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 Negative feedback

# Negative feedback

Negative feedback (shortened to NFB) is the process of feeding back to the input a part of a system's output, so as to reverse the direction of change of the output. This tends to keep the output from changing, so it is stabilizing and attempts to maintain constant conditions.

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## Explanation

The term 'negative' do not refer to desirability, but rather to the sign of the multiplier in the mathematical feedback equation. When a change of variable occurs, a negative feedback system will attempt to re establish equilibrium.

Negative feedback is used in this way in many types of amplification systems to stabilise and improve their amplification characteristics (see e.g., operational amplifiers).

While it has many advantages, such as increased stability of the system, NFB also has disadvantages, like loss of gain.

## Examples

A simple and practical example is a thermostat. When the temperature in a heated room reaches a certain upper limit the room heating is switched off so that the temperature begins to fall. When the temperature drops to a lower limit, the heating is switched on again. Provided the limits are close to each other a steady room temperature is maintained. The same applies to a cooling system, such as an air conditioner, a refrigerator, or a freezer.

Some biological systems exhibit negative feedback such as the baroreflex in blood pressure regulation and erythropoiesis. Many biological process (e.g., in the human anatomy) use negative feedback. Examples of this are numerous, from the regulating of body temperature, to the regulating of blood glucose levels. The disruption of negative feedback can lead to undesirable results: in the case of blood glucose levels, if negative feedback fails, the glucose levels in the blood may begin to rise dramatically, thus resulting in Diabetes.

## NFB in electronic amplifiers

Consider a voltage amplifier (other systems are similar). Without feedback, the output voltage Vout = AO.Vin, where the amplification AO (also known as the open-loop gain) may in general be a function of both frequency and voltage.

The open-loop gain AO is given as

$A_O = \frac{V_{out}}{V_{in}}$ .....(1)

Suppose we have a feedback loop so that a fraction β.Vout of the output is added to the input. β is known as the feedback factor and is determined by the feedback network that is connected around the amplifier. For an operational amplifier just two resistors are required for the feedback network to set the closed-loop gain. This network may be modified using reactive elements like capacitors or inductors to (a) give frequency dependent closed-loop gain as in equalisation/tone-control circuits or (b) construct oscillators.

The input to the amplifier is now V'in, where

V'in = Vin + β.Vout ..... (2)

The closed-loop gain AC is given by,

$A_C = \frac{V_{out}}{V'_{in}}$ ..... (3)

Substituting for V'in from (2),

$A_C = \frac{V_{out}}{V_{in} + \beta.V_{out}}$ ..... (4)

Rearranging, and dividing both sides by Vin,

$1 + \beta.\frac{V_{out}}{V_{in}} = \frac{V_{out}}{V_{in}.A_c}$ ..... (5)

Since $A_O = \frac{V_{out}}{V_{in}}$,

Then $1 + \beta.A_O = \frac{A_O}{A_C}$ ..... (6)

And

$A_C = \frac{A_O}{1 + \beta.A_O}$ ..... (7)

If AO > > 1, then $A_C \approx \frac{1}{\beta}$ and the effective amplification (or closed-loop gain) AC is set by the characteristics of the feedback constant β, thus making linearising and stabilising the amplification characteristics straightforward.

Note also that if there are conditions where β.AO = − 1, the amplifier has infinite amplification - it has become an oscillator, and the system is unstable.

The stability characteristics of the gain feedback product (β.AO) are often displayed and investigated on a Nyquist plot (a polar plot of the gain/phase shift as a parametric function of frequency).

• Improves stability of gain
• Increases input impedance
• Decreases output impedance
• Reduces distortion and internally generated noise
• Increases the bandwidth

• The gain of the amplifier decreases.