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71M6515H Demo Board User’s Manual
2.1.4
CALIBRATION WITH THREE MEASUREMENTS
The simplest calibration method is to make three measurements. Typically, a voltage measurement and two
Watt-hour (Wh) measurements are made.
We assume the voltage measurement has the error E V, and the two Wh measurements have errors E 0 and
E 60 , where E 0 is measured with φ L = 0 and E 60 is measured with φ L = 60. These values should be simple
ratios—not percentage values. They should be zero when the meter is accurate and negative when the
meter runs slow. The fundamental frequency is f 0 . T is equal to 1/f S , where f S is the sample frequency
(2560.62Hz). Set all calibration factors to nominal: CAL_IA = 16384, CAL_VA = 16384, PHADJ_A = 0.
From the voltage measurement, we determine that
1.
A XV = E V + 1
We use the other two measurements to determine φ S and A XI .
2.
E 0 =
IV A XV A XI cos( 0 ? φ S )
IV cos( 0 )
? 1 = A XV A XI cos( φ S ) ? 1
2a.
A XV A XI =
E 0 + 1
cos( φ S )
3.
E 60 =
IV A XV A XI cos( 60 ? φ S )
IV cos( 60 )
? 1 = A XV A XI
cos( 60 ? φ S )
cos( 60 )
? 1
3a.
E 60 =
A XV A XI [ cos( 60) cos( φ S ) + sin( 60) sin( φ S ) ]
cos( 60 )
? 1
= A XV A XI cos( φ S ) + A XV A XI tan( 60 ) sin( φ S ) ? 1
Combining 2a and 3a:
4.
E 60 = E 0 + ( E 0 + 1 ) tan( 60 ) tan( φ S )
5.
tan( φ S ) =
E 60 ? E 0
( E 0 + 1 ) tan( 60 )
φ S = tan ? 1 ? ?
?
6.
?
?
E 60 ? E 0 ?
( E 0 + 1 ) tan( 60 ) ? ?
and from 2a:
7.
A XI =
E 0 + 1
A XV cos( φ S )
Now that we know the A XV , A XI , and φ S errors, we calculate the new calibration voltage gain coefficient from
the previous ones:
CAL _ V NEW =
CAL _ V
A XV
? tan( φ S ) 1 + ( 1 ? 2 ? 9 ) 2 ? 2 ( 1 ? 2 ? 9 ) cos( 2 π f 0 T ) ] ?
[
]
? ( 1 ? 2 ) sin( 2 π f 0 T ) ? tan( φ S ) 1 ? ( 1 ? 2 ) cos( 2 π f 0 T ) ?
We calculate PHADJ from φ S , the desired phase lag:
PHADJ = 2 20 ? ? 9 ? 9 ?
And we calculate the new calibration current gain coefficient, including compensation for a slight gain
increase in the phase calibration circuit.
Revision 2.0
? Copyright 2005 TERIDIAN Semiconductor Corporation
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