# What is Hysteresis? - Definition & Loop

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• 0:03 What Is Hysteresis?
• 1:16 Types of Hysteresis
• 2:48 Magnetic Hysteresis
• 4:48 Lesson Summary
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Lesson Transcript
Instructor: Kip Ingram

Kip holds a PhD in Engineering from The University of Texas at Austin and was an occasional substitute lecturer in engineering classes at that institution.

Hysteresis is a common phenomenon in physical systems and occurs when the system's output depends not only on its present inputs but also on past inputs (when the system exhibits memory so to speak). Learn more in this lesson.

## What Is Hysteresis?

If you pay close attention to your AC unit (set, say, to 78 degrees), you may notice that it turns on when the temperature rises to 79 degrees and off when the temperature falls to 77 degrees. This behavior is called hysteresis, and AC units are designed this way deliberately. If the unit cycled precisely at 78 degrees in both directions, it would switch on and off much more frequently and wear out more quickly. Hysteresis causes the temperature at which the unit switches to depend on the direction the temperature is moving.

Technically, a physical system has hysteresis when its output depends on both present and past inputs. In the case of the AC unit, the behavior at the set point (78 degrees in our example) depends on recent temperature history: if the temperature is rising through 78 degrees, the system will be off until the temperature reaches 79 degrees; but if the temperature is falling through 78 degrees, the system will be on until the temperature reaches 77 degrees. The direction of temperature change matters, and knowing what that direction is requires knowledge not only of the present temperature but of temperatures in the recent past as well.

## Types of Hysteresis

Systems that exhibit hysteresis fall into two categories:

• Systems with rate-dependent hysteresis have a memory of recent inputs that fades with time - if the input stops changing and we wait long enough, the output will eventually reach the same value for that particular input.
• Systems with rate-independent hysteresis retain a permanent memory of certain input patterns, and even the steady state value of the output depends on the nature of the input history.

The AC unit exhibits rate-independent hysteresis - at any given time the set point could be either 77 or 79 degrees, so if the temperature is 78 degrees and you do something 'external' to keep it that way, like open a window, or turn on a heater, the unit's off/on state (which depends on which direction the temperature was moving before we locked it in at 78 degrees) will never change.

If we describe our system with the equation y = F(x), where x is the input, y is the output, and F is 'the system,' we can say that a system with rate-dependent hysteresis has an F that makes use of both present and recent values of x, whereas a system with rate-independent hysteresis has an F that actually changes in response to some input patterns.

The full class of systems with hysteresis (rate-dependent and rate-independent) is very broad. Often an analysis of rate-dependent systems doesn't require the hysteresis concept at all, and some writers define hysteresis as rate-independent hysteresis only.

## Magnetic Hysteresis

One of the most commonly encountered examples of hysteresis occurs in systems that involve magnetic fields: for example, transformers used in electrical equipment and distribution grids. In such systems, a coil of current-carrying wire is used to create a magnetic field, and routing that field through an iron core greatly reduces the current required for a given field strength. However, the iron also introduces hysteresis into the system.

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