REV. 0

ADE7751

–10–

THEORY OF OPERATION

The two ADCs digitize the voltage and current signals from the

current and voltage transducers. These ADCs are 16-bit second

order sigma-delta converters with an oversampling rate of 900 kHz.

This analog input structure greatly simplifies transducer interfacing

by providing a wide dynamic range for direct connection to the

transducer and also by simplifying the antialiasing filter design.

A programmable gain stage in the current channel further

facilitates easy transducer interfacing. A high-pass filter in the

current channel removes any dc component from the current

signal. This eliminates any inaccuracies in the real power calcu-

lation due to offsets in the voltage or current signals—see

HPF and Offset Effects section.

The real power calculation is derived from the instantaneous

power signal. The instantaneous power signal is generated by a

direct multiplication of the current and voltage signals. In order

to extract the real power component (i.e., the dc component), the

instantaneous power signal is low-pass filtered. Figure 2 illustrates

the instantaneous real power signal and shows how the real power

information can be extracted by low-pass filtering the instantaneous

power signal. This scheme correctly calculates real power for

nonsinusoidal current and voltage waveforms at all power factors.

All signal processing is carried out in the digital domain for

superior stability over temperature and time.

LPF

DIGITAL-TO-

FREQUENCY

F1

F2

CH1

MULTIPLIER

PGA

CH2

ADC

V

I

2

V I

V I

2

p(t) = i(t) v(t)

WHERE:

v(t) = V cos( t)

i(t) = I cos( t)

p(t) = V I

2

ADC

TIME

HPF

DIGITAL-TO-

FREQUENCY

CF

INSTANTANEOUS REAL

POWER SIGNAL

INSTANTANEOUS

POWER SIGNAL – p(t)

Figure 2. Signal Processing Block Diagram

The low-frequency output of the ADE7751 is generated by

accumulating this real power information. This low frequency

inherently means a long accumulation time between output

pulses. The output frequency is therefore proportional to the

average real power. This average real power information can in

turn be accumulated (e.g., by a counter) to generate real-energy

information. Because of its high output frequency, and hence

shorter integration time, the CF output is proportional to the

instantaneous real power. This is useful for system calibration

purposes that would take place under steady load conditions.

Power Factor Considerations

The method used to extract the real power information from the

instantaneous power signal (i.e., by low-pass filtering) is still

valid even when the voltage and current signals are not in phase.

Figure 3 displays the unity power factor condition and a DPF

(displacement power factor) = 0.5, i.e., current signal lagging

the voltage by 60

°. If we assume the voltage and current waveforms

are sinusoidal, the real power component of the instantaneous

power signal (i.e., the dc term) is given by:

VI

×









×°

()

2

60

cos

(1)

This is the correct real power calculation.

INSTANTANEOUS

REAL POWER SIGNAL

INSTANTANEOUS

POWER SIGNAL

V I

2

cos(60 )

V I

2

INSTANTANEOUS

POWER SIGNAL

INSTANTANEOUS

REAL POWER SIGNAL

60

CURRENT

VOLTAGE

CURRENT

VOLTAGE

0V

0V

Figure 3. DC Component of Instantaneous Power Signal

Conveys Real Power Information PF < 1

Nonsinusoidal Voltage and Current

The real power calculation method also holds true for nonsinu-

soidal current and voltage waveforms. All voltage and current

waveforms in practical applications will have some harmonic

content. Using the Fourier Transform, instantaneous voltage

and current waveforms can be expressed in terms of their

harmonic content.

vt

V

V

h t

Oh

h

h

()

sin(

)

=+

× ∑

×+

≠

∞

2

0

ωα

(2)

where:

v(t)= The instantaneous voltage

and

h

= The phase angle of the voltage harmonic

it

I

I

h

ht

Oh

h

()

sin(

)

=+

×

≠

×+

∞

∑

2

0

ωβ

(3)

where:

i(t)= The instantaneous current

= The dc component

= The rms value of current harmonic h

and

h

=The phase angle of the current harmonic