Synthesis of a Passive Complex Filter Using Transformers

In this paper, the synthesis of a passive complex filter has been described. First, a normalized real coefficient filter is transformed into a complex coefficient filter, which includes imaginary-valued resistors by using a proposed frequency transformation. Second, a complex filter using passive elements is presented. The proposed circuit consists of terminating resistors, capacitors, and transformers with finite self-inductances and coupling coefficients equal to or less than unity. A third-order complex Chebyshev bandpass filter is designed using practical passive elements, and its frequency response is measured. It is shown that the experimental circuit exhibits bandpass characteristics (90-110 kHz) and an image rejection of 53 dB.