Synthesis of a complex filter with reduced transmission zeros and its leapfrog simulation

In this paper, a synthesis of a complex filter with reduced transmission zeros is proposed. A new characteristic function is proposed. It is described that the element values are obtained from the proposed characteristic function. The proposed prototype complex filter has finite transmission zeros at negative frequency area only. The required elements of the proposed prototype complex filters are fewer than that of the conventional ones with finite transmission zeros. Algorithms for determining the element values is described. The resulting circuit can be simulated without bilinear complex coefficient transfer functions. As an example, a third-order filter with equiripple passband response is designed. The image rejection ratio, sensitivity and the number of required elements are compared with those of the complex filters based on the frequency shifting method. The proposed circuit has the best image rejection ratio in the complex filters based on the frequency shifting method. The validity of the proposed method is confirmed through both of computer simulation and experiment. The experimental circuit exhibits complex bandpass characteristics(1-5kHz) and an image rejection ratio of 40.3 dB. © 2017 The Institute of Electrical Engineers of Japan.