We analyze Feynman’s work on the response of an amplifier performed at Los Alamos and described in a technical report of 1946, as well as lectured on at the Cornell University in 1946–47 during his course on Mathematical Methods. The motivation for such a work was Feynman’s involvement in the Manhattan Project, for which the necessity emerged of feeding the output pulses of counters into amplifiers or several other circuits, with the risk of introducing distortion at each step. In order to deal with such a problem, Feynman designed a theoretical “reference amplifier”, thus enabling a characterization of the distortion by means of a benchmark relationship between phase and amplification for each frequency, and providing a standard tool for comparing the operation of real devices. A general theory was elaborated, from which he was able to deduce the basic features of an amplifier just from its response to a pulse or to a sine wave of definite frequency. Moreover, in order to apply such a theory to practical problems, a couple of remarkable examples were worked out, both for high-frequency cutoff amplifiers and for low-frequency ones. A special consideration deserves a mysteriously exceptional amplifier with best stability behavior introduced by Feynman, for which different physical interpretations are here envisaged. Feynman’s earlier work then later flowed in the Hughes lectures on Mathematical Methods in Physics and Engineering of 1970–71, where he also remarked on causality properties of an amplifier, that is on certain relations between frequency and phase shift that a real amplifier has to satisfy in order not to allow output signals to appear before input ones. Quite interestingly, dispersion relations to be satisfied by the response function were introduced.

中文翻译：

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寻找回应：费曼理论参考放大器的迷人奥秘

我们分析了费恩曼在Los Alamos进行的放大器响应的工作，该工作在1946年的技术报告中进行了描述，并在1946–47年的康奈尔大学数学方法课程中进行了演讲。进行这项工作的动机是费曼参与了曼哈顿计划，因此有必要将计数器的输出脉冲馈送到放大器或其他几个电路中，而每个步骤都有引入失真的风险。为了解决这个问题，Feynman设计了一种理论上的“参考放大器”，从而可以通过每个频率的相位和放大率之间的基准关系来表征失真，并提供了一个标准工具来比较实际频率。设备。阐述了一般理论，从中，他可以从放大器对脉冲或一定频率的正弦波的响应中得出放大器的基本特征。此外，为了将这种理论应用于实际问题，针对高频截止放大器和低频截止放大器，设计了两个杰出的例子。值得特别注意的是，Feynman推出了一种具有最佳稳定性的神秘而卓越的放大器，此处设想了不同的物理解释。Feynman的早期工作随后在1970-71年的休斯关于物理和工程学的数学方法的讲座中进行了介绍，他还谈到了放大器的因果特性，这是真实放大器必须满足的频率和相移之间的某些关系，以便不允许输出信号出现在输入信号之前。非常有趣的是，介绍了响应函数要满足的色散关系。