RMS

root-mean-square. The RMS voltage of a signal is computed by squaring the instantaneous voltage, integrating over the desired time, and taking the square root.

The reason that RMS computation is used for most electronic and physical measurements is that we want to find the power carrying capability of a signal. Therefore the instananeous voltage values are squared, giving power, which is then summed up before converting back to voltage by the square root operation.

The accuracy of an RMS measurement of a noise-free DC signal or sinusoidal signal can often be derived by looking at the accuracy specifications of the instrument. However, you must very carefully examine the signal to make sure that it truly is "clean" or noise free. If significant common mode voltage exists, you must choose an averaging time and measurement technique so that the common mode voltage is suppressed to be at least a factor of three below your desired measurement accuracy.

If you are making an RMS measurement on a noise signal, the error of the measurement will typically be dominated by the effective number of statistical averages you perform, and not as much on the actual "sine wave" (data sheet) accuracy of the instrument. The random error (with 95% confidence) of a measurement on random noise signals is equal to

where B = Bandwidth of the measurement in Hz
and T = the averaging time in seconds.

For example, if you measure random noise with a bandwidth of 100 Hz over 1 second, the error will be equal to

The effect of averaging time on a random signal, can be seen in demo 1. (Requires the the LabVIEW Player.)

If you are measuring a sine wave and there is significant random noise present, the noise will bias the value of the sine wave measurement to be too high. In cases of this nature, it is best to use a spectrum analysis technique where the sine wave component can be separated from the random noise components. The longer the measurement, the more noise can be removed, and the less the value of the sine wave will be affected by the noise. Long measurement times make very narrow spectrum measurements possible. This is illustrated in demo 2.

In demo 3 we illustrate that you can also find sines buried in noise using synchronous averaging.

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