Frequency Symbolic Analysis of High Complexity LPTV Circuits

This paper extends the frequency symbolic method (FS method) for analyzing linear periodically time-varying (LPTV) circuits to highly complex circuits. It has been demonstrated that this extension is achieved by applying the d-tree method to the FS method developed by the authors. At the same time, the d-tree method, based on the nodal voltage method and extended to LPTV circuits, has demonstrated high efficiency, making it possible to analyze circuits of high complexity. The paper considers the problem of transforming a system of linear integro-differential equations describing a circuit into a system of linear differential equations, which requires the application of L.A. Zadeh’s equation in the FS method. Two methods for eliminating integral expressions from a system of differential equations are proposed, one of which (the variable substitution method) is implemented in the UDF MAOPCs program. The reverse transformation to the original variables in the form of nodal voltages is proposed to be performed by differentiating transfer functions or multiplying them by the corresponding values of complex variables associated with individual harmonic components present in the transfer function. The results of analyzing a highly complex LPTV circuit, containing 33 nodes and 32 parametric elements, have been presented.