Foster's seminal treatise on lossless networks has been published almost 100 years ago and a particularly notable conclusion drawn therein, i.e. that the reactance (and susceptance) functions are always monotonically increasing with frequency, is frequently referred to as Foster?s theorem. In this paper we present two variants for an alternative simple derivation of a stronger form of this theorem, which holds for the driving point reactance (susceptance) of general lossless devices, i.e. also configurations without lumped elements. One version introduces a realizable lumped element equivalent circuit approximating the considered circuit in a narrow band around a particularly considered frequency. It turns out that this avenue of proof also facilitates an alternative validation of the realizability of the so called Foster 1 and 2 realizations.

中文翻译：

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福斯特电抗定理的替代路径及其与窄带等效电路的关系

福斯特关于无损网络的开创性论文发表于近 100 年前，其中得出的一个特别值得注意的结论，即电抗（和电纳）函数总是随频率单调增加，经常被称为福斯特定理。在本文中，我们提出了该定理的更强形式的替代简单推导的两种变体，它适用于一般无损设备的驱动点电抗（电纳），即没有集总元件的配置。一个版本引入了可实现的集总元件等效电路，该电路在特定考虑的频率附近的窄带中近似考虑的电路。事实证明，这种证明途径也有助于对所谓的 Foster 1 和 2 实现的可实现性进行替代验证。