Digital Signal Processing Reference
In-Depth Information
open-loop based system. For a single-ended transistor stage, the dc-offset is
determined by the operating point of the transistor. In the majority of the cases,
the output voltage of an amplifier is not compatible with the operating point of
the subsequent stage. Because the in- and output operating point voltage levels
are commonly fixed at different voltages, a dc-coupling between subsequent
stages of a multistage amplifier becomes highly problematic. Then again, in
the small number of cases where the stages are directly coupled, one must pro-
ceed with extreme caution, since a small deviation from the operating point is
treated as a valid input signal by the next stage. This causes the amplifier to
drift away from the intended biasing point, which may cause clipping in the
next stage. It is for this reason that the dc-voltage is removed from the signal
path in almost every high-gain amplifier (e.g. the if-stages of a receiver). This
is commonly achieved by employing ac-coupled circuit sections: coupling ca-
pacitors block the dc-component and pass the higher frequency components
to the next stage.
Coefficient
a
1
from Equation (A.1) represents the linear gain of the amplifier.
For example, the large-signal model for a mos transistor in strong inversion is
described by (A.2):
K
W
V
T
)
2
,
I
ds
=
L
(V
gs
−
(A.2)
where
I
ds
is the drain-source current as a result of the
V
gs
voltage applied over
the gate-source terminals of the transistor. The
W/L
ratio is defined by the
dimensions of the transistor and
V
T
is the threshold voltage. The transconduc-
tance parameter,
K
(units:
A/V
2
), depends on technology parameters such
as electron mobility and oxide capacitance. These characteristics are generally
obtained from measurements. The small-signal linear gain of the mos ampli-
fier can be obtained by choosing the dc-operating point of the mos transistor
in the strong inversion region and then applying a sufficiently small voltage
swing around this operating point. The first order variation of the drain current
is then given by:
i
ds
v
gs
=
·
I
ds
V
gs
−
2
a
1
=
g
m
=
,
(A.3)
V
T
where
v
gs
is the small-signal input voltage and
i
ds
is the resulting output cur-
rent. The fraction
i
ds
/v
gs
is called the transconductance
g
m
(unit:
A/V
)ofa
mos transistor. The capitalized parameters
V
gs
and
I
ds
define the large signal
operating point. One can see that the first order transconductance can be in-
creased in two ways. The first option is an increase of the drain-source current
flowing through the transistor. If the overdrive voltage (
V
gs
−
V
T
) needs to re-
main fixed, this is achieved by changing the
W/L
dimensions of the transistor
