# Control and Feedback in electronic circuits

• Rushers
In summary, a control system in electronics involves a substractor, forward path, and feedback path. The input and output are represented by X and the forward and feedback paths are described by gain functions. The textbook assumes ideal amplifiers, which results in the two Xo values being the same. However, in reality, the phase of the system and frequency response can have a significant impact on the stability and performance of the control system. The "gain" of the circuit represents the fraction of output to input.
Rushers
I'm trying to understand the concept of a control system in electronics.
In a control system, we have a substractor, forward path and feedback path.

The forward path is described by a function g ( a gain function ) and the feedback by another function ( gain again ).
The input is Xi and the output is Xo.

Let's suppose we are controlling the voltage so X is a voltage.
Our sensor in the feedback path reads the value of the voltage. This value is multiplied by B. My question is .Why?

If we want to substract from the reference value at the substractor, why would we multiply by a gain and modify the real value of voltage?

Then we substruct so we get (Xi -BXo) and then multiply by A to get A(Xi - BXo).
This new value is supposed to be the new value of voltage.
Xo = A(Xi -BXo) with TWO values of Xo. We have Xo previous and Xo after the operation of modification.
But in the textbook they say these values are the same and deduce a "gain" of the circuit (A/ (1 + AB)).
Why, if we have two values of Xo, are they taken to be similar?
AND what does this "gain" represent?

This is a really insightful question.

Basically for now, to keep things simple, the textbook is assuming that all the amplifiers are ideal. Or more specifically, that it takes zero time for the signal to pass through the amplifier. If this it true then the two Xo's in the equation are the same. This assumption keeps the math a lot easier.

However, as you mention, this is not true for real amplifiers. It takes some time for the signal to pass through them. The measure of this time is called the phase of the system and it has huge implications on the stability of the control system.

Even more confusing is that for different d(Xi)/dt's the delay (and gain) through the system will be different. Determining this is called finding the frequency response of the system.
http://en.wikipedia.org/wiki/Frequency_response

And I'll bet it is something that your textbook will cover in future chapters as it is hugely important.

For all the why do we do this questions...
There are many good reasons. I recommend reading this introductory chapter. I think it is really good.
http://www.cds.caltech.edu/~murray/amwiki/index.php/Introduction

Last edited:
Oh ya, that gain represents the fraction Xo/Xi.

So: Xo/Xi = (A/ (1 + AB))

## 1. What is the purpose of control and feedback in electronic circuits?

Control and feedback are essential components of electronic circuits that help to regulate the behavior and performance of the circuit. Control refers to the ability to adjust or manipulate certain parameters of the circuit, while feedback involves using information about the output to adjust the input. Together, they help to maintain stability, accuracy, and efficiency in electronic circuits.

## 2. How does negative feedback work in electronic circuits?

Negative feedback is a control mechanism in electronic circuits where a portion of the output signal is fed back to the input to regulate the behavior of the circuit. It works by comparing the output to a reference signal and then adjusting the input accordingly. This helps to stabilize the output and reduce any errors or distortions.

## 3. What is the difference between open-loop and closed-loop control?

Open-loop control refers to a control system where the output is not fed back to the input for adjustment. This means that the input is not regulated based on the output, and the system relies on the initial setpoint. On the other hand, closed-loop control involves using feedback to continuously adjust the input based on the output, resulting in more accurate and stable control.

## 4. How does feedback affect the performance of electronic circuits?

Feedback plays a crucial role in improving the performance of electronic circuits. It helps to stabilize the output and reduce errors, distortions, and fluctuations. It also allows for more precise control and improves the circuit's response time. However, excessive feedback can lead to instability and oscillations, so it must be carefully designed and implemented.

## 5. What are some common examples of control and feedback in electronic circuits?

Control and feedback are used in a wide range of electronic circuits, from simple devices like thermostats to complex systems like robotics and aircraft. In audio amplifiers, feedback is used to improve the linearity and reduce distortion. In voltage regulators, control is used to maintain a constant output voltage despite changes in input or load. In digital circuits, feedback is used for error detection and correction. These are just a few examples of the many applications of control and feedback in electronic circuits.

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