Alternating Current — Question 9

Question 9

A sine-calibrated average meter misreads a square wave

A meter measures mean absolute voltage and multiplies it by a calibration constant so it reports the correct rms for any sine wave. It is then connected to a symmetric square wave with amplitude A.

1. Derive the calibration constant.

2. Find the displayed reading and percentage error relative to the true square-wave rms.

Question 9 - Solution

A sine-calibrated average meter misreads a square wave

(a) Method and calculation

$$\langle|v_{\mathrm{sine}}|\rangle=2V_p/\pi,\quad V_{{\mathrm{sine}},\mathrm{rms}}=V_p/\sqrt2.$$$$\boxed{k=\pi/(2\sqrt2)=1.11072}.$$

(b) Interpretation and further calculation

$$\langle|v_{\mathrm{square}}|\rangle=A=V_{{\mathrm{square}},\mathrm{rms}}.$$$$\boxed{V_{\mathrm{display}}=1.11072A,\quad\text{error}=+11.0721\%}.$$

Physical check

A true-rms instrument and a sine-calibrated averaging instrument need not agree for nonsinusoidal signals.