This letter proposes an entirely new method for performing analogue signal filtering. All circuits are based upon current amplifiers but derived from well-known voltage amplifier circuits. These circuits possess the same sensitivity properties as their voltage amplifier counterparts. However, it is expected that these circuits will operate at higher signal bandwidths, with greater linearity, and have larger dynamic range than their voltage-based circuit counterparts.

All current-mode frequency selective circuits

The success of equilibrium thermodynamics in describing static phenomena has inspired many attempts to develop a rigorous thermodynamics of rate processes

Network thermodynamics: dynamic modelling of biophysical systems

The multivariate Tutte polynomial (known to physicists as the Potts-model partition function) can be defined on an arbitrary finite graph G, or more generally on an arbitrary matroid M, and encodes much important combinatorial information about the graph (indeed, in the matroid case it encodes the full structure of the matroid). It contains as a special case the familiar two-variable Tutte polynomial -- and therefore also its one-variable specializations such as the chromatic polynomial, the flow polynomial and the reliability polynomial -- but is considerably more flexible. I begin by giving an introduction to all these problems, stressing the advantages of working with the multivariate version. I then discuss some questions concerning the complex zeros of the multivariate Tutte polynomial, along with their physical interpretations in statistical mechanics (in connection with the Yang--Lee approach to phase transitions) and electrical circuit theory. Along the way I mention numerous open problems. This survey is intended to be understandable to mathematicians with no prior knowledge of physics.

The multivariate Tutte polynomial (alias Potts model) for graphs and matroids

Homogeneous multivariate polynomials with the half-plane property

It is well known that arbitrary interconnections of passive (possibly nonlinear) resistors, inductors, and capacitors define passive systems, with port variables the external source voltages and currents, and storage function the total stored energy. In this note, we prove that for a class of RLC circuits with convex energy function and weak electromagnetic coupling it is possible to "add a differentiation" to the port terminals preserving passivity - with a new storage function that is directly related to the circuit power. The result is of interest in circuits theory, but also has applications in control as it suggests the paradigm of power shaping stabilization as an alternative to the well-known method of energy shaping. We show in this note that, in contrast with energy shaping designs, power shaping is not restricted to systems without pervasive dissipation and naturally allows to add "derivative" actions in the control. These important features, that stymie the applicability of energy shaping control, make power shaping very practically appealing. To establish our results we exploit the geometric property that voltages and currents in RLC circuits live in orthogonal spaces, i.e., Tellegen's theorem, and heavily rely on the seminal paper of Brayton and Moser in 1964.

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Power shaping: a new paradigm for stabilization of nonlinear RLC circuits

B. D. H. Tellegen was the first to point out (1952, 1953) the generality and wide-ranging usefulness of the theorem that bears his name. Nevertheless, the theorem is still not as widely known as its utility warrants. The authors of this monograph set out to correct this neglect, noting that "There is hardly a basic network theorem that cannot be proved by invoking Tellegen's theorem. The simplicity and generality of the theorem make it attractive pedagogically, and its ability to generalize known results and lead to new results indicates its research value. This theorem definitely should be in every circuit designer's kit of tools."Tellegen's theorem is unusual in that it depends solely upon Kirchhoff's laws and the topology of the network. The theorem thus applies to all electrical networks that obey Kirchhoff's laws, whether linear or nonlinear, time-invariant or time-variant, reciprocal or nonreciprocal, passive or active, single-valued or multiple-valued, hysteretic or nonhysteretic. The excitation is arbitrary--it may be sinusoidal, exponential, periodic, transient, or random. Also, the initial conditions may be arbitrarily chosen. The modern interest in nonlinear and time-variant networks gives Tellegen's theorem a special new importance, because it is one of the very few general theorems that apply to such networks.To demonstrate its range of applications and the theorem's great power in the derivation of other basic and important theorems about electrical networks (and the extent that these other theorems are special cases of Tellegen's), the authors have collected more than 100 such theorems and have shown that they can be proved from Tellegen's theorem. Most of these were known before; but some are extended in their range of validity, and a few are new. (Apart from Tellegen's theorem, this collection of theorems is valuable in its own right.) Applications are given to automated network synthesis and to nonlinear, time-varying, switching, nonreciprocal, and other networks--all the major areas of network theory are covered. In addition, extensions of the theorem to other physical systems are discussed, including applications to the electromagnetic field, electron beams and plasmas, and quantum mechanics.The theorem is proved in its most general form thus far known. In addition, two weaker forms that have useful properties for certain applications are presented. In these weaker forms, the theorem applies to voltages, currents, and wave (or scattering) variables. The use of wave variables in Tellegen's theorem is believed to be new.Oliver Heaviside used a version of the theorem in 1883 to establish a specific result, and others have used its equivalent in a limited range of applications. Others (Weyl, 1923; Bott, 1949) have derived highly abstract and mathematical versions without regard to applications. But Tellegen was the first to devote a full paper to the subject and the first to grasp the theorem's general importance and applicability. In a similar way, the authors of this monograph are the first to devote a book to the subject and the first to collect (or newly present) all of the most important applications of the theorem in the hope of bringing it into the common currency it deserves.

Simon Duinker

Papers

Tellegen's theorem and electrical networks