Circuit Theory, IRE Transactions on
This title ceased production in 1962. The current updated titles are IEEE Transactions on Circuits and Systems I: Regular Papers and IEEE Transactions on Circuits and Systems II: Express Briefs.
Latest Published Articles

Application of complex symbolism to linear variable networks
Apr19 2013 
Effect of rectifier capacitances on the conversion loss of ring modulators
Apr19 2013 
A practical method of designing RC active filters
Apr19 2013 
Analysis of timedependent linear networks
Apr19 2013 
Resistancecapacitance filter networks with singlecomponent frequencycontrol
Apr19 2013
Popular Articles

Stability and PowerGain Invariants of Linear Twoports
Jan06 2003 
The Scattering Matrix in Network Theory
Jan06 2003 
A practical method of designing RC active filters
Apr19 2013 
MaximallyFlat Time Delay Ladders
Jan06 2003 
NegativeImpedance Converters
Jan06 2003
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Popular Articles (November 2014)
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1. Stability and PowerGain Invariants of Linear Twoports
Page(s): 29  32It is shown that the stability of a linear twoport is invariant under arbitrary lossless terminations, under interchange of input and output, and under "immittance substitution," a transformation group involving the arbitrary interchanging of impedance and admittance formulations at both ports. The quantity
k = frac {2 Re (gamma_{11}) Re (gamma_{22})  Re(gamma_{12} gamma_{21})} {gamme_{12} gamma_{21}} (where thegamma may be any of the conventional immittancez, y, or hybridh, g matrix parameters) is the simplest invariant under these transformations, and describes uniquely the degree of stability, providedRe(gamma_{11}), Re(gamma_{22}) geq 0; the largerk is, the greater the stability, and in particulark = 1 defines the boundary between unconditional and conditional stability. The quantityk is thus the basic invariant stability factor. Its definition is also extended to include the effect of terminating immittances, which may be padding resistances or source and load immittances, or both. Certain powergain functions, including the maximum available power gain, are shown to be invariant under immittance substitution, andk is identified as a function of ratios between them, where they exist. This provides a fundamental way of determining k, apart from calculating it from matrix parameters, and indicates that it is a measure of an inherent physical property. View full abstract» 
2. The Scattering Matrix in Network Theory
Page(s): 88  97This paper gives an introductory treatment of the concept and uses of scattering methods in network problems. The scattering parameter description for linear networks is defined and the utility of this formalism for problems involving power flow in terminated networks is discussed. Examples of scattering computations for transformer 4ports, transformerless impedance matching networks and transducers with parasitic capacitance are given. The physical realizability requirements for linear lumped networks in the frequency domain are presented in scattering terms, and some extensions to the realizability of distributed networks are briefly discussed. View full abstract»

3. A practical method of designing RC active filters
Page(s): 74  85IN THE FREQUENCY range below about 30 cps, the dissipation factors of available inductors are generally too large to permit the practical design of inductancecapacitance (LC) or resistanceinductancecapacitance (RLC) filter networks. The circuits described in the following pages were developed and collected to provide an alternative method of realizing sharp cutoff filters at very low frequencies. In many cases the active elements can be simple cathodefollower circuits that have stable gain, low output impedance and a large dynamic range. View full abstract»

4. MaximallyFlat Time Delay Ladders
Page(s): 214  218The drivingpoint impedance for a maximallyflat time delay response is derived. The impedance is synthesized as an infinite lowpass LC ladder that starts with an
epsilon G/omega_0 farad shunt capacitor The ladder elements rapidly taper toward a capacitance of2G/omega_0 farads and an inductance of2R/omega_0 henries. The impulse and step responses of the impedance are derived as a series of Bessel functions. A threeterminal maximallyflat time delay transfer impedance is also considered. The conditions for a smoothlytapering ladder structure are given. The transfer impedance is synthesized as an infinite lowpass LC ladder whose first two shunt capacitors are32G/(9omega_0) andepsilon^{3}G/(9omega_0) farads, respectively. The impulse and step responses of the transfer impedance are also derived. View full abstract» 
5. NegativeImpedance Converters
Page(s): 124  131The conditions under which an active device exhibits an input impedance at one terminal pair which is exactly the negative of the load impedance connected to the other terminal pair are discussed. There are an infinite number of ways by which such a device, which is called a negativeimpedance converter (NIC), can be made. One of the limits of this set is represented by a transistor circuit which was discussed previously by Linvill; the other limit, by a new circuit introduced recently. Practical negativeimpedance converters are not exact; however, they may be made so by the addition of a pair of compensating impedances. The parameters of the NIC which most affect circuit performance are indicated as a guide to NIC design. Two typical transistor NIC circuits are compared on this basis. Experimental results are given. View full abstract»

