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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.

The need for improved ocean shipping service in the South Pacific, as evidenced by recent statements from indigenous political and business leaders and organizations, is cited. The major hypothesis of the research is then presented: "There exists a potential for improvement in shipping service and a reduction in cost-of-service through: a) consolidation and/or expansion of existing routes into regional center-feeder line networks; b) consolidation of capital equipment or merger of existing firms." A possible approach using minimal spanning trees (MST's) is illustrated for selected South Pacific ports. The results are intended to illustrate and establish the methodology. The short paper concludes with a brief description of the research work that remains to be done before the hypothesis can be accurately tested.

This paper describes TRANSIM simulation a a method for solving problems. There is a brief discussion of modeling and its importance. TRANSIM is compared with other general purpose simulators, special purpose simulation, and network analysis techniques such as PERT/CPM. Data requirements for TRANSIM applications are discussed, and a few examples of specific Navy applications are described in a general fashion. In conclusion, the paper details the latest TRANSIM development work in project analysis and output formats for project risk, resource allocation and scheduling.

Formal impact assessment, defined as the identification, description, and evaluation of changes associated with proposed actions, have been mandated by recent legislation relevant to federal water resources agencies. This paper uses an example involving proposed reservoirs in Carmel Valley, California, to demonstrate the various concepts which are introduced. The paper demonstrates how “evaluative factors,” defined as the goals, concerns, constraints, etc., that affected publics and other decision makers consider in ranking alternative actions, can be used in deciding on which impacts to forecast and at what levels of detail. The paper presents a classification of “causative factors” which encourages a systematic examination of the various aspects of a proposed action that may bring about change. Network diagrams of cause-effect relations, and the problems associated with the analysis of indirect impacts are also analyzed. The paper summarizes a number of characteristics of impacts which can be used in describing the results of an impact assessment.

This paper presents a systematic method of obtaining the total sum of all possible tree admittance products of a very complicated network. First, such a network is partitioned into several simple subnetworks by a set of independent cut sets. Then, the relationship between trees or tree admittance products of the network and multitrees or multitree admittance products of each subnetwork is found and presented as the tree expansion theorem. Finally, an effective method for decomposition of the large network into simple subnetworks is discussed. The methods described in this paper are very suitable for use by automatic computation.

This paper deals with the subject of applying different types of systems analysis tools to water quantity studies of multireservoir networks of increasing degrees of complexity. The object is to show how each tool can be used, modified and combined with other tools to solve specific problems and to indicate the degrees of complexity at which more sophisticated tools should be applied. Firstly, several applications and limitations of linear programming and dynamic programming are discussed. Secondly, it is shown that mass curve analysis is useful, can be extended to serve in computing reservoir rules for conventional multireservoir simulation models, and can be applied in conjunction with either historic or generated sequences of hydrologic input data. Thirdly, extended and limiting features of conventional time-interval-by-time-interval multireservoir simulation models are analyzed. And fourthly, a two-model series for problems which defy analysis by more basic tools is described in detail, the first model using network analysis (Out-of-Kilter Algorithm) for all space and time arcs simultaneously and providing data for the second general-purpose model using network analysis each time interval. The importance of efficient computer procedures is stressed. The background for the paper includes systems analysis of water availability and hydro-thermal power studies carried out during the past six years in that part of Canada lying between the Great Lakes and the Rocky Mountain Divide.

A judicious combination of the most suitable of the mathematical techniques now available makes possible the development of a system of programs for analysing electrical circuits which is both more efficient and more accurate than has previously been possible. These improvements are particularly necessary in the field of analogue type circuits, the present requirements for which are not met by existing analysis programs. The complete series of four papers will describe these techniques in detail. The present paper, which is introductory, gives a preliminary survey of the whole material.

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.

The paper is complementary to a paper by G.A. Montgomerie and it suggests that the method of algebraic manipulation proposed by Montgomerie may be considerably improved. In Montgomerie's paper, a closed contact is allotted the symbol unity, and an open ontact the symbol zero. Contacts in series are then treated as if additive, while contacts in parallel are treated as if multiplicative.The present paper shows that, if contacts in series are treated as multiplicative and contacts in parallel as additive, a considerable simplification of algebra results, with a concomitant gain in elegance. This usage avoids the necessity for rules such as 1+0 = 0, 1×0 = 1, which are in direct conflict with those of ordinary algebra. Also, many results which according to the original proposal would be obtained only after considerable manipulation are obtainable at sightusing the methods now proposed.

