Digital Signal Processing Reference
In-Depth Information
harm
2
,x
(j
2
ω)
=
harm
2
,d
(j
2
ω)
·
tf
(j
2
ω)
d
→
x
F(j
2
ω)H
=
harm
2
,d
(j
2
ω)
·
(A.51)
1
+
F(j
2
ω)a
1
H
At this moment, two signals will be present at the input of the nonlinear ampli-
fication stage: the original fundamental component and the homesick second-
order harmonic delivered by the feedback path. In a typical application, the
amplitude of the fundamental component at node
x
is much larger than this of
the second-order harmonic. As a consequence, the closed-loop intermodula-
tion distortion characteristic im
2,z
is solely determined by the amplitude of the
smaller second-order component.
At first glance, this statement may seem somewhat confusing, but can be easily
clarified as follows. Consider the polynomial approximation of the amplifier
where only the linear gain
a
1
and the second-order coefficient
a
2
are taken
into account. The fundamental waveform with amplitude
u
fund
and the second-
order harmonic with amplitude
u
harm2
are applied to the input of this amplifier
(A.52):
a
2
x
2
with
x
a(x)
=
a
1
x
+
=
u
fund,x
·
cos
(ωt)
+
u
harm2,x
·
cos
(
2
ωt)
u
fund,x
+
u
harm2,x
a
2
2
a(x)
=
·
a
1
u
fund,x
+
a
2
u
fund,x
u
harm2,x
+
cos
(ωt)
a
1
u
harm2,x
+
2
u
fund,x
a
2
+
cos
(
2
ωt)
·
+
cos
(
3
ωt)
·
a
2
u
fund,x
u
harm2,x
+···
(A.52)
The output signal of the amplifier contains signals at various frequencies. How-
ever, only two of them are of importance for the calculation of the second-order
intermodulation distortion at node
z
(im
2,z
): the amplitude of the largest com-
ponent at the fundamental frequency
ω
and the amplitude of the
second-order
intermodulation product at frequency
ω
fund
+
3
ω
fund
. The ratio of the
intermodulation product to the amplitude at the fundamental frequency pro-
vides the intermodulation distortion characteristic at node
z
of the amplifier.
Remark that im
2,z
only depends on the amplitude (
u
harm2
) of the second-order
distortion component (A.53):
ω
harm2
=
a
2
u
fund,x
u
harm2,x
a
1
u
fund,x
+
im
2,z
=
a
2
u
fund,x
u
harm2,x
a
2
a
1
·
≈
u
harm2,x
