Digital Signal Processing Reference
In-Depth Information
component. The third-order harmonic distortion (hd
3
)isdefinedastheratio
between the third- and first-order components in the output signal (A.21):
1
2
a
2
a
1
U
hd
2
=
(second-order harmonic distortion)
1
4
a
3
a
1
U
2
hd
3
=
(third-order harmonic distortion)
(A.21)
As expected and confirmed by Formula (A.21), the level of distortion is also
related to the amplitude
U
of the input signal. It follows that, independently
of the amplifier configuration, distortion can always be suppressed by reduc-
ing the input signal level. On the other hand, the input signal is only one part of
the story. The noise floor is also an important factor, since the total harmonic
distortion plus noise (thd
+
n) is a limiting factor for the signal quality, espe-
cially for untuned wideband amplifiers where the noise floor is integrated over
a wide frequency band.
Self-mixing components and dc-offset
Also interesting is the unexpected offset component in the output sig-
nal (underlined in A.21). Usually the term
a
2
/
2
U
2
can be neglected.
For large input signals however, this term causes an unwanted dc-
offset at the output of the amplifier.
For example, in an frequency conversion stage where a large lo-signal
is applied to the input of the mixer, a serious dc-offset may appear
at the output of the mixer. In a direct conversion receiver, where the
rf-signal is converted immediately to a lower frequency band around
dc, this results in the irreversible loss of near-dc signal information,
because it is very difficult to separate the unwanted offset signal and
the signal-of-interest in a nearby frequency band.
The frequency independent time-domain model of the nonlinear amplifier in
Equation (A.19) can be embedded in a negative feedback loop, as is illustrated
by Figure A.6. As a result, the nonlinear characteristics of the active element
a(x)
in the forward path of the loop are suppressed in the overall transfer char-
acteristic. The closed-loop representation of this system can again be reduced
to a polynomial expression of the form (A.22):
y(v
in
)
=
b
0
+
b
1
v
in
+
b
2
v
in
+
b
3
v
in
+
...
,
(A.22)
