# Find the output resistance in a amplifier (MOSFET) small-signal model

• Engineering
• Martel
In summary: R).In summary, the main problem is to determine the output resistance of an invented MOSFET amplifier in saturation region. This can be done by applying a voltage test to the output, measuring the resulting current, and dividing them to obtain the output resistance. However, in this specific problem, the output resistance needs to be expressed as a function of other given variables, including the supply voltage (VS), bias resistance (R), and bias voltage (VDS). The equation for gm, which is K * VDS ^ 2, suggests that these variables are necessary to accurately determine the output resistance.
Martel
Homework Statement
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Relevant Equations
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I have to solve a problem related with an 'invented' (non-real) MOSFET working in its saturation region (amplifier). I have solved all the questions, but I'm unable to get the last one. Basically, I need to determine the output resistance of the amplifier as a function of other given 4 variables. I have read the book and I know that I'm supposed to apply a voltage test to the the amplifier's output, measure the obtained current and divide them to get the output resistance, which in the typical amplifier schema with a load resistor is exactly that load resistor (this is actually the situation in my problem).

The problem is that I need to express this answer as a function of other given 4 variables, and I have tried to do it like 1000 times and there is no way for getting what I need to do. The problem and the question is below:

The main problem's description:

The provided small signal model:

The question:

I have been able to obtain gm, which is K*VDS^2

Still, I just can't get the right result for the output resistance (ro). It should be R, but how can I express it as a function of the mentioned variables (notice I can't use VS).

I don't see any way to avoid referencing the resistance R in your output resistance calculation. It obviously represents a path to (signal) ground via Vs.

alan123hk
In order to know the exact values of gm and ro in the small signal model, it seems unavoidable that the supply voltage (VS) and bias resistance (R) are involved.
According to the obtained equation gm = K * VDS ^ 2, gm is related to the bias voltage (VDS), so the values of the supply voltage (VS) and the bias resistance (R) should be provided to determine the bias voltage.

Note: Obviously, according to the given equation, the value of ro is also forced to depend on the bias voltage (VDS)

Last edited:

## 1. What is the purpose of finding the output resistance in a MOSFET amplifier small-signal model?

Finding the output resistance in a MOSFET amplifier small-signal model is important because it allows us to understand the behavior of the amplifier and make necessary adjustments to improve its performance. It also helps in determining the maximum output current that can be delivered by the amplifier.

## 2. How is the output resistance calculated in a MOSFET amplifier small-signal model?

The output resistance in a MOSFET amplifier small-signal model is calculated by taking the inverse of the slope of the output characteristics curve at the operating point. It can also be calculated by dividing the change in output voltage by the change in output current at the operating point.

## 3. What factors affect the output resistance in a MOSFET amplifier small-signal model?

The output resistance in a MOSFET amplifier small-signal model is affected by several factors such as the drain-source resistance of the MOSFET, the load resistance, and the transconductance of the MOSFET. The output resistance can also be affected by the biasing conditions and the temperature of the circuit.

## 4. How does the output resistance impact the overall performance of the MOSFET amplifier?

The output resistance of a MOSFET amplifier can significantly impact its performance. A higher output resistance can lead to lower voltage gain and reduced output signal swing. It can also cause distortion and affect the overall stability of the amplifier. Therefore, it is important to minimize the output resistance for optimal performance.

## 5. What are some techniques to reduce the output resistance in a MOSFET amplifier small-signal model?

There are several techniques that can be used to reduce the output resistance in a MOSFET amplifier small-signal model. These include using a cascode configuration, implementing feedback, and using current mirrors. Proper biasing and choosing the right load resistance can also help in reducing the output resistance. Additionally, using higher transconductance MOSFETs can also lower the output resistance.

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