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# RMS

Compute true root mean square (RMS) value of signal

## Library

Control and Measurements/Measurements

## Description

The RMS block computes the true root mean square (RMS) value of the input signal. The true RMS value of the input signal is calculated over a running average window of one cycle of the specified fundamental frequency:

$RMS\left(f\left(t\right)\right)=\sqrt{\frac{1}{T}\underset{t-T}{\overset{t}{\int }}f{\left(t\right)}^{2}},$

where f(t) is the input signal and T is 1/(fundamental frequency).

As this block uses a running average window, one cycle of simulation must complete before the output gives the correct value. For the first cycle of simulation, the output is held to this specified initial RMS value.

## Dialog Box and Parameters

True RMS value

Select this check box to have the block compute the true RMS value of the input signal.

Clear this check box to have the block compute the fundamental value of the input signal, divided by sqrt(2).

Fundamental frequency (Hz)

Specify the fundamental frequency, in hertz, of the input signal.

Initial RMS value

Specify the initial RMS value of the output signal.

Sample time

Specify the sample time of the block, in seconds. Set to 0 to implement a continuous block.

## Characteristics

 Sample Time Specified in the Sample Time parameterContinuous if Sample Time = 0 Scalar Expansion Yes, of the parameters Dimensionalized Yes

## Example

The power_RMS_THDpower_RMS_THD example shows two applications of the RMS measurement block. One RMS block calculates the true RMS value of a signal with harmonics, and another one calculates the RMS value of the same signal at the fundamental frequency.

The model sample time is parameterized by the Ts variable set to a default value of 50e-6 s. Set Ts to 0 in the command window to simulate the model in continuous mode.