6. On Nonuniform Sampling of BandwidthLimited Signals
Page(s): 251  257The purpose of this investigation is to examine four special nonuniform sampling processes in detail, and to deduce some interesting properties of bandwidthlimited signals. The main results are contained in four generalized sampling theorems. These theorems not only contain the nature of determination (uniquespecification, overspecification, and underspecification) of signals but also include explicit reconstruction formulas. From the reconstruction formulas, the complexity and accuracy of the nonuniform sampling processes discussed can be estimated. In addition, these theorems lead to observations regarding the allowable shapes, the "prediction," and the "energy" of bandwidthlimited signals in general. A "minimumenergy" signal is introduced which has certain advantages as compared to the ordinary "timelimited" signals when a finite number of sample values are given. Finally, a statement due to Cauchy on the sampling of bandwidthlimited signals is generalized to include a wider class of nonuniform sample point distributions and modified to give more exact information regarding the nature of determination of signals. View full abstract»

7. On the Design of Filters by Synthesis
Page(s): 284  327Following an introduction to the methods and significance of filter design, this paper deals with definitions and filter synthesis according to prescribed attenuation requirements. It shows how the characteristic function for cases of practical importance can be calculated, particularly for the special cases 1) where this function is a power term in the frequency variable (maximally flat), 2) where it is a Tchebycheff polynomial function, and 3) where the effective attenuation in both the pass band and the stop band is of Tchebycheff character, and, also for 4) the general case of Tchebycheff behavior in the pass band with prescribed attenuation poles. The way, and the separate steps, of the determination of the circuitelement values for the realization of reactance laddernetwork filters without mutual inductances are indicated, and the various necessary computation formulas are described. For the first two special cases mentioned above, computation formulas applicable in general are given. New formulas are presented for the transformation of a lowpass into a bandpass configuration with a minimum number of inductances, and into a bandpass with the stray capacitance being taken into consideration. These are illustrated by several numerical examples. Next, the paper deals with the design of filters, taking into consideration additional requirements involving the group delay. Possibilities of solving the problem are described. An actual example, together with the measured results, illustrates the excellent agreement between the theoretical determination and the behavior of the filter constructed accordingly. The Appendix contains a selected section of a table which gives the normalized values of circuit elements for lowpass filters with the effective attenuation in the pass band and the stop band behaving in the Tchebycheff sense, for the degrees
n = 6, 7, 8, 9, 10 , and11 . Graphs are also appended for easy estimation of the degree needed for a filter design and, thereby, the complexity of the resulting structure. View full abstract» 
8. Exact Design of Transistor RC BandPass Filters with Prescribed Active Parameter Insensitivity
Page(s): 313  320The design of lowfrequency bandpass filters by means of RC rejection networks in the feedback path of active elements has long been known. The advent of the transistor has renewed interest in this field and has necessitated a more exact synthesis procedure. The reason for this is that in the classical design, the active element is assumed to be an ideal voltage amplifier with infinite input impedance, zero output impedance, and zero reverse transmission. The transistor satisfies the dual ideal assumptions to a considerably lesser degree than the vacuum tube. The sensitivity of the transistor parameters to temperature also requires that more attention be paid to the effect of parameter variations on the filter response. This paper extends the classical theory in several directions. 1) A synthesis procedure is developed in which the finite input and output impedances and reverse transmission are taken into account. 2) The freedom that exists in the synthesis procedure is used to obtain a design with a least active element. Graphs are presented which provide the values of four of the six required network elements. Two simple equations must be solved for the other two. 3) Expressions are developed for the sensitivity of the filter bandwidth and center frequency to the four lowfrequency active parameters. It is presumed that the design specifications include a statement of the extent of active parameter variation and of the tolerances on the filter response. The procedure for satisfying such specifications is an integral part of the design procedure. An example which includes all of the above features is worked out in detail. View full abstract»

9. Some Extensions of Liapunov's Second Method
Page(s): 520  527>In the study of the stability of a system, it is never completely satisfactory to know only that an equilibrium state is asymptotically stable. As a practical matter, it is necessary to have some idea of the size of the perturbations the system can undergo and still return to the equilibrium state. It is never possible to do this by examining only the linear approximation. The effect of the nonlinearities must be taken into account. Liapunov's second method provides a means of doing this. Mathematical theorems underlying methods for determining the region of asymptotic stability are given, and the methods are illustrated by a number of examples. View full abstract»

