Hysteresis

Hysteresis occurs when a system does not follow the same input-output path during loading and unloading. The current output depends on the current input and on the history of previous inputs. If the input is cycled, the response forms a loop rather than a single curve. The area inside the loop often represents energy dissipated per cycle.

Material examples

In magnetic materials, the relationship between magnetic field strength H and magnetic flux density B forms a hysteresis loop. After the external field is removed, some magnetization remains. Reversing the field is required to bring the flux density back toward zero. This behaviour is central to transformers, motors, inductors, permanent magnets, and magnetic storage. Hysteresis loss becomes heat during each AC cycle.

In mechanical materials, hysteresis appears when stress-strain loading and unloading paths differ. Elastomers, foams, biological tissues, soils, composites, and plastically deformed metals can all show hysteretic response. The loop may come from internal friction, viscoelasticity, microcracking, plasticity, phase transformation, or contact slip. In vibration systems, hysteresis contributes to damping and affects resonance amplitude.

Sensors, actuators, and controls

Hysteresis also appears in measurement and control. A pressure switch may turn on at one pressure and turn off at a lower pressure to avoid chatter. A thermostat uses hysteresis so small temperature noise does not rapidly switch equipment. Sensors can show hysteresis if output differs depending on whether the measured quantity is approached from above or below. Actuators with friction, backlash, magnetic effects, or material memory can require compensation.

In these applications, hysteresis can be useful or harmful. Intentional hysteresis improves noise immunity and switching stability. Unwanted hysteresis reduces accuracy, repeatability, and control precision.

Modelling and measurement

Hysteresis is not captured by a simple single-valued function of the current input. Models may require internal state variables, Preisach operators, Bouc-Wen models, viscoelastic elements, plasticity rules, friction models, or empirical lookup curves. Measurement protocols must define loading rate, amplitude, temperature, cycle count, dwell time, and preconditioning because the loop can change with all of these.

Common mistakes

A common mistake is treating hysteresis as ordinary delay. Delay shifts a response in time; hysteresis changes the path and can produce different outputs at the same input value. Another mistake is quoting a single stiffness, magnetic permeability, or sensor calibration without specifying where on the hysteresis loop it applies. For design reviews, the important questions are whether hysteresis is intentional, how much energy it dissipates, how it changes with cycling, and whether it threatens accuracy, stability, heat generation, or fatigue life.