Showing papers in "IEEE Transactions on Circuits and Systems I-regular Papers in 1961"

A New Theory of Cascade Synthesis

Abstract: This paper presents a new result generalizing Richards' theorem. It is shown that this result leads to a complete, simple and unified theory of cascade synthesis which yields the types A, B, Brune, C and D sections in a direct and natural manner. The element values of the various sections are obtained in closed form in terms of three or six indexes. Thus the extraction cycle is performed once and for all for the whole class of positive-real functions. Several problems are worked out in detail and a chart is constructed to facilitate the computations. The formulas are easily programmed on a digital computer.

High-Frequency High-Power Operation of Tunnel Diodes

Abstract: The operation of oscillators using high-current tunnel diodes above their self-resonant frequency is presented. General stability conditions of the tunnel diode, including external circuits (lumped and distributed), are discussed. Based on a nonlinear analysis of a tunnel-diode oscillator, the power generated by the diode, the power dissipated within the diode and the power delivered to an external load are calculated as a function of frequency and loading conditions. For operation above the self-resonant frequency, the suppression of unwanted LF oscillations is necessary. Experimental results of an oscillator circuit operating at 2-3 Gc with the suppression of LF oscillation are described. Data on the high-current tunnel diodes (50 \sim 100 ma) used are given.

Solving Steady-State Nonlinear Networks of 'Monotone' Elements

Abstract: This 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 current-vs-voltage-drop 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 ("network-topology"), and 2) quantization of the variables (permitting them to take on only a discrete set of values).

Optimum Synthesis of Wide-Band Parametric Amplifiers and Converters

Abstract: This paper derives the theoretical limitation on gain and bandwidth for parametric amplifiers and inverting-type up-converters. It shows that the transducer power gain of an amplifier or a converter can be related to the reflection coefficient of a simple matching network as G_a \approx \frac {\omega_0} {\omega_{0}\prime} G_c \aaprox \frac {1} {4 |p|^2} where G_a and G_c are the power gain of the amplifier and the converter, respectively, \omega_0 and \omega_0 \prime are the center frequencies of the signal and the idler bands, respectively, and \rho is the reflection coefficient which is limited in bandwidth by the following formula: \frac {B} {\omega_0} \ln \arrowvert \frac {1} {\rho} \arrowvert \leq \frac {\pi} {2} \frac {C_1} {C_0} \sqrt{\frac {\omega_0 \prime} {\omega_0}} B is the bandwidth, and C_0 + 2 C_1 \cos\overline{\omega} t represents the variable capacitance. Optimum Butterworth filters are used as the coupling networks. Condition for optimum matching is determined together with element values of the circuit. The theoretical limitation on bandwidth can be approached if the number of elements in the coupling network is increased. The design of optimum wide-band amplifiers and converters becomes straightforward, thus eliminating any cut and try process.

Pulse Networks with Parabolic Distribution of Poles

Abstract: In this paper an attempt is made to find the pole configuration for a transfer function whose zeros are all at infinity and which will yield a transient response showing improvement over both the Butterworth, Thomson or Transitional ButterworthThomson ones Some discussions of the monotonicity conditions of the time response suggest that the poles may conveniently be located on parabolic contours in the left half of the p plane On investigation of such networks, it is found that they show very little or no overshoot, and small rise time Also the overshoot decreases with increase of the order of the network

Topological Considerations in the Realization of Resistive n-Port Networks

Abstract: The topological implications of irreducibility of the admittance or impedance matrix of an n-port network are studied. Special attention is given to the cases when in (n - 1) rows of such a matrix of order n the main diagonal elements are equal to the absolute values of some off-diagonal elements. It is shown that the conditions of realizability of a Y or Z matrix of this type reduce to the known conditions of realizability by means of a network with (n + 1) vertices or exactly n independent circuits. Some examples show realizable Z matrices which cannot be realized as Y matrices and vice versa. Other examples give nonrealizable, paramount Y and Z matrices showing that paramountcy is not a sufficient condition for realizability.

Approximation Theory for Filter-Networks

Abstract: This paper presents a general design theory for filter-networks constructed on the basis of theory of the Abelian Integral. An ideal transmission function is defined to be an Anbelian Integral w(\lambda) with the following properties: 1) Re w(\lambda) = u(\lambda) = A_k in given regions B_k , 2) \{u(\lambda) - \log | \lambda + a_i|\} is regular at any given point a_i , and 3) otherwise u(\lambda) is a harmonic function. The application of appropriate analytic transformation techniques to w(\lambda) leads to a generalized characteristic function \phi(\lambda)) . All kinds of realizable transfer functions can be derived by the use of linear transformations of \{\phi(\lambda)\}^2 with respect to \lambda^2 . Further, this treatise gives the design methods for filter-networks having one or two pass bands, in which they exhibit the Tchebycheff performance. Besides the method is also established to synthesize a reactance band-pass network with the order N using only [(N - 1)/2] coils. Three design examples, such that the band-pass filter comprising only 6 coils for N = 13 and 4 coils for N = 10 , and the double-pass-band filters with N = 8 and 4 coils, are described in quite detail. All of the examples have the Tchebycheff performance in their pass bands.

