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help to calculate the gain

Discussion in 'Homework Help' started by screen1988, Mar 21, 2013.

Mar 7, 2013
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In the first picture is a source follower. I want to calculate the gain of this circuit by using small signal model in the second picture.
In the small signal model, I don't include ro (purposely) and assume that current source is ideal.
Now I need to figure the gain of the circuit but I get stuck here. I can't make a relation between Vin and Vout without V1. Can anyone help?

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2. WBahn Moderator

Mar 31, 2012
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What is the DC bias voltage on the gate? On the source?

Mar 7, 2013
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I think in this case the current source in the source of transistor will bias for the transistor.

4. WBahn Moderator

Mar 31, 2012
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To what voltage? Assume whatever values for the circuit and transistor parameters make it convenient (while keeping things realistic)

Mar 7, 2013
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I have seen the circuit bellow in my textbook. It is a source follower with current
So I think the circuit can be perform without any modificatiions.
Could you see the picture bellow and guide me with some questions?
Does this circuit need to bias to operate?

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6. WBahn Moderator

Mar 31, 2012
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In your original circuit, there is a coupling capacitor between Vin and the gate. As a result the gate is floating and so you can pick whatever voltage you want for the output and their is a gate voltage that it could be that would be consistent with that output voltage.

Here, the input signal is tied directly to the gate and hence it provided the DC bias for the gate. As a result, there is a single, well defined source voltage that the current source has to output to make the Vgs on the transistor just the right value to get the programmed current through the transistor.

Actually, while your first schematic isn't biased properly, the small signal model is correct (since the small signal model ignores bias issues).

So solve that circuit for v_out as a function of v_in. Hint, what does the current output of the controlled current source have to be?

screen1988 likes this.

Mar 7, 2013
310
4
Thanks, I am always confused to know if a problem being considered is in DC or AC model.
You said the gate voltage is floating. Therefore, I think you are said in DC model, right?
With Iss constant but I can't know what is operation region (triode or saturation), how can I know Vout?
If i understand you correctly, in the circuit DC bias is set by current source. It keep the current through DS constant and if the transistor is in saturation then Vgs is constant. Therefore, when Vin varies, the voltage in current source also varies with the same amount to keep Vgs constant.
But could you explain what criterias that I should consider to choose the value of current source?
What assure/make the circuit operating in saturation?
For example, I know the swing of Vin then I assume that the transistor will be in saturation=> The volate drop in GS Vgs with respecto Iss(in this case Iss is unknown and I need to determine the value for it)=> Vout with respect to Iss.
From the swing of Vout I figure out Iss can be allowed?
Is this correct?
I actual cann't figure out the value of V1. In this case the source of transistor
is floating and the controlled current source isn't connected to anything.
Because of V1 unknown, I can't work out the value of the controlled current source which depends on V1.

8. WBahn Moderator

Mar 31, 2012
24,564
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But look at the circuit in which the controlled current source is a part. What is the current?

Given what the current has to be, what does V1 have to be?

Given what V1 has to be, what does Vout have to be?

screen1988 likes this.

Mar 7, 2013
310
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Do you mean that it is open circuit and then i=0 and V1=0?
I thought about it but I am confused because current source always keep current even the circuit is open.

10. WBahn Moderator

Mar 31, 2012
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How?

Remember, this circuit is only the small signal part. There is also the DC bias part. Remember that current source in it? That i in the small signal model would have to go through the bias current source, but since it will be trying to keep the current in it constant, it will simply change it's voltage in order to make V1 equal to zero, thus reducing the i in the small signal model to zero.

So what will Vout be in terms of Vin?

Mar 7, 2013
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I mean that the current source gmV1. This current source has one end is connected to ground and the other end is left open. Then can I say that the current source has a value of 0A.
If it is right, gmV1=0 => V1=0 and Vout=Vin

12. WBahn Moderator

Mar 31, 2012
24,564
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That's correct. So that means that the voltage on the source follows the input voltage, hence the name "source follower".