Digital Signal Processing Reference
In-Depth Information
matching problem in the gain pair, second order components will emerge at
higher frequencies. The
negative
third-order term in (7.5) represents the large-
signal gain compression and is also related to the third-order intermodulation
distortion im
3
in the frequency domain (more information in Section A.1). At
this point, when the differential pair has a resistive load
R
load
, these third-order
terms are directly translated to the voltage domain by
v
out, diff
=
R
load
.Inor-
der to counteract the third-order distortion component, the differential pair has
been loaded with a second pair, which has the same differential voltage-current
conversion characteristic (7.6):
i
od
·
β
gain
/I
bias
v
id
·
β
gain
·
1
8
·
v
id
·
i
od, gain
=
I
bias
−
β
load
/I
load
β
load
·
1
8
·
v
od
·
i
od, load
=
v
od
·
I
load
−
(7.6)
In this formula,
v
id
represents the differential voltage at the input of the am-
plifier, while
v
od
is the voltage across the output terminals of the amplifier. If
the impedance of the load is dominating over all other parasitic impedances
at the output node, all differential current from the input pair will flow through
the loading pair. In first order, the output voltage of the amplifier can thus be
approximated by
v
od
=
gain
·
v
id
and the following equation holds (7.7):
β
gain
/I
bias
v
id
·
β
gain
·
1
8
·
v
id
·
I
bias
−
β
load
/I
load
β
load
·
1
8
·
gain
)
3
=
v
id
·
gain
·
I
load
−
(v
id
·
·
(7.7)
By comparing the first order terms of Equation (7.7), the expression for the lin-
ear gain of the amplifier can easily be found. Comparing the third-order terms
and substituting the expression for the first-order gain leads to the following
precondition for a linear voltage gain between in- and output (7.8):
β
gain
·
I
bias
β
load
·
I
load
gain
=
from the first-order terms of (7.7)
β
gain
I
bias
=
β
load
I
load
gain
3
·
from the third-order terms of (7.7)
⇓
I
bias
=
I
load
precondition for linear voltage gain (7.8)
For a differential pair with mos transistors in operated in the saturation re-
gion, the large-signal third-order distortion component can thus be avoided by
choosing the same tail current for both gain pair and load pair. The voltage gain
can be chosen independently from this requirement, and is determined by the
