RMS Value (Root Mean Square)
The equivalent constant value that gives the heating effect a waveform produces in a resistor. With a chopped PWM waveform the average and the RMS differ: at 25% duty cycle a 20 A peak current has an average of 5 A but an RMS value of 10 A. Heating calculations are always done with the RMS value.
The difference arises because the loss is proportional to the square of the current. When you take the average you simply sum the current; when you take the RMS you first square it, then find its average, then take the square root. Short but tall pulses affect the average little and the heat a lot.
- Square wave example: A current with duty cycle D and peak value I has an average of I×D and an RMS value of I×square root(D). At 25% duty cycle the average is a quarter of the peak while the RMS is half of it.
- Practical consequence: If you read 5 A on your multimeter and pick the cable and fuse accordingly, in reality you will face a heating effect of 10 A.
- Choosing an instrument: Most cheap multimeters read the average and only show correct RMS for a clean sine wave. With a chopped waveform you need a true-RMS instrument.
At the driver output the current is not fully chopped; the motor inductance filters the current, and as the waveform flattens the average and the RMS converge.
Where this term is used: DC Motor Driver Selection Guide