Calculate Ro for CS MOSFET Amp using V'A, L, and ID | Homework Solution

[vermin]

Homework Statement

Supposed to find R_o for a CS MOSFET amp given V'_A=10V/μm, L=0.4μm, and I_D=100μA.

Homework Equations

R_o=r_o=V'_A*L/I_D

The Attempt at a Solution

I say that r_o=10μ*0.4μ/100μ=
10*10^-6*0.4*10^-6/100*10^-6
= 4*10^-8

Book says "10x0.4/.1=40kΩ"

.. what exactly went into that? for one thing (10*0.4)/.1 does not = 40,000.

also if you multiply something in micrometers by something in micrometers, then divide by something in microamps, you should end up with a very small number, I think.

I'm sure 40kΩ makes sense somehow but they're doing a bad job of explaining it.

 

[vermin]

Nevermind, I got it. V'A was in units of V/um, so really 10*(V/um)

[(10*(V/um))(0.4*um)]/(100*uA)=(10*V*0.4)/(100*uA)=40,000 ohm

^ because the um cancels out in numerator, ^ becomes just 4 V