Electronic – Simple NMOS transistor circuit output impedance

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I am having trouble figuring out the best way to determine the output impedance of this simple NMOS transistor circuit:

NMOS transistor circuit

Both transistors are equal, and the body effect is ignored.

What method should I use to find the output impedance? Should I find the transistors' small-signal equivalent and then use Thevenin and simply add resistances of both transistors together, or is there another method I could use?

Also, won't the output impedance vary with the drain current? Will it then be a function of \$V_{\text{ref}}\$?

EDIT:

I have tried to reduce the circuit down to its small signal equivalent using the t-model for an active NMOS. Is this correct?

enter image description here

EDIT 2:

Can the small signal equivalent circuit be reduced using Thevenin into something like this?

enter image description here

I feel like I am missing something here. It just seems too easy to be true.

Best Answer

So I spent some time researching the problem, and I came up with a possible solution:

First we draw the small signal equivalent for the circuit and add a test voltage \$v_{\text{d}}\$:

enter image description here

I have made the assumption that \$r_{\text{ds1}}\$ = \$r_{\text{ds1}}\$ = \$r_{\text{ds}}\$ because the transistors are identical.

We find expressions for \$i_{\text{d}}\$ in the top part:

enter image description here

And for \$i_{\text{d}}\$ in the lower part:

enter image description here

We seperate out \$v_{\text{s}}\$

enter image description here

And insert it into the first expression for \$i_{\text{d}}\$:

enter image description here

We then solve for \$R_{\text{s}}\$:

enter image description here

Which is the output impedance.

If anyone could verify if the answer above is correct or incorrect, that would be great.

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