方波激励下的一阶RC响应的简捷解析

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U m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u c的变化情况,得出u c在u的上升沿和下降沿上的值将分别单调连续地收敛于U m(1-A 1)A 2/(1-A 1 A 2)和U m(1-A 1)/(1-A 1 A 2),其中A 1=e-Tδ/(RC)和A 2=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.

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

When a square wave voltage u with the period T,the amplitude U m and the duty ratioδis used as the excitation,it is deduced explicitly by a simple method that the values of the response,u c,the voltage across the capacitor,on the rising edge and falling edge will converge monotonically and continuously to U m(1-A 1)A 2/(1-A 1A 2)and U m(1-A 1)/(1-A 1A 2),respectively(where A 1=e-Tδ/(RC),A 2=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.