# Negative Feedback System

Negative Feedback System is the most common form of feedback control configuration used in microprocessors and amplification systems.

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Feedback is the process by which part of the output signal, such as voltage or current, is used as input.If this feedback fraction is the opposite of the input signal in value or phase ("anti-phase"), feedback is said to be **Negative Feedback** or *degenerative feedback.*

Negative feedback counters or removes input signals that give it many advantages in the design and stabilization of control systems.For example, if the output of the system changes for any reason, negative feedback affects the input in a way that prevents the change.

Feedback reduces a system's overall gain with the degree of reduction associated with the system's open-cycle gain.Negative feedback also has the effects of reducing distortion, noise, sensitivity to external changes, as well as improving system bandwidth and input and output impedances.

Feedback on an electronic system, whether negative or positive feedback is unilateral.This means that its signals flow only one way from the output of the system to its input.This then makes the system's loop gain independent of G's load and welding impedances.

Because feedback requires a closed loop system, it must therefore have a collection point.In a negative feedback system, this collection point or connection in the input removes the feedback signal from the input signal to create an error signal β that runs the system.If the system has a positive gain, the feedback signal must be removed from the input signal in order for the feedback to be negative as shown.

### Negative Feedback System

Circuit, positive gain, G and feedback represent a system that has β.The aggregation link at the input extracts the feedback signal from the input signal to generate the Vin – βG error signal running the system.

Then, using the basic closed loop circuit above, we can deride the general feedback equation as follows:

### Negative Feedback Equation

We see that the effect of negative feedback is to reduce gain by the following factor: 1 + βG .This factor is called the "feedback factor" or "amount of feedback" and is usually indicated in decibels (dB) with a relationship of 20 log (1+ βG).

## Effects of Negative Feedback

If open cycle gain G is too large, it will be much larger than βG 1, so that the total gain of the system is roughly equal to 1/β.If open loop gain decreases due to the effects of frequency or system aging , provided that βG is still relatively large, the overall system gain does not change much.Therefore, negative feedback tends to mitigate the effects of the gain change, which is generally referred to as "gaining stability".

### Negative Feedback Question Example 1

A system has 80dB gain without feedback.Negative feedback fraction is 1/50.Calculate the system's closed loop gain in dB with the addition of negative feedback.

Then we can see that the system has 10,000 cycle gains and 34dB closed loop gain.

### Negative FeedbackQuestion Example 2

After 5 years, the cycle gain of the negative feedback-free system drops to 60dB and the feedback rate remains constant at 1/50.Calculate the system's new closed-cycle gain value.

Then, from two examples, without feedback, we can see system gain drop from 80dB to 60dB (from 10,000 to 1,000) after 5 years of use, a decrease of about 25% in open cycle earnings.

However, with the addition of negative feedback, system gain fell from just 34dB to 33.5dB, a decrease of less than 1.5%, which proves that negative feedback provides additional stability to system gain.

Therefore, by applying negative feedback to a system, we can see that it greatly reduces its overall gain compared to its non-feedback gain.

Without feedback, the system gain can be very large, but it may not be certain that it can change from one system device to another, then it is possible to design a system with sufficient open loop gain, which, after adding negative feedback, the overall gain matches the desired value.

In addition, if the feedback network is established from passive elements with stable properties, the overall gain becomes very stable and is not affected by changes in open loop earnings inherent in systems.

## Negative Feedback on Operational Amplifiers (op-amp)

Operational amplifiers (op-amps) are the most widely used type of linear integrated circuitry, but they have very high gains.The open loop voltage gain of a standard 741 op-amp is A _{VOL} , voltage gain when no negative feedback is applied, and the open loop voltage gain of an op-amp is the ratio of output voltage, Vout , differential input voltage, Vin , ( Vout/Vin ).

The typical _{A-VOL} for 741 op-amp is more than 200,000 (106dB).Therefore, only an input voltage signal of 1mV causes an output voltage above 200 volts! force the output to saturation immediately.Obviously, this high open loop voltage gain needs to be controlled in some way, and we can do this only using negative feedback.

The use of negative feedback can significantly improve the performance of a transactional amplifier, and any op-amp circuit that does not use negative feedback is considered too unstable to be useful.But how can we use negative feedback to control an op-amp.Consider the following circuit of the Inverting Operational Amplifier.

### Non-Inverting Op-amp Circuit

## Negative FeedbackQuestion Example 3

A transactional amplifier with open loop voltage gain, 320,000 A _{VOL} without feedback, will be used as an inverted amplifier.Calculate the feedback resistors R 1 and R _{2} required to stabilize the circuit with closed loop gain _{of 20.}

The generalized closed loop feedback equation we derived above is as follows:

By rearranging the feedback formula, we get a feedback fraction from the following, β :

Then we put the values A = 320.000 and G = 20 in the equation above to obtain the β value as follows:

In this case, since the open loop gain of op-amp is very high (A = 320,000 ), the feedback fraction, β, the closed loop gain as only 1 value will be roughly equal to 1/G./A will be incredibly small.Then β (feedback fraction) equals 1/20 = 0.05.

As their resistance, R _{1} and R _{2} will somehow be determined by the ratios of these resistors as a simple series voltage potential divisive network along the non-inverter amplifier, the closed loop voltage gain of the circuit:

We assume resistance R _{2} has a value of 1,000Ω or 1kQ after which the resistance value will be R _{1:}

Then, for the nonverting amplifier circuit, which is about to have a closed loop gain of 20, the values of the negative feedback resistors required will be in this case, R _{1} = 19kΩ and R _{2} = 1kΩ, giving us an amplifier that does not reverse. Circuit:

### Non-Inverting Op-amp Circuit

There are many advantages to using feedback in a system design, but the main advantages of using **Negative Feedback** on amplifier circuits are to greatly improve their stability, better tolerance to component variations, stabilization against DC slippage, as well as increase amplifier bandwidth.

Examples of negative feedback in common amplifier circuits include resistance R _{ε} Resistance above, as we have seen in op-amp circuits R _{S} FET-centric amplifiers and resistance, R, _{E} , bipolar transistor (BJT) amplifiers.