10. Recent Developments in Filter Theory
Page(s): 236  252This paper is a review of the most important developments in filter theory during the postwar years. The 57 items contained in the bibliography appended to this paper have been selected either for their intrinsic novelty or because they contain reviews of earlier work with historical references. The integration of the various contributions has been attempted in this paper and several original ideas and results are included. No attempt has been made to comment on the practical value of insertion loss design vs image parameter design. As appears from the review, recent extensions of both methods have brought them closer to each other, and their cross fertilization has contributed to progress towards a unified filter theory. View full abstract»

11. Theoretical Limitations on the BroadBand Matching of Arbitrary Impedances
Page(s): 165First Page of the ArticleView full abstract» 
12. Survey of Some Properties of Linear Networks
Page(s): 70  78An attempt is made to give a brief exposé of some modern works on linear network properties. The concepts treated are the following: passivity, stability, efficiency, and nonreciprocity;
n terminalpair networks and twoterminalpair networks in particular are studied at a fixed frequency. View full abstract» 
13. Kirchhoff's 'Third and Fourth Laws'
Page(s): 8  30The epochmarking publication of Kirchhoff in 1847 is considered in this paper. The rule given by Kirchhoff deserves to be understood by almost all engineers, for it shows how to determine in a simple and straightforward way the system functions of any passive network that contains no transformers. Preliminary to the consideration of the rule and its dual, the basic concepts of combinatorial topology are summarized in the present paper. The rules are then stated in the detail necessary to show that their application can be carried out in a routine and mechanical manner. Application of the rules to problems in analysis and synthesis is illustrated in a number of examples. Included among these examples are the derivation of the necessary and sufficient conditions on RLC networks that have been previously given by Fialkow and Gerst, the analysis of an infinite graph, and the determination of the elements of the chain matrix (or the opencircuit impedance or shortcircuit admittance matrix) by essentially a single calculation. Finally, the Feussner method for simplifying the use of the rules is discussed. View full abstract»

14. Synthesis of a Class of StripLine Filters
Page(s): 104  109This paper describes a design theory for a class of stripline filters on an insertion loss basis. The important part of the paper is the equivalent transformations showing the close correspondence between lumped and coupledline distributed parameter circuits. An introduction is provided for clarification. Line type, lowpass ladder, highpass ladder, and bandpass ladder type filters are realized in coupled striplines. Their physical configurations are depicted. Finally a development is given of characteristicimmittance formulas. View full abstract»

15. A Study of Rough Amplitude Quantization by Means of Nyquist Sampling Theory
Page(s): 266  276Quantization is an operation that takes place when a physical quantity is represented numerically. It is the assignment of an integral value to a physical quantity corresponding to the nearest number of units contained in it. Quantization is like "samplinginamplitude," which should be distinguished from the usual "samplingintime." The probability density distribution of the signal is sampled in this case, rather than the signal itself. Quantized signals take on only discrete levels and have probability densities consisting of uniformlyspaced impulses. If the quantization is fine enough so that a Nyquistsampling restriction upon the probability density is satisfied, statistics are recoverable from the grouped statistics in a way similar to the recovery of a signal from its samples. When statistics are recoverable, the nature of quantization "noise" is understood. As a matter of fact, it is known to be uniformly distributed between plus and minus half a unit, and it is entirely random (first order) even though the signal may be of a higherorder process, provided that a multidimensional Nyquist restriction on the highorder distribution density is satisfied. This simple picture of quantization noise permits an understanding of roundoff error and its propagation in numerical solution, and of the effects of analogtodigital conversion in closedloop control systems. Application is possible when the grain size is almost two standard deviations. Here the dynamic range of a variable covers about three quantization boxes. View full abstract»

16. Negative Impedance CircuitsSome Basic Relations and Limitations
Page(s): 132  139Much of the current interest in negative impedance circuits is directed toward potential applications as components of transmission networksfilters, equalizers, and similar structures. To permit maximum flexibility in the analysis and design of such structures, a complete specification of the characteristics of the negative impedance circuit is required. Four parameters are required for such a specification. The present discussion in terms of the ABCD matrix is particularly useful when a tandem connection of negative impedance circuits and passive networks is to be investigated. The behavior of a practical circuit can be represented as the sum of a matrix stating the ideal behavior and an error matrix. In the cases studied, the elements of the error matrix are inversely proportional to the gain of the amplifier used. Stability of an overall circuit and sensitivity to component variations are expressed in terms of the elements of the scattering matrix. View full abstract»

17. Design Principles for Single Loop Transistor Feedback Amplifiers
Page(s): 145  156The design of single loop transistor feedback amplifiers is considered. A criterion of stability is introduced which is useful for either calculating or measuring the stability margins of transistor amplifiers, and in particular, single loop feedback amplifiers. Expressions are derived for relating sensitivity and impedance to feedback. Practical design techniques are discussed and are illustrated by the design of a onemegacycle carrierfrequency feedback amplifier. It is shown that a transistor feedback amplifier is an excellent wideband video amplifier. View full abstract»

