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# Clarifications Needed For Source Follower

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#### sk.shawn

##### Junior Member level 3
Hi all,

In Razavi's book on the chapter of single-stage amplifiers, I came across the section explaining the non-linearity property of source followers (page 69, paragraph 3). The author mentioned that "...For example, if Vin changes from 1.5V to 2V, Id may increase by a factor of 2 and hence (Vgs-Vth) by square root 2, thereby introducing substantial nonlinearity in the input-output characateristic...

Have 2 Questions (Sorry, could be trivial here but I just can't grasp it)

1) How do we know that Id has increased by a factor of 2 when Vin changes from 1.5V to 2V since Vin is not Vgs itself?

2) How is the nonlinearity effect really manifested through a change in Vin, Id and finally (Vgs-Vth)? I just can't see the link?

Hope someone can weigh in further. Thanks

Regards,
Shawn

I don't have Razavi's book off hand, but my guess is that he was using a resistive load. Notice the words "may" and "For example".
For your first answer, the current is given by (Vin-Vgs)/R. In this case, he was stating the numbers from a hypothetical R load that will give the mentioned figures.
For the second answer, refer to the first one. If the body is not connected to the source, you will have another non-linearity due to the body effect. If it uses a current load, then the output impedance of this current load introduces yet another non-linearity.

but my guess is that he was using a resistive load
Right guessed.

The transfer function is shown in Eq. 3.76 directly below the respective source follower schematic Fig. 3.27. You can also derive it yourself by putting in Eq. 2.13, which describes the saturated MOSFET characteristic.

Body effect isn't considered in this place, but discussed on the following pages.

Hi,

Thanks for the replies.

What is the interpretation of nonlinearity in this context? My interpretation is simply having Vout not linearly proportional to Vin and that's nonlinearity for me. Is this correct or there is a broader meaning to nonlinearity?

Hope to have your thoughts and thanks.

Regards,
Shawn

My interpretation is simply having Vout not linearly proportional to Vin and that's nonlinearity for me.
Yes, more exactly, Vout = a*Vin + b would be required for linearity. That means, a constant offset can be present additionally.

But clearly, the source follower transfer characteristic of the below form can't result in a linear behaviour.
k*(Vin-Vth-Vout)²=Vout

If the load is a resistor and vt is about 0.5V, Id will increase by [(2-0.5)/(1.5-0.5)]^2=2.25. It is close to 2.

Just to be really sure about my fundamentals, I would like to confirm the following

I don't have Razavi's book off hand, but my guess is that he was using a resistive load. Notice the words "may" and "For example".
For your first answer, the current is given by (Vin-Vgs)/R. In this case, he was stating the numbers from a hypothetical R load that will give the mentioned figures.
For the second answer, refer to the first one. If the body is not connected to the source, you will have another non-linearity due to the body effect. If it uses a current load, then the output impedance of this current load introduces yet another non-linearity.

1) Vgs changes everytime with Vin right? Like in the instance of increasing Vin from 1.5V to 2V as stated by the author. If that's the case, then I think it's hard for me to see that the current may even increase by 2 times since Id2/Id1 = (2 -Vgs2) / (1.5 -Vgs1) according to the reasoning pointed out above. Any thoughts?

Yes, more exactly, Vout = a*Vin + b would be required for linearity. That means, a constant offset can be present additionally.

But clearly, the source follower transfer characteristic of the below form can't result in a linear behaviour.
k*(Vin-Vth-Vout)²=Vout

2) I understand now. However, this brings me to another question. How does the nonlinearity of k*(Vin-Vth-Vout)²=Vout relate to the nonlinearity message that the author was trying to establish through a change in Vin, Id and finally (Vgs-Vth)?

Once again, I'm really glad for the great responses. Appreciated.

Regards,
Shawn

How does the nonlinearity of k*(Vin-Vth-Vout)²=Vout relate to the nonlinearity message that the author was trying to establish through a change in Vin, Id and finally (Vgs-Vth)?
Both are the same thing.
k*(Vin-Vth-Vout)²=Vout is the source follower transfer function, based on the quadratic FET characteristic, that's also assumed by Razavi for the present problem. Because Vth and k are constants (k is combining Rs and FET parameters to simplify the expression), you can determine Vout for different Vin values (or vice versa) and get a curve similar to Fig. 3.27b.
it's hard for me to see that the current may even increase by 2 times since Id2/Id1 = (2 -Vgs2) / (1.5 -Vgs1)
If Vgs1 is near to 1.5V, it's easy to see, that the ratio can be even higher. Also Fig. 3.27b can visualize this behaviour.

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