Negative feedback

[edit] Americola's celebrity biographies are provided by AmericolaWiki, a celebrity wiki. You can help contribute to Americola and edit this article.

Negative feedback is a type of feedback in which the system responds in an opposite direction to the perturbation. It is a 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. This often results in equilibrium (in physical science) or homeostasis (in biology) such that the system will return to its original setpoint automatically.

In contrast, positive feedback is a feedback in which the system responds in the same direction as the perturbation, resulting in amplification of the original signal instead of stabilizing the signal. Both positive and negative feedback require a feedback loop to operate, as opposed to feedforward, which does not rely on a feedback loop for its control of the system.

Examples of the use of negative feedback to control its system are: thermostat control, phase-locked loop, hormonal regulation, and temperature regulation in animals.

The negative feedback amplifier was invented by Harold Stephen Black at Bell Laboratories in 1927. Fundamentally, all the electronic devices (vacuum tubes, bipolar transistors, MOS transistors) invented by mankind are nonlinear devices. The greatness of negative feedback is basically sacrificing the gain for higher linearity (or in other words, smaller distortion). Amplifiers with negative feedback can be unstable, or in other words, can oscillate. Harry Nyquist of Bell Laboratories managed to work out a theory regarding how to make it stable.

1 Explanation
2 Examples
3 Negative Feedback in electronic amplifiers
- 3.1 Advantages
- 3.2 Disadvantages
4 See also
5 External links

Explanation

The term 'negative' does 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 stabilize and improve their operating characteristics (see e.g., operational amplifiers). Note that negative feedback is used to "stabilize" the system, not in amplifying the signal, whereas positive feedback is used to amplify the signal itself (which may lead to instability).

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.

Negative Feedback in electronic amplifiers

Consider a voltage amplifier (other systems are similar). Without feedback, the output voltage <math>V_{out} = A_O.V_{in}</math>, where the amplification <math>A_O</math> (also known as the open-loop gain) may in general be a function of both frequency and voltage.

The open-loop gain <math>A_O</math> is given as

<math>A_O = \frac{V_{out}}{V_{in}}</math> .....(1)

Suppose we have a feedback loop so that a fraction <math>\beta.V_{out}</math> of the output is added to the input. <math>\beta</math> 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 <math>V'_{in}</math>, where

<math>V'_{in} = V_{in} + \beta.V_{out}</math> ..... (2)

The closed-loop gain <math>A_C</math> is given by,

<math>A_C = \frac{V_{out}}{V'_{in}}</math> ..... (3)

Substituting for <math>V'_{in}</math> from (2),

<math>A_C = \frac{V_{out}}{V_{in} + \beta.V_{out}}</math> ..... (4)

Rearranging, and dividing both sides by <math>V_{in}</math>,

<math>1 + \beta.\frac{V_{out}}{V_{in}} = \frac{V_{out}}{V_{in}.A_c}</math> ..... (5)

Since <math>A_O = \frac{V_{out}}{V_{in}}</math>,

Then <math>1 + \beta.A_O = \frac{A_O}{A_C}</math> ..... (6)

And

<math>A_C = \frac{A_O}{1 + \beta.A_O}</math> ..... (7)

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

Note also that if there are conditions where <math>\beta.A_O = -1</math>, the amplifier has infinite amplification - it has become an oscillator, and the system is unstable.

The stability characteristics of the gain feedback product <math>(\beta.A_O)</math> are often displayed and investigated on a Nyquist plot (a polar plot of the gain/phase shift as a parametric function of frequency).

Advantages

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

Disadvantages

The gain of the amplifier decreases.