物理实验

方波激励下的一阶RC 响应的简捷解析

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  • 华东师范大学物理与电子科学学院,上海 200241
赵强(1972—),男,新疆奇台县人,华东师范大学物理系副研究员,博士,主要从事物理教学和凝聚态物理研究工作.

收稿日期: 2019-05-16

  修回日期: 2019-09-18

  网络出版日期: 2020-04-20

基金资助

华东师范大学课程建设项目(40400-19202-511232 / 112)资助

A short-cut analysis of the first order RC response under square wave excitation

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  • School of Physics and Electronic Science,East China Normal University,Shanghai 200241,China

Received date: 2019-05-16

  Revised date: 2019-09-18

  Online published: 2020-04-20

摘要

通过简易的数学方法,比较直观地解析描述了RC 电路在周期为T、幅值为Um 和占空比为δ 的方波电压u 激励下的电容器C 上的响应电压uc 的变化情况,得出uc 在u 的上升沿和下降沿上的值将分别单调连续地收敛于Um (1-A1 )A2 / (1-A1 A2 )和Um(1-A1 )/ (1-A1 A2 ),其中A1 = e-Tδ / (RC)和A2 = e-T(1-δ)/ (RC). 同时也对各参数之间的关系进行了分析探讨.所得结论不但有助于理解和分析方波激励下的一阶RC 暂态过程的实验现象,也有助于改善实验设计时对参数的选择.

本文引用格式

赵 强, 孙殿平, 张文倩, 郭超修 . 方波激励下的一阶RC 响应的简捷解析[J]. 大学物理, 2020 , 39(04) : 34 -36 . DOI: 10.16854 / j.cnki.1000-0712.190222

Abstract

When a square wave voltage u with the period T,the amplitude Um and the duty ratio δ is used as the excitation,it is deduced explicitly by a simple method that the values of the response,uc,the voltage across the capacitor,on the rising edge and falling edge will converge monotonically and continuously to Um(1-A1 )A2 / (1-A1 A2)and Um(1-A1 )/ (1-A1 A2 ),respectively (where A1 = e-Tδ / (RC),A2 = e-T(1-δ)/ (RC)).Moreover,the relationships among the parameters are also discussed. The results are not only useful for understanding and analyzing the experimental phenomena of the first-order RC transient process under square wave excitation,but also helpful for improving the experimental design.

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