Digital Signal Processing Reference
In-Depth Information
1
V
E
·
I
L
V
out
=
2
−
L
(3.3)
W
K
p
·
L
(
V
SG
−
V
T
)
The equivalent scheme of this amplifier, presented in Fig.
3.1
uses a resistor
r
L
that represents the output resistance of a non-ideal current source
I
L
. The gain of
this amplifier is given by Eq. (
3.4
):
r
L
v
out
v
in
=
I
C
V
SG
−
2
·
V
E
·
L
g
m
,
1
·
(
r
L
r
0
,
1
)
=
V
T
·
I
C
2
·
V
E
·
L
≈
(3.4)
V
SG
−
V
T
The gain can be increased by biasing the transistor with a small gate overdrive
V
SG
−
V
T
and, on the supposition that
r
L
is high, by increasing
L
of the transistor
while keeping the
W
L
ratio constant.
ogy is a parameter that is sensitive to a set of process and environmental variables.
Therefore it is important to investigate and compare the sensitivity of the ampli-
fier topologies to variations of this parameter. In both Eqs. (
3.2
) and (
3.4
) the factor
(
/
is in the denominator. Moreover this factor is small since the transistor
M
1
is typically biased with
V
SG
close to
V
T
for high gain. Therefore both the DC
output voltage level and the gain are very sensitive to a
V
SG
−
V
T
)
V
T
change.
A figure of merit that is presented in this work to compare the sensitivity of an
amplifier circuit to
V
T
in the input transistors is the threshold voltage suppression
ratio (VTSR) derived in Eq. (
3.5
). It represents the ratio between the gain of the
amplifier and the common-mode gain of a
V
T
excitation in the input transistors.
∂
V
out
∂
A
A
V
T
V
in
=
=
VTSR
(3.5)
∂
V
out
∂
V
T
,
in
=
∂
V
out
∂
V
in
VTSR
se
=
1
=
0
dB
(3.6)
∂
V
out
∂
V
in
where
A
and
A
V
T
are respectively the gain of the amplifier and the
V
T
gain of the
amplifier. In this formula only the
V
T
of the input transistors is included. This is
clarified in Sect.
3.2.3
where the implementation of the load transistors is profoundly
discussed. Since the current through a transistor in saturation is always a function of
the gate overdrive
V
SG
−
V
T
,every
V
T
in
M
1
of the single-ended amplifier has
an identical effect to a
V
in
of the amplifier. Therefore the VTSR
se
for a single-
ended amplifier is 1 or 0 dB, hence the higher the gain, the higher the
V
T
sensitivity
of this amplifier. In this topology there is no degree of freedom that separates the
amplifier behavior from the
−
V
T
sensitivity, whereas there is such an opportunity in
the differential amplifier that is discussed in Sect.
3.2.2
.
