RLC串联电路欠阻尼信号衰减常数可视化测量的评估与修正

Evaluation and Correction of Visual Measurement of Underdamped Signal Attenuation Constant in RLC Series Circuit

采用三种示波器可视化方法测量RLC串联电路欠阻尼信号的衰减常数,并对测量结果进行比较与修正,发现无论是传统包络线法近似测量、还是图解法、比值法精确测量,测得的时间常数都与理论值存在超过10%的较大偏差。Desmos软件拟合欠阻尼图像时,使用图解法和比值法测得的时间常数与理论值相差小于0.1%,说明图解法和比值法的确能够较准确地测量时间常数,实际操作过程中存在的系统误差主要来源于电容和电感的内阻。采用能量损耗方程式,计算损耗电阻,并对理论值进行了修正,修正后的理论值与实验测量值相对误差小于1%,说明了修正的有效性。

The attenuation constant of under damped signal in RLC series circuit is measured by three visualization methods with oscilloscope,and the measurement results are compared and corrected.It is found that whether the traditional envelope method is used for approximate measurement,or the graphic method or the ratio method for accurate measurement,the measured time constant has a large deviation of more than 10%from the theoretical value.Using Desmos software to fit the underdamped image,it is found that the difference between the measured value and the theoretical value is less than 0.1%,which indicates that the graphical method and the ratio method can measure the time constant more accurately.The system error in the actual operation mainly comes from the internal resistance of capacitance and inductance.The energy loss equation is used to calculate the loss resistance,and the theoretical value is corrected.The relative error between the corrected theoretical value and the experimental value is less than 1%,which shows the effectiveness of the correction.