# Impedance of a terminal of a simple NMOS circuit

1. Oct 9, 2014

### Waxterzz

1. The problem statement, all variables and given/known data
Calculate the impedance Zin

2. Relevant equations

3. The attempt at a solution

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

Put in test DC voltage

VTest - 10* ITest = VGS (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:

gm [VTest - 10* ITest ]= gm VGS

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

rearranging

VTest / I Test = 10*gm / (gm - 1/10) = Zin

Zin = 101.01 k Ohm ?

This is probably wrong.

2. Oct 9, 2014

### Staff: Mentor

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.

Last edited: Oct 9, 2014
3. Oct 9, 2014

### Waxterzz

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.

4. Oct 10, 2014

### rude man

You are doing small-signal analysis.
So a small input current i = (vin - vgs)/R.
That small current must equal the increase in drain current (why?).
And small-signal-wise, you are given gm = 10 mA/V. What is the definition of gm?
So you can solve for vgs and then Zin = vin/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.