任意有理函数与多项式在非福斯特电阻-电容-电感网络中的表示
Representation of arbitrary rational functions and polynomials by non-Foster resistor-capacitor-inductor networks
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中文总结 AI 辅助
本文证明取消正性限制后，任意有理函数或多项式均可由含负元件的RLC网络表示，无重根时分解为简单子电路，有重根时采用迭代惠斯通电桥。
中文摘要 AI 辅助
Bott-Duffin定理表明，任意有限阶的正实有理函数（代表一个无源网络）可以用有限个正值的电阻、电容和电感来表示。本文证明，若取消正性限制，则任意阶的任意有理函数或多项式都可以用（可能为负值的）电感、电容和电阻组成的网络来表示。当没有重根时，该表示是若干简单子电路之和，每个子电路包含不超过四个元件。当存在重根时，则需要更复杂的电路，本文采用特殊形式的迭代惠斯通电桥来实现。
英文摘要
The Bott-Duffin theorem shows that any arbitrary positive real rational function of finite order, representing a passive network, can be represented by a finite number of positive value resistors, capacitors and inductors. It is shown here that if the positivity restriction is lifted, any rational function or polynomial of any order may be represented by a network of (possibly negative) inductors, capacitors and resistors. When there are no repeated roots this is a sum of simple sub-circuits each of which contains no more than four components. When there are repeated roots a more complex circuit is required, here featuring iterated Wheatstone bridges of special form.
发表机构
- Universal Electromagnetics Ltd.（通用电磁学有限公司）
机构由 AI 辅助整理，请以论文原文为准。
