
ADE7757A
Preliminary Technical Data
Rev. PrE | Page 14 of 24
DIGITAL-TO-FREQUENCY CONVERSION
As previously described, the digital output of the low-pass
filter after multiplication contains the real power information.
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 . . . and so on.
The magnitude response of the filter is given by
()
2
45
.
4
1
f
H
+
=
(7)
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 (2ω) due
to the instantaneous power calculation.
Figure 25 shows the instantaneous real power signal at the
output of the LPF that still contains a significant amount of
instantaneous power information, i.e., cos(2ωt). This signal is
then passed to the digital-to-frequency converter where it is
integrated (accumulated) over time in order to produce an
output frequency. The accumulation of the signal suppresses
or averages out any non-dc components in the instantaneous
real power signal. The average value of a sinusoidal signal is
zero. Thus, the frequency generated by the ADE7757A is
proportional to the average real power. Figure 25 shows the
digital-to-frequency conversion for steady load conditions,
that is, constant voltage and current.
F1
F2
DIGITAL-TO-
FREQUENCY
CF
DIGITAL-TO-
FREQUENCY
MULTIPLIER
F1
TIME
CF
TIME
FRE
Q
UE
NCY
FRE
Q
UE
NCY
V
I
0
FREQUENCY (RAD/s)
ω
2
ω
COS (2
ω)
ATTENUATED BY LPF
V
× I
2
LPF TO EXTRACT
REAL POWER
(DC TERM)
INSTANTANEOUS REAL POWER SIGNAL
(FREQUENCY DOMAIN)
LPF
05330-015
Figure 25. Real Power-to-Frequency Conversion
Figure 25 shows that the frequency output CF varies over time,
even under steady load conditions. This frequency variation is
primarily due to the cos(2ωt) component in the instantaneous
real power signal. The output frequency on CF can be up to
2048 times higher than the frequency on F1 and F2. This
higher output frequency is generated by accumulating the
instantaneous real 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. Consequently,
some of this instantaneous power signal passes through the
digital-to-frequency conversion. This is not a problem in the
application. Where CF is used for calibration purposes, the
frequency should be averaged by the frequency counter, which
removes any ripple. 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, a lot more averaging of the instantaneous real power
signal is carried out. The result is a greatly attenuated sinusoidal
content and a virtually ripple-free frequency output.