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Circuit Theory, IEEE Transactions on

Issue 2 • Date June 1967

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Displaying Results 1 - 21 of 21
  • High-Q Resistance-Capacitance Ladder Phase-Shift Networks

    Publication Year: 1967 , Page(s): 148 - 153
    Cited by:  Papers (5)
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    Resistance-capacitance ladder lowpass networks, to obtain a phase shift ( \phi ) of 180° between the input and the output, are examined. It is found that there exists a theoretical maximum value of Q , defined by \omega _0/2 |d\phi/d\omega | \omega = \omega _0 where \omega _0 is the frequency at which the phase shift is 180°. This theoretical limit can be approached in actual practice, but never reached. It is attempted to synthesize such networks having as high a Q as possible. In addition, the resulting network possesses the property that the open-circuit input impedance and the short-circuit output admittance are simultaneously maximized. A transformation enables one to get the corresponding highpass structure from the lowpass. View full abstract»

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  • On Unistor Graphs

    Publication Year: 1967 , Page(s): 154 - 159
    Cited by:  Papers (2)
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    There are a number of applications of graph theory to the solutions of problems in electrical networks, switching circuits, and communication nets. These applications involve modeling a system by a graph and describing the properties of the system in terms of this corresponding graph. In this paper it is shown that a linear system can be modeled by a graph of unistors; that is, an oriented edge with flow proportional to the initial vertex. The solution of the system is then obtained by means of products of directed trees. There is no calculation of cofactors as an intermediate step, and no extra calculation to determine the sign of the solution. In order to achieve the result, the relationships between the directed trees forming a unistor graph and their associated incidence matrices are developed and techniques for calculating determinants and cofactors of linear systems by means of directed trees and directed 2-trees are given. View full abstract»

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  • Non-Series-Parallel Realization of Symmetrical and Bisymmetrical Two-Element-Kind Two-Ports to Minimize Multiparameter Sensitivity

    Publication Year: 1967 , Page(s): 159 - 166
    Cited by:  Papers (2)
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    A non-series-parallel synthesis procedure is introduced to realize a class of two-element-kind two-port symmetrical and bisymmetrical network function specifications. Necessary and sufficient conditions for the realizability of the network functions are given. The multiparameter sensitivities of the non-series-parallel realizations and their equivalent conventional realizations are discussed. In particular, RC ladder networks (series-parallel networks) are compared with respect to multiparameter sensitivity with non-series-parallel networks which realize the same network functions. It is shown that the new networks always have smaller values of multiparameter sensitivity than two classes of equivalent ladder networks for all frequencies. Numerical examples computed on the CDC 1604 and the IBM 7094 illustrate the method. View full abstract»

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  • A Systematic Method of Finding All Directed Circuits and Enumerating All DIrected Paths

    Publication Year: 1967 , Page(s): 166 - 171
    Cited by:  Papers (1)
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    A method of obtaining all directed circuits is presented by using a connection matrix. Also obtained is the number of directed paths of each length from any one vertex to another. Finally it is extended to the nonoriented case. View full abstract»

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  • A Topological Method of Generating Constant Resistance Networks

    Publication Year: 1967 , Page(s): 172 - 179
    Cited by:  Papers (5)
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    Zadeh has shown that any self-dual network, fixed or linear time varying, is a constant resistance network. To date, the only known constant resistance networks with self-dual structures are the classical lattice and bridged-T networks. In this paper, we investigate the topological aspect of the problem, with the aim of obtaining new constant resistance network configurations. Let G_{\rho} be a self-dual one-terminal-pair graph with respect to vertices ( i, j ), and with the degrees of ( i, j ) both equal to \rho . It is proved that for \rho \geq q 2, G_\rho can be realized with 8 \rho - 11 edges, but not with fewer edges, if the union of G_\rho and an edge joining ( i, j ) is to be 3-connected. Using these graphs as the basis, a class of constant resistance networks are generated, which include the classical lattice and bridged-T networks as special cases for \rho = 2 . The generation of a constant resistance network for \rho = 3 is shown in detail, with a numerical example illustrating its application in transfer function synthesis. View full abstract»

