The Synthesis of Minimum Sensitivity Networks

The synthesis of networks with minimum sensitivity to element tolerances is studied from a computer viewpoint. The theory of equivalent networks is used to generate a sequence of networks whose transfer functions are identical to that of a given network but whose elements differ from one network to the next by an incremental amount. In the limit, differential equations result whose solution at any value of the independent variable give the elements of an equivalent network. Similarly, differential equations for the sensitivity of the transfer function to changes in each of the elements are derived. The differential equations in both cases are linear homogeneous with the elements of the transformation matrix as the independent variables. As a measure of the optimality of the network, the sum of the squared magnitudes of the sensitivities is chosen as a performance criterion. The method of steepest descent applied to this criterion leads to a simple choice of the transformation parameters which is easily implemented on the digital computer, thereby allowing efficient synthesis of networks with minimum sensitivity to element tolerances.