Approximation of a transfer function with high Q-factor poles by a special transfer function with decreased Qs

This paper presents a method for the approximation of a transfer function with high Q-factor poles by a transfer function whose poles have a lower Q-factor. The ratio of this new transfer function to the given transfer function approximates unity with a minimum deviation over the whole ¿¿-axis. The method is based on rearranging all poles of a given transfer function, lowering the Q of the high Q-factor poles and increasing the Q of the low Q-factor poles by interdependent movement in the s-plane. The resulting transfer function with decreased maximum ¿¿-factor has the same order as the original transfer function and a limit on the amount of Q-factor lowering is shown to exist. The function obtained can be used as a first (and in many cases, sufficient) step of the approximation process. Further reduction of the approximation error is obtained by generating more complicated transfer functions. In these functions the multiplicity of all poles which are the poles of the first-step transfer function with decreased Q is increased simultaneously. The error decreases in a geometric progression with each step. The rapid growth of approximating-function complexity restricts the application of the proposed method to transfer functions with a small number of poles. A method for determining the poles and zeros of the approximating function is described and an example of approximation is given.