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首页> 外文期刊>IEEE Transactions on Automatic Control >Why RLC Realizations of Certain Impedances Need Many More Energy Storage Elements Than Expected
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Why RLC Realizations of Certain Impedances Need Many More Energy Storage Elements Than Expected

机译：为什么某些阻抗的RLC实现需要比预期更多的储能元件

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摘要

It is a significant and longstanding puzzle that the resistor, inductor, and capacitor (RLC) networks obtained by the established RLC realization procedures appear highly nonminimal from the perspective of the linear systems theory. Specifically, each of these networks contains significantly more energy storage elements than the McMillan degree of its impedance, and possesses a nonminimal state-space representation whose states correspond to the inductor currents and capacitor voltages. Despite this apparent nonminimality, there have been no improved algorithms since the 1950s, with the concurrent discovery by Reza, Pantell, Fialkow, and Gerst of a class of networks (the RPFG networks), which are a slight simplification of the Bott-Duffin networks. Each RPFG network contains more than twice as many energy storage elements as the McMillan degree of its impedance, yet it has never been established if all of these energy storage elements are necessary. In this paper, we present some newly discovered alternatives to the RPFG networks. We then prove that the RPFG networks, and these newly discovered networks, contain the least possible number of energy storage elements for realizing certain positive-real functions. In other words, all RLC networks that realize certain impedances contain more than twice the expected number (McMillan degree) of energy storage elements.
机译：从线性系统理论的角度来看，通过已建立的RLC实现程序获得的电阻器，电感器和电容器（RLC）网络在很大程度上显得非常微不足道，这是一个长期存在的重大难题。具体而言，这些网络中的每个网络都包含比其阻抗的麦克米伦度大得多的能量存储元素，并且拥有非最小状态空间表示，其状态对应于电感器电流和电容器电压。尽管存在明显的非最小性，但自1950年代以来，就没有任何改进的算法，Reza，Pantell，Fialkow和Gerst并发发现了一种网络（RPFG网络），这是对Bott-Duffin网络的略微简化。 。每个RPFG网络包含的能量存储元件数量是其阻抗的麦克米伦度的两倍以上，但是，如果所有这些能量存储元件都是必需的，则从未建立。在本文中，我们提出了一些新发现的RPFG网络替代方案。然后，我们证明RPFG网络以及这些新发现的网络包含用于实现某些正实函数的最少数量的能量存储元素。换句话说，所有实现某些阻抗的RLC网络都包含能量存储元件预期数量（麦克米伦度）的两倍以上。

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