Digital Signal Processing Reference
In-Depth Information
introducing a cascode transistor on top of the gain transconductance. However,
this merely relocates the i-to-v conversion problem to the drain terminal of
the cascode transistor. A more convenient solution in this case - and generally
for all amplifiers with a decent low-frequency gain - would be to embed the
entire multistage structure in a closed-loop feedback system. The purpose of
feedback in this case is to push non-idealities of the active gain elements to the
background. Once again, the excess gain available in the forward path is thus
'deployed' to take advantage of the better linearity of passive elements in the
feedback path of the system.
At this point, the reader must realize that the low-frequency voltage gain of
a multistage amplifier is superior to that of a single stage amplifier. It is thus
not surprising that this also shines through in the overall accuracy of the am-
plifier in feedback configuration. At least in the lower frequency region. Since
the high gain prerequisite implies that the signal must pass through a chain of
several cascaded transistors on it's way to the output, it is pretty interesting
to see what kind of impact this has on the speed of the amplifier and - more
specifically - on the linearity in higher frequency bands. The following deriva-
tion was made under the assumption of a two-stage amplifier, but can be easily
expanded to an arbitrary number of gain stages in the forward path of the feed-
back system. In a typical case, only one of the stages of a two-stage amplifier
is dedicated to voltage amplification (Figure A.21). The other one acts as a
buffer stage driving the output, which is commonly a capacitive load in cmos
H
node n
1
sees large virtual
capacitor: C
virt
= g
m2
r
load
C
miller
nVdd
cmfb
r
out
r
out
node sees 1/g
m2
beyond first pole
g
m2
n
f
eedback
n
out
n
1
C
miller
n
inp
r
load
C
load
r
o
g
m1
n
inn
I
bias
Input pair provides voltage
Output stage of amplifier
gain. First pole of two-stage
drives capacitive load. Has a
amplifier located at node n
1
.
low output resistance (1/g
m2
).
Figure A.21.
Example of a two-stage amplifier (cmos Miller ota [Ste90]). The
output stage determines the second pole (
g
m
2
/C
load
)oftheampli-
fier. Then, taking stability into account, one can determine the gbw-
product (gbw
=
g
m
1
/C
miller
). Distortion suppression only starts at
frequencies below the first pole of the closed-loop system (
ω
p1, cl
=
gbw
·
H
).
