Find the input resistance of the following MOSFET circuit

In summary: Hint #2: You can use Thevenin's theorem to solve for the input resistance. In summary, the homework statement is trying to find the input resistance using Thevenin's theorem. However, the author does not seem to understand how to get to the correct result.
  • #1
Jalo
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0

Homework Statement



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

281zq53.png

Homework Equations


The Attempt at a Solution



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

2hwgr3q.png


As we can see the voltage vgs = vi - vo. To find the input resistance I used Thenevin's theorem, placing a DC test voltage, VT, between the output terminals. By finding the relationship between VT 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/gm || ro || Rs. I do not understand how to get to this result tho.. If someone could point me in the right direction I'd appreciate!
 
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  • #2
Looking at your small signal model you can see that the output voltage VT = Vgs.

So the current source gmVgs is actually gmVT.

Then compare ohms law I=V/R with I = gmVT.

What's the equivalent resistance of the current source?

Edit: Sorry I'm not explaining that very well. VT = -Vgs when Vi = 0. See page 5..

http://web.mit.edu/6.012/www/SP07-L20.pdf
 
  • #3
You can't apply a hard voltage to the output and determine the resulting current from your hard voltage source. Why? Because that rides roughshod over the entire circuit. When you change vs you also change vg-vs which changes id etc.

So, question: what is the definition of output impedance really? It obvously has something to do with the following: I put a signal vg on the gate, I get a signal vs on the source. Now I parallel Rs with a test resistor R and the voltage drops to some extent. If the output impedance is zero there is no drop in vs. If the output impedance is 1K then if R = 1K the output voltage drops to one-half. Etc.

So your first (and main!) task is to determine an equation which relates the change in vs to a change in Rs. (I am lumping Ro in with Rs, which is justified by your equivalent circuit. Your equiv. ckt. is OK, use it.

Hint #1: change your Rs and Ro to conductances and work exclusively with conductances, not resistances.
 
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1. What is a MOSFET circuit and how does it work?

A MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor) circuit is an electronic device that is used to switch or amplify electrical signals. It works by controlling the flow of electrons through a channel between the source and drain terminals using an electric field generated by the gate terminal.

2. What is input resistance and why is it important in MOSFET circuits?

Input resistance is the measure of how much resistance a circuit offers to an incoming signal. In MOSFET circuits, it is important because it determines the amount of current that can flow into the gate terminal and affect the device's performance. A higher input resistance allows for better signal amplification and less loading on the circuit.

3. How do you calculate the input resistance of a MOSFET circuit?

The input resistance of a MOSFET circuit can be calculated by dividing the change in voltage at the input terminal by the change in current at the same terminal. This can be represented by the equation Rin = ΔV/ΔI.

4. What factors affect the input resistance of a MOSFET circuit?

The input resistance of a MOSFET circuit can be affected by various factors such as the physical size and material of the transistor, the biasing voltage applied to the gate terminal, and the load connected to the output terminal. Additionally, the type of MOSFET (enhancement or depletion) and its operating mode (saturation or linear) can also impact the input resistance.

5. How can the input resistance of a MOSFET circuit be improved?

The input resistance of a MOSFET circuit can be improved by using a larger MOSFET with a higher channel width, decreasing the biasing voltage, and increasing the load resistance. Additionally, using a cascode configuration (two or more transistors connected in series) or adding a source follower stage can also increase the input resistance of the circuit.

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