Premium
Differential equation description and Chebyshev approximation of linear time‐invariant circuits
Author(s) -
Huang Liang,
Yao Chang
Publication year - 2018
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.2461
Subject(s) - chebyshev filter , chebyshev polynomials , chebyshev equation , mathematics , chebyshev nodes , chebyshev iteration , chebyshev pseudospectral method , differential equation , approximation theory , linear differential equation , mathematical analysis , orthogonal polynomials , classical orthogonal polynomials
Summary 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.