A new proof of Reichert's theorem

Zhang, Sara Y; Jiang, Jason Zheng; Smith, Malcolm

doi:10.1109/cdc.2016.7798656

Cited by 2 publications

(2 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, it can be computed that the impedance is a biquadratic, so D(E) has 6 rows, hence rank(D) ≤ 6. This network has been considered in [10], [19]. Example 5.…”

Section: Examplesmentioning

confidence: 99%

On a concept of genericity for RLC networks

Hughes

Morelli

Smith

2019

Systems & Control Letters

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…In fact, it can be computed that the impedance is a biquadratic, so D(E) has 6 rows, hence rank(D) ≤ 6. This network has been considered in [10], [19]. Example 5.…”

Section: Examplesmentioning

confidence: 99%

On a concept of genericity for RLC networks

Hughes

Morelli

Smith

2019

Systems & Control Letters

Self Cite

View full text Add to dashboard Cite

show abstract

“…This proof was later reworked in [19], and some parts of the argument were expanded. Recently, an alternative proof based on a result in [5] was provided in [40].…”

Section: Enumeration Approachmentioning

confidence: 99%

Electrical Network Synthesis: A Survey of Recent Work

Hughes

Morelli

Smith

2018

Lecture Notes in Control and Information Sciences - Proceedings

Self Cite

View full text Add to dashboard Cite

The field of electrical network synthesis has a number of long-standing unanswered questions. The most perplexing concern minimality in the context of resistor, inductor and capacitor (RLC) network synthesis. In particular, the famous Bott-Duffin networks appear highly non-minimal from a system theoretic perspective. We survey some recent developments on this topic. These include results establishing the minimality of the Bott-Duffin networks and their simplifications for realising certain impedances; enumerative approaches to the analysis of RLC networks within given classes of restricted complexity; and new necessary and sufficient conditions for a (not necessarily controllable) system to be passive. Finally, some remaining open questions are discussed.

show abstract

A new proof of Reichert's theorem

Cited by 2 publications

References 8 publications

On a concept of genericity for RLC networks

On a concept of genericity for RLC networks

Electrical Network Synthesis: A Survey of Recent Work

Contact Info

Product

Resources

About