18. On the Brune Process for nPorts
Page(s): 280  296The Brune process for
n ports, established by Oono, McMillan, and Tellegen, is derived by an alternative method based on successive series and shunt extractions of passiven ports containing fictitious complex resistances, which are finally eliminated by a simple equivalence transformation. The method is also applied to nonreciprocaln ports, thus establishing that such ann port of degreem is realizable with not more thanm reactive elements. For reciprocaln ports, the new derivation of Brune's process clarifies the physical structure of the reactive2n port generalizing Brune's section and yields explicit formulas for its element values. View full abstract» 
19. Synthesis of TransmissionLine Networks and the Design of UHF Filters
Page(s): 325  336Recently, Richards proved the remarkable fact that the synthesis of networks consisting of resistors and lossless transmissionlines with finite electrical length may be treated exactly the same way as in the case of conventional linear passive networks. This paper offers a new synthesis of this kind without mutual induction and its application to the design of uhf filters having Tchebyscheff characteristics in both pass and attenuation bands. The synthesis problem treated here is, in other words, the analog of the socalled Darlington problem in conventional lumped constant networks. Approximation procedures for filter characteristics are based on the wellknown potential analogy. View full abstract»

20. FlowGraph Solutions of Linear Algebraic Equations
Page(s): 170  187A weighted, oriented topological structure, denoted by
G and called a flow graph, is associated with a set ofm equations inn variables, denoted byKX = 0 , such thatK is a connection matrix andX a vertex weight matrix of the associated graph. This same set of equations can be written asA_{v:}^{} C(A+)'X = 0 whereA_{}^{v:} andA^{+} are negative and positive incidence matrices and whereC andX are respectively branch and vertex weight matrices of the graph. By familiar algebraic procedures, an expression for the weightx_p , of a nonreference vertex ofG is obtained as a linear combination of the weights of the reference vertices (vertices with zero negative order) and can be written asx_p = Sigma_{j=1}^{s} zeta p{dot}r_{j}x_{r_j} . To these algebraic results there correspond topological expressions in terms of subgraphs ofG for the coefficients,zeta P{dot}r_j . A similar correspondence is obtained between the topological operation of deleting a vertex from the flow graph and the algebraic operation of eliminating a variable from the set of equations. These results are derived from the algebraic equations written in terms of the incidence and weight matrices of the graph. They are similar to those given for the familiar SignalFlowGraph, although they are more convient to use, since the topological properties of the flow graph depend only upon the algebraic properties of the set of equations. A flow graph can be drawn directly from an electric network diagram, and the flowgraph properties, used to obtain a solution of the network equations. Examples of this for two types of feedback networks are shown. View full abstract» 
21. Subharmonic Oscillations of Order One Half
Page(s): 102  111This paper deals with subharmonic oscillations of order one half, i.e., oscillations whose fundamental frequency is one half that of the applied force. The steadystate solutions are first sought for various combinations of the system parameters, and their stability is investigated. The transient state of the oscillations is then discussed by the phaseplane method. It is a distinctive feature of nonlinear systems that various types of steadystate response may take place even in the same system depending on different values of the initial conditions. Particular attention is, therefore, directed toward obtaining the relationship between the initial conditions and the resulting subharmonic responses. Several patterns of initial conditions leading to subharmonic responses are shown on the phase plane. The theoretical results are compared with the solutions obtained by analogcomputer analysis and found to be in satisfactory agreement with them. View full abstract»

22. A New Design Approach for Feedback Amplifiers
Page(s): 274  284A new design procedure is presented which is based on the rootlocus technique. The realization of the following is possible: a) desired closedloop response bandwidth (or rise time) and gain level (or amount of desensitivity); b) desired response shapes such as flat magnitude or flat delay; and c) desensitivity of both lowfrequency and bandedge responses. The key feature of the rootlocus technique is the proper use and location of phantom zeros (transmission zeros of the feedback path). To illustrate the technique, a shuntshunt feedback configuration is used together with the realization of flatmagnitudetype closedloop responses. The basic amplifier is a threestage
ce transistor cascade. Typical design examples with experimental results are included. View full abstract» 
23. LadderNetwork Analysis Using Fibonacci Numbers
Page(s): 321  322First Page of the ArticleView full abstract» 
24. Definitions of 'Bandwidth' and 'Time Duration' of Signals Which Are Connected by an Identity
Page(s): 286  288In this paper we give definitions of "equivalent time duration"
Deltatau and "equivalent bandwidth"Delta f and show that they are connected by a simple reciprocal identity. An example is given and it is shown that the same concepts can be applied in antenna theory to give useful definitions of "equivalent aperture distribution width" and "equivalent angular spectrum." View full abstract» 
25. Stability of feedback systems using dual Nyquist diagram
Page(s): 35  44This paper introduces a procedure for determing the stability of a feedback system using a dual Nyquist diagram. Such a diagram results when the characteristic equation of the system is interpreted to be the sum of two frequencydependent functions F1(p) + F2(p) instead of the normal expression 1 + G(p)H(p). This diagram then consists of two polar plots; one plot represents the locus of one of the functions which is contained in the characteristic equation, and the other plot is the negative locus of the other function contained in the characteristic equation. Each of these curves may, if desired, be considered as an individual Nyquist diagram. View full abstract»

