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In the May–June issue of Operations Research, Thomas Healy presents findings which he uses to demonstrate that a prescribed subdivision of activities will change probabilities in a PERT network analysis [“Activity Subdivision and PERT Probability Statements,” 9 341–347 (1961)]. As a member of the original PERT team, I would like to call attention to and take issue with some aspects of his paper.

For pedagogical reasons, classroom examples of analysis are usually performed symbolically. A student can frequently attain insight as to the relative effects of various circuit elements when they have symbolic labels. A prototype program has been devised which is capable of determining symbolic equations for a class of circuits. The equations are written in FORTRAN type notation. Although the original intention of the program was to determine circuit state equations, several other applications exist. For instance, dc analysis, such as that which is required for steady-state analysis, may be performed. If a circuit is linear, it is possible to obtain a transfer function for which the s polynomial coefficients are symbolic. Transient responses often yield information which is not discernible from symbolic relationships. For this reason, a companion program which integrates the state equations determined by the preceding program has been written. Currently, the integration routine must be run separately by the user. This entails the insertion of the state equations and other integration control statements. It is believed that a program which relieves the user from this task will be available by the time this paper is published. Numerical examples are also included in the paper.

This paper describes a general theory on the rheological dispersion caused when substances of different sorts are mixed. In rheological researches, it is usual that experimental results are directly connected to molecular structure. The present theory suggests that such a method is premature, because measured dispersions may have been possibly caused by the mixing.As an example, a case of series mixture is treated here. The new dispersion appeared in this case corresponds to the Maxwell-Wagner dispersion in the problem of dielectrics. To discuss the case of a general mixture, the electrical circuit theory is applied.First of all, equivalent circuit model of the general mechanical system is shown. This circuit was already obtained by G. Kron, but as some errors are found in it, they are corrected in this paper. The circuit is composed of ideal transformers and two kinds of elements with admittances of 2μ*Δl and λ*Δl (where μ* and λ* are complex Lame moduli, and Δl is an elementary length). Assuming that the sample body is noncompressible, the elements of the circuit are reduced to only one kind (2μ*Δl). If the sample is made of binary mixture of such substances, the equivalent circuit for the sample are to imply only two kinds of elements. General form of the appearent complex modulus of the mixture is obtained as a function of the moduli of the components, applying the Cauer's theory on 2-terminal impedance of the electrical network composed of two kinds of elements.In the light of the circuit theory, the relaxation frequency of the modulus is equal to the coordinates of the pole of the modulus devided by -2π, provided that the pole means the point where the denominator of the modulus as a function of p(=iω) is equal to zero. The zero of the modulus means the zero point of its numerator. The zero of the modulus is, therefore, the pole of the compliance, which is proportional to the relaxation frequency of the compliance. Considering the moduli of the components to be given as functions of p, the modulus of the mixture which is known above as a function of the moduli of the components is obtained eventually as a function of p. As a result, there are obtained laws on the relative position between zeros and poles of the moduli of components and those of the mixture. The main points of the laws are as follows:If the whole negative real axis of p is divided into sections by the zeros and poles of the moduli of the components, newly produced zeros and poles find themselves in the section at the most right side or in the alternate sections to it. The other sections become prohibited bands. The number of new zeros and poles increases as the mixing becomes more complicated.

The paper presents a general approach to the modeling of linear integrated circuits for computer-aided analysis in the frequency domain. The modeling is done through black boxes whose internal details are ignored and which are characterized only at their external terminals. Lumped and distributed, ideal and experimentally characterized multiterminal devices can be handled. The mathematical characterization is the indefinite admittance matrix. The implementation of the methods discussed is very simple, since no topological matrices are required. The method lends itself to analyzing large circuits by tearing them and then reconnecting the pieces. The method has been implemented in a program entitled BELNAP. A transient counterpart BELTIP and a design program IMPROVE have been in use by designers at Bell Laboratories for some time. An example circuit is solved in detail in the paper using BELNAP.

