JH Technology Application Note AN11001
What is True RMS – and When do I Need It?
Short answer:
RMS expresses the power capability of an AC source. It is not the same as the average voltage, and
the relationship between average and RMS voltage varies for different waveforms. Instruments
which are not true-rms give correct readings for sine waves (such as line voltage) but can be highly
incorrect when used with triac power controllers (chopped sine wave), variable frequency drives
(VFDs), pulsed waveforms and other non-sinusoidal sources. True-RMS is required whenever you
need accurate measurement of such voltages or currents.
Technical detail:
RMS is a way of expressing the average power available from an AC voltage or current.
Instantaneous power is not steady, but cycles up and down with the voltage.
For a steady DC voltage connected to a resistive load, the power is:
Power = E2/R
where E is the voltage and R is the load resistance. Note that power is proportional to the square of
the voltage. Stated another way, the voltage is proportional to the square root of power.
RMS stands for Root Mean Square, or the Square Root of the Mean (average) of the voltage
Squared. For AC the instantaneous power (in a resistive load) is proportional to the voltage squared.
If you calculate the voltage squared at each and every instant, and then average it (find the mean)
over a complete cycle, the result indicates the average power (E2/R). The square root of this average
value, then, is the RMS voltage. (A similar analysis can be made for current, where Power = I2R.)
Here’s a simple example. Figure 1 shows a pulsed DC source: 100 volts half the time, zero the other
half. The average voltage, of course, is 50 volts.
While the voltage is at 100 volts, the power is (100)2/R, or 10,000/R. At zero volts, the power is zero.
Over the full cycle the average power is 5000/R. The equivalent steady-state voltage which would
produce the same power is the square root of 5000, or 707 volts. This is the RMS voltage. Power =
(707 squared) / R, or 5000/R. Note that the RMS voltage is 1.414 times the average.
Next example – sine wave (Figure 2). Actually, since a sine wave spends half its time positive and
half negative its average voltage is zero, but meters and instruments rectify the voltage before
measuring it. Without going into mathematical detail, the average value of this waveform is 0.637
times the peak voltage. The RMS value is 0.707 times the peak. So, the RMS voltage is 1.11 times the
average.
Simple (not true-RMS) meters and instruments respond to the average value but are calibrated to
read as RMS, so when the average is 63.7 volts the reading will be 70.7 (the RMS value). This is fine,
but only for sine waves. In the pulsed example of Figure 1, an average voltage 63.7 volts will read
70.7 even though the actual RMS value is 90.07V – a serious error!
One last example – Triac-controlled sine wave (Figure 3). If the waveform is turned on at 40% of the
cycle (72 degrees) the average voltage turns out to be 0.417 times the peak; RMS is 0.613 times the
peak. RMS is 1.47 times the average so, again, a simple average-responding measurement would
produce a serious error.
Conclusion: Use true-RMS measurement whenever your voltage is not a pure sine wave.
JH Technology offers true-RMS transmitters in DIN-rail, plug-in and field mount styles.
www.jhtechnology.com
SARASOTA, FL 34233 USA
(800) 808-0300 (941) 927-0300
FAX: (941) 925-8774