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Circuit Theory, IRE Transactions on

Issue 4 • Date December 1958

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Displaying Results 1 - 25 of 27
  • Introduction

    Page(s): 234 - 235
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  • Abstracts of articles on circuit theory

    Page(s): 364 - 366
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    Freely Available from IEEE
  • Author's Comment on 'Network Topology'

    Page(s): 367 - 368
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  • Letter on 'Network Topology'

    Page(s): 369
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  • Equivalent circuits for transformers

    Page(s): 370 - 371
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  • Branch transfer functions

    Page(s): 371 - 372
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  • Network decomposition using topological formulas

    Page(s): 373 - 374
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  • A note on four-pole parameters

    Page(s): 375
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  • Computation of Elliptic Functions of Rational Fractions of a Quarterperiod

    Page(s): 352 - 355
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    The evaluation of Jacobian elliptic functions with arguments which are rational fractions of a quarterperiod is often necessary in network design. Conventional methods, using theta functions, are quite satisfactory for this purpose, but, in the more interesting range of the modulusknear unity, they do not represent the best that can be done. A slight modification of the theta functions, together with a change of parameter made possible by the special nature of the rational-fraction form of argument, produces a computing scheme which, in most practical instances, converges more quickly than the classical one. The scheme is illustrated by a numerical example. View full abstract»

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  • Synthesis of Band-Pass Ladder Network

    Page(s): 256 - 264
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    The synthesis of frequency-asymmetrical band-pass filters which do not depend on the reactance-transformation from low-pass filters presents an important problem from the theoretical and practical points of view. In this paper, sufficient conditions are derived for realizing a nondissipative general "band-pass" filter by means of a reactive ladder network which excludes mutual inductance, except for an ideal transformer connected in cascade to one end thereof, and for realizing reactive "band-pass" ladders using a minimum number of inductors (or capacitors). Moreover, the relation between negative values of reactive elements of the filter and its transmission characteristic is investigated. The method of synthesis for these kinds of ladders is presented in detail and some experimental results are included. View full abstract»

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  • Synthesis of Driving Point Impedances with Geometric Symmetry

    Page(s): 359 - 363
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    If a driving point impedance shows geometric symmetry with respect to a center frequencyomega_0, it can be developed in Brune's sense by means of constant resistance lattices and without the use of coupled coils. View full abstract»

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  • Note on Maximally Flat Delay Networks

    Page(s): 363 - 364
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    A general solution in closed form is given for the reflection coefficient of a network with transfer function equal to the reciprocal of annth degree Bessel polynomial. The result is applicable to a Darlington-type synthesis of a maximally flat delay network with unequal resistance terminations. View full abstract»

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  • On the Design of Filters by Synthesis

    Page(s): 284 - 327
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    Following 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 circuit-element values for the realization of reactance ladder-network 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 low-pass into a band-pass configuration with a minimum number of inductances, and into a band-pass 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 low-pass filters with the effective attenuation in the pass band and the stop band behaving in the Tchebycheff sense, for the degreesn = 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»

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  • Four-Port Constant R Network Required by a Two-Way Single Amplifier Repeater

    Page(s): 276 - 283
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    Two-way single amplifier repeaters have some definite advantages for long transmission systems. Such repeaters may be built according to various configurations. This paper concerns itself with only one of the possible configurations, namely, the one usually referred to as the four-filter configuration, and which is shown in Fig. 2. First, the necessary and sufficient conditions for the physical realizability of the associated networks are derived. Second, the approximation technique is described that leads to physical networks having a scattering matrix very close to that required. The network realization proceeds following well-known methods. Finally, a particular design is outlined briefly. View full abstract»

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  • An Iterative Method for the Direct Hurwitz-Factorization of a Polynomial

    Page(s): 347 - 352
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    IfN(p)is an even polynomial inpwith real coefficients, and further, if any zeros ofN(p)on the imaginary axis occur to an even multiplicity,N(p)can be factored in several ways into the formN(p) = Q(p){cdot}Q(-p). The particularQ(p)which has zeros in the left half-plane only, (including, perhaps, the imaginary axis), is of importance in the theory of vibrating systems, and occurs frequently in theoretical methods of network synthesis, as for example, in Darlington's insertion loss method. It is now possible, owing to the work of the German mathematician, Bauer, to factor outQ(p)directly fromN(p), by a method which is well suited to use in digital computers. The first section of this article is essentially a translation of Bauer's original paper; the second summarizes the experience gained by writing a computer program based on his work. View full abstract»

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  • Numerical Determination of Cascaded LC Network Elements from Return Loss Coefficients

