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The Calculation of Transfer Functions of Nonlinear System on Transfer Functions of Blocks


N.D. Pirogova

In scientific operation the method of functional modeling of nonlinear radio systems which is offered is based on usage of differential-Taylor transformation. This method allows to get response of the system as segments of Volterra series in frequency area on a differential-Taylor spectrum of responses of separate blocks, without using a series in series substitutions and turns of series. The cascade connection of blocks of the nonlinear inertial system is considered. Each block of the given system is described by a segment of a functional Volterra series. It is known, that the nonlinear transfer function (NTF) of a inertial circuit represents multiple Fourier transform from Volterra kernels. Besides there is a link between NTF and partial derivatives in expressions for coefficients of many-dimensional Maclaren series. That is why for getting NTF of each block it is offered to use a method of many-dimensional Maclaren series. In operation the interrelation between a differential-Taylor function of complex amplitude of a combinative component of response and NTF of the appropriate order is obtained. Is shown, that NTF also is the Taylor function of many variables, and the values of NTF is the Taylor spectrum of a combinative component of response of the block. Therefore system of differential - Taylor conversions is applied for getting NTF of a cascade connection of two blocks. The expressions for definition of the Fourier-image of a Volterra kernel of a random order of the integrated block of the nonlinear system using a NTF of making blocks are obtained. The values NTF of a cascade connection of blocks at a preset fre-quency assembly of input actions are a differential-Taylor spectrum and, as a matter of fact, also are the parameters of mathematical model of the integrated block. The mathematical model of a multistage tract turns out a sequential association of blocks. Thus, an offered approach allows to get nonlinear transfer functions of a random order of a radio system using NTF of its blocks. The discrete processing makes it formalized for programming. The example of usage of the given approach for modeling of a radio-receiving tract is considered. Matching outcomes of account of a radio-receiving tract by an offered method (using blocks and as a whole) is reduced.

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