Norton Equivalent with Dependency on Open Circuit

Discussion in 'Homework Help' started by coolchriz90, Jan 24, 2010.

  1. coolchriz90

    Thread Starter New Member

    Jan 24, 2010
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    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.
     
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    What do you need to solve for? There is no problem statement - you've simply supplied the circuit.
     
  3. coolchriz90

    Thread Starter New Member

    Jan 24, 2010
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    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.
     
  4. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    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.
     
  5. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    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?
     
  6. coolchriz90

    Thread Starter New Member

    Jan 24, 2010
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    But the current source shouldn't be considered open when finding R_Norton because it is a dependent current source.
     
  7. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    Yep - agreed - my mistake. Well spotted.

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

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