Digital Signal Processing Reference
In-Depth Information
(A.3), the second-order distortion can also be expressed in terms of more prac-
tical design parameters such as the closed-loop transconductance
G
m
, the bias
current
I
ds
and the overdrive voltage
V
gst
(A.33):
i
ds
,peak
I
ds
(V
gs
−
V
T
)
2
I
ds
1
8
hd
2,cl
=
G
m
(A.33)
The closed-loop transconductance
G
m
represents the useful gain that is eventu-
ally available from this system. Furthermore, the bias current
I
ds
will define the
power consumption of the amplifier setup. Note that if the power consumption
is a fixed constraint, the linearity can still be improved by
decreasing
the over-
drive voltage, completely opposite to the intuitive solution suggested earlier.
The reason for this behaviour is that a constant drain-source current leads to
a quadratical increase of the dimensions of the transistor
(W/L)
, thereby also
increasing the small-signal gain
g
m
. A major pitfall of improving the linearity
in this way is that the high-frequency performance of the system will collapse
under the increased load of parasitic capacitances.
The simplified mos transistor model used in these calculations does not con-
tain any third-order coefficients. When the transistor is used in an open-loop
topology, no third-order distortion components will thus appear at the output.
However, from Equation (A.24) it is clear that third-order components appear
in the degenerated amplifier setup after all. By following the same strategy
as for the second-order distortion, and employing the polynomial coefficients
from (A.29) in hd
3,cl
, the following expressions are obtained for the third-
order harmonic distortion (A.34):
v
2
1
32
g
m
R
S
g,peak
(V
gs
−
=
hd
3,cl
V
T
)
2
(
1
+
g
m
R
S
)
4
i
ds
,peak
I
ds
2
G
m
g
m
2
1
32
=
g
m
R
S
(A.34)
While these formulas might look very impressive or confusing for the reader, it
is far more interesting to look back to the closed-loop second-order harmonic
distortion formula of A.32. It seems that the third-order distortion of A.34 is
related to HD
2,CL
in the following manner (A.35):
1
8
G
m
g
m
2
i
ds
,peak
I
ds
hd
3,cl
=
2
g
m
R
S
2
hd
2,cl
2
=
g
m
R
S
=
g
m
hd
2,cl
R
S
2hd
2,cl
=
g
m
h
d
2,c
l
R
S
im
2,
c
l
(
3
)
(A.35)
(
2
)
(
1
)
