System modelling and synthesis of stepped impedance resonators and filters

This study presents system-based models of stepped impedance resonators (SIRs) based on the singularity expansion method. Analytical expressions of the transfer function and the impulse response for two types of dual-band step resonators are derived (open-circuited λ/2 and short-circuited λ/4) for general impedance ratio (K). The accurate physical poles of the structures are acquired using a pole-energy-based refined matrix pencil scheme. Then, the frequency domain expression is used to develop a precise equivalent lumped element circuit model for the dual-band SIRs. Based on that, a direct pole-zero placement synthesis method is applied to design a three-stage dual band-pass filter. Very good matching between the transfer function of the system model and the frequency response data of the synthesised SIR filter is observed. The explored system-based modelling and synthesis procedures can be generalised systematically to design more complex filter structures.