26. The EmitterCoupled Differential Amplifier
Page(s): 51  53The transistor emittercoupled differential amplifier is analogous to the cathodecoupled differential amplifier and gives promise of excellent utility in transistorized circuitry. Expressions are given for 1) the circuit voltage gain, current gain, and input impedance, 2) the commonmode rejection when the circuit is used as a differencing amplifier, and 3) the signal unbalance when the circuit is employed as a singleendedtopushpull amplifier or phase inverter. When the circuit is used as a dc amplifier, drift generated by variations in the temperaturesensitive parameters cancels to a satisfactory degree. View full abstract»

27. Converse of the StarMesh Transformation
Page(s): 491  493First Page of the ArticleView full abstract» 
28. Realizability Conditions on nPort Networks
Page(s): 217  221It is well known that the positive real
(pr) concept is one of the most important in network theory. Its importance derives from the following two facts: 1) A necessary and sufficient condition for a real rational function to be realizable as the drivingpoint impedance of a oneport network is that it be apr function. 2) A necessary and sufficient condition for a symmetric nthorder matrix of real rational functions to be realizable as the opencircuit impedance matrix of ann port network is that it be apr matrix. Sets of necessary and sufficient conditions equivalent to the definition of apr function and a pr matrix have been presented in the literature, In this paper new sets of necessary and sufficient conditions are formulated for a rational function and a matrix of rational functions to bepr . These conditions give insights that may be useful in research on unsolved synthesis problems; some of these problems are now being studied by the authors. When used for testing purposes none of the new conditions requires root solving, and thus in many cases much of the tedium of previous tests is eliminated. View full abstract» 
29. On the Stability of TimeVarying Linear Systems
Page(s): 420  422First Page of the ArticleView full abstract» 
30. Bounded Real Scattering Matrices and the Foundations of Linear Passive Network Theory
Page(s): 102  124In this paper the most general linear, passive, timeinvariant
n port (e.g., networks which may be both distributed and nonreciprocal) is studied from an axiomatic point of view, and a completely rigorous theory is constructed by the systematic use of theorems of Bochner and Wiener. Ann portPhi is defined to be an operator inH_n , the space of alln vectors whose components are measurable functions of a real variablet, ( infty < t < infty) (and as such need not be singlevalued). Under very weak conditions on the domain ofPhi , it is shown that linearity and passivity imply causality. In every case,Phi_a , then port corresponding tophi augmented byn series resistors is always causal (Phi is the "augmented network," Fig. 2). Under the further assumptions that the domain ofPhi_a is dense in Hilbert space andphi is timeinvariant, it is proved thatPhi possesses a frequency response and defines ann times n matrixS(z) (the scattering matrix) of a complex variablez = omega + ibeta with the following properties: 1)S(z) is analytic in Imz > 0 ; 2)Q(z) = I_n  S^{ast}(z)S(z) is the matrix of a nonnegative quadratic form for allz in the strict upper halfplane and almost allomega . Conversely, it is also established that any such matrix represents the scattering description of a linear, passive, timeinvariantn portPhi such that the domain ofPhi_a contains all of Hilbert space. Such matrices are termed "bounded real scattering matrices" and are a generalization of the familiar positivereal immittance matrices. WhenPhi andPhi^{1} are singlevalued, it is possible to define two auxiliary positivereal matricesY(z) andZ(z) , the admittance and impedance matrices ofPhi , respectively, which either exist for allz in Imz > 0 and almost allomega or nowhere. The necessary and sufficient conditions for anm>n times n matrix A_{n}(z) to r epresent either the scattering or immittance description of a linear, passive, timeinvariantn portPhi are derived in terms of the real frequency behavior ofA_{n}(omega) . Necessary and sufficient conditions forPhi_a to admit the representationi(t) = int_{infty}^{infty} dW_{n}(tau)e(t  {tau}) for all integrablee(t) in its domain are given in terms ofS(z) . The last section concludes with a discussion concerning the nature of the singularities ofS(z) and the possible extension of the theory to active networks. View full abstract» 
31. A Note on the Admittance and Impedance Matrices of an nTerminal Network
Page(s): 70  75First Page of the ArticleView full abstract» 
32. Solving SteadyState Nonlinear Networks of 'Monotone' Elements
Page(s): 99  104This paper treats the problem of finding the steadystate currents and voltage drops in an electrical network of twoterminal elements, each of which has the property that its currentvsvoltagedrop graph, or "characteristic," is a curve going upward and to the right. (Thus, "tunnel diodes" are excluded, but nonlinear resistances, current and voltage sources, rectifiers, etc. are permitted.) The construction methods are specifically designed for digital computation techniques (either automatic or manual). The principal tools are: 1) the application of theorems from graph theory ("networktopology"), and 2) quantization of the variables (permitting them to take on only a discrete set of values). View full abstract»

