Abstract-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.

SUMMARYThis paper describes a method of configuration of a complex R i CR filter with coupled Chebyshev characteristics. The frequency shift method is a well-known method of obtaining a complex filter from a real filter, in which the transfer characteristic of the real filter is shifted along the frequency axis. The complex coupled Chebyshev filter obtained by the frequency shifting of a coupled Chebyshev filter has an excellent attenuation characteristic, but the number of constituent elements for active realization is large and the circuit is complex. In the proposed method, the complex coupled Chebyshev filter is first transformed to a complex R i CR filter so that the number of constituent elements for active realization is reduced and the circuit is simplified. In this paper, a method is presented for transforming the complex coupled Chebyshev filter to a complex R i CR filter. The attenuation characteristics and the numbers of constituent elements of the complex filter designed by the proposed method, the complex coupled Chebyshev filter, and the conventional complex R i CR filter, are compared for confirmation of the effectiveness of the proposed method.

SUMMARYIn general, signals with 90° phase difference from an orthogonal phase oscillator or a phase difference detector are used for measurement of the frequency characteristics of a complex coefficient filter with two input terminals for the real part and the imaginary part. However, since the phase splitter is designed by an approximate method, the phase difference of its output signal has an error. This paper describes the effect of the phase difference of the input signal on the error in the measurement of the frequency characteristics of a complex coefficient filter. Next, two new methods are described for deriving the frequency response of the complex coefficient filter without using an orthogonal phase oscillator or a phase splitter. The proposed method can be realized by providing the in-phase and out-of-phase signals to two input terminals or by providing the signal only to one of the terminals while the other is grounded. Finally, the frequency response of the complex coefficient filter is measured with the proposed method and its effectiveness is confirmed.

No abstract

No abstract