Digital Signal Processing Reference
In-Depth Information
Appendix A
Distortion analysis of feedback amplifiers
In this appendix, the theory of distortion suppression in feedback systems is
reviewed briefly. Feedback is commonly used to suppress the non-ideal char-
acteristics of the active gain stage, such as a poorly defined gain factor or a
nonlinear transfer function between in- and output. The ability of feedback
to mask the imperfections of the gain stage rely on the availability of a cer-
tain amount of excess loop gain. Unfortunately, exactly the lack of loop gain at
higher frequency bands prevents feedback-based amplifiers to be used in wide-
band applications. In order to get some insight in this matter, this chapter starts
with a general review of the theory on feedback and linearity. While the cal-
culations in the first few sections will deliberately ignore all non-ideal effects
which are encountered in practical amplifier implementations, non-idealities
such as a finite output resistance of the transistors, bandwidth limitations or
the issues caused by stability requirements are gradually introduced and dis-
cussed in more detail in the subsequent sections.
To get off to a good start, consider a transistor amplifier that is used within it's
weak nonlinear operating region. The time-domain input signal is represented
by
x(t)
and the output signal of the amplifier is given by
y(t)
. The frequency
independent relationship between the in- and output of this system is being
described by (A.1):
a
2
x
2
(t)
a
3
x
3
(t)
y(t)
=
a
0
+
a
1
x(t)
+
+
+
...
(A.1)
Coefficient
a
0
represents the dc-current at the output of the amplifier, which is
independent from the signal applied to the input. At first sight, the dc-output
of the amplifier may seem a somewhat pointless detail, but it will become
clear later on that this offset voltage is a major headache for the designer of an
