ADE7752/ADE7752A

Rev. C | Page 18 of 24

DIGITAL-TO-FREQUENCY CONVERSION

After multiplication, the digital output of the low-pass filter

contains the real power information of each phase. Because this

LPF is not an ideal brick wall filter implementation, however,

the output signal also contains attenuated components at the

line frequency and its harmonics (cos(hωt), where h = 1, 2, 3,

and so on).

power signal. The average value of a sinusoidal signal is zero.

Thus, the frequency generated by the ADE7752 is proportional

to the average real power. Figure 27 shows the digital-to-

frequency conversion for steady load conditions, constant

voltage, and current.

Figure 27

As can be seen in

The magnitude response of the filter is given by

()

2

8

1

1

|

|

⎭

⎬

⎫

⎩

⎨

⎧

+

=

f

f

H

(8)

, the frequency output CF varies

over time, even under steady load conditions. This frequency

variation is primarily due to the cos(2ωt) components in the

instantaneous real power signal. The output frequency on CF

can be up to 160 times higher than the frequency on F1 and F2.

The higher output frequency is generated by accumulating the

instantaneous real 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 conse-

quence, 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. This

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, much 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.

where the −3 dB cutoff frequency of the low-pass filter is 8 Hz.

For a line frequency of 50 Hz, this would give an attenuation of

the 2ω(100 Hz) component of approximately –22 dB. The

dominating harmonic is twice the line frequency, cos(2ωt), due

to the instantaneous power signal. Figure 27 shows the

instantaneous real power signal at the output of the CF, 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 component in the instantaneous real

LPF TO EXTRACT

REAL POWER

(DC TERM)

Σ

Σ

MULTIPLIER

LPF

MULTIPLIER

LPF

MULTIPLIER

LPF

Σ

DIGITAL-TO-

FREQUENCY

DIGITAL-TO-

FREQUENCY

F1

F2

CF

VA

IA

VB

IB

VC

IC

CF

TIME

F1

ω

cos(2

ωt)

ATTENUATED BY LPF

2

ω

FREQUENCY – RAD/S

2

V

× I

0

INSTANTANEOUS REAL POWER SIGNAL

(FREQUENCY DOMAIN)

|X|

|X|

|X|

ABS

TIME

Figure 27. Real Power-to-Frequency Conversion