Negative Feedback

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 .

'Positive' and 'negative' do not refer to desirability, but rather to the sign of the multiplier in the mathematical feedback equation. The negative feedback loop tends to bring a process to equilibrium, while the positive feedback loop tends to accelerate it away from equilibrium.

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

Some biological systems exhibit negative feedback such as the .

IN AMPLIFIERS

Consider a voltage Amplifier (other systems are similar).

Without feedback, the output voltage V_out = A_O.V_in, where the amplification A_O (also known as the open-loop Gain ) may in general be a function of both frequency and voltage.

The open-loop gain A_O is given as

A_O = rac{V_{out}}{V_{in}}

.....(1)

Suppose we have a feedback loop so that a fraction ''β.V_out'' 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 Capacitor s or Inductor s 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} = V_{in} + \beta.V_{out}

..... (2)

The closed-loop gain A_C is given by,

A_C = rac{V_{out}}{V'_{in}}

..... (3)

Substituting for V'_in from (2),

A_C = rac{V_{out}}{V_{in} + \beta.V_{out}}

..... (4)

Rearranging,

V_{in} + \beta.V_{out} = rac{V_{out}}{A_C}

..... (5)

Dividing both sides of (5) by V_in,

1 + \beta.rac{V_{out}}{V_{in}} = rac{V_{out}}{V_{in}.A_c}

..... (6)

Substituting for V_out/V_in from (1),

1 + \beta.A_O = rac{A_O}{A_C}

..... (7)

And hence

A_C = rac{A_O}{1 + \beta.A_O}

..... (8)

If A_O >> 1, then A_C ≈ 1/β and the effective amplification (or closed-loop gain) A_C 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.A_O = -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.A_O) are often displayed and investigated on a Nyquist Plot (a polar plot of the gain/phase shift as a parametric function of frequency).

These are the advantages of NFB, but there is the primary disadvantage, of loss of gain:
# Improves stability of gain
# Increases input impedance
# Decreases output impedance
# Reduced distortion and noise
# Increases the bandwidth
Disadvantage: The gain of the amplifier decreases.

SEE ALSO

Stability Criterion

Nyquist

Closed Loop

Positive Feedback

Cybernetics

EXTERNAL LINKS

http://www.biology-online.org/4/1_physiological_homeostasis.htm

	CATEGORIES ABOUT NEGATIVE FEEDBACK

	control theory

	cybernetics

	electronic feedback

	control systems

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Negative Feedback