A new original formulation of all pole low-pass filter functions is proposed in this article. The starting point in solving the approximation problem is a direct application of the Christoffel-Darboux formula for the set of orthogonal polynomials, including Gegenbauer orthogonal polynomials in the finite interval [−1, +1] with the application of a weighting function with a single free parameter. A general solution for the filter functions is obtained in a compact explicit form, which is shown to enable generation of the Gegenbauer filter functions in a simple way by choosing the value of the free parameter. Moreover, the proposed solution with the same criterion of approximation could be used to generate Legendre and Chebyshev filter functions of the first and second kind as well. The examples of proposed filter functions of even (10th) and odd (11th) order are illustrated. The approximation is shown to yield a good compromise solution with respect to the filter frequency characteristics (magnitude as wel...

New class of filter functions generated most directly by Christoffel-Darboux formula for Gegenbauer orthogonal polynomials

The generation of the summed-sensitivity invariants for the case of active networks is presented. On using the new method of proof, the summed-sensitivity invariants can be generated also for general physical systems.

Summed-sensitivity invariants and their generation

The results of Holt and Fidler for the summed sensitivity of RC passive networks are obtained by an alternative method which allows the results to be conveniently extended to active RC networks and gyrator-RC networks. The effect of these results on the minimum value of Schoefler's sensitivity criterion is discussed.

Summed sensitivity of active networks

The paper presents a survey of the literature as it pertains to the problem of multiparameter sensitivity in network theory. In particular, a critical appraisal is made of several multiparameter sensitivity functions, and the problems involved in their computation are considered. Several procedures for their evaluation are described, with attention focused on the auxilliary network approach of Leeds and Ugron and the adjoint network approach of Director and Rohrer. Another approach considered is the so-called direct approach, in which an algorith, is used to obtain directly the partial derivaties of the network function.

Multiparameter sensitivity problems in network theory

Bounds on the sum of element sensitivity magnitudes for transfer immittances, transfer voltage, and current ratios are established for networks consisting of resistors, capacitors, inductors, and gyrators. For RC and LC networks these bounds are given in terms of relevant driving-point functions and their frequency sensitivities. Further, for two-element-kind networks, bounds are given for the quadratic sensitivity index \phi .

https://www.cs.ou.edu/~thulasi/Misc/01083536.pdf

Bounds on the sum of element sensitivity magnitudes for network functions

An expression for the sum of the sensitivities of a network function with respect to the network components is derived. This is shown to be directly related to the network function in certain cases.

Summed sensitivity of network functions

The constraints on LC transfer-function coefficients are investigated for networks to be optimally sensitive according to Schoeffler's criterion considered by Leeds and Ugron.

Optimally sensitive networks

A tree and 2-tree generation method which does not suffer from most of the common restrictions, and which is ideally suitable for programming for the digital computer, is described.

J.K. Fidler

Papers

Summed sensitivity of network functions

Summed sensitivity of active networks

Optimally sensitive networks

Efficient tree-generation method suitable for computer programming