Users of nonlinear transient network-analysis programs, which use explicit integration procedures, have reported that excessive computer time is required to compute the transient response of networks containing widely separated time constants. Several recent papers have shown that for these problems significant computation-time reductions can be obtained by using implicit integration formulas. This paper is concerned with the selection and implementation of an implicit integration formula used in the CIRPAC nonlinear transient network-analysis program. Time-comparison data presented here indicate that the integration system that is described in this paper is significantly faster than the integration system of a network-analysis program that uses an explicit integration algorithm.

A judicious combination of the most suitable of the mathematical techniques now available makes possible the development of a system of programs for analysing electrical circuits which is both more efficient and more accurate than has hitherto been possible. These improvements are particularly necessary in the field of analogue type circuits, the present requirements for which are not met by existing analysis programs. The first paper 1 , which was introductory, gave a preliminary survey of the whole material. The second paper 2 commenced the detailed description of the techniques of linear analysis. Paper three 3 completed the description of linear techniques and commenced an account of the method of steady state nonlinear analysis based on a Picard iteration using the Fast Fourier Transform. The present paper, which ends this series, concludes the description of nonlinear steady state analysis by describing a method of steady state sensitivity analysis. It then considers certain methods of dealing with the problems of transient analysis of nonlinear circuits and concludes by surveying the position which has now been achieved in the field as a whole and discussing some of the problems which remain outstanding.

In engineering and scientific problems one of the most commonly used tools is Fourier analysis. With the increasing availability of analog, hybrid, and digital computers, it is useful to examine special techniques applicable to these machines. This paper presents: 1) methods for evaluating the required integrals on either a digital or an analog computer and 2) an analysis which results in guidelines for choosing the sampling interval when the problem is done digitally. Parts of the material presented in this paper can be found in other sources although there are some refinements included here that make the implementation of the theory considerably easier. The theory is valid for any machine, but minor modifications may have to be made in hybrid computer patching or in the digital program to conform with equipment restrictions.

A conceptual framework is erected which will give better control, it is hoped, to the designer of unbalanced RLC networks that are to realize prescribed, minimum-phase or nonminimum-phase transfer functions. Maneuverability is achieved by introducing a set of "elementary sections," which are constructed from the individual factors of the prescribed transfer function. The rules for the interconnection of these sections are derived from an equivalent-network scheme which contains "generalized, ideal transformers," but mutual inductance is absent altogether from the synthesized networks. The majority of design deliberations can take place in terms of network concepts discussed in Sections II-IV, while the role of purely formal, algebraic manipulations is intentionally minimized. Four different illustrative designs, which realize new networks for transfer functions previously used by E. C. Ho and L. Weinberg, are carried out step by step. In each of the four cases the network designed in Section V of this paper exhibits substantial improvements. The approach chosen in this paper is put into perspective with regard to pertinent synthesis papers by E. C. Ho, G. L. Matthaei, R. H. Pantell, and L. Weinberg, and the equalizer design techniques of O. Zobel and H. W. Bode. This makes it necessary also to examine the relationship between some of these papers, which is done primarily in Appendix I.

This paper is concerned with the development of a general and rigorous broad-banding theory for varactor parametric amplifiers. We first show that the parametric device exhibits some inherent network properties which are not shared with other twoterminal active devices. When the varactor is embedded in an arbitrary passive environment, it presents an impedance that can be characterized by a positive function rather than a positive-real function. The broad-banding theory presented takes into account also the interaction between the signal and sideband circuits through the frequency coupling action of the variable capacitor. Realizability conditions on the transducer power-gain function of a varactor parametric amplifier are derived. It is shown that the prescribed transducer power-gain function must satisfy a set of restrictions derived in part from the parasitic elements of the varactor. The main results of this paper are embodied in Theorems 1 and 2 which describe a synthesis method for the realization of broad-banding parametric amplifiers using varactors. It is shown that the synthesis requires, in general, two factorizations of the prescribed transducer power-gain function.

