# CMOS Inverter Electronics Question

#### jegues

Joined Sep 13, 2010
733
I'm having trouble with this question. (See figure attached)

How do I go about showing that the expression provided is indeed the maximum current that the inverter can sink under the mentioned constraints?

After I figure that part out I will make an attempt at the second portion of the question.

Thanks again!

#### thatoneguy

Joined Feb 19, 2009
6,359
How do I go about showing that the expression provided is indeed the maximum current that the inverter can sink under the mentioned constraints?
I don't see any work from you, only scans from a bookk?

#### jegues

Joined Sep 13, 2010
733
I don't see any work from you, only scans from a bookk?

$$i_{dmax} = 0.075kn'(\frac{W}{L})_{n}V_{DD}^{2}$$

$$V_{OL} = 0.1V_{DD}$$

To be honest with you, I don't have a good enough feel of where to start to give any reasonable attempt.

Can you give me a shove in the right direction?

I have no problems with making attempts at the solution as long as I have something to work from.

#### thatoneguy

Joined Feb 19, 2009
6,359
I believe you are to work the given answer backwards from the end where it is stated that $$k^'_n=\frac{115\mu A}{V^2} @V_{DD}=2.5V$$

Make a simultaneous equation to find $$(\frac{W}{L})_n$$ while current is 7.5mA

Since, as I read it, the technology at $$0.2V_{DD}$$ allows 7.5mA with that same $$k'_n$$

That's my shot in the dark, it's been a while since college, and there are several statements intermixed with questions in that little paragraph they show.

Are the terms or methods of deriving $$K'_n$$ and $$\frac{W}{L}$$ defined somewhere on that same page outside of this question?

#### jegues

Joined Sep 13, 2010
733
I believe you are to work the given answer backwards from the end where it is stated that $$k^'_n=\frac{115\mu A}{V^2} @V_{DD}=2.5V$$

Make a simultaneous equation to find $$(\frac{W}{L})_n$$ while current is 7.5mA

Since, as I read it, the technology at $$0.2V_{DD}$$ allows 7.5mA with that same $$k'_n$$

That's my shot in the dark, it's been a while since college, and there are several statements intermixed with questions in that little paragraph they show.

Are the terms or methods of deriving $$K'_n$$ and $$\frac{W}{L}$$ defined somewhere on that same page outside of this question?
Before making equations for W/L I need to show how the equation they've given me comes to be.

That's what I'm trying to figure out before I crunch out W/L.

#### thatoneguy

Joined Feb 19, 2009
6,359
Before making equations for W/L I need to show how the equation they've given me comes to be.

That's what I'm trying to figure out before I crunch out W/L.
I thought (hoped?) that would have been covered in the book or in class.

I guess we need to wait for t_n_k to arrive. #### t_n_k

Joined Mar 6, 2009
5,455
Use the general relationship

$$I_D=\frac{K'W}{L}$(V_{GS}-V_T)V_{DS} -\frac{V_{DS}^2}{2}$$$

For the NMOS on state ...

Substitute

$$V_{GS}=V_{DD}, \ V_T=0.2V_{DD}\ & \ V_{DS} =0.1V_{DD}$$

and you should obtain the required relationship.