Digital Signal Processing Reference
In-Depth Information
|TF(f)| [dB]
v
in
x
a
1
ω
p1
open-loop gain
30
a
1
H
a
1
H
Transfer function from v
in
a
1
Hω
p1
20
to node x. A lower value
1/H
results in less distortion.
closed-loop gain
10
Distortion suppression
begins to improve below
1
closed-loop pole frequency.
0
a
1
H
v
in
→ x
Distortion suppression
−
10
1/a
1
H
deteriorates starting from
the first open-loop pole.
frequency [GHz]
10
−1
10
0
10
1
Figure A.11.
Transfer function from
v
in
to intermediate node
x
for a single-pole
amplifier. Distortion suppression is only available below the closed-
loop pole of the system, from where the excess loop gain reduces the
signal level at node
x
.
ω
2ω
distortion
d
v
in
x
z
y
a
1
F(j
ω)
H
Figure A.12.
The principle of distortion injection in a closed-loop system. From the
input signal at node
x
, the distortion amplitude at node
d
can be calcu-
lated. The final distortion level at output node
y
is then found using the
transfer function from
d
to
y
.
with the most important frequency marks. Also, this figure clearly illustrates
once more that gain may be traded for linearity. But as soon as the available
excess gain (
a
1
H
) drops due to the limited bandwidth of the active element,
the linearity performance starts to degrade.
Starting from the transfer function from input terminal
v
in
to node
x
at the in-
put of the active element, the amplitude of the fundamental component at the
output of the amplifier (node
z
in Figure A.12) is found by a multiplication
with the linear gain
a
1
of the amplifier. In an open-loop setup, the magnitude
of the harmonic components would then easily be determined using the hd
2
,
ol
and hd
3
,
ol
formulas of (A.21). In the closed-loop system however, distortion
must be regarded as a brand new signal component that is injected in the sys-
tem, as illustrated by Figure A.12. The second- or third order distortion signal
