Digital Signal Processing Reference
In-Depth Information
a smaller second-order component is present. It is this factor that will con-
tribute to both the second- and third-order distortion components when the
transistor is embedded in the resistive degenerated feedback system. Based on
Formula (A.29), one could conclude that an increase of the overdrive voltage
V
GST
is the correct way to tackle distortion. The reality, which is of course
a little bit more complex, requires a more subtle shaded answer, depending
on some boundary conditions. Based on the closed-loop distortion formula
(A.24) and from the polynomial coefficients of the MOS transistor (A.29), the
second-order distortion performance of the degenerated MOS stage can be ap-
proximated by (A.30):
1
4
v
g,peak
V
gs
−
1
hd
2,cl
=
,
(A.30)
V
T
(
1
+
g
m
R
S
)
2
relative swing
loop gain
from which it is clear that the distortion at the output of the amplifier is de-
pendent on the relative voltage swing (w.r.t. the overdrive voltage) at the input
and the loop gain
g
m
R
S
. In a discrete amplifier setup, where fixed transistor
dimensions
(W/L)
are a constraint, increasing the overdrive voltage
V
gst
or
the series resistance
R
S
are appropriate choices to improve the linearity of the
single transistor amplifier.
The calculations for the harmonic distortion can also be referred to the current
amplitude
i
ds
at the output of the system. A combination of the mos transistor
parameters from (A.29), the output-referred second-order distortion formula in
Equation (A.25) and some unpleasant calculations may lead the reader to the
following expression for the output-referred second-order distortion (A.31):
1
8
i
ds
,peak
I
ds
1
hd
2,cl
=
(A.31)
1
+
g
m
R
S
relative swing
loop gain
Then, keeping the closed-loop transconductance of the overall system in mind
(Formula (A.28)), the output-referred distortion from above can also be refor-
mulated as (A.32):
G
m
g
m
1
8
i
ds,peak
I
ds
hd
2,cl
=
(A.32)
The last factor in this expression indicates the ratio between the closed-loop
transconductance
G
m
and the open-loop gain
g
m
that is available from the tran-
sistor. It is thus again confirmed by this observation that gain can be traded for
linearity in a feedback system. Using the approximation of
g
m
introduced by