Predicting the reliability of a redundant system with repair is considerably simplified when the system can be subdivided into mutually independent subsystems. Results can be obtained without knowing the failure of repair time distributions of the subsystems. In this paper formulae are developed for the ``steady-state'' availability and MTBF of a complex system in terms of the availabilities and MTBF's of its constituent subsystems. The basic concepts required are introduced and discussed in a review of a simplex system. These concepts are then applied to a complex system to obtain the main results of the paper. Finally, two examples are given to illustrate the application of these results.

This paper describes the mathematical formulation of a computer program for automatic transient analysis of electronic networks. The formulation is based on the "state-variable" approach to network analysis and differs from other such programs primarily in the way that the network equations are manipulated to produce a solution. SCEPTRE includes a number of features aimed at providing greater flexibility and convenience for users of the program. Important among these features is that no prescribed equivalent circuit for active elements is required for program operation. Also, linearly dependent voltage and current sources in a network can be handled by the program, and provision has been made to allow a free-form format for input data. The paper includesa discussion of the program's ability to solve networks containing time-varying passive elements, and considers the factors that influence program running time.

This paper describes an efficient version of NASAP (Network Analysis for Systems Application Program) that has been developed by Northeastern University for batch and on-line solution of circuit problems. Problem coding, using a free-form input format, may be facilitated by use of mark-sense cards. The program provides a multiple-transfer function representation of a linear, lumpedparameter network. Output options useful to the student or designer include routines for frequency and time response and parameter sensitivity.

This paper attempts to summarize and place in perspective some of the recent contributions to stability theory. The major emphasis is on work which relates closely to applications in control, circuit theory, and aerospace systems. The frequency domain stability criteria for nonlinear and time-varying feedback loops are discussed in some detail. A large number of references describing both theoretical developments and applications are included.

Methods for the automatic analysis and design of microwave circuits using a digital computer in batch mode are given. The methods are capable of handling microwave components modeled by ordinary R, L, C, M, CS elements pins transmission lines and multiterminal black-boxes whose characteristics have been determined theoretically or experimentally. The analysis-optimization program, IMPROVE (Integrated and Microwave Program for Optimizing Variable Elements), implementing the methods presented in this paper is described and its use illustrated with a practical design problem.

This paper presents an example of the broad applicability of techniques developed initially for use in a specialized field. Describing-function techniques, which are useful in the analysis of nonlinear circuits, are applied to the analysis of thermally selfexcited mechanical oscillators. The amplitude and frequency behavior predicted by this method of analysis are in qualitative agreement with the observed behavior of typical oscillators.

In many actual network flow situations, nodes as well as arcs have limited capacities. This paper presents, for such a network, an algorithm for maximizing flow from a source node to a sink node. The algorithm allows us to treat these situations without introducing artificial arcs and nodes, as has been done in the past. Eliminating the artificial arcs and nodes simplifies network analysis since it always results in half as many nodes, as well as less than half as many arcs if the original arcs are undirected. In addition, the following generalization of Ford and Fulkerson’s max-flow, min-cut theorem is presented and proven. Consider two subsets of the nodes, X and Y, whose union is the set of all network nodes and such that the source node is a member of X, and the sink node is a member of Y. Then, forming a cut set separating the source and sink are the nodes in the intersection of X and Y, and the set of all arcs (i, j), such that i is a member of X − Y, and j is a member of Y − X. Letting a cut set's value be the sum of the capacities of all its arcs and nodes, it follows that the maximum flow is equal to the minimum value of all cut sets separating the source and sink.

This paper develops a procedure for determining a lower bound to the reliability of multiple-line redundant networks. The procedure is general in that there are no restrictions on the interconnection pattern between the functions of the network, and it allows, within limitations, different parts of the network to take on different orders of redundancy. The approximation to reliability is very good if the reliabilities of the circuits in the network are close to unity.

