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

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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.

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  • \$\begingroup\$ 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 : ) \$\endgroup\$ – Verbal Kint Jan 4 at 13:53
  • \$\begingroup\$ Take a look at this example electronics.stackexchange.com/questions/295771/… \$\endgroup\$ – G36 Jan 4 at 19:48
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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
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