Approximate Synthesis of a Complex RiCR Filter Using Grounded Imaginary Resistors

Abstract

Many techniques concerned with complex analog filters have been proposed. The complex filters have asymmetrical frequency response with respect to D.C. This property is important for the orthogonal communication systems. In this paper, an approximate synthesis of a complex RiCR filter using grounded imaginary resistors is proposed. The proposed complex RiCR filter is obtained through the frequency shifting method and an equivalent transformation using $\pi$ -connected imaginary gyrators composed of capacitors. The frequency characteristics of the proposed circuit with high selectivity are similar to those of the prototype one. The number of the required active elements of the proposed complex RiCR filter is smaller than that of the conventional one. A third-order complex RiCR filter is designed and its frequency response is measured. The experimental circuit exhibits complex bandpass characteristics and an image rejection ratio of 51 dB.