Digital Signal Processing Reference
In-Depth Information
A designer has several options to achieve the required transconductance ratio.
During design time, the transconductance of each pair can be altered by choos-
ing the appropriate w/l dimensions for each transistor. It is also possible to
dynamically adjust the tail current at runtime: a lower tail current of the diode-
connected load pair results in a higher output impedance and thus an increased
voltage gain. How tempting it may look to have stepless control over the gain
stages, the tail current will not be used as an extra degree of freedom in the
last four to five stages of the amplifier chain: it is precisely the tail current ra-
tio which plays a crucial role in the optimization of linearity of the open-loop
amplifier.
This is clarified by the following intuitive analysis. Suppose that both the gain-
and the loading pair are perfectly symmetrical, which also applies to their tail
currents. The voltage gain of this setup is very close to unity.
1
The nonlinear-
ities of the transconductance gain stage are suppressed thanks to the inverse
i-to-v characteristic of the active load. Now, in order to increase the gain, the
w/l dimensions of the loading pair are slightly decreased,
without
altering the
tail current of the loading pair. As a result of the reduced 1
/g
mo
impedance of
the diode-connected pair, the voltage gain of the amplifier will increase with
same factor.
At this point though, the proposed distortion cancellation mechanism needs
some extra attention, because the signal swing applied to the active load has
become larger than the signal swing over the input terminals of the amplifier.
At first sight it may seem that, due to the larger signal swing at the output,
the increased third-order nonlinearity of the active load will cause problems.
However, it is important to remember that, although the w/l dimensions of the
load were decreased, the tail current was kept constant. As a result, the over-
drive voltage (
V
gs
−
V
t
) of the active load will increase automatically, which
in turn results in an improved linearity [San99]. Summarizing, the increase of
distortion resulting due to the larger signal swing at the output is counteracted
by a larger overdrive voltage of the active load.
The outcome is that, after some fine-tuning of the tail currents, third-order dis-
tortion is still effectively suppressed by the inverse i-to-v characteristic of the
active load. Remark that, even though the proposed linearization technique is
not based on any form of feedback, the quality of the linearization mecha-
nism still deteriorates near the 3 dB cut-off frequency of the core amplifiers: at
higher frequencies, a substantial portion of the output current of the gain pair
is absorbed in the parasitic load capacitance at the output terminals. It follows
that the neutralization of the imperfections of the transconductance become
1
Provided that the drain resistance of the transistors is sufficiently high so that the 1
/g
m
resistance of the
diode-connected load dominates the output impedance.
