GB753085A - Improvements in or relating to electrical wave transmission networks - Google Patents

Abstract

753,085. Filters. WESTERN ELECTRIC CO., Inc. June 4, 1954 [June 8, 1953]. No. 16596/54. Class 40 (8). An active electrical filter comprises two passive networks 1, 2 and a negative impedance converter 3 connected in tandem between them, the networks having at their ends facing the converter driving-point impedances which at one or more prescribed natural frequencies of the filter are related to each other by a numerical factor equal in magnitude to the impedanceconversion ratio of the converter. The impedance-conversion ratio is always negative and in the examples given in the Specification has a magnitude of unity. It is defined as the ratio of M e to M i where M i is the ratio of input current to output current and Me is the ratio of input voltage to output voltage. Either M e or M i is negative and the choice of magnitudes for these ratios determines the gain factor of the converter. The converter may be of the vacuum-tube type or of the transistor type described in Specification 743,450, [Group XL (c)]. The Specification gives in detail mathematical design procedures for a filter in accordance with the invention. As an example, a desired transfer function is prescribed for the filter (which is e.g. a high-pass filter) in the form where N(p) and D (p) are polynomials in p = # + j#. The natural frequencies of the filter must occur at complex frequencies corresponding to the zeros of D(p). At each of these frequencies the sum Z of the impedance - Z 11 b seen looking into the converter 3 at its input terminals 9, 10 and the driving point impedance Z 22 a of the network 1 at the same terminals is zero. Z 11 b is the driving-point impedance of the network 2 at terminals 11, 12 and the impedance conversion ratio of the converter 3 is assumed to be - 1. Therefore we may write where D(p) is the denominator of the expression for Z T and # 1 , # 2 , # 3 ... are points on the complex frequency plane corresponding to the poles of Z. If each of the networks 1, 2 is an R-C structure these poles will fall on the negative real axis and their selection is arbitrary so far as the transfer impedance of the filter is concerned. The expression for Z is expanded in partial fractions and the terms divided into a first group with positive residues and a second group with negative residues. The residues are always real. It is known that any function with simple poles on the negative real axis and positive real residues in those poles is the driving-point impedance of an R-C network. Therefore the first group of terms is associated with the impedance Z 22a of the network 1 and the second group with the impedance Z 11b of the network 2. Although the network 2 can only provide positive residues in the poles of Z 11 b, they will appear as negative residues when viewed from the terminals 9, 10 of the converter 3. It is assumed that the networks 1 and 2 will be ladder structures comprising resistors and shunt capacitors. The required values are found by making a Cauer synthesis. The Specification also describes design procedure for low-pass and band-pass filters using lattice and twin-T structure for the passive networks 1, 2. U.S.A. Specifications 2,106,785 and 2,549,065 also are referred to.