A New Design Approach for Feedback Amplifiers

Abstract: A new design procedure is presented which is based on the root-locus technique. The realization of the following is possible: a) desired closed-loop 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 low-frequency and bandedge responses. The key feature of the root-locus technique is the proper use and location of phantom zeros (transmission zeros of the feedback path). To illustrate the technique, a shunt-shunt feedback configuration is used together with the realization of flat-magnitude-type closed-loop responses. The basic amplifier is a three-stage c-e transistor cascade. Typical design examples with experimental results are included.

On the Realization of an nth-Order G Matrix

Abstract: Synthesis of a single-element-kind network from a given short-circuit parameter matrix of order n, leading to a topological configuration involving n + 1 nodes, is now known, having been given by the author and several others working on this problem almost simultaneously. This form of realization is, however, not completely general, and therefore it is possible for a given matrix to be physically realizable even though the (n + 1) -node realization procedure fails. The present paper discusses this more general problem and leads to some useful results which do not, however, represent a complete solution.

On the Synthesis of Resistive N-Port Networks

Abstract: A new approach to the problem of the synthesis of resistive n -port networks with (n + 1) nodes is given. First it is shown that, given a conductance matrix G of order n , the signs of its elements define the complete tree of the n port uniquely (if it exists). The case of two (or more) ports in "series" is exceptional: the order of such ports in the complete tree can be found by comparing the absolute values of a couple (or more couples) of elements of G . Once the complete tree has been determined, the synthesis becomes very simple, since the G matrix can be transformed into another matrix Go referred to a set of node-to-datum independent voltages, whose conditions of realizability are well known.

Broad-Band Matching Between Load and Source Systems

Abstract: This paper discusses impedance matching between an arbitrary load and a particular type of source network, by means of a lossless two-terminal-pair matching network. The source network consists of an LC ladder in series with a generator resistance. This study is devoted principally to theoretical considerations of low-pass systems utilizing lossless matching networks between source networks and arbitrary load impedances. The present effort is one possible extension of previous work of Fano. Fano's system, however, did not include a two-terminal-pair source network. The value of the present work is derived from an investigation of constraints imposed by the source system and the load, rather than just the load itself.

Zero Cancellation Synthesis Using Impedance Operators

Abstract: Through an extension of Richards' theorem, an RLC driving-point impedance function, Z , is synthesized by a prescribed, realizable, four-terminal network terminated with another drivingpoint impedance function, \zeta , four less in rank than Z . Z is completely arbitrary except that it may not have a pole or a zero at the origin or infinity. The initial four-terminal network consists of a capacitor, a perfectly-coupled transformer, and an ideal gyrator. Other equivalent networks are derived which do not require transformers and gyrators but in which the cascade nature of the synthesis is lost.

Design of Lossy Ladder Filters by Digital Computer

Abstract: Nonavailability of ideal elements is a major drawback in the development of filters having some prescribed characteristic. In this paper, a method for designing lossy filters built with elements having unequal dissipation factors using a high-speed digital computer as the main tool is presented along with the results of a preliminary study of the method. The magnitude function, within the first order, is shown to be a multilinear function of the element values for very small change in the element values. The basic idea is to perturb the element values of the lossy filter with the aim of making the magnitude function of the lossy filter proportional to that of the ideal filter. An error function is defined as the sum of squared differences between the magnitude characteristic of the lossy filter and the same of the ideal filter (multiplied by a suitable constant factor) at some discrete frequencies in the passband and the stop band. The error function is then minimized by the steepest descent method of minimization. Results of using the suggested method in designing a lossy Tchebycheff filter of degree 9 are included. It is found that the minimization of the pass-band ripple is associated with a decrease in the stop-band attenuation. The paper also includes details on programming methods.

Analysis and Synthesis Techniques of Oriented Communication Nets

Abstract: An oriented communication net is a communication network in which channel capacities between pairs of terminals are not symmetrical. Such a system can be represented by an oriented graph. The concept of a minimum-valued cut is used to determine the terminal-capacity matrix which gives the maximum possible communication between any ordered pair of terminals. Necessary conditions for a terminal capacity matrix to be realizable as an oriented communication network are obtained. These conditions are shown to be sufficient when the order of the terminal capacity matrix is three or less. They are not sufficient for higher-order cases in general. Synthesis techniques based on matrix partition and matrix addition are used to realize any three-by-three terminal capacity matrix with extensions to some higher-order cases.

