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Design >> Analog Design >> Expression for gds as a function of VGS in weak inversion?
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Message started by spectrallypure on May 31^st, 2018, 11:24pm

Title: Expression for gds as a function of VGS in weak inversion?
Post by spectrallypure on May 31^st, 2018, 11:24pm

Hi! I am writing a paper and I need a way to show analytically that the output conductance of a MOS decreases as the VGS decreases in WEAK INVERSION. Classical books provide expressions only for STRONG INVERSION, like

gds = IDS/Va = lambda*IDS

Does anybody know is such an expression exists FOR WEAK INVERSION?. I need something of the form:

gds = gds(VGS), in weak inversion.

Thanks, Jorge.

Title: Re: Expression for gds as a function of VGS in weak inversion?
Post by spectrallypure on Jun 1^st, 2018, 8:59pm

Actually, I need a general expression that would hold both in strong an weak inversion. So far the best I have found is the following expression from Tsividis' book "Operation and Modelling of the MOS transistor" (eq. 8.2.48 in the 2nd edition / eq. 7.2.58 in the 3rd edition):

gds = (W/L)uCox*[Vgb-VFB-PSIsL-gamma*sqrt(PSIsL)]

(PSIsL is the surface potential at the drain) which I guess can be rewritten in terms of Vgs as:

gds = (W/L)uCox*[Vgs-Vsb-VFB-PSIsL-gamma*sqrt(PSIsL)]

However, I'm not sure if this expression is valid all the way from strong to weak inversion and in linear and saturation regions (that would be great). Can someone please confirm this?

Note that I am not interested in the modelling of the Ids dependence on Vds (channel length modulation, DIBL, etc): I just need an expression to show that, when Vgs diminishes, the drain-to-source conductance diminishes too!

Thanks, Jorge.