Root Mean Square (RMS)

Root Mean Square is a way of comparing arbitrary waveforms based upon their equivalent energy. RMS voltage is the contant (DC) voltage that would be required to produce the same heat in a resistive load, indicating equivalent ability to do work. You can't use a simple "average voltage": Consider that a sine wave has positive and negative phases that would average to zero, yet it still generates heat regardless of the polarity of the voltage.

The RMS method takes the square of the instantaneous voltage before averaging, then takes the square root of the average. This solves the polarity problem, since the square of a negative value is the same as the square of a positive value. For a sine wave, the RMS value thus computed is the same as the amplitude (zero-to-peak value) divided by the square root of two, or about 0.7071 of the amplitude. For a repetitive waveform like this, an accurate calculation can be done by averaging over a single cycle of the wave (or an integer number of cycles), but for random noise sources the averaging time must be long enough to get a good representation of the characteristics of the source.

For noise or signal bursts, the RMS value is still the effective heating value, but of course it is reduced because the signal is not always present. If you know the RMS value of the continuous signal, the true RMS of the burst will be the continuous RMS times the square root of the fraction of the time the signal is on.

Root-Square Summation of Components:

The Root-Square method is used to compute a single value that represents the composite of different sine wave components whose amplitudes you already know. You just square each of the values and sum them together, then take the square root of the total. If the original values were RMS, the result will be also be an RMS value. If the originals were zero-to-peak amplitudes, then the result will be the equivalent amplitude of a sine wave having the same energy as the sum... you can multiply this by 0.7071 to get the RMS value of the composite.

This is the method used to find the total energy in a band of Spectrum output frequencies using the Sigma mode of the cursor readouts.

If you have a set of values that are in dB, you can find the effective combined dB by first converting each back to volts squared, summing them all together, and converting back to dB. This is the method used in the RMS "Sum" of dB Values topic, which includes a discussion of the dB_Sum macro supplied with Daqarta.