Maxim Integrated 71M6534 Energy Meter IC Family Software - Manual (Page 60)

71M653X Software User’s Guide
Here's how it is derived:
To calculate phase correction:
tan (Φ) = -VARh_measured/Wh_measured
The value of tan(Φ) can be used directly without calculating trigonometric values.
For 60Hz metering, from the data sheet,
ce_phase_corr = 1048576 * ((0.02229 * tan(Φ))/(0.1487 - (0.0131 * tan(Φ))))
For 50Hz metering, from the data sheet,
ce_phase_corr = 1048576 * ((0.0155 * tan(Φ))/(0.1241 - (0.009695 * tan(Φ))))
For the volts:
V_gain = Volts_applied/Volts_measured
But, the CE’s value for unity is 16,384, so:
ce_v_gain = 16384 * V_gain
For the current:
The meter's signal is a vector sum of the real (Wh) and imaginary (VARh) parts of the power. i_gain, the current gain,
needs scaling to eliminate power errors, and rotation in the complex plane to eliminate phase error.
Let Φ be the phase adjust angle.
A vector is rotated by multiplying by a 2x2 matrix:
cos(Φ) -sin(Φ)
sin(Φ) cos(Φ)
The linear adjustment vector is:
{Wh_applied/(Wh_measured * V_gain), VARh_applied/(VARh_measured * V_gain)}
i_gain is the real part of multiplying the rotation matrix by the linear adjustment vector.:
i_gain = cos(Phi)(Wh_Applied/(Wh_measured * V_gain))
+ sin(Phi)(VARh_Applied/(VARh_measured * V_gain))
But, the applied signal's VARh_applied = 0, so that term is negligible:
i_gain = cos(Phi)(Wh_Applied/(Wh_measured * V_gain))
Further, cos(Phi) = Wh_measured/VAh_measured; So substituting, one gets a classic fast current-calibration equation
for a meter:
i_gain = Wh_applied / (VAh_measured * V_gain)
VAh_measured is easy to calculate, and the meter's signal processing gives it good linearity and repeatability, so we
keep it and calculate it:
VAh_measured = sqrt(Wh_measured^2 + VARh_measured^2)
The CE's value for unity is 16384. Substituting:
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