Electrical Network Synthesis: A Survey of Recent Work

Hughes, Tim; Morelli, Alessandro; Smith, Malcolm

doi:10.1007/978-3-319-67068-3_21

Cited by 8 publications

(6 citation statements)

References 31 publications

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“…For the damped spring, the mechanical parameters of H ( f ) are the damping, mass, and most importantly the spring constant arranged in a series structure. However, many different structures have the same frequency response function H ( f ) . Thus, the topology of the network and the values of its parameters cannot be determined without additional information.…”

Section: Theorymentioning

confidence: 99%

H-Bonds in Crambin: Coherence in an α-Helix

Minh

Eisenberg

2023

ACS Omega

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We applied coherence analysis�used by engineers to identify linear interactions in stochastic systems�to molecular dynamics simulations of crambin, a thionin storage protein found in Abyssinian cabbage. A key advantage of coherence over other analyses is that it is robust, independent of the properties, or even the existence of probability distributions often relied on in statistical mechanics. For frequencies between 0.391 and 5.08 GHz (corresponding reciprocally to times of 2.56 and 0.197 ns), the displacements of oxygen and nitrogen atoms across α-helix H-bonds are strongly correlated, with a coherence greater than 0.9; the secondary structure causes the Hbonds to effectively act as a spring. Similar coherence behavior is observed for covalent bonds and other noncovalent interactions including H-bonds in β-sheets and salt bridges. In contrast, arbitrary pairs of atoms that are physically distant have uncorrelated motions and negligible coherence. These results suggest that coherence may be used to objectively identify atomic interactions without subjective thresholds such as H-bond lengths angles and angles. Strong coherence is also observed between the average position of adjacent leaves (groups of atoms) in an α-helix, suggesting that the harmonic analysis of classical molecular dynamics can successfully describe the propagation of allosteric interactions through the structure.

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Section: Theorymentioning

confidence: 99%

H-Bonds in Crambin: Coherence in an α-Helix

Minh

Eisenberg

2023

ACS Omega

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“…Of particular interest and importance is the concept of minimality. Notably, it is not known how to find an electric circuit to realise an arbitrary given impedance function minimally (i.e., using the least possible number of elements) [4,9,12]. Surprisingly, well-known networks which are apparently non-minimal in this sense, such as the Bott-Duffin realisation and its simplifications, have in fact recently been shown to be minimal for certain impedance functions [7,8].…”

Section: Introductionmentioning

confidence: 99%

On a concept of genericity for RLC networks

Hughes

Morelli

Smith

2019

Systems & Control Letters

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A recent definition of genericity for resistor-inductor-capacitor (RLC) networks is that the realisability set of the network has dimension one more than the number of elements in the network. We prove that such networks are minimal in the sense that it is not possible to realise a set of dimension n with fewer than n − 1 elements. We provide an easily testable necessary and sufficient condition for genericity in terms of the derivative of the mapping from element values to impedance parameters, which is illustrated by several examples. We show that the number of resistors in a generic RLC network cannot exceed k + 1 where k is the order of the impedance. With an example, we show that an impedance function of lower order than the number of reactive elements in the network need not imply that the network is non-generic. We prove that a network with a non-generic subnetwork is itself non-generic. Finally we show that any positive-real impedance can be realised by a generic network. In particular we show that sub-networks that are used in the important Bott-Duffin synthesis method are in fact generic.

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“…[15, p. 3]. The synthesis procedure developed by Bott and Duffin [6] resolves this drawback and does not need any transformers, however the number of reactive elements in the synthesized circuit is larger than the McMillan degree in general, while improvements are available, see also [15][16][17]30].…”

Section: Introductionmentioning

confidence: 99%

“…The present paper does not deal with the synthesis problem, but with the structural properties of an implicit operator (represented by G(s)) describing the dynamics of a given and fix RLC network which we aim to analyze. We stress that, in particular, there is no overlap with the works [15][16][17]30] which are concerned with network synthesis. Also note that the latter refers to realization issues of transfer functions of single-input, single-output (SISO) systems; in our approach we consider properties of the implicit internal transfer function that has no inputs and no outputs.…”

Section: Introductionmentioning

confidence: 99%

“…Also note that the latter refers to realization issues of transfer functions of single-input, single-output (SISO) systems; in our approach we consider properties of the implicit internal transfer function that has no inputs and no outputs. Apart from this fundamental difference between implicit internal models (discussed here) and the realization of SISO systems discussed in network synthesis (e.g., [15][16][17]30]), there are some common issues such as the McMillan degree, but this is where the similarity stops.…”

Section: Introductionmentioning

confidence: 99%

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The Pseudo-McMillan Degree of Implicit Transfer Functions of RLC Networks

Berger

Karcanias

Livada

2018

Circuits Syst Signal Process

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We study the structure of a given RLC network without sources. Since the McMillan degree of the implicit network transfer function is not a suitable measure for the complexity of the network, we introduce the pseudo McMillan degree to overcome these shortcomings. Using modified nodal analysis models, which are linked directly to the natural network topology, we show that the pseudo McMillan degree equals the sum of the number of capacitors and inductors minus the number of fundamental loops of capacitors and fundamental cutsets of inductors; this is the number of independent dynamic elements in the network. Exploiting this representation we derive a minimal realization of the given RLC network, that is one where the number of involved (independent) differential equations equals the pseudo McMillan degree.

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Electrical Network Synthesis: A Survey of Recent Work

Cited by 8 publications

References 31 publications

H-Bonds in Crambin: Coherence in an α-Helix

H-Bonds in Crambin: Coherence in an α-Helix

On a concept of genericity for RLC networks

The Pseudo-McMillan Degree of Implicit Transfer Functions of RLC Networks

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