DESIGN OF BAND-PASS FILTERS WITH NON-EQUIRIPPLE FREQUENCY RESPONSES

Abstract

Introduction. Band-pass filters circuit elements can be calculated by converting low-pass filter (LPF) parameters, which is the prototype of the designed band-pass filter. The conversion causes problems in case calculated values of circuit elements (resistors and capacitors) are out of standard values determined by the GOST standard. Obviously, frequency characteristics of band-pass filters are distorted when replacing the calculated values of circuit elements by the standard ones. The number of circuit elements with values different from standard can be reduced to zero by solving an additional system of equations that connects parameters of designed and reintroduced non-equiripple frequency responses. Objective. The objective of this work is to develop a calculation method of band-pass ladder filters with values of circuit elements corresponding to standard ones. Materials and methods. The filter design process includes two stages. The first stage is a parameters calculation of a polynomial LPF prototype. The calculated parameters are determined as a system of equations solution set. The equations are formed by equating coefficients of variables raised to the same powers in transfer function (TF) expressions of designed and realized filters. Initial characteristics are the filter order and frequency response unevenness. The transition to the standard values of circuit elements can be done when solving another system of equations that connects LPF converted parameters with unknown parameters of reintroduced non-equiripple frequency response. Results. TF of LPF prototypes up to the fifth order and frequency responses of band-pass filters (BPF) and bandrejection filters up to the tenth order are presented. Analytical expressions of non-equiripple and equiripple frequency responses are used to estimate distortions of the latter when a band-pass filter center frequency is tuned by using variable inductors or capacitors. The integral quadratic function of a variable is taken as a measure of real frequency response distortions. The tenth order BPF calculation example is given. Conclusion. The presented calculation methods of band-pass filters and given example demonstrate possibilities of the filter design method based on the systems of non-linear equations solution. In contrast to approximation methods of ideal filter frequency response by using special functions and tabular filters design, the presented method allows high-order filter calculation for any initial requirements without using reference data.