Differential equation description and Chebyshev approximation of linear time-invariant circuits

The approximation technology of analogue circuit functions is crucial to the computer-aided simulation, analysis, and design automation of electronic circuits. Chebyshev polynomials and various differential equations are proposed in this paper to approximate the functions of linear time-invariant circuits. The coefficient calculation methods of the Chebyshev expansion and the differential equation matrices are thoroughly deduced, and the construction methods employed in the functions and the actual time mapping of the linear time-invariant circuits are presented in this paper. An example of an analogue filter verifies the effectiveness and accuracy of the proposed approximation algorithm and elaborates on the selection process of the order number and the time step length of the Chebyshev expansion according to the demanded truncation error.