33. Directions of Mathematical Research in Nonlinear Circuit Theory
Page(s): 542  553In this paper we wish to present a potpourri of problems of some interest and difficulty arising in the field of nonlinear circuit theory. Perhaps the only sensible way to catalogue scientific problems is in terms of "solved or unsolved." Yet this classification is itself a very subjective one, dependent upon the times and the fashions. Recall the dictum of Poincaré that the solutions of one generation are the problems of the next. In this paper, we have attempted, for the sake of convenience, to group categories of problems under the headings of "descriptive," "control," "stochastic," and so forth. Convenient as some of this nomenclature is, it should be regarded with a certain amount of suspicion. Most significant problems blithely cut across these artificial boundaries within fields of specialization, and within science itself. In these days of rapidly and dramatically changing technology it would be rather brash to attempt to predict the type of mathematics that will be most urgently required even ten years from now. It is, however, fairly safe to look about and note the requirements of the present and of five years back. The difficulties that abound render a certain time lag inevitable, and it may well be that new scientific developments may render fields obsolete and mathematical solutions for problems within those fields unnecessary before they are even obtained. View full abstract»

34. Topics in the Design of Insertion Loss Filters
Page(s): 337  346This paper combines the theory of scattering matrices and the design of filters on an insertion loss basis. It is not intended to add substantially new results. Its purposes are to simplify the presentation of the insertionloss theory, with the help of the scattering parameters, and to study a number of particular cases serving as a guide in practical design and as a starting point of approximate formulas for numerical work. The particular cases and approximate formulas give the designer an appreciation of the influence of various parameters, before the design is crystallized and the accurate computations are begun. The first part of the paper develops properties of general reactance networks, terminated in resistances, and of the special class of such networks which are either "symmetric" or "antimetric." Then the general theory is applied to the design of filters with Tchebycheff behavior in the pass band. View full abstract»

35. Polynomial Decomposition in Active Network Synthesis
Page(s): 270  274This paper deals with the use of polynomial decomposition as a basis for the synthesis of active RC networks. The first part briefly reviews the formation and important properties of the Horowitz decomposition. Next, the relationships between the decompositions of two polynomials are presented in the form of three basic theorems. Significant in the development of these theorems is the use made of the theory of positive real functions. The active network function is treated as the even or the odd part of a positive real impedance, and hence the wealth of information available on positive real functions is brought to bear on the problem of active synthesis. The tie between active and passive synthesis is then illustrated by means of a method of active driving point synthesis, which closely parallels the synthesis of lossless terminated passive networks. View full abstract»

