# Calculate the Transconductance for a MOSFET, given W,L,Vg,Vd,u,Cox but not Vth

1. Aug 23, 2011

### genxium

1. The problem statement, all variables and given/known data

This problem is given to me by programme inductor, and I just copy the whole description here so every given element is the same as what he/she gives. I'm confused with the given conditions.

1) What is the transconductance (gm) of a MOSFET biased at W=L=1um,
uCox=0.01A/V^2, Vg= 1V and Vd=1V?

2) For the same transistor with a load resistance of 100ohm, what is the
voltage gain?

2. Relevant equations

Triode mode or linear region, When VGS > Vth and VDS < ( VGS – Vth )

$$I_D=\mu_nC_{ox}\frac{W}{L}((V_{GS}-V_{th})V_{DS}-\frac{V_{DS}^2}{2})$$

Saturation or active mode, When VGS > Vth and VDS > ( VGS – Vth )

$$I_D=\frac{\mu_nC_{ox}}{2}\frac{W}{L}(V_{GS}-V_{th})^2(1+\lambda (V_{DS}-V_{DSsat}))$$

or

$$I_D \approx \frac{\mu_nC_{ox}}{2}\frac{W}{L}(V_{GS}-V_{th})^2$$

The derivation is http://ecee.colorado.edu/~bart/book/book/chapter7/ch7_3.htm" [Broken].

3. The attempt at a solution

I'm afraid the threshold voltage Vth should be given to do the calculation, besides, Vg=Vd=1V here so the transistor should be in Saturation Mode , should I assume the value of Vth by myself or just assume that Vg-Vth is approximately equal to Vd ?

Last edited by a moderator: May 5, 2017
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