General Analytic Solution of the Telegrapher’s Equations and the Resulting Consequences for Electrically Short Transmission Lines

S. Kühn
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引用次数: 6

Abstract

Based on classical circuit theory, this article develops a general analytic solution of the telegrapher’s equations, in which the length of the cable is explicitly contained as a freely adjustable parameter. For this reason, the solution is also applicable to electrically short cables. Such a model has become indispensable because a few months ago, it was experimentally shown that voltage fluctuations in ordinary but electrically short copper lines move at signal velocities that are significantly higher than the speed of light in a vacuum. This finding contradicts the statements of the special theory of relativity but not, as is shown here, the fundamental principles of electrical engineering. Based on the general transfer function of a transmission line, the article shows mathematically that an unterminated, electrically short cable has the characteristics of an ideal delay element, meaning that an input signal appears at the output with a slight delay but remains otherwise unchanged. Even for conventional cables, the time constants can be so small that the corresponding signal velocities can significantly exceed the speed of light in a vacuum. The article also analyses the technical means with which this effect can be conveyed to very long cables.
电短传输线电报方程的一般解析解及其结果
基于经典电路理论,本文提出了电报机方程的一般解析解,其中电缆长度被明确地包含为一个可自由调节的参数。因此,该解决方案也适用于电短路电缆。这样的模型变得不可或缺,因为几个月前,实验表明,普通但电短的铜线中的电压波动以明显高于真空中光速的信号速度移动。这一发现与狭义相对论的说法相矛盾,但与这里所示的电气工程的基本原理不矛盾。基于传输线的一般传递函数,本文从数学上表明,未端接的短电缆具有理想延迟元件的特性,这意味着输入信号在输出端出现轻微延迟,但在其他方面保持不变。即使对于传统的电缆,时间常数也可能很小,以至于相应的信号速度可能大大超过真空中的光速。文章还分析了将这种效应传递到超长电缆上的技术手段。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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