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# Elements of network synthesis

01 Jan 1963-

About: The article was published on 1963-01-01 and is currently open access. It has received 63 citations till now.

##### Citations

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18 Jun 1969

TL;DR: The realisation of negative-impedance convertors and invertors using the bridge-type circuit using the nullor to infinite-gain controlled sources is briefly surveyed and a relevant theorem concerning passivity is proved.

Abstract: The realisation of negative-impedance convertors (n.i.c.s) and invertors (n.i.i.s) using the bridge-type circuit is briefly surveyed. An equivalence relating the nullor to infinite-gain controlled sources is first proved, and is then used for the derivation of nullator-norator equivalent circuits for n.i.c.s and n.i.i.s. Some properties of networks containing singular elements, which are used in the realisation of gyrators, are investigated. Nullator-norator equivalent circuits for gyrators are derived by using the n.i.c.s and n.i.i.s. They are converted into physical networks by using the proved equivalence. Gyrator circuits are obtained by replacing nullors by operational amplifiers. A stability analysis of the gyrator circuits is produced and a relevant theorem concerning passivity is proved. The feasible Qfactors and the accuracy of the gyrator circuits are indicated by some experimental results. A generalised-impedance convertor (g.i.c.) is defined by generalising the n.i.c. theory, and it is shown that the gyrator circuits described can be used as g.i.c.s. The application of the gyrator and g.i.c. circuits in the synthesis of RC-active networks is considered. Finally, a highpass filter using gyrators and a bandpass filter using g.i.c.s are designed, and the experimental results are given.

252 citations

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IBM

^{1}TL;DR: In this paper, the transient response of an n-conductor, coupled transmission-line system, which is characterized by multiple propagation modes of unequal phase velocities, is computed.

Abstract: This paper presents an effective method for computing the transient response of an n-conductor, coupled transmission-line system, which is characterized by multiple propagation modes of unequal phase velocities. To derive the computational algorithm, an equivalent circuit consisting of n decoupled transmission lines in conjunction with two congruence transformers was constructed and converted into two disjointed resistive n-ports. It is shown that the electrical behavior of the coupled transmission lines can be completely described by the static capacitance matrices of the conductor system. The experimental result obtained on a three-conductor, microstrip printed circuit was found to be in excellent agreement with the computed result.

235 citations

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TL;DR: In this paper, the authors show the equivalence of irreducible realization in control theory and degree of rational matrix in network theory and show that the degree of a rational matrix is a function of the number of nodes in a graph.

Abstract: Equivalence of irreducible realization in control theory and degree of rational matrix in network theory

180 citations

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TL;DR: In this article, special numerical integration formulas are developed which transform a differential equation into a difference equation, such that the differential equation and the corresponding difference equation are both stable or else they are both unstable.

Abstract: A differential equation is stable if the roots of the characteristic polynomial are in the interior of the left half plane. Likewise a difference equation is stable if the roots of the characteristic polynomial are in the interior of the unit circle. This paper concerns algorithms which test polynomials for these properties. Also of concern is the relationship between the two problems. In particular, special numerical integration formulas are developed which transform a differential equation into a difference equation. These formulas are such that the differential equation and the corresponding difference equation are both stable or else they are both unstable.

58 citations

### Cites background from "Elements of network synthesis"

...Here T is the forward translation operator defined as (4) TU(t) = U(t + h) and h is the spacing of the grid points....

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