On the Synthesis of R Networks

Abstract: A study is made of a class of real symmetric matrices, and a new set of necessary and sufficient conditions are defined on the entries of these matrices such that they can be synthesized, without using ideal transformers, as an R-network with a minimum number of terminals. The conditions are stated in terms of the terminal graph used in representing the terminal characteristics of multiterminal components. The new class of matrices then represents "terminal equations" corresponding to a path-tree terminal graph. It is also shown that one of the well-known class of matrices, referred to as dominant matrices, represent the terminal equations for a Lagrangian-tree terminal graph. It is further indicated that any such class of real symmetric matrices is distinguishable by a particular terminal graph. For the cases when a real symmetric matrix of order n cannot be synthesized by an R network with (n + 1) terminal vertices, an "enlarged" matrix is formed, and the necessary and sufficient conditions for realizability of these matrices are given.

Synthesis of Active RC Networks

Abstract: Synthesis procedures are presented which establish that one grounded 3-terminal negative-impedance converter, embedded in an unbalanced grounded RC structure, is sufficient to realize 1) any driving-point function, 2) any two of the four short-circuit admittance parameters of a two-port network, and 3) certain sets of n short-circuit admittance parameters of an (n + 1) -terminal network, where each of the parameters is specified as the ratio of any two polynominals in the complex-frequency variable, with real coefficients. Furthermore, the required RC networks can always be made to take the form of grounded ladder-type structures, some of which, in particular cases, reduce to two-terminal admittances.

Optimal Synthesis of a Communication Net

Abstract: This paper gives solutions to the problem of realizing a communication network at minimum cost. The network is composed of a set of nodes connected by a set of branches. Every branch has associated with it a capacity. The required amount of flow between every pair of nodes is specified. The unit costs of the branch capacities are given. The problem is to find the network and the branch capacities such that the total cost is minimum. The set of branch capacities and the set of terminal demands are shown to satisfy a set of linear inequalities. Linear programming is used to obtain the optimal solution. In the case of identical unit costs, several realizations are given which require fewer branches than previously reported.

Stability Margins and Steady-State Oscillations of ON-OFF Feedback Systems

Abstract: Exact methods of determining the steady-state oscillations in feedback systems incorporating one nonlinear element of the ON-OFF type have been developed by Hamel and Tsypkin. It is shown that these methods are not generally applicable. A general method is developed which overcomes these limitations and suitable stability margins are derived.

The Seg: A New Class of Subgraphs

Abstract: The linear graph, after a delay of about a hundred years from its conception by Kirchhoff, is today rapidly assuming a dominant position in the foundation of electric network theory. This paper is a presentation, by definition and properties deducible therefrom, of a new class of subgraphs (segs) which includes stars and cut sets as special cases. The matrix associated with the seg can be shown to be the general coefficient matrix of the Kirchhoff current equations. Hence, in addition to adding to the structure of linear graph theory, the results in this paper broaden the base of knowledge of currents in electric networks. This broadened base has already permitted the opening of a new phase of network theory and can certainly be expected to open others.

Synthesis of All-Pass Delay Equalizers

Abstract: A systematic-synthesis technique has been developed whereby a given delay characteristic is approximated within a given error with a small number of all-pass network sections. The method is a generalization of Darlington's using the Tchebycheff polynomial series. As an application, a three-section delay equalizer for color television was designed which had better performance than a four-section equalizer now in use.

Two Extensions of the Darlington Synthesis Procedure

Abstract: Two methods are presented which make it possible to synthesize a driving-point impedance function by a Darlington-type synthesis without surplus factors One method relies on the use of nonreciprocal devices (gyrators) in the synthesized network The additional constraints due to presence of gyrators are discussed It is shown that the residue condition for physical realizability now becomes k_{11} k_{22} - k_{12}^2 - \beta^2 > 0 ( \beta is the coefficient of the z_{12} term which is of the form \beta \omega_{0}/(s^2 + \omega_{0}^2)) It is shown also that two real-part conditions now exist In addition to the usual Brune real-part condition Re z_{11} Re z_{22} - (Re(z_{12} + z_{21}))^2/4 > 0 for reciprocal elements, there exists another restriction Re 1/y_{11} Re 1/z_{22} - (Re(z_{12} - z_{21})/2z_{22})^2 \geq 0 on the j -axis (the equal sign is dropped for Res > 0 ) The second method relaxes the cascade network requirement, and from a study of E v Z(s) allows the synthesis of the network by a Darlington-type synthesis Examples are given of both new methods

Conditions for the Realizability of a Conductance Matrix

Abstract: It is shown that it is possible to determine whether a given conductance matrix of order n is realizable by a network with n + 1 nodes without going through the actual realization of the tree. This realizability criterion requires only a proper arrangement of the rows and columns of the sign matrix, corresponding to the assigned conductance matrix.

Impedance Transformation Using Lossless Networks

Abstract: Two impedances are said to be compatible if one of them can be realized as the input impedance to a two-terminal-pair lossless network terminated in the other impedance. A uniqueness property of the Darlington realization procedure and the methods of cascade synthesis are used to determine a simple, concise set of necessary and sufficient conditions under which two given realizable impedances can be compatible. Applications are discussed.