ADE7761B
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 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. As a consequence, some of this instantaneous
power signal passes through the digital-to-frequency conversion.
This is not a problem in the application.
DIGITAL-TO-FREQUENCY CONVERSION
As described in the Active Power Calculation section, the digital
output of the low-pass filter after multiplication contains the
active 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
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, such as in a microprocessor-
based application, the CF output should also be averaged to calcu-
late power. Because the F1 and F2 outputs operate at a much
lower frequency, much more 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.
1
H( f ) =
(6)
1 = ( f /4.5Hz)2
For a line frequency of 50 Hz, this gives an attenuation of the 2ω
(100 Hz) component of approximately −26.9 dB. The dominating
harmonic is at twice the line frequency, cos(2ωt), due to the
instantaneous power signal.
Figure 27 shows the instantaneous active power signal output of
the LPF, 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 non-dc components in
the instantaneous active power signal. The average value of a
sinusoidal signal is zero. Therefore, the frequency generated by
the ADE7761B is proportional to the average active power.
TRANSFER FUNCTION
Frequency Output F1 and Frequency Output F2
The ADE7761B calculates the product of two voltage signals
(on Channel V1 and Channel V2) and then low-pass filters this
product to extract active power information. This active power
information is then converted to a frequency. The frequency
information is output on F1 and F2 in the form of active high
pulses. The pulse rate at these outputs is relatively low, for
example, 0.37 Hz maximum for ac signals with S0 = S1 = 0
(see Table 8). This means that the frequency at these outputs
is generated from active power information accumulated over
a relatively long period. The result is an output frequency that
is proportional to the average active power. The averaging of the
active power signal is implicit to the digital-to-frequency conver-
sion. The output frequency or pulse rate is related to the input
voltage signals by
F
1
DIGITAL-TO-
FREQUENCY
F
F
1
2
V
TIME
MULTIPLIER
CF
DIGITAL-TO-
FREQUENCY
LPF
I
CF
LPF TO EXTRACT
ACTIVE POWER
(DC TERM)
6.13×Gain×V1rms ×V2rms × f1−4
(7)
F , F Frequency =
1
2
2
VREF
where:
F1, F2 Frequency is the output frequency on F1 and F2 (Hz).
V1rms is the differential rms voltage signal on Channel V1 (V).
V2rms is the differential rms voltage signal on Channel V2 (V).
Gain is 1 or 16, depending on the PGA gain selection made
using Logic Input PGA.
TIME
0
ω
2ω
FREQUENCY (Rad/s)
INSTANTANEOUS ACTIVE POWER SIGNAL (FREQUENCY DOMAIN)
Figure 27. Active Power to Frequency Conversion
VREF is the reference voltage (2.5 V 8%) (V).
f1–4 is one of four possible frequencies selected by using Logic
Input S0 and Logic Input S1 (see Table 6).
Figure 27 also shows the digital-to-frequency conversion for
steady load conditions: constant voltage and current. As can be
seen in Figure 27, 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
active power signal.
Rev. 0 | Page 16 of 24
ADI [ ADI ]
