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# Synthesis of Passive Networks

15 Jan 1957-

About: The article was published on 1957-01-15 and is currently open access. It has received 567 citations till now.

##### Citations

More filters

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HRL Laboratories

^{1}TL;DR: In a tutorial exposition, the following topics are discussed: definition of a matched filter; where matched filters arise; properties of matched filters; matched-filter synthesis and signal specification; some forms of matched filter.

Abstract: In a tutorial exposition, the following topics are discussed: definition of a matched filter; where matched filters arise; properties of matched filters; matched-filter synthesis and signal specification; some forms of matched filters.

1,138 citations

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TL;DR: The main contributions of the paper are the introduction of a device, which win be called the inerter, which is the true network dual of the spring, which contrasts with the mass element which, by definition, always has one terminal connected to ground.

Abstract: The paper is concerned with the problem of synthesis of (passive) mechanical one-port networks. One of the main contributions of the paper is the introduction of a device, which win be called the inerter, which is the true network dual of the spring. This contrasts with the mass element which, by definition, always has one terminal connected to ground. The inerter allows electrical circuits to be translated over to mechanical ones in a completely analogous way. The inerter need not have large mass. This allows any arbitrary positive-real impedance to be synthesized mechanically using physical components which may be assumed to have small mass compared to other structures to which they may be attached. The possible application of the inerter is considered to a vibration absorption problem, a suspension strut design, and as a simulated.

1,118 citations

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01 May 2001TL;DR: In this review paper various high-speed interconnect effects are briefly discussed, recent advances in transmission line macromodeling techniques are presented, and simulation of high- speed interconnects using model-reduction-based algorithms is discussed in detail.

Abstract: With the rapid developments in very large-scale integration (VLSI) technology, design and computer-aided design (CAD) techniques, at both the chip and package level, the operating frequencies are fast reaching the vicinity of gigahertz and switching times are getting to the subnanosecond levels. The ever increasing quest for high-speed applications is placing higher demands on interconnect performance and highlighted the previously negligible effects of interconnects such as ringing, signal delay, distortion, reflections, and crosstalk. In this review paper various high-speed interconnect effects are briefly discussed. In addition, recent advances in transmission line macromodeling techniques are presented. Also, simulation of high-speed interconnects using model-reduction-based algorithms is discussed in detail.

645 citations

### Cites background from "Synthesis of Passive Networks"

...A network with admittance matrix represented by is passive iff [83], [84], [154]–[157]:...

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TL;DR: This report describes a new approach to nonlinear RLC-networks which is based on the fact that the system of differential equations for such networks has the special form T/-x di dP(i, v) .

Abstract: This report describes a new approach to nonlinear RLC-networks which is based on the fact that the system of differential equations for such networks has the special form T/-x di dP(i, v) ., dv dP(i, v) L(i) dt ~ ~di~ • C(-V)dt dv The function, P(i, v), called the mixed potential function, can be used to construct Liapounov-type functions to prove stability under certain conditions. Several theorems on the stability of circuits are derived and examples are given to illustrate the results. A procedure is given to construct the mixed potential function directly from the circuit. The concepts of a complete set of mixed variables and a complete circuit are defined. Introduction. A. In the extensive theory of electrical circuits many impressive advances have led to a powerful tool for the engineer and the designer. For a wide class of problems one is able to construct a circuit with required properties using a rather complete theory which is available in several textbooks (see, e.g., [1], [2]). Most of these theories are based on the linear differential equations of electrical circuits. However, in recent times many engineering problems have led to the study of nonlinear networks which cannot appropriately be approximated by linear equations. Typical examples in this direction are the so-called flip-flop circuits which have several equilibrium states. Since a linear circuit obviously admits only one equilibrium, a flip-flop circuit can only be described by nonlinear differential equations. The main difference between such circuits and linear ones lies in the nonmonotone character of the voltage-current relations for the resistors. It will be a main point in the following to admit such \"negative resistors\". B. The electrical circuits considered in this paper are general RLC-circuits in which any or all of the elements may be nonlinear. One of the purposes of this paper is to show that the differential equations of such electrical circuits have a special form which has its ultimate basis in the conservation laws of Kirchhoff. It will be derived that under very general assumptions the differential equations have the form di„ dP L> dt di,' (p C'dtt=-%I' ('-r+l,-,r + .). (1) *Received May 29, 1963. The results reported in this paper were obtained in the course of research jointly sponsored by IBM and the Air Force Office of Scientific Research, Contract AF49(638)-1139. 2 R. K. BRAYTON AND J. K. MOSER [Vol. XXII, No. 1 where the i„ represent the currents in the inductors and v, the voltages across the capacitors. The function P(i, v) describes the physical properties of the resistive part of the circuit. Since it has the dimension of voltage times current, it will be called a potential function. This function can be formed additively from potential functions of the single elements similar to the way that the Hamiltonian is formed in particle dynamics from the potential energy and the kinetic energy of the different particles. However, it should be observed that equations (1) do not represent a Hamiltonian system since the latter describes nondissipative motion while in equations (1) the potential P contains dissipative terms. Also, the transformation properties of the above equations are different from Hamiltonian equations in that equations (1) preserve their form under coordinate transformations which leave the indefinite metric -Zi«2+ E ca(dv«)2 (2) p = 1 „ = 0. (1.2) loop Another way of describing this loop law is that to every node one can assign a voltage level such that v„ equals the difference of the defined voltage levels between the end node and initial node.* In the investigation of the circuit dynamics it will be of first importance to know how restrictive Kirchhoff's laws are. They form a set of linear equations, and we study first which of the currents and voltages can be chosen independently. More precisely, we call a set of variables i\\ , • • • , ir , vr+1 , • • ■ , vr+** \"complete\" if they can be chosen independently without leading to a violation of Kirchhoff's laws and if they determine in each branch at least one of the two variables, the current or the voltage. The problem is to describe a complete set of variable

424 citations

### Cites background from "Synthesis of Passive Networks"

...That a circuit can be constructed for any such function is easily shown and can be found in the same paper of Foster (see also Guillemin [11])....

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Alcatel-Lucent

^{1}TL;DR: The use of Krylov-subspace methods for generating reduced-order models of linear subcircuit models that preserve the passivity of linear RLC subcircuits are described.

420 citations

### Additional excerpts

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