The current unbalance in a 500-kV double-circuit and a 138-kV triple-circuit, paralleled and untransposed transmission line is analyzed comprehensively. This paper establishes that the magnitudes of individual circuit current unbalances resulting from currents circulating between the paralleled circuits are more significant than the net through system unbalance. Since the former were not considered in previous investigations, the criteria established there for proper phase configurations is shown in this paper to lead to maximum circulatimg current unbalance. The influence of series capacitor-line compensation is also shown and the ramifications of these unbalances are discussed and evaluated on a present worth of annual loss basis.

This paper presents a discussion and analysis of short circuits for low-voltage distribution systems. Many distribution systems are supplied from transformers connected in delta on the low-voltage side with the mid-tap of one secondary winding, or with one corner of the delta, connected to ground. As a result, short circuits on these systems often involve failure to ground, and an accurate analysis for these faults is of value. An original analysis of power-leg-to-ground and light-leg-to-ground short circuits is presented together with formulas for line-to-line and three-phase faults. A study of short circuits on the secondary circuits of single-phase transformers supplied from three-phase systems is also included, thereby giving a comprehensive treatment of distribution short circuits. The paper also includes a discussion of the effects of resistance in limiting short-circuit currents and the voltage rise of the secondary neutral above ground potential caused by transformer failure and resistance to ground.

The past two decades have witnessed profound changes in the composition, functions and the level of complexity of electrical as well as electronic systems which are employed in modem technology. As a result, classical RLC network theory, which was the mainstay of electrical engineering at a time when RLC networks were the bread and butter of the electrical engineer, has been and is being increasingly relegated to the status of a specialized branch of a much broader discipline-system theory-which is concerned with systems of all types regardless of their physical identity and purpose. This paper presents a brief survey of the evolution of system theory, together with an exposition of some of its main concepts, techniques and problems. The discussion is centered on the notion of state and emphasizes the role played by state-space techniques. The paper concludes with a brief statement of some of the key problems of system theory.

From an abstract point of view, both electric circuits and switching circuits may be considered as weighted nonoriented graphs. There are two main differences between electric and switching circuits from this point of view. The first of these is the algebra to which the weights belong. In electrical network theory the weights belong to the complex number field or to the field of rational functions of a complex variable since they are impedances or admittances. In switching theory they are Boolean functions. The second difference is that one is interested, in electrical network theory, in the circuits or the "loops" in the system, whereas in switching theory one is interested in the paths. This paper seeks to relate the two theories by means of topological considerations. Formulas are derived relating the switching function and the driving point admittance function of a two-terminal network. Certain relations between dual networks are also established. The paper concludes with a synthesis procedure for a type of switching circuit of academic interest, the single contact switching circuit, and statements of some important unsolved problems.

In this paper integral restrictions on the time delay of linear phase, low-pass matching networks are derived. These networks operate between a resistive generator and a load involving parasitic elements. The restrictions relate the minimum group delay, size of the parasitic elements, and order of the matching network (number of elements of the system) with the level of the overall gain. This paper is limited to the case in which the load has a zero of transmission at infinity. The restrictions involve the Appell integral. In the case of unit gain at dc, this integral becomes the Riemann Zeta function. The restrictions are derived by assuming a Gaussian amplitude characteristic. The synthesis procedure is based on the fact that the Gaussian amplitudes are asymptotic forms of Bessel polynomials which were investigated by Thomson and Storch.

Starting from the definition of a determinant and using a few of its elementary properties, this paper gives an independent derivation of the optimum formula for the gain of a flow graph. Thus, a simpler path is shown to Coates' important result. This paper is self-contained, so that no previous knowledge of flow graphs is required. For motivation, the reader is referred to some well kmown papers and books.

In this paper a systematic procedure is proposed to obtain the n -port structure appropriate to the Y matrix of a resistive network containing exactly n + 1 nodes. The method presents: A set of necessary conditions which may eliminate quickly a large class of matrices from further consideration for realization; A simple procedure for the determination of a port structure in the case the Y matrix contains a few or no zero elements; A realization procedure which is particularly convenient in case the Y matrix contains a large number of zero elements. This procedure is also extended to the realization of Z matrices. It is shown that sometimes there exists more than one network with n + 1 nodes realizing a given matrix Y with different port structures. An evident application of the method presented in this paper is the realization of fundamental circuit matrices and fundamental cut-set matrices of oriented graphs.

