This paper focuses on the problem of using the symbolic frequency method for the determining the time dependency of output signals of linear periodically-time-variable circuits by applying the inverse Fourier transform (for a steady-state mode) or the Laplace transform (for a transition mode) to the images of these signals obtained using the transfer functions.

The frequency symbolic method allows us to calculate the conjugate parametric transfer functions of linear periodically-time-variable circuits. Such transfer functions link the input signals with the output signals in the form of approximating polynomials of Fourier in trigonometric or complex form. By the same polynomials of Fourier are approximated the normal parametric transfer functions which are the basis of assessment of the asymptotic stability of the circuit. To determine the conjugate and normal parametric transfer functions, there are the appropriate functions in the system of software functions Multivariate Analysis and Optimization of the Parametric Circuits (MAOPC), The system of software functions MAOPCs based on the frequency symbolic method and is implemented in the environment of MATLAB software.

The paper presents the results of computational experiments obtained by the system of software functions MAOPCs which show the adequacy of the definition of steady-state and transient modes of linear periodically-time-variable circuits in the time domain using the transfer functions determined by frequency symbolic method.

The coincidence of the results obtained by the system of software functions MAOPCs and the Micro-Cap7.0 program demonstrates the adequacy of applying the inverse Fourier and Laplace transforms for the investigations of linear periodically-time-variable circuits in the steady and transient modes in the MAOPCs environment.

- Yu. Shapovalov, B. Mandziy, and S. Mankovsky, “The peculiarities of analysis of linear parametric circuit performed by frequency-symbolic method”,
*Przeglad Elektrotechniczny*, vol.86, no 1, pp. 158-160, 2010. - Yu. Shapovalov, B. Mandziy, and S. Mankovsky, “Peculiarities of frequency-symbolic method applied to parametric circuit analysis”,
*Przeglad Elektrotechniczny*, vol.87, no 5, pp. 155-159, 2011. - Yu. Shapovalov,
*Symbolic analysis of linear electrical circuits in the frequency domain. Fixed and variable parameters*. Lviv, Ukraine: Lviv Polytechnic National University publication, 2014. - A. Solodov and F. Pietrov,
*Linear Automatic Systems with Varying Parameters.*Moscow, Russia: Nauka, 1971. (Russian) - Yu. Shapovalov and B. Mandziy “Frequency symbolic analysis of linear periodicallytime-varying circuits with many parametric elements”,
*Przeglad Elektrotechniczny*, vol.90, no 5, pp. 64-66, 2014. - Yu. Shapovalov, B. Mandziy, and D.Bachyk “The system functions MAOPCs for analysis and optimization of linear periodically time-variable circuits based on the frequency symbolic method”,
*Przeglad Elektrotechniczny*, vol.91, no 7, pp. 39-42, 2014. - V.D.Razevig,
*C**ircuit simulation using the Micro-Cap 7.*Moscow, Russia: Horiachaya liniya-Telekom, 2003. (Russian) - G. Korn and T. Korn,
*Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review*. New York, USA: Dover Publications, 2000. - Yu. Shapovalov, B. Mandziy, and D.Bachyk, “Investigation of stability reserve of linear periodically-time-variable circuits by the frequency symbolic method”, in
*Proc. IEEE International Conference on Computation Problems of Electrical Engineering CPEE-2015,*Lviv, Ukraine, pp. 181 – 184, DOI:10.1109/CPEE.2015.7333370, 2015.