Digital Signal Processing Reference
In-Depth Information
H
i
o
A
Figure A.3.
Basic feedback amplifier. Factor
A
is the active gain element of the feed-
back circuit, while
H
is called the feedback element. For linearity rea-
sons, the feedback element is a passive circuit in most applications.
|TF(f)| [dB] (out / in)
A
0
: Low-frequency gain
of the active element in
the forward path.
ω
p1
o
pen-loop
30
A
0
slope: 20dB/decade
1/H: Closed-loop gain
25
excess gain : A
0
H
of the ideal system with
H in the feedback path.
20
Α
0
Ηω
p1
1/H
closed-loop
15
H
10
A
0
H
A
0
5
ω
p1
i
o
0
f
T
H
-1
A
0
H
ω
p1
10
−1
10
0
10
1
frequency [GHz]
Figure A.4.
Transfer characteristic of an amplifier with a single pole in an open loop
(solid) and in a closed-loop (dashed) configuration. In closed-loop con-
figuration, the excess gain suppresses non-ideal characteristics of the
active element in the forward path.
of this feedback system can be approximated by 1
/H
for sufficiently large
values of the forward gain factor
A
. As mentioned before, a practical amplifier
implementation exhibits one or more poles beyond which the gain factor
A
starts to decrease. An amplifier setup with a single pole filter in the forward
path is introduced in Figure A.4. This time, the transfer function of the single
pole feedback system is given by Equation (A.15), where the ideal amplifier
A
is substituted by it's frequency dependent counterpart:
A
0
A(f )
=
(A.16)
ω
ω
p
1
1
+
j
For a sufficiently large dc loop gain (
A
0
H
1), the application of a single-
pole (
ω
p
1
) amplifier in a feedback system results in a new single-pole system,
