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

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SUMMARY

The discussion focuses on calculating the output resistance (Ro) for a common source (CS) MOSFET amplifier using the parameters V'A=10V/μm, L=0.4μm, and ID=100μA. The correct formula for Ro is Ro=V'A*L/ID, leading to Ro=40kΩ when properly applying unit conversions. The confusion arose from misinterpreting the units, but the resolution clarified that the micrometer units cancel out, resulting in a straightforward calculation. The final output resistance is confirmed as 40,000 ohms.

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Homework Statement


Supposed to find Ro for a CS MOSFET amp given V'A=10V/μm, L=0.4μm, and ID=100μA.

Homework Equations



Ro=ro=V'A*L/ID

The Attempt at a Solution



I say that ro=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.
 
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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