Analog Integrated Circuits and Signal Processing 5, 175181 (1994)
© 1994 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands.
An Improved Analysis for the Nonlinear Performance
of BodyDriven Analog MOSFET Circuits
MUHAMMAD TAHER ABUELMA'ATTI
King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Received January 4, 1993; Revised April 22, 1993.
Abstract. This article discusses the nonlinear performance of bodydriven analog longchannel MOSFET circuits.
Analytical expressions are obtained for the nonlinear distortion products resulting from sinusoidal excitation of
the body terminals. The special case of a single sinusoid excitation is considered in detail, and conditions for har
mordc suppression are obtained.
1. Introduction
The MOSFET, shown in figure 1, is a fourterminal
device with source, drain, gate, and substrate (body).
In ~e standard textbook treatment the derivation of the
basic equations always assume that the substrate of the
MOSFET is connected to the source. Although this is
the case in most digital applications, a number of im
portant exceptions to this case occur in analog circuits
using MOSFETS [15]. The sourcesubstrate voltage
affects the threshold voltage and thus the drain current
IDS
:[6]. Thus an accurate analytical model for the
MOSFET characteristic must include the effect of the
substratesource voltage. On the other hand, the inver
sion layer mobility is a function of the traverse field.
Using a firstorder approximation for the transverse
fielddependent inversion layer mobility, the current
voltage characteristic of a longchannel MOSFET can
be expressed as [7]
IDS
:=
K f
VDs
(1 + XV)
(Vos

VTO
,JO
+ 7x/~B 
V 
3"~/V 
VBS + 2CkB) dV
(1)
where
Vr
=
Vro +
3'(42~

Vss 
242~B),
K = #0 Cox
W/L,
3' = ~/Cox,
Wis the channel width, L is the channel length (about
100 microns, long enough that longitudinal mobility
modulation can be neglected),
NA
is the substrate dop
ing concentration, Cox is the gate oxide capacitance
per unit area, e is the silicon dielectric constant, q is
G
'
O
So~CC
t5
Fig. 1.
MOSFET is a fourtemdnal device.
the electron charge, V~0 is the threshold voltage with
zero substratesource voltage, 2¢~8 is commonly token
to be the Fermi potential, but is actually several kT/q
higher than this value [8], and/z 0 is the zero voltage
carrier mobility in the channel.
By standard integral tables [9], (1) yields
1
IDS = K{(Vas 
VTO + "y 2x~B) VDs  ~ V~s
2
 ~ "Y(VDs  VBS +
2~bB) 3/2 + 3 3' (24~n 
VSS) ~n
+ x ~(v~  V~o + v24~.) v:o~3
31 v~s
2~5 (3VDs + 2VB s  40B)(Vos  V,s
+
2q~B) 3/z
+4~
(VBs 
20B)(2q~B  VBS) 3n] }
(2)
I
D
J
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176
Abuelma ' atti
Equation (2) shows the nonlinear dependence of
los
on
VBS
and
los.
However, in its present form it cannot
yield closedform expressions for the nonlinear perfor
mance of bodydriven analog longchannel MOSFET
circuits. By specializing their interest into the case of
a signal of amplitude
flVDs
superimposed on the body
terminal, expanding (2) in a Taylor series about
VDS
= 0, and retaining terms up to the third power of
Vos,
Patterson and Shoucair [7] obtained approximate
closedform expressions for the secondharmonic and
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 Integrated Circuit, Signal Processing, The Land, longchannel MOSFET, Analog MOSFET Circuits, BodyDriven Analog MOSFET, analog longchannel MOSFET

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