Synthesis and design of asymmetrical dual‐band bandpass filters with modified Richard's transformation

An exact synthesis method for asymmetrical dual‐band bandpass filter (BPF) designs is presented with the proposed modified Richard's transformation (MRT). The MRT parameters are calculated first. Next, the filtering response is obtained according to the filter design specifications. Then, the component values of the LC circuit are obtained by an optimisation method. Finally, the LC circuit is transformed to its corresponding transmission line circuit. The discussions on the MRT are divided into two aspects. From the filtering response side, a set of parameters of the MRT is used so as to map a normalised symmetrical to an asymmetrical filtering response. By doing so, the bandwidths and the frequency ratio of the two passbands can be obtained with their desired values. From the circuit side, given that the classical Richard's transformation is a function of tan( θ ) while the proposed MRT is a function of tan( θ / n d ), dual‐section commensurate transmission lines are used instead of the commonly used single‐section ones. As synthesis and design examples, two second order and a cascading asymmetrical dual‐band BPFs are demonstrated in a step‐by‐step procedure. Their experimental results are in a good agreement with the predicted ones thereby verifying the MRT‐based synthesis procedure.