A judicious combination of the most suitable of the mathematical techniques now available makes possible the development of a system of programs for analysing electrical circuits which is both more efficient and more accurate than has previously been possible. These improvements are particularly necessary in the field of analogue type circuits, the present requirements for which are not met by existing analysis programs. The first paper, 1 which was introductory, gave a preliminary survey of the whole material. The second paper 2 commenced the detailed description of the techniques of linear analysis. The present paper concludes this description and commences the description of techniques for nonlinear analysis.

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.

An experimental study carried out on a 12-ft x 12-ft hypar roof cable network model is described, and the results are compared with those obtained by using an approximate theoretical procedure for linear analysis of prestressed cable networks. A reasonably good correlation between the two sets of results is established, and on this basis it is recommended that, within the limitations specified, the theory can be used for preliminary design calculations. A considerable saving can thus be effected in the effort required in employing a nonlinear analysis procedure. It is also concluded that prestressed cable networks are not likely to exhibit a marked degree of nonlinearity when subjected to loads within the practical range. The details of the theory do not form part of this paper and can be found in existing literature (4,8) on the subject. However, the assumptions in the theory are reviewed. The paper gives the details of the experimental set-up. The procedure for prestressing the network, which may be found useful in the construction of cable roof networks is also described.

Most recent papers on sparse matrix methods in circuit analysis are written to describe large problem capability, but usually the illustrations given are for relatively small problems. In this paper a computer program for frequency domain analysis of large RLCM networks is described. It is regularly used on 3000-4000 node networks with many large sets of mutually coupled inductors. Timing and storage figures are given for a 3300 node problem. In the first part, the generation of the admittance description for networks with mutual inductors is described. Then the sparse matrix techniques are discussed. Some are standard, but the unique use of storage utilized in the construction of the LU factorization makes it possible to solve very large problems in a reasonable amount of core storage and time.

The application of the grid-controlled gasfilled, or "thyratron," electronic tube to relay practice, principally for the protection of transmission lines, is considered in this paper. Several different types of these relays are discussed under the 2 principal classifications of "normal" design and high speed relays. This paper by Doctor Wideroe, based upon European practice, should be of considerable interest in this country.

This paper considers the problem of global asymptotic stability of a system S of nonlinear networks I (i), j = 1, - ,n, interconnected by lossless transmission lines. Each 0(i) consists of a linear time-invariant lumped-parameter multiport network with a nonlinear element (resistor or capacitor) in parallel or (resistor or inductor) in series with each of its output ports. The voltage-current, voltage-charge, and current-flux linkage relationships for the nonlinear elements are assumed to lie in a sector. The transmission lines introduce time delays in the overall system as well as loading effects at the terminals of the networks. On the assumption that the linear system obtained by deleting (appropriately shorting or opening) the nonlinear elements is asymptotically stable by satisfying, for example, Brayton's conditions, this paper develops a frequency-domain condition that guarantees global asymptotic stability of the system S. This result is achieved by suitably modifying and extending the result of Popov and Halanay.

A general trend for the use of silicon controlled rectifiers (SCR) in television line-scanning generators leads, in principle, to new circuit configurations /1/, in which the deflection coils are driven during the retrace via a switching element. Instead of the SCR, transistors may be used as well, In the present paper, optimum working conditions of this circuit diagram are determined and equations derived enabling a simple engineering design of this generator. The wiring diagram mentioned in the paper has a high-voltage circuit part designed in an unique way.

