Find the input resistance of the following MOSFET circuit

[Daniel San]

1. The problem statement, all variables and given/known data

Given the following circuit find the input resistance as seen through vo.

2. Relevant equations



3. The attempt at a solution

To solve this problem I started by drawing the signal equivalent circuit:

As we can see the voltage v_gs = v_i - v_o. To find the input resistance I used Thenevin's theorem, placing a DC test voltage, V_T, between the output terminals. By finding the relationship between V_T and the current that passes throught it I hoped to find the value of the input resistance.

This, however, didn't take me to the correct result. I was told the result was equal to 1/g_m || r_o || R_s. I do not understand how to get to this result tho.. If someone could point me in the right direction I'd appreciate!

 

[Audioguru]

You are confusing resistance and impedance.
Resistance is DC. Impedance is AC that you are talking about.

The Mosfet amplifies the source resistor value of Rs by its amount of gm. Then R1 and R2 are in parallel with the result to give the input impedance.

 

[The Electrician]

You are confusing resistance and impedance.
Resistance is DC. Impedance is AC that you are talking about.

The Mosfet amplifies the source resistor value of Rs by its amount of gm. Then R1 and R2 are in parallel with the result to give the input impedance.

He says he needs to "...find the input resistance as seen through vo.". The result he's given makes it clear that he really wants what you and I would call the output impedance.

And I see that he's another poster who asks for help on multiple forums:

https://www.physicsforums.com/showthread.php?t=730288