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Technology / Technical guide
Schmitt Hysteresis: Thresholds, History & Retained State
A single switching threshold can produce repeated state changes when an input moves back and forth nearby. A Schmitt-style relationship uses different thresholds for opposite transitions and retains state between them. The central feature is memory of the previous state, rather than a claim that noise has disappeared from the input.
The same input can correspond to two retained states.
Two thresholds define a state-dependent relationship; their separation differs from timing delay and physical sensor error.
01 / Two thresholds
Opposite transitions use different boundaries.
Texas Instruments describes Schmitt hysteresis through a higher rising transition threshold and a lower falling transition threshold.
Texas Instruments describes Schmitt hysteresis through a higher rising transition threshold and a lower falling transition threshold. Their difference is the hysteresis width. This general concept is distinct from any numerical limits or implementation inside a particular controller.
Use an abstract input x and states A and B. Let H exceed L. In the example relationship, A changes to B when x is at least H, while B changes to A when x is at most L. These are mathematical labels, not turbine commands.
02 / State memory
Inside the interval, history supplies the answer.
For an input strictly between L and H, the example retains its current state.
For an input strictly between L and H, the example retains its current state. If it entered the interval from state A, it stays A; if it entered from state B, it stays B. Consequently, x alone is insufficient to determine the represented state.
An initial state must therefore be part of the model. Starting inside the interval without a known state does not imply either answer. Real analogue thresholds can also have specified ranges and variation; the ideal two-number example is not a component tolerance specification.
03 / Toy sequence
One invented history illustrates the retained state.
Suppose L = 2 and H = 4 arbitrary units, beginning in A.
Suppose L = 2 and H = 4 arbitrary units, beginning in A. For successive input values 1, 3, 4, 3 and 2, the states are A, A, B, B and A. Equality belongs to the transition in this explicitly chosen convention.
The input value 3 appears twice but corresponds to different states because the histories differ. The hysteresis width is 2 units. It is not an actual yaw deadband, voltage threshold or recommended protection value, and the sequence represents no physical operation.
04 / Noise meaning
Retaining state is different from eliminating disturbance.
Small excursions within the interval do not cause a transition in the example.
Small excursions within the interval do not cause a transition in the example. However, an excursion reaching the applicable boundary can still change state. A two-threshold relationship therefore changes how the input becomes a state, rather than removing noise from the original quantity.
The result depends on the disturbance’s amplitude and the current state. It cannot be summarised by saying that every noisy signal is cleaned. A wide interval also represents more history-dependent ambiguity; hysteresis has a consequence beyond reducing repeated switching near one level.
05 / Other concepts
A dead zone and a dwell rule represent different mechanisms.
A memoryless dead zone maps an input region to a specified output without retaining the preceding state.
A memoryless dead zone maps an input region to a specified output without retaining the preceding state. The Schmitt example retains either A or B inside its interval. Equal-looking boundary numbers do not make the two relationships equivalent.
Time qualification adds another dimension: an input can satisfy an amplitude condition yet fail a duration rule. Conversely, this ideal hysteresis model contains no minimum duration. Physical sensor hysteresis, where the measured response depends on approach direction, is also a different source of behaviour.
06 / Scope
State logic is not a verified protection design.
A mathematical transition rule does not determine fault handling, missing-input treatment, reset permission or a safe operating response.
A mathematical transition rule does not determine fault handling, missing-input treatment, reset permission or a safe operating response. Those questions require additional relationships. Selecting H and L without that context would not follow from the conceptual example.
No MARSTON Schmitt function, hysteresis width or threshold is confirmed. This page supplies no protection settings or control modifications. The debounce guide examines time qualification as a separate signal concept.
Related technical guides: Signal Debouncing: Persistence, Sampling & Event Timing · Phase-Locked Loops: Phase, Frequency & Synchronisation · Model Residuals: Prediction Gaps & Ambiguous Causes.
General background: Texas Instruments: Understanding Schmitt Triggers — hysteresis definition. These references explain industry concepts; they are separate from the applicable MARSTON product and project documents.
Key concepts and conditions.
Read each quantity with its reference, units and stated conditions. A general relation does not establish a model-specific value.
| Concept / quantity | Meaning / relation | Conditions / limits |
|---|---|---|
| Upper H | Boundary for A-to-B in the example | H exceeds L; equality convention stated |
| Lower L | Boundary for B-to-A in the example | Applies to the opposite current state |
| Width H−L | Input units rather than seconds | Does not itself define a timing delay |
| Retained state | A or B inside the interval | Needs known history or an initial state |
| Time qualification | Duration or observation rule | Additional logic, not implicit hysteresis |
Engineering questions.
What is the key feature of Schmitt hysteresis?
Opposite thresholds and retained state between them.
Can the same input have different states?
Yes. Inside the interval, the previous state matters.
Is hysteresis width a time delay?
No. It has the units of the input quantity.
Does hysteresis remove all noise?
No. It changes the state mapping without eliminating the disturbance.
Is it identical to a dead zone?
No. A memoryless dead zone does not retain the preceding state.
Are the example thresholds actual protection settings?
No. They describe an abstract relationship only.
Technical enquiry
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