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  • Active RC Synthesis for Significant Reduction in Magnitudes of Reactive Elements

    Publication Year: 1967 , Page(s): 179 - 187
    Cited by:  Papers (3)
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    Active elements may be used to significantly reduce the total reactance required in a network. This paper presents two active RC synthesis techniques for this purpose. One method employs a negative-impedance-converter to realize any number of system poles and reduces the total required capacitance to any desired extent. The resulting design is, however, very sensitive to active and passive parameter values. The second method also permits any prescribed total capacitance but employs a cascade of isolated second-degree sections. Two such sections are presented and optimized with respect to a figure of merit C_{t}AS_{A} , being the product of total capacitance, required active element gain and system sensitivity to the latter. System transmission zeros may be accommodated to a certain extent. View full abstract»

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  • Simplified Multiple Parameter Sensitivity Calculation and Continuously Equivalent Networks

    Publication Year: 1967 , Page(s): 188 - 191
    Cited by:  Papers (18)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (459 KB)  

    A method of efficiently calculating the sensitivity functions of a single output variable with respect to all the parameters in a reciprocal network is described. The method reduces the problem of obtaining these sensitivity functions to the simple problem of solving one additional network easily derived from the given network. A distinct advantage of the method is that currently available digital computer network analysis programs can be used with little modification and calculation of the sensitivity functions. Next, the frequency dependence of the sensitivity of continuously equivalent networks is examined. The results of this study allows one to make three hypotheses about continuously equivalent networks. 1) The continuously equivalent network resulting from a minimization of the sum of the magnitudes squared of the sensitivity functions at a given frequency is the network with minimum sum of the magnitudes squared of the sensitivity function at all frequencies. 2) The sum of the magnitudes squared of the sensitivity functions decreases as the number of elements increases in continuously equivalent networks. 3) The sum of the sensitivity functions is invariant with respect to the various equivalent networks. The most important hypothesis is the first since if true for all continuously equivalent networks, then a great simplification of the computation problem results. Even if a limited class of continuously equivalent networks exhibit this property, then the result is worthwhile. Experimental results show that such a class does exist. These experimental results do not prove that all continuously equivalent networks have these three properties. View full abstract»

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  • Analysis and Synthesis of Multivalued Memoryless Nonlinear Networks

    Publication Year: 1967 , Page(s): 192 - 209
    Cited by:  Papers (9)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2071 KB)  

    This paper presents a simple but general method-the Iterative Piecewise Linear Method-suitable for the analysis and synthesis of multivalued memoryless nonlinear networks that may contain multivalued nonlinear resistors, controlled sources, ideal transformers, gyrators, negative impedance converters, etc. The method itself is an algorithm, and therefore it can be easily programmed in a computor. Part I, Analysis of Multivalued Memoryless Networks, considers the operating point problem and the determination of driving-point and transfer characteristic plots. Part II, Piecewise Linear Synthesis of dc Memoryless Nonlinear Networks, describes a simple procedure to synthesize a nonlinear lattice network having a prescribed driving point, and transfer as well as nonlinear load characteristics. An analytical procedure for realizing a nonlinear voltage divider with multivalued transfer characteristics is also given. View full abstract»

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  • Computation of the Step Response of a General Nonuniform RC Distributed Network

    Publication Year: 1967 , Page(s): 219 - 221
    Cited by:  Papers (4)
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  • Circuit Transformation for Crystal Ladder Filters

    Publication Year: 1967 , Page(s): 221 - 224
    Cited by:  Papers (1)
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  • Generation of Concave Node-Weighted Trees

    Publication Year: 1967 , Page(s): 229 - 230
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  • Hamilton circuits in directed-tree graphs

    Publication Year: 1967 , Page(s): 231 - 233
    Cited by:  Papers (2)
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  • Constant Resistance, Wide-Sense Solvability, and Self-Duality

