First do it using hand analysis. Using the gm formula you can substitute the values for VOD and gm to find W/L. Then simulate the transistor to fine tune your calculated value for W/L.

Dear Adeel,

welcome,

At first I agree with Mostafa.

Knowing that

I = (kp/2) (w/l) ( VGS-Vtn)^2,

assuming the transistors is operating in the saturation mode which is the case

when it is working as an amplifier.

Then gm= dI/d VGS= kp (w/l) (VGS-Vtn)

The last term is the overdrive voltage VOD= (VGS-Vtn),

kp is known from the technology = mun Cox where un is the mobility of the electrons and cox= epsilon od/ tox.

All these are technological parameter s that can be taken from the technology file.

Best wishes

Dear Adeel Ali,

According to the drain current formula,

ID = (Kp/2) (W/L) ( VGS-Vtn)^2

Kp and Vtn are available from the 65nm technology file if you choose the desired VGS you can have (W/L) ratio.

On the other hand, it is needed to decide about VGS value according to the desired region of MOSFET, then the (W/L) will result.

Regards.

I recommend you to consider investing your time in learning the gm/Id (transconductance efficiency) design method. Is not that complicated and the initial results can be very near what you need. For an opamp is not that simple to apply the method, as the opamp itself is not a simple circuit.

Basic things you need to keep in mind are:

1) What's the amplifier purpose?

2) Do you need to consume low power?

3) Speed is an important thing?

4) High gain is desired?

5) Which are your circuit layout needs? Or is it just a simple schematic issue?

6) What's the desired/allowed signal swing at the output?

All of these questions (and other ones) will define your aspect ratio for all transistors.

For the method, I would recommend the original work: Article A gm/ID based methodology for the design of CMOS analog circ...

And the book from Jespers and Murmann: https://www.cambridge.org/br/academic/subjects/engineering/circuits-and-systems/systematic-design-analog-cmos-circuits-using-pre-computed-lookup-tables?format=HB#lYTbK6kWEmxcEgmA.97#resources

At last, but not least, this is the analog design field: there are hundreds of solutions to a problem. Many of them as good as another 20 ones. Which one will you choose? You may narrow your search by answering the questions above.

Best regards,

Patrick.

Dear Adeel Ali,

1. Assuming MOSFET is in saturation, Id = (k'/2) (W/L) ( Vgs-Vt)^2 , where k' is kp or kn.

2. The respective transconductance is given by gm= ∂Id/ ∂Vgs keeping Vds constant will give you a gm = k’ (W/L)(Vgs – Vt) = k’ (W/L) Vov, where Vov is overdrive voltage.

3. In the above equation you know the value of gm and Vov , the unknown term is k' that you can determine from the 65nm technology MOSFET models.

Note that these calculations will give approximate W/L ratios. It is very much essential to consider second order effects under sub nm technology nodes. You need to tweak the calculated W/L ratios based the second order effects.