The transfer function of general two terminal-pair RC networks

Fialkow, Aaron; Gerst, Irving

doi:10.1090/qam/49081

Cited by 81 publications

(16 citation statements)

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“…These results constitute an extension of those obtained in a previous paper [5], for networks containing two kinds of elements only. In part, our present techniques depend upon the ideas and methods employed in [5] to which reference will be made in the course of the proofs.…”

Section: Introductionsupporting

confidence: 85%

“…The argument of [5, Appendix B] may be used here to show the existence of a Hurwitz polynomial")" U (actually the zeros of U may be taken to be negative real and distinct except that in the special case where N and D are both even functions of p we may use a non-Hurwitz polynomial U having only pure imaginary zeros distinct from the zeros of D and from each other) such that in A(p) = KUN/UD = G/H "This restriction on To is easily removed but we do not stop to do this here. **Of the synthesis procedures mentioned in [5], the last alternative method in the footnote on p. 120 which was later given in detail in [4] usually yields a simpler network.…”

Section: Introductionmentioning

confidence: 99%

“…For an examination of the proof in [5,Appendix B] shows that in addition to (iii), (iv) and (v) of Theorem 1, use was made only of the fact that the zeros of D were not positive real or zero, and this is guaranteed by (i) of Theorem 1. This common factor technique achieves positive coefficients in the transfer function as is stated in (2.6).…”

Section: Introductionmentioning

confidence: 99%

“…This is hardly justified, for examination of these and other references reveals at best a superficial similiarity to our method. Furthermore, in view of his statement it is surprising that in none of the literature on transfer functions prior to [5] including his own thesis [9] has our or a similar method been employed, (bj) Synthesis: Case I.…”

Section: Introductionmentioning

confidence: 99%

“…Hence by-(A) the functions^ = G'JH'e , A2 = GJH. In view of (2.1) the corresponding *The method used here is analogous to the last alternative procedure mentioned in [5], footnote on page 120 and given in [4]. Similarly, techniques based on the other procedures given in [5] may also be employed here.…”

Section: Introductionmentioning

confidence: 99%

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The transfer function of networks without mutual reactance

Fialkow¹,

Gerst²

1954

Quart. Appl. Math.

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Section: Introductionsupporting

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The transfer function of networks without mutual reactance

Fialkow¹,

Gerst²

1954

Quart. Appl. Math.

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Realization of a transfer function as a passive two‐port RC ladder network with a specified gain

Wang

Chen

2017

Circuit Theory & Apps

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Summary This paper is concerned with the realization problem for a class of high‐pass as well as low‐pass transfer functions as a two‐port RC ladder network with a specified gain, which requires that the actual gain of the realization configuration is equal to the gain of the given transfer function. From a cascade realization approach, it is shown that any transfer function belonging to the class under investigation can be realized as a two‐port RC ladder network with any specified gain in a continuous interval. Finally, a numerical example is presented to illustrate the result. Copyright © 2017 John Wiley & Sons, Ltd.

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On rlc network matrices

Fialkow¹

1973

Circuit Theory & Apps

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SUMMARYA generalization of the coefficient conditions which hold for an RLC network as well as of the paramount property obeyed by the matrix of a resistance network is derived. This result is a property of either the nodal or mesh matrices for either the admittances or impedances of a general RLC network. It states that if P is any principal minor or such a matrix and Q any other minor constructed from the same rows (columns) as P then P, P + Q , P-Q are rational functions of the complex frequency variable which, before cancellation of common factors, have only non-negative coefficients.Much has been written concerning RLC (transformerless) multiport networks. Nevertheless the basic realization problem remains unsolved except for special cases such as the RC and RLC voltage transfer function4" and the resistance n-port having exactly n + 1 ~e r t i c e s .~ Even necessary conditions which derive peculiarly from the transformerless character of the network are rather scarce. Two such properties of some generality which are inherent to networks without transformers are (i) the coefficient conditions for RLC 2-ports,' (ii) the paramount character of the node admittance matrix and of the mesh impedance matrix and their inverses for a resistance network.2 The purpose of this paper is to derive a generalization of these properties which includes both of them. PRELIMINARIESWe first summarize some results of graph theory and their application to electric network theory which are needed in the sequel. The details inherent in this summary are given in References 2 and 6. Let be a connected RLC (transformerless) network with b branches and n + 1 nodes. Of course, b > n. Any complete tree T ofThe two nodes of each branch of T define a port, so that an n-port N is thus defined by means of T Similarly, each link may be associated with the loop formed by it and the unique path in T between the vertices of the link. In this way, the system of fundamental loops or meshes M is defined by means of T (formed by deleting one row from the incidence matrix) and B the (6 -n ) x 6 fundamental loop matrix corresponding to the loops of M . Both A and B are unimodular ; that is, the determinant of any square submatrix of either A or B is -1, + 1 or 0.has n branches and b -n links.Let A be the n x 6 reduced incidence matrix ofThe n x n nodal admittance matrix Y, and the nodal impedance matrix Z, of the n-port are given byHere Y is the diagonal matrix of branch admittances, enumerated in the same order as the columns of A, and the prime denotes the transpose of the matrix. Since A, Y are of rank n, 6 respectively, Y, must be nonsingular. For the fundamental loop system M , the (b -n) x ( 6 -n ) mesh impedance matrix Z, and the mesh admittance matrix Y , are given by Z, = BZB', Y, = Z,'

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The transfer function of general two terminal-pair RC networks

Cited by 81 publications

References 3 publications

The transfer function of networks without mutual reactance

The transfer function of networks without mutual reactance

Realization of a transfer function as a passive two‐port RC ladder network with a specified gain

On rlc network matrices

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