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All guys are right exept you, This formula is only for strong inversion.
If you'd like be more advanced in analog design take a look for Gm/Id methodology. There're many guys on forum who are interested in.
It would have been really nice if gm/Id was equal to 2/(Vgs-Vt) everywhere. This way you make very small overdrive voltage and you get huge efficiency of the transistor - analog designer's dream. Seriously, however, you should probably know that when transistor is in saturation it can be either in strong inversion or weak inversion or inbetween those two. That formula is based on the square law of operation of the MOS transistor and valid in strong inversion only. For modern technologies even in strong inversion and long channel devices there is probably 15-30% discrepancy too, because of velocity saturation. It is definitely not true in moderate inversion and weak inversion. In weak inversion MOS transistor works like a bad bipolar transistor and hence current is exponentially changing with Vgs. For bipolar transistors gm/Id=q/kT and for MOS in weak inversion it is q/nkT where n=1 to 2.
And in moderate inversion it should be somewhere inbetween those asymptotes.
Hope this helps.
haoyun said:
Hi yschuang,
I think , gm/Id=2/(Vgs-Vt) is valid for all inversion.
But by simulation I don't understand why it's no valid.
EKV and ACM models provide accurate extrapolation functions of gm/Id; This allows developing quite accurate automated synthesis routines to be developed using Matlab-like tools.
It's true - you can not use this simple expression, except as a first-order approximation
If you look at the full expression for Id, and make derivative with respect to Vgs (keeping in mind all the variables that are Vgs dependent), you'll realize that the expression you use is approximation. The key point is to start from the "full" expression of current, taking into account all of the second-order effects. It's also important to realize which variables are Vgs dependent.
That's exactly what simulator does. (OK, not "exactly" )
It's true , gm/Id=2/(Vgs-Vt) is only used for hand-anaylsis.
In Cadence simulation for short channel , gm/Id=2/(Vgs-Vt) is invalid even if its operation is in strong inversion.
The Ids formula in text book is the simplified version for learners. the hspice higher end version will have Ids formula with many other Vgs dependeancies. When we differentiate Ids wrt to Vgs the resulting expression Gm is not as simplfied.
It would have been really nice if gm/Id was equal to 2/(Vgs-Vt) everywhere. This way you make very small overdrive voltage and you get huge efficiency of the transistor - analog designer's dream. Seriously, however, you should probably know that when transistor is in saturation it can be either in strong inversion or weak inversion or inbetween those two. That formula is based on the square law of operation of the MOS transistor and valid in strong inversion only. For modern technologies even in strong inversion and long channel devices there is probably 15-30% discrepancy too, because of velocity saturation. It is definitely not true in moderate inversion and weak inversion. In weak inversion MOS transistor works like a bad bipolar transistor and hence current is exponentially changing with Vgs. For bipolar transistors gm/Id=q/kT and for MOS in weak inversion it is q/nkT where n=1 to 2.
And in moderate inversion it should be somewhere inbetween those asymptotes.
Hope this helps.
All guys are right exept you, This formula is only for strong inversion.
If you'd like be more advanced in analog design take a look for Gm/Id methodology. There're many guys on forum who are interested in.
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