2.4 RMS Voltage Measurement

For the A/C power supply, RMS is equal to the value of the direct current that would produce the same average power dissipation in a resistive load. The RMS value gives the equivalent DC measurement of the A/C power. Mathematically, the root mean square is defined as the square root of the mean square (the arithmetic mean of the squares of a set of numbers). In alternating signals, RMS can be defined as an integral of the squares of the instantaneous values during a cycle.

In the application, the RMS voltage is calculated by the arithmetic mean of the square of a set of numbers on a phase of the three-phase input signal.

Figure 2-3. Sample Signal for RMS Voltage Calculation

Equation for calculating RMS voltage:

$V r m s = \sqrt{\frac{\sum V n}{(N)}}$

Here,

N is the total number of samples
n is the sample number and the possible values are 1, 2, 3, 4...n

$V_{n} = {((A D C C_S T E P_S I Z E) * ({ADCCOUT}_{n}))}^{2}$

Here,

V₁, V₂, V₃...V_n represent the voltage (in mV) of the sampled data points
ADCCOUT_n is the equivalent digital output value for each sampled input signal
ADCC Step Size is,
$A D C C_S T E P_S I Z E = \frac{V ref}{2^{R}}$
Here the ADCC is provided by a reference voltage (V_ref) of 3.3V. It provides a 10-bit binary result using successive approximation, which gives the Resolution (R) of ADCC equal to 10.
Therefore, value of ADCC step size is,
$A D C C_S T E P_S I Z E = \frac{3.3 V}{2^{10}} = 0.00322V = 3.22 mV$