Digital Signal Processing Reference
In-Depth Information
but this time the cut-off frequency of the compound system is given by
ω
cut-off
=
A
0
Hω
p
1
(A.17):
1
H
·
1
A
cl
(f )
=
(A.17)
1
A
0
Hω
p
1
1
+
jω
A summary of the transfer characteristics of both the open-loop amplifier and
the same amplifier in feedback configuration is given in the magnitude plot of
Figure A.4. When applied to the single transistor current amplifier, the 0 dB
crossover point is defined by the
f
T
of the mos transistor, while the open-loop
gain
A
0
is then defined by
g
m
r
ds
.
The excess gain factor
A
0
H
, shown in Figure A.4, can be employed to suppress
imperfections of the active gain element. In a closed loop topology, nonlin-
earities that are present in the characteristics of the transistors are being sup-
pressed thanks to the excess gain that is available in the feedback loop. While
the gain of the ideal closed loop system is only defined by the feedback fac-
tor (1
/H
), the relative deviation of the actual closed loop gain
A
cl
from this
1
/H
-characteristic is determined by the excess loop gain (A.18):
1
/H
−
A
cl
1
rel
=
=
1
/H
1
+
A(jω)H
ω
ω
p
1
1
+
j
1
=
+
A
0
H
·
(A.18)
ω
A
0
Hω
p
1
1
1
+
j
The frequency response of the error curve is shown in Figure A.5. At the lower
end of the frequency spectrum, the relative error on the gain is solely defined
by 1
/(
1
A
0
H)
.However,atthefirstpole
ω
p
1
of the active gain stage in the
forward path of the amplifier, the deviation from the correct gain factor has
already risen to 1
.
4 times the error at dc. For even higher frequencies, the
relative error gradually rises to 100%, which in fact means that there is no
output signal at all.
+
Distortion in feedback amplifiers
Not only the unpredictable and finite gain
A
0
of the non-ideal amplifier is sup-
pressed in a closed-loop system, but also the linearity requirements of the am-
plifier are relaxed. For an increasing open-loop excess gain
A
0
H
, the nonlinear
characteristics of the closed-loop system are left to the - commonly passive -
elements in the feedback path. It should be easy to understand that the extent