    Page(s): 356 - 359
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    The data for describing the behavior of a lossless network and for synthesizing a network which exhibits that behavior can be presented in many ways. One of the lesser used descriptions is the Taylor series expansion insof the return loss about a transmission zero. As is well known, a return loss is the natural logarithm of the reciprocal of the reflection coefficient as measured between a resistance termination and the remainder of the network. While it is realized that the return loss expansion is not so immediately useful a network function as, for example, the input impedance or the reflection coefficient, the analytical aspects are very interesting in themselves and may well find application in future work. If the low-pass LC ladder network ofnelements starting with a seriesLis considered, the first(2n - 1)coefficients of a given return loss expansion about the transmission zero at infinity contain all the necessary information for finding numerical values of the ladder elements. It can be shown that the first coefficient depends on the first ladder element, the third coefficient depends on the first and second elements, etc. Formulas for finding up to four elements from the return loss expansion are available. However, a recursion form for extending the range of these formulas is not immediately evident from these available formulas. Two general equations, one for the seriesL's and one for the shuntC's are presented. The equations depend only on a knowledge of the Taylor coefficients for the particular type of ladder network under consideration. The method of finding theL's andC's is a straightforward algebraic approach and is novel only in that the elimination of redundant information leads to simple expressions for theL's andC's. Application of the equations leads to a recursion method for alternately finding anL, the succeedingC, the nextL, etc. Accumulated results from one equation are used in finding the next equation. View full abstract»

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  • On the Realizability of Ladder Filters

    Page(s): 253 - 255
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    For practical design, it is useful to be able to determine in advance, from design parameters alone, the condition under which mutual inductances will not appear in ladder networks designed on the image-parameter or on the insertion loss basis. The present paper starts with some comments on Fujisawa's criterion and extends it to a class of image-parameter band-pass filters. It expresses Fujisawa's criterion in terms of the design parameters for the symmetrical, low-pass filter having Tchebycheff behavior in both the attenuation and transmission ranges and for some degenerate cases. Various approximations yield simple results of great practical importance. View full abstract»

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  • Recent Developments in Filter Theory

    Page(s): 236 - 252
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    This 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»

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  • Synthesis of Three-Terminal Networks with Two Kinds of Elements

    Page(s): 267 - 275
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    The present paper is concerned with the synthesis of LC, PC, and RL-three-terminal networks without mutual inductance. It shows that the immittance matrices which satisfy the following sufficient conditions may be realized as networks of these kinds: (sufficient condition for RC case) 1) Admittance (or impedance) matrix satisfies the realizability conditions as a four-terminal RC network. 2) Numerator ofy_{12} (z_{12})is a polynomial with nonnegative coefficients whose zeros are restricted to the left half of the complex frequency plane including boundary, where the denominator is assumed to be a polynomial with nonnegative coefficients. 3)(y_{11} - y_{12}): (y_{22} - y_{12}) = 1 :n [(z_{22} - z_{12}): (z_{11} - z_{12}) = 1 :n)]. The theory may be applicable to the two important problems in network synthesis; that is, to the synthesis of filter circuits as three-terminal reactance networks and to the realization of RC transfer functions as three-terminal RC networks without mutual inductance. Furthermore, for the case of a symmetrical circuit, the theory offers the theoretical method of transforming from a symmetrical lattice to an unbalanced form. View full abstract»

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  • Transient Responses of Conventional Filters

    Page(s): 333 - 347
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    Much of the tedium of filter design has been eliminated by previously published tabulations of element values, pole locations, polynomial coefficients, and similar data for several conventional types of filters. The transient responses of some of the same types of filters have been computed and plotted in this paper. The curves presented are the normalized impulse and step responses of the first ten orders of the low-pass and high-pass Butterworth (maximally-flat) and Tchebycheff (equal-ripple) types, with band-pass ripple of 0.5, 1, and 2 db for the latter, and the low-pass Bessel (maximally-flat time delay) type. The method of calculation of the responses is described in detail, and some interesting properties of the pole loci are explained. The calculations were performed with a digital computer. View full abstract»

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  • A Modification of Brune's Method for Narrow-Band Filters

    Page(s): 264 - 267
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    If a given driving point immittanceZ(p)represents a narrow-band filter it can be developed into a ladder network without closely coupled coils by a modification of Brune's method. The method is applicable to filters with phase or amplitude characteristic which are not symmetric with respect to the band center frequency.Z(p)is represented by the ratio of two polynomials inpwith complex coefficients. A fictitious low-pass equivalent network is developed, which contains frequency independent imaginary components. This network becomes realizable after a low-pass, band-pass transformation is made. It then represents a narrow-band approximation to the exact solution. View full abstract»

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