Question

The full triode region equation: (Eq.1) gives a nonlinear relationship between Vps and in, due to the vps2 term. Assuming the Vps term to be negligible allowed us to approximate the relationship between Vps and in as linear, which gives a resistive behavior: (Eq.2) Several people have asked, what is a "small enough" vos? The answer depends on how accurate you need to be. As vns gets larger, the difference between Eq.I and Eq.2 gets larger (see Figure 2.0 below). Find a value for the fraction Vps / (VGS-Vt), for which the current in predicted by the resistive approximation of Eq.2 is within 10% of the actual current value given by the full triode model of Eq.1? For what fraction is the error less than 1%? iD E9.2 (RESISTIVE) L-ERROR Eq.1 (TRIODE) VDS Figure 2.0

Answer 1

The answers with a detailed explanation and calculation is given below. The question has been solved for both the cases of 10% and 1% error. Ask for queries if any.

The full triode region equation of is for an NEMOS is given by: - km) [Co. - VW - 4wt] -0 Assuming vos term is negligible, the current s is lineas and it is: Ups - rou *** Ki (W) (www-vo] is kn' (W) . (ugs - Vz). Vos - ③ What is small enough Vos? As of my knowledge, small ups means, Vos < (VGs - Vt) and depends on the accuracy we need to be as mentioned. As 'Vos crosses (Ugs - Vt) the NMOs will go to saturation and equations 0 ① and ② are no longer valid. Subracting equations 0 and ② Ad kn (W) / 105 4 Egns 4 divided by 6 → Aid - 2 2 105 - un v) Vos - 12 ups

(Vay V4) - I los (2.Cey=MO) - 12(Vgs - 4 or less w.rit actual current For every to be 10% given by triode model, Mail.com (EX) -1 0 - [2 (*)-1=10 () Vas Vor - Vt within 103 Jos - V S 25 for enor to ( 0.182) sool (1%) , similiaaly we get For Uds for error to a within 1%. I (3 x 0.148