# Output Resistance - Small-Signal MOSFET

I am doing a question (I have broken the problem down to this sub-problem) which requires me to find the output resistance below:

I tried to do the small-signal analysis to find it by adding an extra voltage source and finding Vx and Ix. However, I'm stuck now. I can solve the problem if just ro2 was there, but the ro3 to GND is making it difficult to find the current Ix.

• To determine a resistance or an impedance, you have to stimulate the circuit with a current source $I_T$ while the response $V_T$ appears across its terminals. In your case, once the current source is installed instead of your voltage source, express the $I_T$ current versus the other elements and $V_T$. Then factor the whole thing to have $\frac{V_T}{I_T}=...$ and this is the resistance you want. A quick SPICE simulation showing operating points with $I_T$ set to 1 A will confirm your results - or not : ) – Verbal Kint Jan 4 at 13:53
• Take a look at this example electronics.stackexchange.com/questions/295771/… – G36 Jan 4 at 19:48

Vgs(th) =Vt has a wide Mfg. and temperature tolerance 50%? Measured at some arbitrary low std current threshold.

• yet 1-Vgs/Vt= k controls both Ron or RdsOn =1/gm.
• source output impedance = Ron +Rd =Rout here
• RdsOn is usually rated around k = 2.5 to 5. Or both where the difference is small.
• thus for Vt = 2 to 4V , Ron might be rated at 10V ( these are all the old enh FETs )
• newer Fets with lower Vt were designed for “Logic level” thus rated at 3V or 5V for Vgs and Ron
• there is also a strong temperature shift included in this tolerance of Vt.

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• So you get the idea , that computing it is not so easy but you expect Ron to be <= Rd in a linear design and < 2% of Rd for an efficient switch.
• Yet I have given you hints to solve Rout
• but if you make Ron << Rd then you must be aware that Coss * Ron is somewhat constant in a given design so that can affect turn off time.
• So choose your FET Ron wisely, otherwise you need your thermodynamic skills to design the heatsink