Digital Signal Processing Reference
In-Depth Information
about 3V. The linearity of the
V
T
shift is valid for a very large interval, reaching
over several tens of volts, and in this way the backgate can enable the free choice of
the DC level of the gate contact without changing
I
SD
or
V
SD
of the transistor. This
technique is applied for DC connecting consecutive differential amplifier stages in
2.4.3.2 Gate-Backgate Connected Transistors
A second and probably more powerful technique that fully turns the backgate to
advantage is obtained by connecting the backgate contact with the gate contact.
The technique in this work is also referred to with the term
backgate steering
.Inthis
technique the
V
T
of the transistor is shifted during operation by the gate voltage itself.
The result of this
V
T
shift on the
V
G
−
I
D
curve is plotted in Fig.
2.19
a. The gray curves
correspond to the measured
V
G
−
I
D
curves of the 4-contact 140
µ
m/5
µ
m transistor
with a fixed backgate voltage that is stepwise varied between 10 and
10V. Each of
these lines include one dot where
V
G
equals
V
BG
. All those dots also correspond to
the curve of the transistor with its gate and backgate connected. As such the curve
of the gate-backgate connected transistor is graphically derived. The black curve
corresponds to the measured
V
G
−
−
I
D
curve of this transistor and logically coincides
with the graphically derived curve. The acquired transistor curve is clearly steeper
than the original curves, i.e., more current flows through the same transistor under
the same
V
SG
and
V
SD
and moreover a higher transconductance
g
m
is obtained. This
behavior can be derived from Eq. (
2.9
) and the result is presented in Eq. (
2.17
).
W
L
(
2
I
SD
,
sat
=
μ
C
ox
×
V
SG
+
ξ
×
V
SBG
−
V
T
,
0
)
(
with
V
SBG
=
V
SG
)
⇓
V
SG
−
V
T
2
W
L
V
T
,
0
1
2
where
V
T
I
SD
,
sat
=
(
1
+
ξ)
×
μ
C
ox
×
(
=
+
ξ
)
(2.17)
The striking conclusion from this equation is that the transistor current still follows
the quadratic current law in saturation, which facilitates themodeling of this behavior.
According to the measured value of 350mV/V for
, an increase of the transistor
constant
K
P
with 82% is experienced. Furthermore, the
V
T
of the transistor is slightly
moved by this technique. The increase of the current is logically passed on to the
transconductance, where an identical increase is experienced when the gate overdrive
V
SG
−
ξ
V
T
is kept constant, as can be seen in Eq. (
2.18
):
2
I
SD
V
SG
−
2
g
m
=
V
T
=
(
1
+
ξ)
×
g
m
,
0
(2.18)
where
g
m
,
0
is the original
g
m
value of the 4-contact transistor with fixed backgate. It
must be noted that this comparison is interpreted for identical gate overdrive voltages,
