ADE7755
Figure 12 shows the instantaneous real power signal at the
output of the CPF, which still contains a significant amount of
instantaneous power information, i.e., cos (2 wt). 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 will suppress or average out any
non-dc components in the instantaneous real power signal. The
average value of a sinusoidal signal is zero. Hence, the frequency
generated by the ADE7755 is proportional to the average real
power. Figure 12 shows the digital-to-frequency conversion for
steady load conditions, i.e., constant voltage and current.
0.30
0.25
0.20
0.15
0.10
0.05
0
–0.05
–0.10
F1
DIGITAL-TO-
FREQUENCY
0
100 200 300 400 500 600 700 800 900 1000
FREQUENCY – Hz
F1
F2
ꢇ
V
Figure 10. Phase Error between Channels (0 Hz to 1 kHz)
LPF
TIME
TIME
MULTIPLIER
I
DIGITAL-TO-
FREQUENCY
FOUT
0.30
0.25
0.20
0.15
0.10
0.05
0
ꢇ
CF
LPF TO EXTRACT
REAL POWER
(DC TERM)
V ꢁ I
2
cos(2ꢆt)
ATTENUATED BY LPF
ꢆ
2ꢆ
0
FREQUENCY – RAD/S
INSTANTANEOUS REAL POWER SIGNAL
(FREQUENCY DOMAIN)
–0.05
–0.10
Figure 12. Real Power-to-Frequency Conversion
40
45
50
55
60
65
70
FREQUENCY – Hz
As can be seen in the diagram, the frequency output CF is seen
to vary over time, even under steady load conditions. This
frequency variation is primarily due to the cos (2 wt) 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 accumu-
lating the instantaneous real power signal over a much shorter
time while converting it to a frequency. This shorter accumula-
tion period means less averaging of the cos (2 wt) component.
As a consequence, some of this instantaneous power signal passes
through the digital-to-frequency conversion. This will not be a
problem in the application. When CF is used for calibration
purposes, the frequency should be averaged by the frequency
counter. This will remove any ripple. If CF is measuring energy,
e.g., 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, 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.
Figure 11. Phase Error between Channels (40 Hz to 70 Hz)
DIGITAL-TO-FREQUENCY CONVERSION
As previously described, the digital output of the low-pass filter
after multiplication contains the real power information. How-
ever, since this LPF is not an ideal “brick wall” filter implemen-
tation, the output signal also contains attenuated components
at the line frequency and its harmonics, i.e., cos(hwt) where
h = 1, 2, 3, and so on.
The magnitude response of the filter is given by:
1
|H( f )|=
(5)
1+( f /8.9 Hz)
For a line frequency of 50 Hz this would give an attenuation of
the 2w (100 Hz) component of approximately –22 dBs. The
dominating harmonic will be at twice the line frequency, i.e.,
cos (2 wt), and this is due to the instantaneous power signal.
REV. 0
–13–
ADI [ ADI ]
