The criterion for invulnerability of a network based on the connectivity of a graph is well treated in literature. We define a criterion for survivability of a network in terms of the independence number of a graph. The following problems are then considered. 1) Find an -connected graph, with vertices and edges, whose independence number is the minimum possible, where denotes the greatest integer less than or equal to ) Given positive integers , and , find the realizability conditions for a graph with vertices and edges, whose connectivity is at least and independence number is at most .
An iterative method is proposed for obtaining a solution to the problem of l_{p^m} approximation by exponentials. The method always converges and has the advantage that the samples need not be equidistant. Using the proposed method and allowing p to increase yields, in a much easier way, results that are comparable to those obtained by Fischl for the Chebyshev approximation.
The use of the second-generation current conveyor as the active element in realizing all-pass transfer functions is illustrated by two circuits.
A new method is presented for obtaining network functions in which some, none, or all of the network elements are represented by symbolic parameters (i.e., symbolic network functions). Unlike the topological tree enumeration or signal flow graph methods generally used to derive symbolic network functions, this new process uses fast, efficient, numerical-type algorithms to determine the contribution of those network branches not represented by symbolic parameters. A computer program [Network Analysis Program Using Parameter Extractions (NAPPE)] that incorporates all of the concepts discussed in this paper has been written. Several examples illustrating the usefulness and efficiency of NAPPE are included.
The advanced statistical analysis program (ASTAP) is a general-purpose network-analysis program which performs nonlinear transient, dc, and ac analyses and provides statistical simulation to determine the distribution of circuit outputs due to parameter variations. The program combines a user-oriented input language capable of describing completely general nonlinear devices with the latest advances in numerical and programming techniques: variable-order implicit integration, tableau formulation, and sparse-matrix solution methods. This paper describes how these techniques have been implemented in the ASTAP program. Attention is focused on the computational algorithms.
Brown's procedure for the synthesis of an n th-order symmetric positive entry matrix as the resistance matrix of an n -port network is extended so as to make it applicable to matrices having negative and zero entries also.
This paper considers the problem of designing networks whose function is the simultaneous transmission of independent signals over vertex-disjoint paths ( -transmission). All paths are assumed to consist of two edges and to traverse an intermediate vertex (bus). Necessary and sufficient conditions are given, lower bounds are established, and optimal designs are exhibited.
Necessary and sufficient conditions are given for the compactness of the open-circuit impedance (or short-circuit admittance) matrix of a passive reciprocal RC two-port network when the specified short-circuit admittance (or open-circuit impedance) matrix of the network is compact. The conditions are applicable to unsymmetrical as well as to symmetrical reciprocal RC two-ports.
The philosophy and features of the designer-oriented computer-aided design (CAD) are presented and discussed from both the economic and technical standpoint. Dedication of the CAD system is proposed for efficient design with the minicomputer being the economical choice. Some novel techniques suitable for minicomputers are proposed and a CAD system tailored for designer-oriented operation is described. Based on a 16 k minicomputer, the system generates for each design problem a custom program containing a set of simulated test instruments, thus reproducing the familiar laboratory environment for the designer. A sample problem is given.
The basic problem associated with the design of active filters is the sensitivity of filter characteristics to variations in filter component values. Utilization of a digital computer and the pole sensitivity concept provides a technique for filter design which incorporates sensitivity and filter turning as an integral step in the design procedure.
A method is described for the tolerance analysis of linear circuits with large element variations. It utilizes the adjoint network concept to set up a reduced system of equations, solvable by either Gaussian elimination or iteration. The process appears to be considerably more economical than simple repeated analysis of the circuit, provided that not all circuit elements are toleranced.
The properties of traditors are examined and a classification system for traditor types is established. It is demonstrated than an n -degree basic traditor can be defined by 2^n Lagrangians which yield 2n different traditor types.
Two well-known active all-pass networks can be arranged to give a constant-resistive input impedance at one of their ports merely by making two resistance values equal. Sensitivity to termination errors is thus reduced with no sacrifice in the basic properties of the network.
A new approach to star-polygon transformations is introduced. For star-connected -networks and for a certain class of polygon-connected -networks the "terminal value" is defined. This concept allows for an elegant derivation of the necessary and sufficient conditions for the existence of a polygon-into-star transformation. The related formulas appear to be simple and easy to remember. More important, the terminal value turns out to be a useful tool in the search for planar equivalents and in the recognition of transformable polygon structures. Simplicity is the only reason for the restriction to resistance networks. The study of the general RLC case does not bring out any new aspects.
A class of active RC networks is presented with which an all-pass transfer function of arbitrary order, having simple negative real poles, has been realized by combining the output of a threeterminal RC network with a portion of its input in a differential amplifier. A synthesis procedure for such an all-pass function is also indicated. This class of networks has the advantage that the gain constant of the all-pass function may be varied by varying the gain of the differential amplifier.
A new biquadratic active filter configuration is described which requires only two resistors, two capacitors, and two finite gain summing amplifiers. The circuit is shown to have zero -sensitivity to the resistors and capacitors and extremely low - sensitivity to the amplifiers.Other sensitivities of interest are also shown to be low. Practical realizations using one operational amplifier and additional resistors for each summing amplifier are given for bandpass, low-pass, high-pass, and notch filtering.
The problem of interconnecting several identical filters so as to obtain a filter which is both nominally closer to ideal and has lower sensitivity than the original filter is studied. A feedforward design for such a redundant filter is given which is applicable to filters having any specified passband, and the results of simulations illustrating the improvement in nominal behavior and sensitivity resulting from redundancy are presented.
The MOST model of Pao and Sah is extended to take into account the two-dimensional nature of the electrostatic potential. By keepig the current one dimensional, the basic equations can be cast into a form suitable for Gummel's iterative scheme. The numerical model is based on a finite-difference approximation to Poisson's equation and a closed-form expression for the current flow. The model is verified by comparing its results with experimental data. Good agreement is obtained. Deviations of the threshold voltage from the conventional expression for short-channel structures outside the range of the gradual channel approximation are investigated. In particular, the dependence of threshold voltage on channel length, drain-source, and substrate-source bias are illustrated with numerical and experimental results. Practical results from these investigations are summarized in graphical form.
