![](http://datasheet.mmic.net.cn/310000/ADE7754_datasheet_16240613/ADE7754_17.png)
REV. PrG 01/03
PRELIMINARY TECHNICAL DATA
ADE7754
–
17
–
ROOT MEAN SQUARE MEASUREMENT
Root Mean Square (RMS) is a fundamental measurement of
the magnitude of an AC signal. Its definition can be both
practical and mathematical. Defined practically, the RMS
value assigned to an AC signal is the amount of DC required
to produce an equivalent amount of heat in the same load.
Mathematically: the RMS value of a continuous signal f(t) is
defined as:
F
T
f
( )
rms
T
∫
0
=
1
2
(1)
For time sampling signals, rms calculation involves squaring
the signal, taking the average and obtaining the square root:
F
N
f
i
rms
=
=
∑
1
2
1
( )
(2)
The method used to calculate the RMS value in the ADE7754
is to low-pass filter the square of the input signal (LPF3) and
take the square root of the result.
With
V t
V
t
rms
( )
sin
=
(
)
2
ω
then
V t
V t
V
V
t
rms
rms
( )
( )
cos
×
=
(
)
2
2
2
ω
The RMS calculation is simultaneously processed on the six
analog input channels. Each result is available on separate
registers.
Current RMS calculation
Figure 18 shows the detail of the signal processing chain for
the RMS calculation on one of the phases of the current
channel. The current channel RMS value is processed from
the samples used in the current channel waveform sampling
mode. It should be noticed that the APGAIN adjustment
affects the result of the RMS calculation - see Current RMS
Gain adjust. The current RMS values are stored in an
unsigned 24-bit registers (AIRMS, BIRMS and CIRMS).
One LSB of the current RMS register is equivalent to one
LSB of a current waveform sample. The update rate of the
current RMS measurement is CLKIN/12.
With the specified full scale analog input signal of 0.5V, the
ADC will produce an output code which is approximately
±2,684,354d - see
Current channel ADC
. The equivalent
RMS values of a full-scale AC signal and full scale DC signal
are respectively 1,898,124d (1CF68Ch) and 2,684,354d
(28F5C2h).
With offset calibration, the current rms measurement pro-
vided in the ADE7754 is accurate within +/-2% for signal
input between Full scale and Full scale/100.
Note:
A crosstalk between phases can appear in the ADE7754
current rms measurements. This crosstalk follows a specific
pattern: Current rms measurements of Phase A are corrupted
by the signal on the Phase C current input, Current rms
measurements of Phase B are corrupted by the signal on the
Phase A current input and Current rms measurements of
Phase C are corrupted by the signal on the Phase B current
input. This crosstalk is only present on the current rms
measurements and does not affect the regular Active power
measurements. The level of the crosstalk is dependent on the
level of the noise source and the phase angle between the noise
source and the corrupted signal. The level of the crosstalk can
be reduced by writing 0x01F7 to the address 0x3D. This 16-
bit register is reserved for factory operation and should not be
written to any other value.
When the current inputs are 120° out of phase and the register
0x3D is set to 0x01F7, the level of the current rms crosstalk
is below 2%.
24
LPF3
FS
Current Signal - i(t)
-100% to +100% FS
Irms(t)
1CF68Ch
00h
IRMS
IA
S
+
SGN21121029
222120
IRMSOS[11:0]
24
AAPGAIN
HPF
00000h
400000h
28F5C2h
C00000h
D70A3Eh
+ FS
- FS
ADC Output
word Range
0000h
EB8520h
1CF68Ch
147AE0h
+ 100% FS
+ 70.7% FS
- 100% FS
- 122.5% FS
E30974h
DC8713h
+ 122.5% FS
- 70.7% FS
2378EDh
AAPGAIN[11:0]
000h
7FFh
800h
Current Channel (RMS)
Figure 18 - Current RMS signal processing