# [SOLVED]Mismatch Parameters for 65nm UMC.

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#### Ans5671

##### Member level 1
I am wanting to design a current steering DAC in UMC65. Can someone let me know how to find the technology mismatch technology parameters Avth and Aβ. I know that they are to be found in the Spice/Spectre file, how do I identify. There are a lot of terms in that I don't understandnd?

#### sleepless_nights

##### Junior Member level 1
Hi,

I'm not sure if I got your question, but I believe the best way is to extract a statistical distribution from a Monte Carlo simulation. I believe that those values you mentioned are nothing but threshold voltage and beta variances.

I hope this help and I'm sorry in advance if I got it wrong.

Kind regards,
Vitor

### deep_sea

Points: 2

#### Ans5671

##### Member level 1
Okay. so my question is, Abeta and Avth are foundry specific mismatch parameters. Where to find them.
My understanding is that the statistical distribution from a Monte Carlo simulation would give variations for a particular design. Whereas these parameters are generic of foundry.

#### timof

Electrical Design Rule Manual?

#### Ans5671

##### Member level 1
Is it there in electrical design rule manual? I don't know.

#### timof

It should be there.

#### deep_sea

##### Full Member level 1
I agree with sleepless_nights. You will not even find Vth and $\beta$ in electrical rules. What you will find is the current at a specified (W,L; VGS, VDS). The best way is to characterise your devices by simulator and extract these parameters. It would be better if you use gm/ID instead of square law but this another story.
You can plug a transistor into a testbench. Use sufficiently large L and try to extract the parameters. If you use then Monte-Carlo simulation, you can see how much the current deviates for 3 $\sigma$. Using your equation, you can infer how much was $\sigma$ assuming you have only one cause of deviation (dominated either by Vth or $\beta$ ).

#### timof

By the way, for current steering DAC, do not forget about other sources of the mismatch - for example, Vgs mismatch caused by the metal debiasing of the ground net that feeds to the current sources (different IR drop --> different Vs --> different Vgs --> systematic current mismatch).

Also, if you scale your current sources (e.g. binary) by increasing the number of fingers - there may be systematic mismatch induced by the edge finger effect.

#### Ans5671

##### Member level 1
Yes. Thank you for the heads up. I would look for other sources of mismatches. The Abeta and Avth would give a starting point for design. As I have seen in papers using the Pelgrom's formula. I guess as @deep_sea has said. I would have to simulate and obtain the parameters.

#### Ans5671

##### Member level 1
@deep_sea You have mentioned using gm/Id method for designing a DAC core, is there any reference for that. I am finding mainly amplifier designs. THanks.

#### deep_sea

##### Full Member level 1
gm/ID is a general methodology to use instead of traditional square law. It uses gm/ID as biasing indication to know how your biasing is far from strong, intermediate, weak inversion.
In traditional square law, you say I have Vth=0.4 V and I have VGS=0.6 V and translate this into Vov=0.2 V. In gm/ID, you classify your biasing by gm/ID or V*.
I have not personally designed a DAC and the design of a complete DAC looks for me as a task for group of designers or a complete PhD thesis.
But what I meant is that using square law
$ID= (\beta /2) (W/L) (VGS-Vth)^2$
is not going to give you even a good estimation for hand calculations.

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