IEEE Solid-States Circuits Magazine - Summer 2018 - 48

Biasing for
Zero Distortion
Using the EKV/BSIM6 expressions

T

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Willy Sansen

he EKV/BSIM6
model is well
suited to find the
optimum biasing
point of a metal-oxide-semiconductor transistor (MOST)
for zero third-order intermodulation
(IM 3) distortion. This article provides
a derivation of a simple expression for
this biasing point, for all possible regions of operation, i.e., the weak inversion (wi), the strong inversion (si), the
velocity saturation (vsat), and all their
crossover regions. Because the expressions are relatively simple, this overview provides, at the same time, a set
of EKV/BSIM6 model expressions to
be used for design and educational purposes.

An Introduction to the
MOST Device Model

Digital Object Identifier 10.1109/MSSC.2018.2844607
Date of publication: 13 August 2018

48

su m m e r 2 0 18

For nanometer complimentary metal-
oxide-semiconductor (CMOS) devices,
the EKV model offers many advantages [1]-[3]. If the design variable,
i.e., inversion coefficient (IC), is used

IEEE SOLID-STATE CIRCUITS MAGAZINE

instead of VGS -VT , then the MOST
parameters g m, g m /I DS , and fT all give
straight lines on log-log scales [3]. As
a result, it is easier for the designer to
gain insight, which is essential to optimize MOST circuitry within the speednoise power compromise.
The EKV model also allows easy
prediction of the distortion. Because
distortion is a specification that many
designers struggle with, it is derived
here in detail. The same model is used
as before, and the same independent
variable IC. These curves lead to the
optimum IC when distortion is one
of the most important specifications.
However, because a gate voltage is
applied to the MOST itself, these
curves have to be converted first.
Some specific biasing values of IC
are of great interest for a designer.
There is a value of IC where the IM 3
becomes zero. This zero distortion
point is most useful in circuits such as
high-frequency, low-noise amplifiers
[4]. IM 3 is given by the second-order
derivative of the transconductance,

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IEEE Solid-States Circuits Magazine - Summer 2018

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Contents
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