Direct Calculation of Band-Pass Filters

Abstract

Introduction. When calculating band-pass filters (BPF), the circuit elements can be determined by converting the parameters of prototype low-pass filters (LPF). In a number of cases, the synthesized BPF does not have a direct prototype in the low-frequency range. Such filters include, e.g., BPFs with nodes tied to zero potential and other types of filters. Filters can be calculated directly by equating the coefficients of the synthesized filter transfer function (TF) and the realized TF obtained from the low-pass filter TF by the frequency conversion followed by solving the corresponding system of equations.Aim. To develop a methodology for direct calculation of band-pass filters with attenuation poles.Materials and methods. The simplest scheme of BPF with attenuation poles can be formed by two sequentially connected Г-shaped half-links on parallel circuits. Such a filter is realized only at certain requirements upon attenuation characteristics. When switching to BPF schemes with an additional parallel circuit in the transverse branch and a sequential circuit in the longitudinal branch, these restrictions are removed. In this paper, we develop a method for calculating inverse and quasi-elliptical BPF of П-shaped and T-shaped type, which have no restrictions when selecting the minimum attenuation and unevenness of the amplitude-frequency response (AFR).Results. The TF analytical expressions of the 6th and 10th order BPF were derived. Relations were obtained that allow the number of equations of the system for determining the filter parameters to be reduced. For П- and T-shaped 6th order BPFs, representations of circuit inductances through the central frequency and filter capacitances were obtained. This made it possible to express transfer functions through capacitances, at the same time as reducing the number of equations of the system. Examples of direct calculation of the 6th and 10th order PPFs were given.Conclusion. When converting TF of LPF, the frequencies of the realized AFR at both sides of the central BPF frequency are connected by certain relations. This fact makes it possible to eliminate the equations of the system that equate the coefficients of transfer function numerators, thereby reducing the total number of equations. Parameters, whose number exceeds that of the equations of the system, are selected arbitrarily from a number of standardized values. As a result, the accuracy of reproducing the realized frequency response is significantly improved.