Digital Signal Processing Reference
In-Depth Information
(3)
(1)
ω
0
3ω
0
g
m
(2)
2ω
0
R
S
Figure A.9.
The origins of third-order distortion in a mos transistor amplifier with re-
sistive degeneration. Second-order distortion components (1) appear at the
output, reenters into the input of the system (2) and finally cause third-order
distortion which is the result of the intermodulation mix product between the
input signal and the second-order distortion components.
The latter method of formulating hd
3
provides a better insight in the distortion
generating mechanism of the resistive degenerated amplifier. The amplitude of
the second-order component in the output current
i
ds
is taken into account by
the first factor
(
1
)
in Equation (A.35). This small-signal current is transformed
to a voltage by
R
S
(
2
)
which is subsequently fed back to the input of the sys-
tem. When re-entering the loop, this second-order distortion component will
be mixed with the fundamental input signal (single tone at
ω
0
).
Second-order
intermodulation distortion (im
2
), represented by factor
(
3
)
, will finally gener-
ate frequency components at 2
ω
0
±
ω
0
. The sum of these components finally
results in the third-order distortion. The whole process is once again illustrated
in Figure A.9.
A.2
Frequency dependent distortion in feedback systems
The linearity calculations in the previous section have assumed that the active
element in the forward path of the feedback loop has a frequency-independent
characteristic. All real-world amplifier implementations however, exhibit one
or more poles beyond which the gain is reduced. The loop-gain of the feedback
system embedding such a frequency-limited amplifier is dependent on the op-
erating frequency and as a result, also the distortion suppression capabilities
will reduce at the higher end of the spectrum. Calculations of the distortion
parameters of such a nonlinear closed-loop system are not straightforward. For
linear time-invariant systems, the frequency dependent behaviour of the feed-
back system is easily described in the frequency domain. But for nonlinear
systems, a complete description in terms of interdependent eigenvectors (i.e.
a set of sinusoidal in- and outputs) is not possible. Rather than elaborating on
a thorough mathematical description of the frequency dependent behaviour of
nonlinear systems, a lot of insight in the internals of a feedback system can
already be obtained by some well-considered reasoning.