In this paper certain magnetic amplifier circuits will be illustrated and their circuit equations presented subject to certain assumptions. The equations will be interpreted in as clear a manner as the author thinks possible and some conclusions will be drawn. Since the mathematics of analysis of magnetic amplifiers is quite complex as viewed from continuous theory a clearer period by period interpretation will be pursued during which periods the equations may be considered as a continuous, elementary and reasonably accurate representation of the phenomena. The two periods which will be used are those during which the amplifier output current is large (conducting period); and during which the amplifier output current is of the order of the magnetizing current (nonconducting period). Equivalent circuits for each period will be set up. The final conditions of one period will represent the initial conditions of the following period. The two assumptions utilized in this analysis are ``ideal'' magnetization curves for the core materials, Figure 1, and ``ideal'' rectifiers. The best core materials and rectifiers manufactured today rather closely approximate these assumed conditions. A resistive load impedance will be used for simplification of the mathematics. The conclusions drawn from these elementary considerations will form a basis for predicting the performance of examples of certain novel circuits which shall have properties of an unusual nature. Practical discussion of these circuits is beyond the scope of this paper and will be presented elsewhere.

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.

The development of new solid-state active elements, such as variable-capacitor diodes and tunnel diodes, has stimulated the network theorist to consider the negative resistor as an additional basic circuit element to be included in problems of linear network analysis and synthesis. In this paper it is first shown that if the negative resistor is added to the usual set of lumped passive building blocks, then it is possible to represent as a network any linear relation between n-port voltages and currents prescribed in terms of real, rational functions of a complex-frequency variable. This leads to the synthesis of some novel pathologic circuits which have neither immittance nor scattering representations, such as a one-port, which is simultaneously an open circuit and a short circuit (v=i=0, the "nullator"), and the linear network in which voltages and currents at the ports are completely arbitrary (the "norator," the unique, linear nonreciprocal, one-port). These elements are shown to be basic linear circuit building blocks. The second part of the paper considers the synthesis in the frequency domain of a real, rational n×n immitance matrix in which pole locations and pole multiplicities are completely arbitrary. It is shown that such a matrix can always be realized with lossless elements and at most n positive and n negative resistors.

This paper consists of two parts. The first part is tutorial and describes at an elementary level one of the contributions made by Darlington. This is the design theory of electrically symmetrical reactive (lossless) networks with particular attention to filters which exhibit Tchebycheff type performance in the pass and stop bands. The second part of the paper is the presentation, in "handbook" style, of step-by-step procedures to be followed in the design of filters of the above type. Emphasis is placed on the use of rapidly converging series in the computations in place of elliptic function tables.

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 deals with the lengths of codes for several simultaneous channels in a general formulation. The paper is almost self-contained, and requires for its reading no prior knowledge of information theory.

Brief reference is made to recent applications of topology in structural analysis. Kron’s methods, developed for the analysis of large networks, are examined and applied to various structures, including the Wilson-Maney bent. This paper is an extension of two previous papers which attempt to facilitate the formulation and solution of large structures using digital computers.

Although computer-aided circuit analysis has advanced quite rapidly in the last few years, there is considerable room for applications of network theory to the computer-aided design of electronic networks. In this paper the scope of network theory is generalized to include multiterminal networks in which the voltages and currents are related by inequality as well as equality relations. Two classes of new singular elements useful in electronic network design are introduced. The first class generalizes the allowed v-i pairs of a nullator and its multiterminal counterparts. The second constrains the allowed pairs of the norator and its multiterminal counterparts. The new singular elements are used to constrain network variables and to represent bounded adjustable elements. In this way the role of the objectives and element constraints are handled in a unified scheme. By imbedding these elements in a network, the synthesis problem is transformed into a problem of analysis of a circuit containing singular elements. Although the method is applicable to a wide variety of circuits, only the dc linear case is treated here. By keeping a linear formulation throughout, the analysis can be done with linear programming techniques with the corresponding theoretical and computational advantages. On-line programs for interactive time-share use have been written, and their flow charts are given in the paper. They provide a very efficient on-line design system that avoids the iterative analysis optimization approach. The gains achieved in computation time are of several orders of magnitude, and the solutions are guaranteed to be found.

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.

Electrical and thermal interactions in silicon integrated circuits provide a means for realizing large effective time constants and, correspondingly, low cutoff frequencies in filters. This paper describes a method of analyzing the behavior of a general configuration of lumped or distributed heaters and sensors in an integrated circuit. The method yields results that are amenable to computer evaluation, and that also indicate how heaters and sensors should be shaped to obtain a particular type of response. A practical synthesis procedure is given for filter applications, and experimental results are presented that show close agreement with calculated values for examples of both analysis and synthesis of filters.