Linear graph theory has received wide application in electrical network theory. This paper extends the well-known methods of network analysis by exploiting the linear relationship between current and carrier density that exists in the lumped (large-signal) model of the bipolar transistor. The lumped model is described briefly and a linear graph is drawn for the lumped model. Relations between the trees and two-trees of this graph and the incrementals ?, Ico, and Ieo are then derived. A lumped model for a double emitter transistor is also considered and its graph is drawn. Linear graphs are then used to determine the lumped parameters of a and reverse currents for two conditions: 1) emitter one as the input and emitter two open circuited and 2) emitter one as the input and emitter two shorted. Each condition leads to its own graph which may then be used to find the applicable a and reverse currents. Methods for determining the circuit parameters are fully outlined and some sample calculations are given.

This paper describes the results of predicting the reliability of a circuit at different radiation levels. The conditional mean and variance of circuit output and the conditional reliability are predicted using Sceptre and test data on components exposed to different levels of radiation. These predictions are compared with the results of tests of the circuit. The difference between predictions and tests are examined and explained. The conclusions suggest a minor modification of the proposed method. We also suggest that this method of computer-aided reliability prediction can be a valuable design aid. This is especially true when there is a significant effect due to environmental variation, such as the effect of radiation on semiconductors.

Signal flow-graph techniques provide not only numeric but also symbolic expressions for network functions in terms of component parameters; these procedures are also useful in obtaining sensitivity coefficients. The paper presents the method of analysis of circuits using signal flow-graphs. The development includes the determination of transfer functions, sensitivity coefficients, worst case analysis and tolerance analysis. Two examples illustrate the method.

This paper describes the study and development of a linear, variable-pass network system which is controlled by the Fano short-time autocorrelation function of the input. Given an input function, the message, whose short-time power spectrum varies in an unpredictable manner with time, and to which there has been added a different function, the disturbance, whose short-time power spectrum is either time-invariant or varies in a completely known manner, a linear, input-controlled, variable-pass network can be specified which minimizes the mean-square error between the message input and the total output, taking network delay into account. Methods for mathematical computation of the mean-square error have been devised. The linear, input-controlled, variable-pass network has been found to have a lower mean-square error than that attainable with an optimum-mean-square, linear, fixed, selective network, for certain types of input messages.

This paper describes microwave circuit analysis programs techniques for general purpose which perform frequency domain analyses. Differing techniques used in two programs are described. The first uses transfer matrix analysis and is limited to networks having tree structured topologies and two-port devices such as transmission lines, stubs and lumped elements. It runs on a time-shared computer and is used for interactive design. The second program can analyze any linear network including those with multiport elements such as coupled transmission lines. This uses a nodal representation for the circuit and relies on inverting an admittance matrix to perform the analysis. In the first program the user describes his circuit in terms of topology as well as circuit elements. By this technique, a considerable reduction in computer size needed to run this program is effected. A 60 element circuit can be run on a commercial time-sharing service with less than 6K words of available core. The second program requires a large computer; for example, 32K words or core storage are required to analyze a 50 node circuit.

Characterization of devices for high speed ACP (Advanced Circuit Program) circuits demands an accurate study of transients and switching delays. This paper describes (a) the large-signal transistor model evolved for the purpose of carrying out such an analysis; (b) methods of measuring device parameters with relevant theory; (c) computational techniques most adaptable; and (d) correlation between predicted and observed transients. Many new ideas in the development of the device model, measurements, and computational procedure are reported and could be used for any general circuit analysis.

The objective in the courses described herein was to teach circuit analysis, optimization, and design in a way that recognizes the important role of computers, but does not become overpowered by the myriad subtleties and irrationalities of real-world computers. This paper discusses the author's experience in using existing interactive computer facilities to teach graduate and undergraduate circuits subjects, and suggests promising directions in which to go and not to go. Questions raised concern the role of omnibus circuit analysis programs, if any, how to teach numerical analysis without quite, time-sharing economics, and the use of a computer in teaching machine mode someday.

