Transfer function of NMOS schematic

[dalarev]

Homework Statement

Attachment titled Clapp Schematic is what I am finding the transfer function of. Results are obtained with small signal, low frequency, equivalent circuit for a common-source NMOS.

Homework Equations

I have derived two different formulas, looking at Vo in 2 different ways.

The Attempt at a Solution

My 2 results are in the last 2 images attached, where I derive 2 different expressions for Vo/Vi.

Having the transfer function, we set Im[H(s)] = 0 to find resonant frequency, but as can be seen from my derivation, it is not possible.

 

[LightHero]

I'm not sure if this means something is wrong with my derivation, or there is no resonant frequency for this circuit? Any help would be appreciated.Thanks!

 

[Mene]

I would first commend the student for their thorough work in deriving two different formulas for the transfer function of the NMOS schematic. This shows a strong understanding of the underlying principles and a willingness to explore different approaches to problem solving.

In terms of the results obtained, it is important to note that the transfer function may not always lead to a simple and straightforward solution, as seen in this case where setting Im[H(s)] = 0 does not provide a resonant frequency. This could be due to the complexity of the circuit or potential errors in the derivation process.

To further investigate this issue, it may be helpful to compare the derived transfer function with known solutions or to simulate the circuit using software such as SPICE. Additionally, considering the limitations and assumptions made in the small signal, low frequency equivalent circuit approach could also provide insights into the discrepancies in the results.

Overall, it is clear that the student has put in a lot of effort and critical thinking into their work, and I would encourage them to continue exploring and questioning their results to gain a deeper understanding of the transfer function of the NMOS schematic.