ADE7769
Rev. A | Page 10 of 20
FUNCTIONAL DESCRIPTION
THEORY OF OPERATION
The two ADCs in the ADE7769 digitize the voltage signals from
the current and voltage sensors. These ADCs are 16-bit Σ-Δs
with an oversampling rate of 450 kHz. This analog input
structure greatly simplifies sensor interfacing by providing a
wide dynamic range for direct connection to the sensor and by
simplifying the antialiasing filter design. A high-pass filter in
the current channel removes any dc component from the
current signal. This eliminates any inaccuracies in the real
power calculation due to offsets in the voltage or current
signals.
The real power calculation is derived from the instantaneous
power signal. The instantaneous power signal is generated by
a direct multiplication of the current and voltage signals. To
extract the real power component (the dc component), the
instantaneous power signal is low-pass filtered.
Figure 15
illustrates the instantaneous real power signal and shows how
the real power information can be extracted by low-pass
filtering the instantaneous power signal. This scheme correctly
calculates real power for sinusoidal current and voltage
waveforms at all power factors. All signal processing is carried
out in the digital domain for superior stability over temperature
and time.
TIME TIME
ADC
ADC
CH1
CH2
MULTIPLIER
F1
F2
DIGITAL-TO-
FREQUENCY
CF
DIGITAL-TO-
FREQUENCY
INSTANTANEOUS REAL
POWER SIGNAL
INSTANTANEOUS
POWER SIGNAL – p(t)
LPF
HPF
05332-005
Figure 15. Signal Processing Block Diagram
The low frequency outputs (F1 and F2) are generated by
accumulating this real power information. This low frequency
inherently means a long accumulation time between output
pulses. Consequently, the resulting output frequency is propor-
tional to the average real power. This average real power
information is then accumulated (by a counter) to generate real
energy information. Conversely, due to its high output frequen-
cy and shorter integration time, the CF output frequency is
proportional to the instantaneous real power. This is useful for
system calibration, which can be done faster under steady load
conditions.
Power Factor Considerations
The method used to extract the real power information from
the instantaneous power signal, that is, by low-pass filtering, is
still valid even when the voltage and current signals are not in
phase.
Figure 16 shows the unity power factor condition and a
displacement power factor (DPF) = 0.5, that is, current signal
lagging the voltage by 60°. Assuming that the voltage and
current waveforms are sinusoidal, the real power component of
the instantaneous power signal (that is, the dc term) is given by
(
°×
⎟
⎠
⎞
⎜
⎝
⎛
×
60cos
2
IV
)
(1)
This is the correct real power calculation.
V × I
2
0V
POWER
CURRENT
VOLTAGE
POWER
TIME
TIME
VOLTAGE CURRENT
V × I
2
COS (60°)
0V
INSTANTANEOUS
POWER SIGNAL
INSTANTANEOUS REAL
POWER SIGNAL
INSTANTANEOUS
POWER SIGNAL
INSTANTANEOUS REAL
POWER SIGNAL
60°
05332-006
Figure 16. DC Component of Instantaneous Power Signal Conveys
Real Power Information, PF < 1
Nonsinusoidal Voltage and Current
The real power calculation method also holds true for
nonsinusoidal current and voltage waveforms. All voltage
and current waveforms in practical applications have some
harmonic content. Using the Fourier transform, instantaneous
voltage and current waveforms can be expressed in terms of
their harmonic content.
(
h
0h
h
0
αthωVVtv +××+=
∑
∞
≠
sin2)(
)
(2)
where:
v(t) is the instantaneous voltage.
V
0
is the average value.
V
h
is the rms value of voltage harmonic h.
α
h
is the phase angle of the voltage harmonic.
