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gm is proportional to W/L or sqrt (W/L)?

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raj2004

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Trying to learn CMOS:

I have a basic question gm is proportional to W/L or sqrt (W/L)? gm can be written as
gm=K*W/L*(Vgs-Vth)=sqrt(2*K*W/L*Id)

and Id increases as Vgs-Vth increases. Could you please explain whats the right way to think?

thanks.
 

If the transistor is biased with a fixed Vgs, then you use the first form. If it's biased with a fixed current, then you use the second form.
 

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    raj2004

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Thanks. But mostly people refer to gm being proportional to sqrt(W/L) that means they are talking about fixed current bias. Just wondering is there any scenario where fixed voltage bias is used as it would give more gm improvement with W/L scaling (sure the current and hence power consumption would increase)?
 

There is no contradiction. You keep the overdrive constant - Vgs-Vth and the gm scales with W. You keep the current constant and then it is sqrt dependence. If you change both W and current the same amount, the overdrive remains constant and your gm is proportional to W or rather to the factor by which you modify W and I. This same result you can get from the sqrt expression for your gm.
It can happen that for ex. in diff pairs you increase only the tail current and then you have the sqrt dependence.
 

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    raj2004

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Thank you both checkmate and sutapanaki. I have donated points for you. Can you please refer me to any book that explains how to properly choose the device size ,gm etc while desiging analog circuits using CMOS. someone who explains with examples. ( other than baker or razavi).
 

Razavi's book is not bad. There's a new book out, about gm/Id design methodology. I haven't read it yet, but expect to be helpful. Also, you can check out the video lectures of ee240 from UC Berkeley website, especially those of prof.Boser from 3-4 years ago.
 

Its so interesting. since few days I have been listening to prof boser e240 itself. looks like i am on right track:) Which new book are you referring? also is there a book other than gray and meyer that shows the design methodology changes between cmos and bjt?
 

The book is "he gm/Id methodology, a sizing tool for low-voltage analog CMOS circuits" Paul Jespers.

I think Gray and Meyer is good enough for this.
 

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