There is a constant need for diode circuits employing rectangular waveguide. Coupling of the diode to the guide by using an inductive post is a popular method. The microwave circuit analysis of the equivalent circuit has been explored by complete theoretical analyses in the literature, but the results have been sufficiently difficult to apply that, in practice, recourse is often made to empiric characterization. This paper derives a simplified equivalent circuit based on a small perturbation approximation. The method is verified by experiment and is then used to evaluate a practical Gunn oscillator cavity.

The paper describes a method of supplementing network analysis by taking a global view of project planning. The sequencing constraints normally found in a project are condensed into restrictions on the quantity of work performed by any stage in its duration. The objective is to minimise cost, where cost is considered to vary both with project duration and with the instantaneous rate of change of resource. Variational methods are used to produce optimal work-time and resource-time project profiles. The form of some constraints likely to arise in a project is considered, and the best profiles subject to certain constraints are derived and discussed. The techniques have been used to obtain a lower bound to project cost and to estimate ideal project duration.

This tutorial paper presents an introduction to the application of hybrid computation and optimization to the direct design of linear dynamic circuits using a simple optimization technique that does not require sophisticated computer programming. The chief merit of such simple techniques is that the user can easily verify the execution by stepping through the program in a manner that permits him to mentally check the logical decisions implemented by the optimization algorithm. This type of operation is economically feasible because of the development of a hybrid computer system which permits these techniques to be demonstrated at minimum capital cost.

An apparatus has been developed for monitoring the instantaneous surface potential of photoconductive insulators during illumination. In addition, instrumentation methods have been evolved for measuring the effective photoinduced discharge current, transit time, and mobility of charge carriers in such materials. The device has proved useful and convenient for qualitative evaluation of the photoinduced discharge characteristics of electrophotographic paper and plate materials under dynamic conditions. It also provides means for precise quantitative measurement for theoretical study of the photoconductive properties of such media. Circuit analysis and theory of operation of the apparatus are described. Discussions are given on the accuracy and usefulness of the techniques presented for monitoring the effective photoinduced discharge current to yield insight into the electrical and optical properties of photoconductive insulators. Test data are shown and discussed.

In the design and application of electronic circuits there is a need for a practical means for predicting the performance of circuits. In this paper a quasi-empirical method is presented for mathematically relating the performance parameter of interest to the pertinent variables. The technique is demonstrated for a medium-speed switching circuit. This circuit is described, the selection of models and the statistical design of the experiment are explained, descriptive component parameter and performance data are presented, models for rise time and delay time as a function of the component parameters are developed, and an analysis of these models is given. Methods for predicting the characteristics of the performance parameter distribution are presented along with a brief discussion of other uses of the models.

Probability theory is used to solve both a complex network situation and a pilot plant evaluation, proving it is an essential tool in decision-making processes. THE ect, outcome whether of every laboratory research or projpilot ect, whether laborat ry or pilot plant scale, is uncertain to some degree. Even so, necessary decisions can normally be made without undue fuss. The purpose of this paper is to illustrate techniques that can be used to organize and analyze situations worth the time and effort required to think hard and systematically about different courses of action. Situations of special interest concern uncertainties, either because the consequences of a particular action are not apparent, or because events may intervene that cannot be controlled or forecast with certainty. Raiffa 1 suggests that, in general terms, the analysis of a decision problem under uncertainty requires that

This paper analyzes the time and space evolution of the current density distribution in an inhomogeneous bulk "S-shaped" negative differential conductivity (SNDC) element and the response of the surrounding lumped element circuit. The SNDC element, in series with a package inductance, is in parallel with a package capacitance, the loop being in series with a load resistance and a battery. First the presence of isothermal current density filamentation in SNDC elements is demonstrated. By approximating the SNDC element as an appropriate conductive voltage curve in series with an appropriate intrinsic inductance, it is next shown that various modes of behavior (switching, relaxation oscillations, and a bias induced transition between the two) can all occur in the same SNDC element for appropriate values of the circuit parameters. A major aspect of the circuit theory is that it transforms directly between S and N shaped NDC elements when the important reactive components are identified in each case (duals). The techniques used are applicable to all SNDC elements, such as p-n-p-n and p-i-n diodes, and Ovonic threshold switches; emphasis is placed on the latter.