    Publication Year: 1967 , Page(s): 233 - 234
    Cited by:  Papers (1)
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  • A Simple Calculation of the Determinant Polynomial of General Networks

    Publication Year: 1967 , Page(s): 234 - 236
    Cited by:  Papers (5)
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  • Nonlinear Distortion in Periodically Time-Variable Circuits

    Publication Year: 1967 , Page(s): 236 - 239
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  • Transfer Function Realizability of Grounded \overline {URC} Networks

    Publication Year: 1967 , Page(s): 129 - 139
    Cited by:  Papers (7)
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    Necessary and sufficient conditions for the realization of a short-circuited transfer admittance by means of a grounded \overline {URC} network are presented. The approach used to determine the realizability conditions is similar to that employed in lumped transformerless networks but, in this case, the conditions upon realizability are directly related to the short-circuited transfer admittance ( y_{12} ), rather than the open-circuited voltage transfer ratio. Similarly, if y_{12} satisfies the realizability conditions, surplus factors may have to be used before synthesis can be performed. Finally, the procedure used in testing for realizability and synthesis is demonstrated by a nontrivial worked example. View full abstract»

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  • Statistical Properties of Ramplike Random Processes

    Publication Year: 1967 , Page(s): 209 - 218
    Cited by:  Papers (1)
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    The work of Lampard and Redman [5] on the statistical properties of the integral of a binary random process is generalized and extended to include more general ramplike random processes z(t) . These ramplike processes are defined to be ramps of random slope that switch slope at random times. Both the intervals between switching times and the slopes of the ramp segments are assumed to be independent random variables. The general properties of the one-dimensional and multidimensional probability density functions of z(t) are discussed. A Laplace transform technique is employed to obtain the Laplace transform of the characteristic function of these probability density functions in terms of the Laplace transform of the characteristic function of the ramp slopes multipled by the probability functions of the switching times. For Poisson switching times, these expressions are relatively compact. However, the inversion problem is formidable, and closed form results are presently available only for a binary slope probability density function (a previously known result). Due to the properties of characteristic functions, the moments of z(t) are obtained by a single Laplace inversion of the derivative of the Laplace transform expressions. These moments may be used to characterize the probability density functions of z(t) with a series expansion involving the Gaussian density function and its derivatives. Examples are given for the cases of Gaussian and rectangular slope probability density functions with Poisson switching times. View full abstract»

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  • Visualizing the Operation of Electronic Circuits

    Publication Year: 1967 , Page(s): 239 - 242
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  • Synthesis of RC Bandpass Filters

    Publication Year: 1967 , Page(s): 140 - 148
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    The technique of the conformal transformation is used in the design of RC bandpass filters. An elliptic-function transformation that transforms the complex-frequency plane into a rectangle is used. In the transformed plane, poles and zeros can be located to produce several useful bandpass characteristics. Key quantities, such as the passband ripple, the equal-ripple bandwidth, and the half-power bandwidth, of these filters can be calculated in terms of a few parameters in closed form. Some design charts are presented. Several design examples and experimental filters are given. View full abstract»

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  • Transient Response of Equal-Element Bandstop Filters

    Publication Year: 1967 , Page(s): 224 - 229
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  • Synthesis of Active and Passive Compatible Impedances

    Publication Year: 1967 , Page(s): 118 - 128
    Cited by:  Papers (7)
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    This paper is concerned with the following problem: given two rational functions Z_1(s) and Z_0(s) , otherwise arbitrary but for which R + Z_1(s) has no zeros in the right-half plane, Z_1(s) is to be realized as the driving-point impedance of a lossless coupling two-port terminated in the impedance Z_0(s) . This problem had been previously considered and solved by Schoeffler and by Wohlers when Z_1(s) and Z_0(s) are positive real functions and the coupling network is reciprocal. Necessary and sufficient conditions are given here for realizability in the contemplated form when neither of the two impedances are necessarily positive real and when the coupling network may be reciprocal or nonreciprocal, but still lossless. A realization procedure is described and examples are given to illustrate the approach. View full abstract»

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