Digital Signal Processing Reference
In-Depth Information
a
2
a
1
2
1
2
1
1+a
1
h
U
y
h
HD
2,CL
=
v
in
y
x
2a
2
2
h
a
3
(1+a
1
h)
a(x)
1-
a
3
1
4
U
y
2
HD
3,CL
=
a
1
3
1+a
1
h
a(x) = a
0
+a
1
x+a
2
x
2
+a
3
x
3
+...
HD
2,OL
= 1/2 a
2
/a
1
U
x
HD
3,OL
= 1/4 a
3
/a
1
U
x
2
Figure A.6.
Distortion in a basic feedback amplifier with a frequency independent
nonlinear active element in the forward path. Note that the level of dis-
tortion suppression of the feedback system is (in first order approxima-
tion) inverse proportional to the feedback factor
h
.
where the coefficients
b
0
...b
3
can be approximated by expressions (A.23):
a
0
b
0
=
(A.23a)
1
+
a
1
h
a
1
b
1
=
(A.23b)
1
+
a
1
h
a
2
b
2
=
(A.23c)
(
1
+
a
1
h)
3
2
a
2
h
a
3
(
1
+
a
1
h)
−
b
3
=
(A.23d)
(
1
+
a
1
h)
5
From the dc-coefficient
b
0
of Equation (A.23a), it is easy to understand that the
offset voltage of the active element is suppressed by the first order loop gain
a
1
h
. It is also well-understood that the first-order gain
b
1
of the closed-loop
system (A.23b) reduces to the expression 1
/h
if a sufficiently large excess
gain (
a
1
h
) is available in the loop. On the other hand, it is a little bit less
evident to grasp why the second- and third-order coefficients of the closed-loop
polynomial decline with the third and the fourth power of
a
1
h
, respectively. In
order to simplify matters, the problem is split in two stages.
As a start, by using the definitions of the second- and third-order harmonics
introduced in Equation (A.21), it is fairly straightforward to find out that the