This paper presents a method for determining the transfer function coefficients of a system from its frequency response. The method is based on Bush's transfer function decomposition technique and Chen-Shen's response conversion formulas. It involves no prejudgment and therefore has no cumulative error.

The design of low-noise broadband microwave integrated amplifiers is particularly suited to the application of optimization techniques. Circuit theory is incapable of synthesizing these circuits, and bread-boarding is expensive as well as difficult. The analytical solution of microwave integrated circuits has been developed, and though complicated, is suitable for computer solution. It is then possible for the engineer to use a computer model of a circuit as a breadboard; however, with the many variables and the conflicting objectives of high flat broadband gain and low-noise figure it is best to leave the tuning of this breadboard to an optimization routine. This paper presents an objective function for the optimization of low noise broadband amplifiers. The effectiveness of this technique is demonstrated with examples.

This paper briefly describes the Bias program1 and its application in reliability analysis. Except in the simplest of networks, the calculation of parameters for reliability analyses is not easily achieved. Because of the easy temperature variation and other features of the network analysis program Bias, it is extremely well suited to at least three commonly used reliability analysis procedures: failure mode and criticality, drift failure, reliability prediction (catastrophic failures).

This survey describes the major optimization techniques of compilers and groups them into three categories: machine dependent, architecture dependent, and architecture independent. Machine-dependent optimizations tend to be local and are performed upon short spans of generated code by using particular properties of an instruction set to reduce the time or space required by a program. Architecture-dependent optimizations are global and are performed while generating code. These optimizations consider the structure of a computer, but not its detailed instruction set. Architecture-independent optimizations are also global but are based on analysis of the program flow graph and the dependencies among statements of source program. The paper also presents a conceptual review of a universal optimizer that performs architecture-independent optimizations at source-code level.

While the concept of a biological system as a balanced network of chemical transformations is not a new one, experimental definition of specific systems has been lacking. This paper defines theoretically and experimentally a number of such networks and their behavior and response to some limited environmental changes.

A graphical analysis is developed for the solution of transient response in nonlinear systems. The nonlinear system is first represented by its equivalent circuits with linear and nonlinear R, L, C circiut elements. By applying Kirchhoff's rules of circuit analysis with properly chosen variables, a set of nonlinear differential equations of the desired form is obtained. To solve the equations, integrations are performed on the phase plane with the graphical method proposed in the paper. This method of analysis possesses the following advantages: (1) The nonlinear functions can be obtained directly from exprimentally determined curves. Analytical expressions are not re quired. (2) The calculation is relatively easy and only simple tools are used. (3) Satisfactory accuracy is obtainable. This method of analysis is applied, in particular, to calculate the transient response of basic circuits of tunnel-diodes. Results are in good agreement with the experiments and with those obtained by electronic computer.

Simple acoustical systems may often be treated as acoustical networks with lumped elements if the linear dimensions of the elements are small compared with the wavelength. At higher frequencies this circuit theory method becomes less practical, and it is then necessary to use a field theory where the medium is considered continuous. It is sometimes difficult to decide whether to use the circuit theory approach or the field theory approach, because the accuracy obtainable with the circuit theory and lumped elements is not immediately apparent. It is shown in the paper that much uncertainty may be resolved by careful analysis of the elements used in the circuit theory. This is demonstrated by means of a simple example. In the design of sound radiators it is often convenient to represent the radiation impedance as a lumped element network, and such representations are well known for simple sound sources. When an extended definition of radiation impedance is used it becomes possible to find a simple network representation of spherical sound sources of arbitrary order n. Examples are given for n = 0,1,2 … 7. A simple network representation is also possible for the input impedance of exponential and hyperbolic horns. The physical significance of these representations is discussed.

Transformations to convert lowpass systems to highpass, bandpass and band-elimination systems in the case of pulse transfer functions of digital filters are given in this paper. It is believed that these results, for z plane transformations, are the first ones to be published in this field.