REV. B

AD7755

–10–

THEORY OF OPERATION

The two ADCs digitize the voltage signals from the current and

voltage transducers. These ADCs are 16-bit second order

sigma-delta 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 simplifying the antialiasing filter design. A

programmable gain stage in the current channel further facili-

tates 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 calculation

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 20

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

INSTANTANEOUS REAL

POWER SIGNAL

MULTIPLIER

PGA

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

Figure 20. Signal Processing Block Diagram

The low frequency output of the AD7755 is generated by accu-

mulating this real power information. This low frequency inher-

ently 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 infor-

mation. Because of its high output frequency and hence shorter

integration time, the CF output is proportional to the instanta-

neous 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 21 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 wave-

forms are sinusoidal, the real power component of the instanta-

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

VI

×









2

× cos (60°).

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

CURRENT

VOLTAGE

0V

0V

VOLTAGE

Figure 21. 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 har-

monic content.

vt

V

Vh

h t

h

O

h

( )

sin(

)

=+

×

×

+

≠

∞

∑

2

0

ωα

(1)

where:

v(t)

is the instantaneous voltage

is the average value

Vh

is the rms value of voltage harmonic h

and

h

is the phase angle of the voltage harmonic.

it

I

Ih

h t

h

O

h

( )

sin(

)

=+

×

×

+

≠

∞

∑

2

0

ωβ

(2)

where:

i(t)

is the instantaneous current

is the dc component

Ih

is the rms value of current harmonic h

and

h

is the phase angle of the current harmonic.