Some methods of estimating the magnitude of total sensitivities for the transfer characteristics of a reactance filter

Abstract

AbstractThis paper proposed two methods (the decision theory method and the probability method) for estimating the approximate magnitude of the tolerances of the transfer characteristics which are caused by the deviation of elements of a reactance filter. The first method estimates the total element sensitivities of the filter by an estimation measure which gives an upper bound of the absolute sum of the second‐order element sensitivities for the attenuation characteristic of the reactance filter. The estimation measure is represented by the various quantities which can be derived from the characteristic function of the filter only. Therefore, the element sensitivities of the filter can be estimated by its characteristic function only before actually constructing the network. The second method is for determining the statistical mean value and variance of the tolerance of the transfer characteristics for a reactance ladder filter. A calculation algorithm for this method is proposed. The transfer characteristics include the attenutation characteristic and phase characteristic as well as the real and imaginary parts of the characteristic function expressed in nepers. The analytical technique is based on Taylor's series expansion. The first‐order to third‐order terms and the mean value of the fourth‐order term are used. The second method differs from the first in that the former utilizes the information about the internal structure of the network.