RF Filter Design Using Coupled Co-axial Resonators

This paper describes the operation, design, implementation and performance of RF coupled resonator filters. It starts by considering discrete parallel inductor/capacitor resonators and then moves on to discuss the implementation of this style of filter at higher frequencies using short circuit co-axial resonators in place of the inductors. Introduction Shunt mounted resonators, comprising a discrete inductor and capacitor in parallel; can be used to realise RF bandpass filters. Two or more resonators are normally coupled together to achieve the desired frequency response. This type of filter has found common use at lower RF frequencies in narrow band receivers for applications such as paging and PMR. As operating frequencies increase practical considerations result in it becoming increasingly difficult to realise such filters. One way of implementing this style of filter at higher frequencies is to use short circuit co-axial resonators in place of the inductors. This paper starts by considering the fundamental performance of a single parallel inductor/capacitor (LC) resonator. It then describes how such resonators can be used to design RF bandpass filters. The implementation and achievable performance are then discussed and a means of extending the practical operating frequency range by the use of short-circuit co-axial resonators is detailed. Simulated performance and practical examples of coupled co-axial resonator filters are also presented. Single parallel LC resonator A simple resonant circuit can be formed from a parallel inductor (L) and capacitor (C). The resonant frequency of such a structure is given by Equation 1. Below resonance this structure is predominantly inductive, above resonance it is predominantly capacitive and at resonance it is high impedance. Equation 1 : C L Fo ⋅ ⋅ ⋅ = π 2 1 The loaded Q of such a resonant structure is dependent on the load and source impedance and the Q of the inductor and capacitor themselves. If a single shunt-mounted resonator is considered, between a source of impedance RS and a load of impedance RL, then the loaded Q is given by Equation 2.