ADE7752B_15 datasheet(18/24 Pages) AD

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ADE7752B

Rev. 0 | Page 18 of 24

DIGITAL-TO-FREQUENCY CONVERSION

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

contains the active power information of each phase. 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 …

The magnitude response of the filter is given by

()

⎭

⎬

⎫

⎩

⎨

⎧

(11)

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

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

(100 Hz) component of approximately −22 dB. The dominating

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

the instantaneous power signal. Figure 23 shows the instantane-

ous active 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 nondc component in the instantaneous active

power signal.

The average value of a sinusoidal signal is zero. Thus, the

frequency generated by the ADE7752B is proportional to the

average active power. Figure 23 shows the digital-to-frequency

conversion for steady load conditions, that is, constant voltage

and current.

The frequency output CF varies over time, even under steady load

conditions (see Figure 23). This frequency variation is primarily

due to the cos(2ωt) components in the instantaneous active power

signal. The output frequency on CF can be up to 160× higher than

the frequency on F1 and F2. The 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. Therefore, some of this instantaneous power signal

passes through the digital-to-frequency conversion.

Where CF is used for calibration purposes, the frequency counter

should average the frequency to remove the ripple and obtain a

stable frequency. If CF is being used to measure energy, for

example, 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, significant 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 on F1 and F2, which are used to measure energy

in a stepper motor-based meter.

LPF TO EXTRACT

REAL POWER

(DC TERM)

MULTIPLIER

LPF

MULTIPLIER

LPF

MULTIPLIER

LPF

DIGITAL-TO-

FREQUENCY

DIGITAL-TO-

FREQUENCY

TIME

2ω

FREQUENCY (RAD/sec)

V × I

INSTANTANEOUS REAL POWER SIGNAL

(FREQUENCY DOMAIN)

|X|

ABS

TIME

cos(2ωt)

ATTENUATED BY LPF

Figure 23. Active Power-to-Frequency Conversion

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