REV. A

ADE7757

–9–

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 har-

monic content. Using the Fourier Transform, instantaneous

voltage and current waveforms can be expressed in terms of

their harmonic content.

vt

V

2

0

×

×

+

()

≠

∞

Σ

ho

hh

Vh t

sin

ωα

(1)

where:

v(t) is the instantaneous voltage.

it

I

0

×

×

+

()

≠

∞

2

Σ

ho

hh

Ih t

sin

ωβ

(2)

where:

i(t) is the instantaneous current.

Using Equations 1 and 2, the real power P can be expressed in

PP

P

H

=+

1

where

PV

I

11

1

1

11

1

=×

=

cos

–

φ

φα

β

(3)

and

PV

I

H

h

hh

h

hh

h

=∑

×

=

≠

∞

1

cos

–

φ

φα

β

(4)

As can be seen from Equation 4, a harmonic real power compo-

nent is generated for every harmonic, provided that harmonic is

present in both the voltage and current waveforms. The power

factor calculation has previously been shown to be accurate in

the case of a pure sinusoid. Therefore, the harmonic real power

must also correctly account for power factor since it is made up

of a series of pure sinusoids.

Note that the input bandwidth of the analog inputs is 7 kHz at

the nominal internal oscillator frequency of 450 kHz.

ANALOG INPUTS

Channel V1 (Current Channel)

The voltage output from the current sensor is connected to the

ADE7757 here. Channel V1 is a fully differential voltage input.

V1P is the positive input with respect to V1N.

The maximum peak differential signal on Channel V1 should be

less than

±30 mV (21 mV rms for a pure sinusoidal signal) for

specified operation.

+30mV

–30mV

V1

DIFFERENTIAL INPUT

30mV MAX PEAK

COMMON-MODE

6.25mV MAX

+

–

V1P

V1N

V1

+

–

AGND

Figure 5. Maximum Signal Levels, Channel V1

The diagram in Figure 5 illustrates the maximum signal levels

on V1P and V1N. The maximum differential voltage is

±30 mV.

The differential voltage signal on the inputs must be referenced

to a common mode, e.g., AGND. The maximum common-

mode signal is

±6.25 mV, as shown in Figure 5.

Channel V2 (Voltage Channel)

The output of the line voltage sensor is connected to the

ADE7757 at this analog input. Channel V2 is a fully differen-

tial voltage input with a maximum peak differential signal of

± 165 mV. Figure 6 illustrates the maximum signal levels that

can be connected to the ADE7757 Channel V2.

+165mV

–165mV

V2

DIFFERENTIAL INPUT

165mV MAX PEAK

COMMON-MODE

25mV MAX

+

–

V2P

V2N

V2

+

–

AGND

Figure 6. Maximum Signal Levels, Channel V2

Channel V2 is usually driven from a common-mode voltage,

i.e., the differential voltage signal on the input is referenced to a

common mode (usually AGND). The analog inputs of the

ADE7757 can be driven with common-mode voltages of up to

25 mV with respect to AGND. However, best results are achieved

using a common mode equal to AGND.