36. Synthesis of Active RC Networks
Page(s): 260  269Synthesis procedures are presented which establish that one grounded 3terminal negativeimpedance converter, embedded in an unbalanced grounded RC structure, is sufficient to realize 1) any drivingpoint function, 2) any two of the four shortcircuit admittance parameters of a twoport network, and 3) certain sets of
n shortcircuit admittance parameters of an(n + 1) terminal network, where each of the parameters is specified as the ratio of any two polynominals in the complexfrequency variable, with real coefficients. Furthermore, the required RC networks can always be made to take the form of grounded laddertype structures, some of which, in particular cases, reduce to twoterminal admittances. View full abstract» 
37. An Extension of Wiener Filter Theory to Partly Sampled Systems
Page(s): 362  370The growing use of digital computers as components of control systems has given great importance to the study of linear systems which are partly sampled and partly continuous. This paper treats the problem of optimizing the simplest possible mixed system consisting of an input filter with transfer function
K(s) , a sampler with sampling intervalT , and an output filter with transfer functionL(s) . Given the power spectra of the input signal and the noise, the object is to find a realizableK andL which in combination minimize the mean square difference between the outputh anda "desired output"h_d .h_d is defined by a "desired transfer function"{G_d}(s) , not necessarily realizable, which would produceh_d from the input signal if the noise were absent.KL will in general contain factors periodic ins with period2 pi j/T , and such factors may be moved to either side of the sampler without changing the final output, thus introducing a considerable arbitrariness inK andL . However, since these periodic factors represent linear operations on discrete data (such as might be performed inside a digital computer), it is appropriate to separate them out. There are then three functions to be determined: the nonperiodic part ofK , the nonperiodic part ofL , and the remaining (periodic) factor ofKL . Methods for determining these three functions are given. The interesting theoretical point is that the determination is not always unique. In general, there will be a finite number of distinct but equivalent solutions. View full abstract» 
38. Unit Real Functions in Transmission Line Circuit Theory
Page(s): 247  250A new class of functions is introduced which has a direct physical significance in transmission line theory. These are called "unit real" (u. r.) and are derivable by bilinear transformations from positive real (p. r.) functions. The complex reflection coefficient is a unit real function of the "line vector"
exp(2jtheta) , wheretheta is the electrical length of a section of line in a resistortransmission line circuit. Just as in lumped constant circuit theory the impedance is a p.r. function of the complex frequency. U.r. and p.r. functions are compared. A new proof and a discussion of Richards' theorem are also presented. View full abstract» 
39. Maximum available power gain of linear fourpoles
Page(s): 375  376First Page of the ArticleView full abstract» 
40. Solution of a Transistor Transient Response Problem
Page(s): 54  57The transient response of the exact current transfer function,
alpha(omega) , of a groundedbase junction transistor operating in the shortcircuited output condition is compared with the transient response derived from the conventional approximate form foralpha(omega) . The response to both a unit impulse and a unit step is calculated, and it is shown how the results may be readily adapted to yield a rapid oscilloscope method of determining thealpha cutoff frequency and several of the transistor material and dimensional constants. View full abstract» 
41. RC Active Networks Using Current Inversion Type Negative Impedance Converters
Page(s): 140  144The RC active filter, which has been established by J. G. Linvill, has a circuit configuration of a negative impedance converter sandwiched between two RC networks. This paper deals with a new circuit also using two RC networks and a converter, but its configuration is based on the parallel or series connection and the converter must be a currentinversion type. The main results obtained here are as follows: 1) The filter characteristic function which has attenuation poles at finite frequency can be realized by the synthesis of only RC twoterminal impedances without using twin
T circuits. 2) The characteristic allpass function is realized by the same method as a filter characteristic. 3) A currentinversion type converter, which uses a pair of unction transistors or vacuum tubes, is obtained. 4) Some design examples and experimental results are reported on filters and phase shifters. View full abstract» 
42. Evaluation of Oscillator Quality
Page(s): 261  268A general type of oscillator is considered, which results from the combination of an active element with a selective network. Amplitude and frequency are deduced by a simple method, valid for quasisinusoidal oscillation. If the oscillator is perturbed, relative amplitude and frequency variations can be calculated. Their product depends only upon the perturbation itself and a coefficient which is a function of the selective network. It seems apt to choose this coefficient as the figure of merit of the oscillator. For ordinary LC oscillators it is approximately equal to the Q. Values are calculated for certain RC oscillators. Some experiments confirm the results. View full abstract»

43. Bias Considerations in Transistor Circuit Design
Page(s): 194  202It is well known that the operating point of a transistor has a tendency to shift with temperature. An analysis is made of the factors contributing to this shift. It is found necessary to define two stability factors for an adequate formulation of the bias problem. These factors, together with the voltage and current defining the operating point, are used in the design of bias networks. Various stabilization circuits are considered in detail, and design procedures set up for these schemes. A comparison is made of the various schemes; in particular, direct and feedback stabilization are compared on the basis of battery drain, ac gain, and variation of operating point with battery voltage. The stabilization of directcoupled stages is also discussed, and the design of a bias circuit for a twostage directcoupled pair is taken up in detail. Nonlinear techniques for temperature stabilization are also discussed. These are useful in special applications such as highpower output stages, where the temperature changes are extreme, or in lowlevel circuits where extremely stable operation is required, e.g., in oscillators. View full abstract»

44. Stability of Circuits With Randomly TimeVarying Parameters
Page(s): 260  270This paper is concerned with the stability, in a stochastic sense, of circuits or systems described by ordinary differential equations with randomly time varying parameters. Sufficient conditions for stability in the mean square are obtained by an extension of "Lyapunov's Second Method" to stochastic problems. The general result while appliable to nonlinear as well as linear systems, presents formidable computational difficulties except for a few special cases which are tabulated. The linear case with certain assumptions concerning the statistical independence of parameter variation is carried out in detail. View full abstract»

