A range of ultracompact bandpass filters (BPFs)exploited circular-substrate-integrated waveguide (CSIW) with low insertion loss (IL) and high selectivity are proposed based on through-silicon via s (TSVs) for Ku-/Ka-band application in this article. Since the distribution of electromagnetism fields inside CSIW cavities is centrosymmetric, the 1/n mode CSIW can be divided with various central angles of alpha, which leads to significant reduction of the cavity size compared with the full-mode SIW (FMSIW) resonator. Consequently, a second-order BPF centered at 17.96 GHz is designed with alpha=10 degrees underelectrical excitation. The simulated and measured IL are 0.29 and0.85 dB, respectively, with a total area of 0.36 lambda(2)(g). The capacitive coupling realized by a slot line and inductive coupling achieved by the mutual inductance of perturbed TSVs (PTSVs) constitute the electromagnetic hybrid coupling, which results in transmission zeros (TZs) and is analyzed based on the equivalent circuit of the BPF. Furthermore, two compact dual-band BPF prototypes with different central angles and orders are proposed. The total area of the BPFs centered at 16.16/40.14 GHz and 16.86/30.24 GHz are 0.45 lambda(2 )(g)and 0.53 lambda(2)(g), respectively. The measured results verify the analytical method presented in this article well.