Digital Signal Processing Reference
In-Depth Information
capacitors was then combined in the following expression for the capacitive
load at the output terminal of the open-loop stage (7.17):
C
in
A
v, si
ngl
e stag
e
C
out
=
kC
in
+
+
xC
in
,
(7.17)
next stage
loading pair
where the fairly constant factor
k
(
3) embodies the combined parasitic capac-
itance of the pmos bias transistors (a), the offset compensation circuitry (b)
and some interconnect wiring (c). The gate-source capacitance of the diode-
connected pair is equal to that of the gain pair for unity voltage gain. Higher
gains are achieved by a proportional reduction of the width of the loading pair.
This is taken into account by the second term. The last section in Formula
(7.17) denotes the input capacitance of the subsequent gain stage, which is
upscaled with a factor
x
. The approximate bandwidth of the nonlinear loaded
open-loop stage, when it is embedded in a tapered structure is given by (7.18):
≈
1
r
load
C
out
=
1
C
in
k
x
ω
3dB, single stage
=
g
mo
·
1
+
A
v, single stage
+
g
mi
A
v, single stage
·
1
ω
3dB, single stage
=
C
in
k
x
1
+
A
v, single stage
+
g
mi
C
in
1
=
·
,
(7.18)
1
+
A
v, single stage
[
k
+
x
]
f
T
, input
where
g
mi
and
C
in
are the transconductance and the gate-source input capaci-
tance of the first gain stage. It follows from the last expression in (7.18) that
the bandwidth of the amplifier can be expressed as a function of
f
T
, the cut-off
frequency of the input transistors. Remark that this frequency is not necessar-
ily equal to the maximum achievable
f
T
in a certain technology: the nonlinear
loaded amplifier achieves a better distortion suppression for a higher output
resistance of the transistors: increasing the channel length of the input pair in-
creases the channel-induced output resistance of the gain pair. For example, in
the design presented in this section, the physical length of the input transistors
was increased from 0
.
12 to 0
.
24
m. Doing so, the parasitic output impedance
r
o
of the non-ideal transconductance is increased with a factor 3. This is, of
course, at the expense of the cut-off frequency, which dropped from 100 GHz
μ