45. A New Kind of Matched Filter
Page(s): 14  29In this article, an attempt is made to bring together the method of frequency filters, designed to separate signals whose spectra are nonoverlapping without regard to the statistical properties of the signals being separated, and the method of "optimum filters" (Wiener, ZadehRagazzini) where the desired signal and the interference are specified by their power spectral densities or their autocorrelation functions. Thus a class of new filters is defined; their fundamental properties are studied and a number of examples are furnished. Finally, a comparison is made, referring to a particular case, with the method of Zadeh and Ragazzini. View full abstract»

46. Design of Unsymmetrical BandPass Filters
Page(s): 33  40The paper presents a new approach to the synthesis of bandpass filters, in particular of filters with electrical characteristics which are not symmetrical with respect to their center frequency when plotted on an arithmetic frequency scale. The synthesis proceeds in three steps: approximation, representation by means of fictitious network elements in the lowpass domain, and subsequent lowpass, bandpass transformation. The approximation process leads to network functions defined by polynomials containing complex coefficients. It is shown that these functions can be handled with available synthesis procedures, if suitable modifications are made. This technique is based upon the properties of quasiHurwitz polynomials, treated in the Appendix. These procedures then lead to a network representation in the lowpass domain, which includes two fictitious network elements, namely constant positive or negative imaginary quantities. After a lowpass, bandpass transformation has been applied the network becomes physically realizable. It is shown that unsymmetrical lossless networks can be developed into canonic forms in the lowpass domain. A practical example is given. View full abstract»

47. On the Identification Problem
Page(s): 277  281The identification problem involves the determination of the identity of a black box from the observation of its responses to a set of input signals. In this paper attention is focused on the identification of zeromemory multipoles and twopoles of class
n_1 . The test signals are sine waves of different amplitudes and frequencies, and the measured quanity is the describing function of the device. In the case of twopoles of classn_1 , it is found that the describing function is related to the characteristic function by an integral equation of second order which can be solved explicitly by the use of the FourierHankel transformation. View full abstract» 
48. Matrix Analysis of Oscillators and Transistor Applications
Page(s): 181  188The use of matrix techniques leads to the classification of feedback, harmonic oscillators into four basic types. The oscillator is considered to be made up of two twoport networks: one contains the active element; the other, the feedback network. The equations for oscillation are expressed in terms of the twoport parameters. The method is applied specifically to the Hartley and Colpitts oscillators and their duals. The use of matrices in the analysis brings out the similarities between the oscillators. The Colpitts and Hartley circuits are of one class and require a small L/C ratio to reduce the effect of the active element upon frequencies, whereas their duals require a small C/L ratio. While the equations are derived for the low frequency case, two methods of highfrequency analysis are presented. The application of the equations to transistors is considered and several practical circuits for the dual oscillators are given. A short discussion of the bias elements and their effect on frequency and starting conditions is also included. View full abstract»

49. Noise in NegativeResistance Amplifiers
Page(s): 166  170Negativeresistance amplifiers that consist of a noisy negative resistance imbedded in a lossless threeterminalpair linear network to make a twoport amplifier are analyzed. It is shown that Haus and Adler's noise measure
M_{e} , is not constrained to lie between two eigenvalues of a noise matrix, as is the case for bona fide twoport amplifiers. Instead, it is always equal to its optimum value, and is independent of the (lossless) imbedding network used. As a corollary of this, the noise figure of such an amplifier fails to equal its optimum value only insofar as the exchangeable gain is not high. The single value of noise measure may be computed from any simple lossless circuit at hand, or else from the exchangeable noise power of the noisy negative resistance. View full abstract» 
50. Transient Response of a Transmission Line Containing An Arbitrary Number of Small Capacitive Discontinuities
Page(s): 151  157A uniform, lossfree transmission line, across which an arbitrary number of lumped capacitors have been connected at equal intervals, is subjected to an exponential step without a carrier
[1  e{beta t}] and to an exponential step which is superimposed upon a carrier:[1  e{beta t}] sin omega t . The response of the line is evaluated analytically and numerically. The results can be applied directly to situations where long transmission lines with many discontinuities, such as insulators or flanges, are used. A typical application is the response of the coaxial transmission line between a TV transmitter and its antenna. View full abstract»
Aims & Scope
This title ceased production in 1962. The current updated titles are IEEE Transactions on Circuits and Systems I: Regular Papers and IEEE Transactions on Circuits and Systems II: Express Briefs.
Further Links
Persistent Link: http://ieeexplore.ieee.org/servlet/opac?punumber=8148 More »
Frequency: 4
ISSN:
00962007
Subjects
 Components, Circuits, Devices & Systems