Datasheet

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
Vhtsin ωα
(1)
where:
v(t) is the instantaneous voltage.
V
0
is the average value.
V
h
is the rms value of voltage harmonic h.
␣
h
is the phase angle of the voltage harmonic.
it I
0
()
=+ × × +
()
≠
∞
2 Σ
ho
hh
Ihtsin ωβ
(2)
where:
i(t) is the instantaneous current.
I
0
is the dc component.
I
h
is the rms value of current harmonic h.
␤
h
is the phase angle of the current harmonic.
Using Equations 1 and 2, the real power P can be expressed in
terms of its fundamental real power (P
1
) and harmonic real
power (P
H
).
PPP
H
=+
1
where
PV I
111 1
111
=×
=
cos
–
φ
φαβ
(3)
and
PVI
H
h
hh h
hhh
=∑ ×
=
≠
∞
1
cos
–
φ
φαβ
(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
V
CM
V1
DIFFERENTIAL INPUT
ⴞ30mV MAX PEAK
COMMON-MODE
ⴞ6.25mV MAX
+
–
V1P
V1N
V1
+
–
V
CM
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
V
CM
V2
DIFFERENTIAL INPUT
ⴞ165mV MAX PEAK
COMMON-MODE
ⴞ25mV MAX
+
–
V2P
V2N
V2
+
–
V
CM
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.