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ADE7753
–19–
REV. PrF 10/02
PRELIMINARY TECHNICAL DATA
sec. Equation 3 gives an expression for the instantaneous
power signal in an ac system.
()
( )
t
V
t
v
ω
sin
2
=
()
( )
t
I
t
i
ω
sin
2
=
where
V = rms voltage,
I = rms current.
()
() ()
()
( )
t
t
p
ω
cos
VI
VI
=
T he average power over an integral number of line cycles (n)
is given by the expression in Equation 4.
(1)
(2)
t
i
t
v
p
×
=
(3)
0
1
nT
P
p t dt
VI
nT
=
=
∫
(4)
where T is the line cycle period.
P is referred to as the Active or Real Power. Note that the
active power is equal to the dc component of the instanta-
neous power signal
p(t)
in Equation 3
, i.e., VI. T his is the
relationship used to calculate active power in the ADE7753.
T he instantaneous power signal
p(t)
is generated by multiply-
ing the current and voltage signals. T he dc component of the
instantaneous power signal is then extracted by LPF2 (Low
Pass Filter) to obtain the active power information. T his
process is illustrated graphically in Figure 31.
Voltage
√
2
×
V
×
sin(
ω
t)
Current
√
2
×
I
×
sin(
ω
t)
Instantaneous
Power Signal
Active Real Power
Signal = V x I
V. I.
00000h
19999Ah
CCCCDh
p(t) = V
×
I-V
×
I
×
cos(2
ω
t)
Figure 31– Active Power Calculation
Since LPF2 does not have an ideal “brick wall” frequency
response—see Figure 32, the Active Power signal will have
some ripple due to the instantaneous power signal. T his
ripple is sinusoidal and has a frequency equal to twice the line
frequency. Since the ripple is sinusoidal in nature it will be
removed when the Active Power signal is integrated to
calculate Energy – see
Energy Calculation
.
Frequency
1.0Hz
3.0Hz
30Hz
100Hz
-24
-20
-16
-12
-8
-4
0
d
Figure 32 —Frequency Response of LPF2
F igure 33 shows the signal processing chain for the
ActivePower calculation in the ADE7753. As explained, the
Active Power is calculated by low pass filtering the instanta-
neous power signal. Note that for when reading the waveform
samples from the output of LPF2,
T he gain of the Active Energy can be adjusted by using the
multiplier and Watt Gain register (WGAIN[11:0]). T he
gain is adjusted by writing a 2’s complement 12-bit word to
the Watt Gain register. Below is the expression that shows
how the gain adjustment is related to the contents of the Watt
Gain register.
×
=
Power
Active
WGAIN
Output
+
1
12
2
WGAIN
For example when 7FFh is written to the Watt Gain register
the Power output is scaled up by 50%. 7FFh = 2047d,
2047/2
12
= 0.5. Similarly, 800h = -2048 Dec (signed 2’s
Complement) and power output is scaled by –50%.
Shown in Figure 34 is the maximum code (in hex) output
range for the Active Power signal (L PF2). Note that the
output range changes depending on the contents of the Watt
Gain register. T he minimum output range is given when the
Watt Gain register contents are equal to 800h, and the
HPF
LPF2
Current Signal - i(t)
Voltage Signal - v(t)
Instantaneous
Power Signal - p(t)
19999Ah
MULTIPLIER
Active Power
Signal - P
CCCCDh
I
V
000000h
WGAIN[11:0]
Σ
+
2
-6
2
-7
APOS[15:0]
sgn
2
-8
2
6
2
5
32
24
+
For Energy
Accumulation
For Waveform
Sampling
19999h
24
Figure 33– Active Power Signal Processing