The need to determine the sum of all tree admittance products occurs in almost all applications of topological network theory. This paper describes a method of obtaining this sum through an iterative factorization of the sum of tree admittance products of successively more complex subnetworks. Computational efficiency is achieved in that: (1) it is not necessary to test sets of branches for the presence of circuits; and (2) it is not necessary to calculate each tree admittance product.A digital computer program has been developed for use on an IBM-704 which accommodates any network with complex branch admittances and up to 14 nodes. Far more complex networks may be analyzed, however, if they are first decomposed into two-terminal subnetworks. A detailed description and flow chart of the program are included.

Design automation techniques have been successfully used in wiring board layouts, circuit design analysis, and other areas. Simulation techniques have been used by system analysts to evaluate complex computer systems. In the early stages of a computer system design a designer will find an interactive package, which gives him real-time solutions for queueing models of complex computer systems, extremely useful. In the first few passes at a design, detailed simulation studies are too expensive and too slow. A conversational package which evaluates arbitrary configurations and gives approximate results is preferable to a slow, expensive, though accurate simulation. This paper is concerned with the real-time analysis of complex queueing network models which have been extensively used in computer systems analysis. In this paper we present the theory, algorithms and some programs for a system which departs radically from previous attempts at computer design aids for queueing network analysis in two ways: firstly the design automation system proposed here will give both algebraic and numerical answers to queries put forward by the analyst. For instance, the analyst may want to find out an algebraic expression for the throughput of a network as a function of several parameters. Or the analyst may want the output in the form of a graph of throughput as a function of a parameter. The system discussed in this paper will satisfy both types of requests. Secondly, the system allows the analyst to evaluate arbitrary networks constructed from a set of specified “building blocks.” The “building blocks” are quite general—they include queues with devices (servers), branches, joins, and so on. The analyst is allowed to use as many building blocks as he pleases, and he can interconnect these building blocks in any pattern he chooses. Thus the system is moderately flexible and allows the analyst greater freedom in choosing the models best suited for his system.

Summary form only given. This paper is a report of an investigation which included measurements of relevant 2NG8 PNP-power-transistor parameters and the developmetlt of a method for the design of high-power switrhing circuits with good trigger sensitivity and dc stability over wide temperature ranges. These design techniques can similarly be used for NPN power transistors. The relevant parameters of the simplified dc equivalent circuit are found. The methods and results of the measurements of these parameters are presented, including their variation with temperature and current. This data enables the designer to design a flip-flop circuit for a particular bias condition with temperature considerations as follows. When the ambient temperature is raised, excessive thermal collector current will cause the emitter junction of the OFF transistor to inject carriers. This is a cumulative effect resulting in the OFF transistor turning ON. A means of compensating for this instability is to use a suitable base bias to keep the OFF emitter from injecting carriers. On the other hand, excessive compensating.bias results in a circuit that will not have a stable ON state.

The purpose of this paper is to describe an application program written by the International Business Machines Corporation to couple the existing Electronic Circuit Analysis Program(1) with the IBM 2250 cathode ray tube display scope. The program which, in this paper, will be referred to as 2250 ECAP is a Type III program available from IBM(2). 2250 ECAP has been in use at Beckman Instruments, Inc., Fullerton, California, for approximately four months. This paper will detail some of the experiences available from the use of this program, some of the pitfalls of its use, as well as human factor education relative to the displayed image generated throughout the application.

In integrated-circuit resistors current never flows unidirectionally. Indeed, for many integrated-circuit resistors three spatial coordinates are needed to specify the flow lines at any point within the resistor. This occurs because electrical contacts are made on the top face rather than on the ends of the resistor and because often the contacts do not extend all the way to the bounding surfaces of the resistor. This paper describes a method for determining the resistance of integrated-circuit resistors that accounts for the three-dimensionality of the current flow. The method involves solving the three-dimensional boundary value problem for the electroslatic potential. From the gradient of the potential one then finds the current that flows for a given voltage applied between the terminals. The work in this paper contrasts sharply with previous treatments of integrated-circuit resistors, none of which has accounted for three-dimensional flow.

