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Analog Integrated Circuits and Signal Processing 5, 175-181 (1994) © 1994 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands. An Improved Analysis for the Nonlinear Performance of Body-Driven 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 body-driven analog long-channel 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 four-terminal 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 [1-5]. The source-substrate 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 substrate-source voltage. On the other hand, the inver- sion layer mobility is a function of the traverse field. Using a first-order approximation for the transverse field-dependent inversion layer mobility, the current- voltage characteristic of a long-channel 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 four-temdnal device. the electron charge, V~0 is the threshold voltage with zero substrate-source 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 closed-form expressions for the nonlinear perfor- mance of body-driven analog long-channel 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 closed-form expressions for the second-harmonic and
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