On the Adequacy of Analysis of Linear Periodically Time-Variable Circuits by the Frequency Symbolic Method Using Matrix D-Trees

the frequency symbolic method (FS method) of steady-state analysis of linear periodically time-variable circuits is used to form their transfer functions in the frequency domain. A Fourier polynomial approximates the transfer function and contains the complex variable, the time variable, and the parameters of the circle elements in the form of symbols. The coefficients of such Fourier polynomials using the FS method are unknown in the symbolic systems of linear algebraic equations (SSLAE) and are defined as their solutions in symbolic form. A well-known drawback of solving such SSLAEs is the significant increase in the required computer time when the number of unknowns increases. This shortcoming has been corrected by using one of the methods of sub- circuits namely, the topological method of d-trees.The matrix d-trees method, provides close to optimal rendering of similar in-formed expressions. This is the reason for the significant reduction in the time of their formation, the reduction of the required amount of memory and the high speed of the symbolic matrix d-trees method in general.The FS method, which uses the matrix d-trees method, has been implemented in the system of user-defined functions MAOPCs. The article presents the results of computer experiments that show the adequacy of the system.Four programs have been used to compare the calculation results: Micro-Cap 12.2.0.4, NI Multisim 14.24, and Simulink 10.6(R2022b). The system of user-defined functions MAOPCs showed the highest speed when modelling complex parametric circles containing hundreds and thousands of parametric elements (this is not a typo).