converting mathematical into plot like extraction of W/L params

[yefj]

Hello , I am trying to follow the example shown in the manual below.
In step 3 they find the proper W/L using mathematical expressions.
However I know that these formulas are aproximations ,the realistic way is to usr characteristic plots.
What caractestics plots you reccomend me to use in order to get the proper W/L?
https://aicdesign.org/wp-content/uploads/2018/08/lecture19-150211.pdf
Thanks.

 

[dick_freebird]

If you have the model params for the equations
then you probably have enough to populate a
basic SPICE model. So why not SPICE?

Otherwise, a spreadsheet will grind and plot
if you do the work of setting up tabular I-V
expressions -> tables -> plots.

 

[yefj]

Hello,In the manual below they have a design example.
In step 3 shown below they find mathematickly the W/L assuming 50uA flows threw it and Vsg=0.5.
Because mathematical expressions of a mosfet are aproximations ,I wanted to find using a simulation given Vsg=0.5 the values of W/L that causes Ids=50uA threw it.
As you can see below , thats what I was trying to do ,100uA splits in half and we have Vsg=0.5.
this is the best I could think of representing the mathematical equation.
In the manual they represent drain voltage purely without load to want the PMOS sees, they just say Vtn1 is 0.7 and thats it.
they plug the numbers into Vsg of M3 and thats it.
How can I find the W/L in simulation way?
Thanks.
https://aicdesign.org/wp-content/uploads/2018/08/lecture19-150211.pdf
LTspice file is attached.

 

[dick_freebird]

If you apply 0.5V against a VT of 0.7, then you
are in subthreshold and the equations get
messier (subthreshold slope varies widely
and is modeled kinda "fudgey" - alter the
"surface states" param until you get what
you saw).