AD7755
0.30
0.25
0.20
PHASE – Degrees
0.15
0.10
0.05
0
–0.05
–0.10
Figure 30 shows the instantaneous real power signal at the output
of the CPF which still contains a significant amount of instanta-
neous 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 fre-
quency. 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 AD7755 is proportional to the
average real power. Figure 30 shows the digital-to-frequency
conversion for steady load conditions, i.e., constant voltage and
current.
0
F1
DIGITAL-TO-
FREQUENCY
V
MULTIPLIER
F1
F2
DIGITAL-TO-
FREQUENCY
CF
LPF TO EXTRACT
REAL POWER
(DC TERM)
FREQUENCY
100
200
300
400 500 600 700
FREQUENCY – Hz
800
900 1000
Figure 28. Phase Error Between Channels (0 Hz to 1 kHz)
LPF
TIME
0.30
I
0.25
0.20
V
2
0.15
0.10
0.05
0
–0.05
–0.10
40
0
2
FREQUENCY – RAD/S
cos(2 t)
ATTENUATED BY LPF
I
FOUT
FREQUENCY
PHASE – Degrees
TIME
INSTANTANEOUS REAL POWER SIGNAL
(FREQUENCY DOMAIN)
45
50
55
60
FREQUENCY – Hz
65
70
Figure 30. Real Power-to-Frequency Conversion
Figure 29. 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(hωt) where
h
= 1, 2, 3, . . . etc.
The magnitude response of the filter is given by:
|
H
(
f
) |
=
1
1
+
(
f
/ 8.9
Hz
)
(5)
For a line frequency of 50 Hz this would give an attenuation of
the 2ω (100 Hz) component of approximately –22 dBs. The
dominating harmonic will be at twice the line frequency, i.e.,
cos (2ωt) and this is due to the instantaneous power signal.
As can be seen in the diagram, the frequency output CF is seen
to vary over time, even under steady load conditions. This fre-
quency variation is primarily due to the cos (2
ωt)
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
ωt)
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. Where CF is used for calibration
purposes, the frequency should be averaged by the frequency
counter. This will remove any ripple. If CF is being used to
measure 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, 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.
REV. B
–13–
AD [ ANALOG DEVICES ]
