# Mathematical proof for positive feedback

• anb2020
In summary, a mathematical proof for positive feedback is a rigorous and logical demonstration of the exponential growth or instability of a system. Positive feedback in mathematics refers to a process where the output of a system is used as an input, leading to an increase in the output. Mathematical proof is important for understanding and predicting the behavior of systems with positive feedback. Common examples of positive feedback in mathematics include population growth, compound interest, and the spread of diseases. Mathematicians use positive feedback to solve problems by identifying systems that exhibit this behavior and using mathematical models to analyze and predict their behavior. This allows them to find solutions to real-world problems and make accurate predictions about the future behavior of these systems.
anb2020
Is there a mathematical proof that the positive feedback makes the op-amp saturated?

http://i.imgur.com/71PNh.png

Do you understand why it saturates (non-mathematical seat of the pants explanation)?

Let's clarify this by specifying positive DC feedback drives the opamp into saturation. Positive AC feedback makes it oscillate.

the_emi_guy said:
Do you understand why it saturates (non-mathematical seat of the pants explanation)?

Yes of course

There is indeed a mathematical proof that positive feedback can cause an operational amplifier (op-amp) to become saturated. This can be seen by analyzing the gain equation for an op-amp in a positive feedback configuration.

The gain equation for an op-amp in a closed loop configuration is given by A = A0 / (1 + βA0), where A0 is the open loop gain and β is the feedback factor. In a positive feedback configuration, the feedback factor is greater than 0, meaning that the denominator of the gain equation is less than 1.

When the feedback factor is small, the gain of the op-amp is approximately equal to the open loop gain A0. However, as the feedback factor increases, the gain decreases and eventually becomes 0 when the feedback factor is equal to 1. This means that the output voltage of the op-amp will be equal to the input voltage multiplied by the open loop gain A0, resulting in saturation.

Furthermore, the gain equation also shows that as the feedback factor approaches 1, the gain of the op-amp approaches infinity. This is known as the "infinite gain" phenomenon, where even a small change in the input voltage can cause a large change in the output voltage, leading to saturation.

In conclusion, the mathematical proof for positive feedback causing op-amp saturation lies in the gain equation, which shows that as the feedback factor increases, the gain decreases and eventually becomes 0, resulting in saturation.

## What is a mathematical proof for positive feedback?

A mathematical proof for positive feedback is a rigorous and logical demonstration that a system with positive feedback will exhibit exponential growth or instability.

## What is positive feedback in mathematics?

Positive feedback in mathematics refers to a process in which the output of a system is used as an input, leading to an increase in the output. This results in exponential growth or instability in the system.

## Why is mathematical proof important for positive feedback?

Mathematical proof is important for positive feedback because it provides a solid foundation for understanding and predicting the behavior of systems with positive feedback. It allows us to make accurate and reliable predictions about the behavior of these systems.

## What are some common examples of positive feedback in mathematics?

Some common examples of positive feedback in mathematics include population growth, compound interest, and the spread of diseases. In each of these cases, the output of the system (population, money, or number of infected individuals) is used as an input, resulting in continuous growth or increase.

## How do mathematicians use positive feedback to solve problems?

Mathematicians use positive feedback to solve problems by first identifying systems that exhibit this type of behavior. They then use mathematical models and equations to analyze and predict the behavior of these systems. By understanding the underlying mechanisms of positive feedback, mathematicians can find solutions to real-world problems and make accurate predictions about the future behavior of these systems.

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