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Id equation with channel length modulation

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urian

urian

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Hi!
Recently I am reading books written by Martin and Baker, where I find the Id equation with CLM in their book is

Code: 
Id=½β * (Vgs-Vth)²(1+λ(Vds-Vdssat))

But in Gray and Razavi's books,the Id equation is

Code: 
Id=½β * (Vgs-Vth)²(1+λVds)

I wonder why they are different by -Vdssat?Which is more valid?

Regards²
 

The absolutely precise equation between the two you mentioned is the one given by Martin and Baker.Take a look at Chapter1,page 26 of Analog Integrated Circuit Design (by Jones,Martin) and see how they prove the equation by using Taylor Series.

Gray and Razavi books give the same equation in another way.They have moved the reference point of Vds measurement from the point (0,0)-that is the point of section of Id and Vds axis-to the (Vdsat,0) point.

Summarizing :

--If you want to calculate the Ids when you have measured the Vds from point (0,0) you use the 1st equation of Jones,Martin and Baker.
--If you want to calculate the Ids when you have measured the Vds from point (Vdsat,0) you use the 2nd equation of Gray,Razavi.
 
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    urian

    urian

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Hi,jimito13
Does the Vds in Martin's book equal Vd-Vs as you said?


Gray and Razavi books give the same equation in another way.They have moved the reference point of Vds measurement from the point (0,0)-that is the point of section of Id and Vds axis-to the (Vdsat,0) point.
Click to expand...

What's the meaning?Does the Vds equal Vd-Vdssat?
 

In Martin's book : Ids=...*[1+λ(Vds-Vdsat)] , where Vds=Vd-Vs=Vdrain-Vsource , as you say.

In Gray-Meyer's book : Ids=...*(1+λVds) , where for Vds you should substitute the quantity Vds-Vdsat=Vd-Vs-Vdsat=Vdrain-Vsource-Vdsat .
 
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    urian

    urian

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In Gray-Meyer's book : Ids=...*(1+λVds) , where for Vds you should substitute the quantity Vds-Vdsat=Vd-Vs-Vdsat=Vdrain-Vsource-Vdsat
Click to expand...

What a amazing!! I haven't thought it before and just take Vds=Vd-Vs in Gray's book!
I must return to the book and check this significant point.Thanks a lot!
 

You can't find any clarification for this in Gray-Meyer's book unless you perform by hand the proof of the equation as it exists in Martin's book.
 

I think the second one is correct.

urian said:
Hi!
Recently I am reading books written by Martin and Baker, where I find the Id equation with CLM in their book is

Code: 
Id=½β * (Vgs-Vth)²(1+λ(Vds-Vdssat))

But in Gray and Razavi's books,the Id equation is

Code: 
Id=½β * (Vgs-Vth)²(1+λVds)

I wonder why they are different by -Vdssat?Which is more valid?

Regards²
Click to expand...
 

Hi,guys
I find in Gray and Razavi's books,when they use the Id equation to calculate,they simply replace the Vds with Vd-Vs,rather than Vd-Vs-Vdssat and seems giving no notification.Should I follow them when I calculate Id for someone else?

Regards
 

Gray's book is always very inaccurate when it introduces Early voltage / channel modulation effect (both in the BJT and CMOS sections), using = signs when it should clearly state those are approximations; in addition as -jbaker pointed out- Gray's formula for drain current in (CMOS) saturation is discontinuous wrt to the formula for linear region (unless you introduce an ad hoc correction factor) so Martin and Baker are correct, while Gray&Meyer should review the math throughout their book for their next edition
 
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    urian

    urian

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May be they don' use = sign for a reason. Can someone who is really interested in the accuracy of that formula compare the hand calculations for the drain current with the two formulas against the simulation? May be then you can see which one is correct or maybe both of them are incorrect.
 

sutapanaki said:
May be they don' use = sign for a reason. Can someone who is really interested in the accuracy of that formula compare the hand calculations for the drain current with the two formulas against the simulation? May be then you can see which one is correct or maybe both of them are incorrect.
Click to expand...

Neglecting the fact that you are stating the opposite of what I said (namely that they use the = sign where what comes next is actually an approximation), there is still no reason for undisclosed floppy math when you are developing a model, no matter how obsolete is the model compared to today's devices
 

You can not blame a model of being sloppy when it is only an approximation. And a bad one, nowadays. All models are approximations and as such not true. They are only good for the purpose they were created for.
 

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