Help with a MOSFET exercise - Id and Rout

[knightmetal]

Homework Statement

I must admit I'm a noob when it comes to Analog Circuits, I need help! it actually took me a while to understand what the problem is and how to explain it to you guys.

I'm given the attached exercise and I'm asked to calculate voltage gain and output resistance, both with written computations and with a simulation of the circuit in MicroCap. The purpose is basically to compare the values and discuss possible discrepancies.

I have two questions about the calculation of output resistance. It seems like an easy task but I think the consultation I had not long ago with my teacher confused me even more.

2. Homework Equations and The attempt at a solution

I found this equation:

  Rout = 1 / (λ * Kp (Ugs - Ut)^2) = 1 / (lambda * Id)

I also found that when W and L are given

 Id = 1/2 * Kp * W / L * (Ugs - Uth)^2

My first confusion and question is that if λ = 0, as you can see in the picture, it automatically means that Rout goes off to infinity, but why would my teacher give me such an exercise to compute?

Second question. Assuming that λ is different from 0. I've been trying to find 'Rout' with the two equations I know but there's always something wrong while solving. I don't know how to find Id. My teacher told me that

 Ugs = (5 - Rs * Id)

but then if

Id = 1/2 * Kp * W / L * (Ugs - Uth)^2

and

 Ugs = (5 - Rs * Id)

Does the equation above make sense? why do I have two Id's on both sides of the equation? assuming this is right, the result for 'Id' I get does not make sense.

Another confusion is that in the exercise C3 is not given. In the MicroCap simulation this capacitor, as you may know, regulates the value of 'Id' but then I get totally confused because Id depends on C3 but C3 is nowhere in the equations. I hope this is clear and I'm sorry if the answer is too simple.

If there's anybody who can help me clarify this I'd really appreciate it. I really struggle with this course badly, this is for sure because of my poor background.

Thanks a lot in advance.

 

[KataKoniK]

Hello there,

I can understand your confusion with this exercise. It is common for students to struggle with analog circuits, especially when they are new to the subject. Let me try to help you with your questions.

Firstly, about the calculation of output resistance, it is important to note that λ is the channel-length modulation parameter, which is typically a small value. So, even if it is equal to 0, it does not necessarily mean that Rout goes off to infinity. It just means that the output resistance is very high, but not infinite. Your teacher may have given you this exercise to help you understand the concept of output resistance and how it is affected by different parameters in the circuit.

Moving on to your second question, the equation that you have written for Id is correct, but it is not necessary to solve for Id in order to find Rout. You can use the equation for Id to find the output resistance directly. Also, the equation Ugs = (5 - Rs * Id) is not correct. It should be Ugs = (5 - Rs * Id - Uth), where Uth is the threshold voltage. This is because Ugs is the gate-source voltage, which is equal to the voltage at the gate minus the voltage at the source. So, in this case, it should be 5V - (Rs * Id) - Uth.

Regarding the confusion with C3, I believe it is not necessary to include it in the equations for finding Rout. C3 is a coupling capacitor, which is used to block DC signals and only allow AC signals to pass through. It does not have a direct effect on Rout, but it may affect the value of Id in the circuit.

I hope this helps clarify your doubts. If you have any further questions, please feel free to ask. Don't worry, with practice and a good understanding of the concepts, you will be able to solve these types of problems easily. Keep working hard and don't give up!