# Finding W and L of transistors from DC operating point.

1. ## Finding W and L of transistors from DC operating point.

Hi guys,
I have a schematic of OTA amplifier:

I want to know the W and L that were used to design this OTA. I don't have more information other than the ones provided in this picture.
since all transistors are in saturation, I thought about using the saturation current equation to find (W/L) ratio.
by assuming that I know un*Cox and up*Cox. but the problem that I don't know them. but I have the same technology and same cadence version on which this OTA was designed. which means by running an extra circuit, I can deduce what un*Cox and up*Cox are since I know all the parameters for the other circuit.(also by using saturation current equation because I don't known how to find un*Cox and up*Cox from the cadence tool ) and by substituting them in saturation current equation for the first circuit, I can find W/L ratio.

the question is if un*Cox and up*Cox are the same for all simulations used in the same technology?
or there is some other way to find W and L or the ration between them depending on the information in the picture only?

Note: I'm using 28n technology.

thanks
Firas

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2. ## Re: Finding W and L of transistors from DC operating point.

Wouldn't it be easier to just design the circuit yourself such that at least it produces the same gm and Vdssat, gain for the bias currents that you see on the picture?

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3. ## Re: Finding W and L of transistors from DC operating point.

The negative image could not be seen with daylight so I changed it to be a positive image:

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4. ## Re: Finding W and L of transistors from DC operating point.

the question is if un*Cox and up*Cox are the same for all simulations used in the same technology?
I think only IF the simulation models are from the same technology AND from the same foundry (e.g. TSMC) AND of the same version released (e.g. v1.0.7) then you can be sure the elements are the same.

As suggested above, you might be better to start off from scratch to match the same performance. That being said, if you insist on reverse engineering the circuit, you basically have 2 unknowns, the u*Cox (let's call it K) and W/L, you also have 2 equations you can form based on the fact that Ids (sat) and gm is known, you can form these 2 equations and solve for the 2 variables. And then you can try them on different transistors of the same type (NMOS to NMOS) and check if you can get the right Ids & gm.

Note that you technically have also the channel length modulation effect which introduce another variable (lambdha) into the equations if you want to include them.

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