This paper reviews the state of the art of methods and techniques suitable for use in the automatic optimization of microwave circuits by digital computer. A number of significant recent developments in the rapidly developing area of computer-oriented circuit theory and design which may be directly applied to high frequency or distributed circuits are emphasized. A fairly extensive classified bibliography on optimization methods and on some applications, primarily in the microwave area, is included. The principal aim of this paper is to bring the microwave circuit designer up to date with developments in computer-oriented optimization methods and techniques and their application to microwave circuit design. To achieve this, the state of the art is reviewed in a tutorial manner, highlighting the talk with material taken from a variety of recent research papers, published during the last year or so. Promising areas for future work are indicated. A fairly extensive classified bibliography on optimization methods and on some applications, primarily in the microwave area, concludes the paper. Papers and books not necessarily in the microwave area are referenced if it is felt that the subject matter is, nevertheless, relevant. The first question that a microwave circuit designer might have is what material should he read to convince himself that he can solve a wide variety of design problems using optimization techniques. Five articles [1]-[5] are referenced under the heading of Reviews of Network Optimization which should probably be found most useful.

THE CURRENT ADVANCES in automation have done little to relieve the extensive manual analysis required for the synthesis of specific systems from off-the-shelf items. This paper represents a brief progress report on a study to develop manual and automatic aids for this task. In the space available, it is possible only to outline the basic concepts of Procedure Network Analysis. Details will be left for further publication. Hardware designers have long found logic network analysis a useful technique. The Procedure Network is a more general interpretation of this technique. The basic hypothesis of this study is that Procedure Network Analysis can serve as a useful tool in the synthesis and evaluation of system designs. Furthermore, this analysis can also fill several vital monitoring roles for operational systems. Two examples are: The diagnosis of failures, and the selection of alternatives in the face of a failure. These techniques are not restricted to hardware systems. They may be applied to any discipline which involves the selection and organization of logically related elements. Computer programs are an example close to the interests of the ACM. In the current context, a program is a system synthesized from a set of routines or procedures.

In a previous paper this writer postulated an ideal topological transmission element (unitor) and has shown in subsequent papers its conceptual value over the entire field of nonreciprocal network analysis and synthesis. Later writers have employed the nullor, which, in its threeterminal form, is externally equivalent to the unitor. Now that wide-band linear differential-input operational amplifier units are readily available in compact solid-state form, It has become practicable to obtain convenient and useful realizations of the unitor (or nullor). In this paper we give the basic circuit technique.

In the first paper of this issue, the attention of our membership is directed to some remarkable results published by H. Takahasi in 1951. It appears that unbeknownst to most of us, Takahasi gave at that time a complete and unified solution of a family of filter problems for which piecemeal results have been sprinkled through the literature for the last third of a century. The objective of this species of problem was to obtain closed-form solutions for design of wave filters with resistive terminations. Two general approaches emerged which may be descriptively designated as the "maximally flat" and "equal ripple" cases. These terms apply to the way constant loss was approximated in the pass band. The reader may further observe that the second and third articles in this issue also deal with contributions from Japan. This does not signify that a special issue has been attempted, but rather that this order for the regularly accepted papers has been chosen as a reminder of the steady flow of high level contributions from Japanese authors which has continued since the beginning of our journal.

The paper employs a ladder-network method for calculating the voltages and currents at the lamp junctions in a major road-lighting scheme. The lighting circuit is dealt with in unit lengths of one mile, and, (partly to demonstrate the method), use is made of a step-up transformer at the supply point with simple chokes at the lamp positions. Only by the use of circuit theory can the minimal size of cable become known, and the paper suggests that an increase in the supply voltage might further assist in reducing the size and cost of the cable, at the same time giving the lamp designer greater scope in the development of more efficient lamps. Planning the lighting scheme in unit lengths would necessarily introduce a measure of standardisation, with resulting economy. Further economies might be made possible by the use of low-cost conductors in road-lighting circuits, and by the use of cheaper joints and looping techniques which such conductors could bring in their train. Consequent upon the enforced use of crash barriers, a simple procedure for laying cables on the centre reservation of motorways is put forward in the paper.