ADE7752B
DIGITAL-TO-FREQUENCY CONVERSION
After multiplication, the digital output of the low-pass filter
contains the active power information of each phase. However,
because this LPF is not an ideal brick wall filter implementation,
the output signal also contains attenuated components at the line
frequency and its harmonics, that is, cos(hωt), where h = 1, 2, 3 …
The average value of a sinusoidal signal is zero. Thus, the
frequency generated by the ADE7752B is proportional to the
average active power. Figure 23 shows the digital-to-frequency
conversion for steady load conditions, that is, constant voltage
and current.
| H ( f ) | =
? f ?
1 + ? ?
The magnitude response of the filter is given by
1
2
? 8 ?
(11)
The frequency output CF varies over time, even under steady load
conditions (see Figure 23). This frequency variation is primarily
due to the cos(2ωt) components in the instantaneous active power
signal. The output frequency on CF can be up to 160× higher than
the frequency on F1 and F2. The higher output frequency is
generated by accumulating the instantaneous active power signal
where the ?3 dB cutoff frequency of the low-pass filter is 8 Hz.
For a line frequency of 50 Hz, this gives an attenuation of the 2ω
(100 Hz) component of approximately ?22 dB. The dominating
harmonic is twice the line frequency, that is, cos(2ωt), due to
the instantaneous power signal. Figure 23 shows the instantane-
ous active power signal at the output of the CF, which still contains
a significant amount of instantaneous power information,
cos(2ωt).
This signal is then passed to the digital-to-frequency converter
where it is integrated (accumulated) over time to produce an
output frequency. This accumulation of the signal suppresses or
averages out any nondc component in the instantaneous active
power signal.
over a much shorter time, while converting it to a frequency. This
shorter accumulation period means less averaging of the cos(2ωt)
component. Therefore, some of this instantaneous power signal
passes through the digital-to-frequency conversion.
Where CF is used for calibration purposes, the frequency counter
should average the frequency to remove the ripple and obtain a
stable frequency. If CF is being used to measure energy, for
example, in a microprocessor-based application, the CF output
should also be averaged to calculate power. Because the outputs F1
and F2 operate at a much lower frequency, significant averaging of
the instantaneous active power signal is carried out. The result is a
greatly attenuated sinusoidal content and a virtually ripple-free
frequency output on F1 and F2, which are used to measure energy
in a stepper motor-based meter.
VA
LPF
ABS
MULTIPLIER
IA
|X|
DIGITAL-TO-
FREQUENCY
F1
VB
MULTIPLIER
IB
VC
MULTIPLIER
LPF
LPF
|X|
|X|
DIGITAL-TO-
FREQUENCY
F1
F2
CF
CF
TIME
TIME
V×I
IC
LPF TO EXTRACT
REAL POWER
(DC TERM)
2
cos(2 ω t)
ATTENUATED BY LPF
0
ω
2 ω
FREQUENCY (RAD/sec)
INSTANTANEOUS REAL POWER SIGNAL
(FREQUENCY DOMAIN)
Figure 23. Active Power-to-Frequency Conversion
Rev. 0 | Page 18 of 24
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