I have been struggling with this problem for the last couple hours and haven't been able to figure it out.

I know in general how to solve a Norton equivalent problem (short circuit current and Equivalent resistance) but having a the dependent source be dependent on the voltage drop across this open circuit has thrown me for a loop.

Thanks for any assistance.

 

What do you need to solve for? There is no problem statement - you've simply supplied the circuit.

 

Sorry about that. I guess I've become slightly brain dead with how long I've been staring at this problem. I am trying to find the Norton Equivalent of this circuit.

 

Sorry I didn't read your question carefully. You want the Norton Equivalent.

If you short terminals a and b you will have the Norton Current (=isc)

Vi=Vgs+isc*Rs
Vgs=Vi-isc*Rs -----(1)

Suggest converting the current source in parallel with ro to a Thevenin Equivalent - hence

Vth=gm*Vgs*ro
Rth=ro

isc=gm*Vgs*ro/(ro+Rs) -----(2)

Eliminate Vgs by solving (1) & (2) simultaneously to give isc in terms of Vi.

If you take Vab (open) as Vth you should be able to go from there to find the Norton resistance.

 

In fact Rnorton is found by inspection rather than unnecessary calculation. What do you "see" looking into terminals a-b with the current source open?

 

But the current source shouldn't be considered open when finding R_Norton because it is a dependent current source.

 

But the current source shouldn't be considered open when finding R_Norton because it is a dependent current source.

Yep - agreed - my mistake. Well spotted.

You have to find Vab(open) and divide by isc.

I get Rnorton=ro+Rs+gm*ro*Rs