thresholdhysteresis

Threshold hysteresis is a property of a system in which the input level required to switch from one state to another depends on the direction of the change. In practical terms, the threshold for turning a signal on is not the same as the threshold for turning it off, which creates a loop when input versus output is plotted. The region between the two thresholds is called the hysteresis band. This mechanism reduces sensitivity to noise and small fluctuations around a single threshold, at the cost of a deliberate lag or a small delay in switching.

In electronics, threshold hysteresis is most commonly implemented with a Schmitt trigger, a comparator circuit with positive feedback that yields two distinct switching thresholds, often denoted as V_TH+ (upward) and V_TH− (downward). When the input rises past V_TH+ the output flips to a high state; when the input falls below V_TH− the output flips to a low state. The width of the hysteresis band, ΔV = V_TH+ − V_TH−, determines the amount of noise immunity and the stability of the transition.

Mathematically, a threshold-hysteretic system can be described by a state variable and a set of switching rules: if in state 0 and the input exceeds the upper threshold, switch to state 1; if in state 1 and the input drops below the lower threshold, switch to state 0; otherwise maintain the current state. Dynamic versions may feature thresholds that depend on the current state or on recent output.

Threshold hysteresis is widely used to convert noisy or slowly varying signals into clean digital transitions, to implement memory and stability in sensors and control systems, and in various signal-conditioning and timing applications. Related concepts include hysteresis, Schmitt trigger, positive feedback, and latching.