PRELIMINARY TECHNICAL DATA

REV. PrC.

ADE7757

–8–

THEORY OF OPERATION

The two ADCs digitize the voltage signals from the cur-

rent and voltage sensors. These ADCs are 16-bit sigma-

delta with an oversampling rate of 450 kHz. This analog

input structure greatly simplifies sensor interfacing by

providing a wide dynamic range for direct connection to

the sensor and also simplifies the antialiasing filter design.

A high pass filter in the current channel removes any dc

component from the current signal. This eliminates any

inaccuracies in the real power calculation due to offsets in

the voltage or current signals. Because the HPF is always

enabled, the IC will only operate with AC Input—see HPF

HPF

HPF

HPF

HPF

and Offset Effects.

and Offset Effects.

and Offset Effects.

and Offset Effects.

and Offset Effects.

The real power calculation is derived from the instanta-

neous 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 compo-

nent (i.e., the dc component), the instantaneous power

signal is low-pass filtered. Figure 11 illustrates the instan-

taneous real power signal and shows how the real power

information can be extracted by low-pass filtering the in-

stantaneous power signal. This scheme correctly calculates

real power for sinusoidal 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

INSTANTANEOUS REAL

POWER SIGNAL

MULTIPLIER

CH2

ADC

INSTANTANEOUS

POWER SIGNAL- p (t)

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

PGA

Figure 11. Signal Processing Block Diagram

The low frequency outputs (F1, F2) of the ADE7757 is

generated by accumulating this real power information.

This low frequency inherently means a long accumulation

time between output pulses. Consequently, the resulting

output frequency is proportional to the average real power.

This average real power information is then accumulated

(e.g., by a counter) to generate real energy information.

Conversely, due to its high output frequency and hence

shorter integration time, the CF output frequency is pro-

portional to the instantaneous real power. This is useful

for system calibration, which can be done faster 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 12 displays the unity power factor condition

and a DPF (Displacement Power Factor) = 0.5, i.e., cur-

rent 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:

)

60

(

cos

2

I

V

°

×







 ×

This is the correct real power calculation.

INSTANTANEOUS REAL

POWER SIGNAL

INSTANTANEOUS

POWER SIGNAL

INSTANTANEOUS

POWER SIGNAL

INSTANTANEOUS REAL

POWER SIGNAL

CURRENT

CURRENT

VOLTAGE

0V

0V

VOLTAGE

POWER

POWER

TIME

TIME

°

60

°

60

2

I

V

×

)

60

(

cos

2

I

V

°

×

Figure 12. 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

nonsinusoidal 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.

∑

∞

≠

α

+

ω

×

×

+

=

0

h

h

0

)

h

t

h

(

sin

V

2

V

)

t

(

v

(1)

where:

v(t) is the instantaneous voltage

is the average value

is the rms value of voltage harmonic h

and

h

is the phase angle of the voltage harmonic.

∑

∞

≠

β

+

ω

×

×

+

=

0

h

h

0

)

h

t

h

(

sin

I

2

I

)

t

(

i

(2)

where:

i(t)

is the instantaneous current

is the dc component

is the rms value of current harmonic h

and

h

is the phase angle of the current harmonic.