n-ch mosfet output resistor

mosfet rds on linear region

In n-ch mosfet small-signal model, Rds is output impedance of N-ch mosfet.

when gate voltage of N-ch mosfet is changed,

output impedance of N-ch mosfet, Rds ( resistance between drain and source),

is it changed, too ? or it is not changed, always have ideally infinite impedance?

if Rds don't have infinite value, tell me whether Rds is changed or not.

mosfet vt rds lambda

we assume gate impedance as infinte, not the source or drain

Of course rds is a function of Vgs (very strong).
You can find the relation from the current equations:
1. Linear region
Id=beta((Vgs-Vt)Vds-0.5*Vds^2)
now rds is defined as dVds/dId
Hence the derivative
rds=1/(dId/dVds)=1/(beta(Vgs-Vt-Vds))
generally, it is assumed that Vds is very small (Near zero) Hence we arrive to the famous equation for linear region
rds=1/(beta(Vgs-Vt))
So as it is clear from the equation above rds=f(Vgs)
2. Saturation Region
Id=0.5*beta*(Vgs-Vt)^2(1+lambdaVds)
(This model 2 MOS equation)
Hence
1/rds=dId/dVds=0.5*beta*(Vgs-Vt)^2*lambda
Hence
rds=1/(0.5*beta*(Vgs-Vt)^2*lambda)
Generally it is assumed that lambdaVds<<1
hence, under this assumption you can simplify the
saturation expression as
Id=0.5*beta*(Vgs-Vt)^2
And here comes the famous expression
rds=1/(lambda*Id)
We can also conclude from here that The reason the rds modulation within the saturation region is due to the drain current variation of the transistor
So again
rds=f(Vgs)