Conditions for the physical realizability of a typical component z(y)-matrix of a matching quadrupole of a general form in a concentrated elemental basis

Abstract

When solving problems of broadband matching, very often there is a need for a certain form of the amplitude-frequency characteristic. In connection with this, the problem comes up of synthesizing broadband matching devices that simultaneously have correcting properties, i.e. having a given frequency dependence of the power conversion coefficient in the operating frequency band. The use of broadband reactive matching - correcting circuits in most practical cases is difficult because of the reflected power. This leads to the problem of the synthesis of broadband matching-correcting circuits with arbitrary immittances of the signal source and load in an elemental basis of a general form, containing along with reactive and active elements, which has not been adequately solved. Therefore, it becomes necessary to find the conditions for the physical realizability of a typical component of the immitance matrix of a two-port network of general form containing poles in the left half-plane of complex frequencies. In this paper the necessary and sufficient conditions are defined for the physical realizability of the immitance matrix of a typical component of a subclass of two-terminal networks of general form in a lumped elemental electric basis, when the poles of the Eigen functions in the Foster representation can be in the left half-plane of complex frequencies, excluding the imaginary and real axes. This allows to synthesis of broadband dissipative matching, matching-correcting circuits and matched attenuators in an elemental basis of a general form with arbitrary immitances of the signal source and load from a single point of view.