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On the interchanging of the second‐order network with high Q ‐factor poles by low Q ‐factor stages
Author(s) -
Filanovsky I. M.,
Stromsmoe K. A.
Publication year - 1979
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.4490070203
Subject(s) - mathematics , transfer function , chebyshev filter , square (algebra) , function (biology) , complex conjugate , order (exchange) , factor (programming language) , modulus , mathematical analysis , computer science , geometry , finance , evolutionary biology , programming language , engineering , electrical engineering , economics , biology
This article presents a method for the interchange of a second‐order network with high Q ‐factor poles by a more complicated network that consists of several low Q ‐factor stages. The transfer function square modulus of this new network approximates in a Chebyshev manner the square modulus of a given transfer function if the zeros of a given network are complex conjugate and not located on the α‐axis. In the other cases an error of the square modulus approximation is a Chebyshev kind also, but with the weight that depends on the zero locations of the given second‐order network and given maximum Q ‐factor. It is shown that all low Q ‐factor pairs of the poles must coincide when we apply the proposed method directly. The approximation error decreases in a geometric progression with the growth of the number of low Q ‐factor stages. A method for determination of the numerator zeros of the approximating transfer function is described and examples of interchanging are given.