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# Finding lambda channel length modulation of nmosfet in spice

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#### imperza

##### Junior Member level 3
Hi all,
I really don't know how to find lambda and other parameter like RDS or Ro.
My tool is spice.
thank you.

In your plot, you have taken two points and have the slope between them. From the following equation
Id = 0.5 Kn (W/L) (Vgs - Vth)2 (1 + λ Vds)

For two different points,
Id2 - Id1 = 0.5 Kn (W/L) (Vgs - Vth)2 (λ (Vds2 - Vds1))

Therefore the slope that you have is (Id2 - Id1) / (Vds2 - Vds1) = 0.5 Kn (W/L) (Vgs - Vth)2 * λ.

Use the above to calculate λ.

Or you can just use the equation Id = 0.5 Kn (W/L) (Vgs - Vth)2 (1 + λ Vds)
Do the simulation for Different Id, Vgs, Vds, You have two unknowns Kn and λ which you can then calculate.
These values will change with the operating conditions. λ will vary with Vds and Id and a lot of other parameters.
You might have to do a bunch of simulations and get a bunch of values. You can take a average of them or keep all the values and use each when when required.
Ro or Rds or Gds of a transistor is provided in the dc operating point solution.
Or you can use the equation Ro = 1/(λ*Id)

""Ro or Rds or Gds of a transistor is provided in the dc operating point solution.
Or you can use the equation Ro = 1/(λ*Id)""

After I run simulation, the data on picture attached is displayed. Can i Just pick up Gds and Id value and insert it into the formula Lambda= Gds/ IDS?

Im not sure it is correct data, and does Id= Ids in this case tq.

Can i Just pick up Gds and Id value and insert it into the formula Lambda= Gds/ IDS?

Yes you can do this.
Id and Ids is the same.
You will get different λ for different points that you choose.

Why did I get lambda almost the same that is at 0.0103 for various transistor length and width parameter? Even IDS and GDS is different when doing calculation lamda is same? Is it wrong?

Dude, don't worry, your value of λ looks OK. The variation will be small, probably in the 3rd or 4th significant digit. For a higher length, (L > 0.5um), the transistor is quite close to the ideal square law and hence the variation is minimum. For lower lengths the variation is more.

λ is inversely proportional to Length though. That is why Higher lengths give higher Ro.

What lengths have you used?

I have used L=1 W= 100, L=5 and W=100 and L=10 W=10.

Actually, to get 0.0104 I need to use the formula = Ids/ Gds.

Otherwise if i use formula Gds/ Ids, value would be 95 something. thank you.

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