ADE7761ARS-REF datasheet(18/28 Pages) AD

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ADE7761

Rev. A | Page 18 of 28

DIGITAL-TO-FREQUENCY CONVERSION

As previously described, 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

)

(

)

(

(6)

For a line frequency of 50 Hz, this gives an attenuation of the 2ω

(100 Hz) component of approximately –26.9 dB. The dominat-

ing harmonic is at twice the line frequency, cos(2ωt), due to the

instantaneous power signal.

Figure 25 shows the instantaneous active power signal output of

the LPF, which still contains a significant amount of instantane-

ous 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 ADE7761 is proportional to the

average active power.

Figure 25 also shows the digital-to-frequency conversion for

steady load conditions: constant voltage and current. As can be

seen in Figure 25, 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.

DIGITAL-TO-

FREQUENCY

DIGITAL-TO-

FREQUENCY

MULTIPLIER

LPF

FREQUENCY (Rad/s)

LPF TO EXTRACT

ACTIVE POWER

(DC TERM)

TIME

FOUT

INSTANTANEOUS ACTIVE POWER SIGNAL (FREQUENCY DOMAIN)

Figure 25. Active Power to Frequency Conversion

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.

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 calculate power. Because the outputs F1 and F2

operate at a much lower frequency, a lot 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.

TRANSFER FUNCTION

Frequency Outputs F1 and F2

The ADE7761 calculates the product of two voltage signals (on

Channel 1 and Channel 2) and then low-pass filters this product

to extract active power information. This active power infor-

mation 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, 0.34 Hz maximum for ac signals with S0 = S1 = 0 (see

Table 7). This means that the frequency at these outputs is

generated from active power information accumulated over a

relatively long period of time. 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

conversion. The output frequency or pulse rate is related to the

input voltage signals by the following equation:

REF

rms

Frequency

−

(7)

where:

F1 − F2 Frequency is the output frequency on F1 and F2 (Hz).

V1rms is the differential rms voltage signal on Channel 1 (V).

V2rms is the differential rms voltage signal on Channel 2 (V).

VREF is the reference voltage (2.5 V ± 8%) (V).

F1–4 is one of four possible frequencies selected by using the

logic inputs S0 and S1 (see Table 5).

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