Optimization Research on Frequency-Domain Simulation Method of Low-Frequency Circuits Based on Interpolation of Variable-Step Runge-Kutta 45 Algorithm

In the simulation of low-frequency circuits, the Runge-Kutta 45 algorithm is a commonly used method for solving differential-algebraic equations, and the Fast Fourier Transform (FFT) is a key means for analyzing the frequency domain characteristics of circuits. Aiming at the problem of low computational efficiency of the traditional fixed-step Runge-Kutta 45 algorithm, this paper proposes an optimization method: using the cubic spline curve fitting technique, the calculation results of the variable-step Runge-Kutta 45 algorithm are interpolated to convert the non-uniformly spaced data into the form of uniformly spaced data required by the FFT, and then the FFT operation is carried out. In this paper, some typical low-frequency circuit simulation models are built, and relevant systematic comparisons are made between the traditional fixed-step direct FFT method and the proposed FFT method after variable-step interpolation in terms of two dimensions: computational efficiency and simulation accuracy. The simulation experiments show that, compared with the traditional fixed-step direct FFT method, the proposed method improves the computational efficiency by about 40% and can ensure the reliability of the frequency domain analysis results.