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Equivalent resistance from source to drain in such configuration

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simbaliya

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The gate resistor value is R, can somebody help me understand how to calculate the equivalent Rds?
 

Rds=Vds/Id.

This is the formula we can calculate Rds.
 

Rds=Vds/Id.

This is the formula we can calculate Rds.

I tried to use small signal model and introduce a measuring voltage between source and drain, but I can not get a solvable equation of Vds/Id or V_measure/I_measure.
 

You get a non-linear relation Vds=f(Ids), you need to specify either Vds or Ids to calculate a small signal rds = dVds/dIds or large signal Rds = Vds/Ids. In any case, they don't depend on gate resistor R.
 

Rds=Vgs(off)/[2Idss(Vgs-Vgs(off))]

Think this could be helpful to you.
 

You get a non-linear relation Vds=f(Ids), you need to specify either Vds or Ids to calculate a small signal rds = dVds/dIds or large signal Rds = Vds/Ids. In any case, they don't depend on gate resistor R.

Thank you for the reply, but could you please explain more on why gate resistor will not affect Rds?
 

No current through gate = no voltage drop at R. The circuit simply makes Vgs = Vds.
 
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