Editing Positive feedback (section)

== Overview ==
Positive feedback enhances or amplifies an effect by it having an influence on the process which gave rise to it. For example, when part of an electronic output signal returns to the input, and is in phase with it, the system [[Gain (electronics)|gain]] is increased.<ref>{{cite web|title=Positive feedback|url=http://www.oxforddictionaries.com/definition/english/positive-feedback|work=Oxford English Dictionary|publisher=Oxford University Press|access-date=15 April 2014|url-status=dead|archive-url=https://web.archive.org/web/20140302160045/http://www.oxforddictionaries.com/definition/english/positive-feedback|archive-date=2 March 2014}}</ref> The feedback from the outcome to the originating process can be direct, or it can be via other state variables.<ref name=theorymodelling/> Such systems can give rich qualitative behaviors, but whether the feedback is instantaneously positive or negative in sign has an extremely important influence on the results.<ref name=theorymodelling/> Positive feedback reinforces and negative feedback moderates the original process. ''Positive'' and ''negative'' in this sense refer to [[loop gain]]s greater than or less than zero, and do not imply any [[value judgement]]s as to the desirability of the outcomes or effects.<ref>{{cite web|title=Feedback|url=http://metadesigners.org/Feedback-Glossary|work=Glossary|publisher=Metadesigners Network|access-date=15 April 2014|url-status=live|archive-url=https://web.archive.org/web/20140416183720/http://metadesigners.org/Feedback-Glossary|archive-date=16 April 2014}}</ref>  A key feature of positive feedback is thus that small disturbances get bigger. When a change occurs in a system, positive feedback causes further change, in the same direction.

=== Basic ===
[[File:Ideal feedback model.svg|thumb|A basic feedback system can be represented by this block diagram. In the diagram the + symbol is an adder and A and B are arbitrary [[causal system|causal]] functions.]]

A simple feedback loop is shown in the diagram.  If the loop gain AB is positive, then a condition of ''positive'' or ''regenerative'' feedback exists.

If the functions A and B are linear and AB is smaller than unity, then the overall system gain from the input to output is finite but can be very large as AB approaches unity.<ref name=smith>Electronics circuits and devices second edition. Ralph J. Smith</ref>  In that case, it can be shown that the overall or loop gain from input to output is:

:<math>G_c = A/(1-AB)</math>

When AB > 1, the system is unstable, so does not have a well-defined gain; the gain may be called infinite.

Thus depending on the feedback, state changes can be convergent, or divergent.  The result of positive feedback is to [[wikt:augment|augment]] changes, so that small perturbations may result in big changes.

A system in equilibrium in which there is positive feedback to any change from its current state may be unstable, in which case the system is said to be in an [[unstable equilibrium]]. The magnitude of the forces that act to move such a system away from its equilibrium is an [[increasing function]] of the ''distance'' of the state from the equilibrium.

Positive feedback does not necessarily imply instability of an equilibrium, for example stable ''on'' and ''off'' states may exist in positive-feedback architectures.<ref name="ReferenceA">{{cite journal|last1=Lopez-Caamal|first1=Fernando|last2=Middleton|first2=Richard H.|last3=Huber|first3=Heinrich|title=Equilibria and stability of a class of positive feedback loops|journal=Journal of Mathematical Biology|date=February 2014|pages=609–645|doi = 10.1007/s00285-013-0644-z|pmid=23358701|volume=68|issue=3|s2cid=2954380}}</ref>

=== Hysteresis ===
{{main|Hysteresis}}

[[File:Hysteresis sharp curve.svg|thumb|Hysteresis causes the output value to depend on the history of the input.]]

[[File:Op-Amp Schmitt Trigger.svg|thumb|In a [[Schmitt trigger]] circuit, feedback to the non-inverting input of an amplifier pushes the output directly away from the applied voltage towards the maximum or minimum voltage the amplifier can generate.]]

In the real world, positive feedback loops typically do not cause ever-increasing growth but are modified by limiting effects of some sort. According to [[Donella Meadows]]:

::"Positive feedback loops are sources of growth, explosion, erosion, and collapse in systems. A system with an unchecked positive loop ultimately will destroy itself. That's why there are so few of them. Usually, a negative loop will kick in sooner or later."<ref name=meadows>
Donella Meadows, [http://www.sustainabilityinstitute.org/pubs/Leverage_Points.pdf ''Leverage Points: Places to Intervene in a System''] {{webarchive|url=https://web.archive.org/web/20131008160618/http://www.sustainabilityinstitute.org/pubs/Leverage_Points.pdf |date=2013-10-08 }}, 1999</ref>

Hysteresis, in which the starting point affects where the system ends up, can be generated by positive feedback. When the gain of the feedback loop is above 1, then the output moves away from the input: if it is above the input, then it moves towards the nearest positive limit, while if it is below the input then it moves towards the nearest negative limit.

Once it reaches the limit, it will be stable. However, if the input goes past the limit,{{clarify|date=June 2012}} then the feedback will change sign{{dubious|date=June 2012}} and the output will move in the opposite direction until it hits the opposite limit. The system therefore shows [[bistability|bistable]] behaviour.