Synthesis of essential‐regular bicubic impedances

Abstract

Summary This paper provides a complete realisation of a special class of positive‐real bicubic impedances. The problem is motivated by the concept of the inerter, which is the mechanical dual of a capacitor. This device allows mechanical network synthesis, by completing the electrical mechanical analogy. With mechanical synthesis, the emphasis is to minimise the number of elements required to allow feasible implementation. The definitions of simple‐series‐parallel networks and essential‐regular positive‐real functions are introduced. The simple‐series‐parallel minimum‐reactive networks that can realise all essential‐regular bicubics are identified and grouped into six network quartets. One of the advantages of these networks is that they contain the minimal number of reactive elements. The necessary and sufficient realisability conditions for all these networks, as well as corresponding element values, are then derived. Finally, numerical examples are provided to illustrate the validity of the theoretical results. In the course of the argument, interesting conclusions regarding essential‐regular bilinear and biquadratic functions have also been presented. Copyright © 2017 John Wiley & Sons, Ltd.

Synthesis of low‐complexity mechanical networks with constrained element values

“…Since the invention of a mechanical element named “inerter,” research interest in synthesis of passive networks has revived due to the control approach utilizing passive mechanisms . As an important branch of system theory, passive network synthesis experienced its “golden era” during the 1930s to the and after the 1970s, its research interest declined despite some new developments .…”

“…It is noted that the velocities related to an inertial system, which is denoted as the mechanical ground . Using the force‐current analogy, the capacitor can be completely analogous to the inerter, and the analogy between passive electrical and mechanical networks is completed . Therefore, passive network synthesis can be completely transplanted into passive mechanical network design.…”

“…The minimal realization problems of low‐degree functions have been widely investigated in the years 2002‐2017 . In addition to the total number of elements, it is also significant to restrict the number of dampers and inerters, since the cost and construction complexity of dampers and inerters are much higher than those of springs.…”

“…Since the invention of a mechanical element named "inerter," 1 research interest in synthesis of passive networks has revived due to the control approach utilizing passive mechanisms. [2][3][4][5][6][7][8][9][10][11][12][13] As an important branch of system theory, passive network synthesis experienced its "golden era" during the 1930s to the [14][15][16][17][18][19][20][21][22][23] and after the 1970s, its research interest declined despite some new developments. [24][25][26][27][28][29][30] This field is to investigate the physical realization of passive systems as networks containing only passive components such as resistors, inductors, and capacitors and how to reduce the realization redundancy.…”

Schwarz lemma for driving point impedance functions and its circuit applications

“…The aim of this study is to perform boundary analysis of derivative of PRFs. Derivative of PRFs are mainly used in network synthesis, [4][5][6][7] in control systems 8,9 and control theory, 10 signal processing, 11,12 and in microwave engineering. 13,14 As an exemplary application, Hazony has used the derivative of PRF to design a gyrator.…”