Impedance of a terminal of a simple NMOS circuit

[Waxterzz]

Homework Statement

Calculate the impedance Zin[/B]

Homework Equations

The Attempt at a Solution

[/B]

I cut V_DD and the DC current source at the top.

Put in test DC voltage

V_Test - 10* I_Test = V_GS (because voltage "after" the resistor = the voltage at the gate and the drain, and source is to ground.

times gm to find current trough NMOS:

g_m [V_Test - 10* I_Test ]= g_m V_GS

This equals V_Test / 10 (current through resistor would be the same as current through NMOS

rearranging

V_Test / I _Test = 10*gm / (gm - 1/10) = Z_in

Z_in = 101.01 k Ohm ?This is probably wrong.

 

[NascentOxygen]

This equals VTest / 10 (current through resistor

This could be true only if the drain voltage was approximately zero, and you haven't demonstrated that it is. So you need to determine the right relationship.

Remember, $\mathtt {\frac 1 g_m}$ has units of Ohms.

Your method of approach is along the right lines, nonetheless. Caution: you are going to be tripped up sooner or later if you continue to write 10k as 10 in formulae.

 

[Waxterzz]

This could be true only if the drain voltage was approximately zero, and you haven't demonstrated that it is. So you need to determine the right relationship.

Remember, $\mathtt {\frac 1 g_m}$ has units of Ohms.

Your method of approach is along the right lines, nonetheless. Caution: you are going to be tripped up sooner or later if you continue to write 10k as 10 in formulae.

Hi, according to my calculations the voltage at the drain should be the same as the gate right, they share the same node.

But in the small signal model, its a current source so current following through resistor and the MOS should be the same not?

And yes, I'm aware of the problem with the possibility that writing 10k as 10 can go wrong. I will check on that in the future.Also, another approach could be given by Blackmans formula, but I don't know how to do that. U could choose between blackman (don't know anything about it) or the Vtest / Itest.

 

[rude man]

You are doing small-signal analysis.
So a small input current i = (v_in - v_gs)/R.
That small current must equal the increase in drain current (why?).
And small-signal-wise, you are given g_m = 10 mA/V. What is the definition of g_m?
So you can solve for v_gs and then Z_in = v_in/i.
The answer is a number not much greater than the resistor (10K).

Note that all parameters are small-signal deviations from the dc bias condition.

You do need to pay attention to units as previously advised. I suggest sticking to SI.