THE ALGORITHM OF CALCULATING THE STEADY–STATE PERIODIC REGIMES IN LINEAR AUTONOMOUS ELECTRIC CIRCUITS BASED ON THE LAPLACE INTEGRAL TRANSFORMATION AND THE RELATIONSHIP OF THE COEFFICIENTS OF POWER AND TRIGONOMETRIC SERIES

The algorithm of calculating the steady-state periodic mode in linear electrical circuit with concentrated stationary parameters is proposed. The calculation scheme of the algorithm determines the possibility to consider all the harmonics of a periodic external action described by a trigonometric polynomial simultaneously. The algorithm is based on forming the Laplace-transform images of the required solutions of the circuit dynamic equations and subsequent decomposition of the images of the solutions’ regular components in Laurent series in the neighborhood of an infinitely distant point. Calculated on the basis of the coefficients of Laurent series, the coefficients of Taylor series for the regular components of solutions are divided into two component parts, one of which corresponds to the free and the other to the forced components of the circuit reaction. Using the «equations of relationship» between the known coefficients of the Taylor series and the harmonic indices of trigonometric polynomials for periodic forced components of the circuit reactions, one can calculate the amplitude and phase parameters of the harmonics of these components.

Authors: Yu. A. Bychkov , S. V. Sherbakov

Direction: Electrical Engineering

Keywords: The electric circuit, the response circuit, the dynamic equations of the circuit, periodic steady state, Laplace transform, Laurent series, Taylor series, trigonometric polynomial, the amplitude and phase of the harmonics indicators

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