Solving an n-channel MOSFET Homework Problem

[roeb]

Homework Statement

http://img195.imageshack.us/img195/3056/mosfetj.jpg

An n-channel enhancement MOSFET for which V_t = 2 V and K = 100 uA/V² is operated from a 9 V supply using a drain resistor R_D of 60kohms and the feedback bias scheme depicted. What drain current results? What is V_D What is the largest sine wave output signal for which operation in the saturation region is maintained?

Homework Equations

The Attempt at a Solution

I'm able to the first two questions but I'm having difficulty with the last sine wave part.

To find Vd and Id, I simply solved (9 - Vd)/60k = (100uA/V^2)(Vd - 2)^2, where I get Vd = 3 V and Id = .1 mA.

To maintain saturation in a n-channel MOSFET this condition: vds >= vgs - vt has to be satisfied. vds >= 3 - 2 = 1. Since Vd = 3 V at DC, then I would think that the sine wave could be +/-2 volts. Unfortunately, the book states the answer is 1.85 volts peak. I think this has to do with the feedback that I may not be correctly taking into account. Does anyone see what I am doing incorrectly?

 

[KataKoniK]

Thank you for your question. It seems like you have a good understanding of the basic concepts involved in solving this problem. However, there are a couple of factors that you may have overlooked when trying to find the largest sine wave output signal for which operation in the saturation region is maintained.

Firstly, when operating a MOSFET in the saturation region, the drain current (Id) is typically limited by the gate-source voltage (Vgs) rather than the drain-source voltage (Vds). This is because, in saturation, the channel is already fully formed and the drain-source voltage has little effect on the current. Therefore, in order to maintain saturation, the gate-source voltage must be kept above a certain threshold.

In this case, the threshold voltage (Vt) is given as 2 V. This means that in order to maintain saturation, the gate-source voltage (Vgs) must be kept above 2 V. Using the equation you provided, Vgs can be expressed as Vd - Id * RD. Substituting in the values you found for Vd and Id, we get Vgs = 3 V - 0.1 mA * 60 kohms = 3 V - 6 V = -3 V. This means that the largest sine wave output signal that can be applied while still maintaining saturation is 3 V peak-to-peak, with a peak voltage of 1.5 V.

Additionally, it is important to consider the effect of the feedback bias scheme on the gate-source voltage. This bias scheme uses a resistor (R1) to provide a voltage divider, which reduces the voltage at the gate (Vg) compared to the voltage at the source (Vs). This means that the gate-source voltage (Vgs) will be even lower than the value calculated above, further limiting the largest sine wave output signal that can be applied.

To find the exact value of the largest sine wave output signal, we would need to know the values of R1 and R2 in the feedback bias scheme. However, we can make some assumptions based on the values provided in the problem. Since the gate-source voltage (Vgs) needs to be at least 2 V to maintain saturation, we know that the voltage drop across R1 must be at least 2 V. This means that R1 must be greater than or equal to (Vgs - Vt) / Id. Using the values we found above

 

[Mene]

I would first commend you for attempting to solve the problem on your own and seeking help when you encountered difficulties. This shows that you are actively engaged in your learning and willing to put in the effort to understand the material.

In terms of the problem, it seems that you have correctly solved for Vd and Id. However, the sine wave part may require a more detailed analysis taking into account the feedback bias scheme. Without knowing the specifics of the scheme, it is difficult to determine where the discrepancy in your answer lies.

I would suggest going back to the fundamentals of the feedback bias scheme and carefully analyzing the circuit to see how the sine wave input affects the operation of the MOSFET. You may also want to double check your calculations and equations to ensure they are correct.

If you are still having trouble, I would recommend seeking help from your instructor or a classmate who may have a better understanding of the feedback bias scheme. Additionally, there are many online resources and forums where you can ask for help and clarification on specific homework problems.

Overall, solving problems in science requires a combination of understanding the fundamentals and being able to apply them in different scenarios. Keep practicing and seeking help when needed, and you will continue to improve your problem-solving skills.