ADE7761B

Rev. 0 | Page 16 of 24

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

2

)

Hz

5

.

4

/

(

1

1

)

(

f

f

H

=

=

(6)

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.

CF

DIGITAL-TO-

FREQUENCY

DIGITAL-TO-

FREQUENCY

MULTIPLIER

LPF

V

I

0

ω

2ω

FREQUENCY (Rad/s)

LPF TO EXTRACT

ACTIVE POWER

(DC TERM)

TIME

TIME

CF

INSTANTANEOUS ACTIVE POWER SIGNAL (FREQUENCY DOMAIN)

Figure 27. Active Power to Frequency Conversion

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.

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 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.

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

2

2

1

13

.

6

,

REF

4

1

rms

rms

V

f

V2

V1

Gain

Frequency

F

F

−

×

×

×

×

=

(7)

where:

is the differential rms voltage signal on Channel V1 (V).

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.

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

is one of four possible frequencies selected by using Logic

Input S0 and Logic Input S1 (see Table 6).