Hysteresis

Definition: Hysteresis is a nonlinear behavior of a system that its output response curve does not map directly to the same input values but rather dependent on history of input values in terms of how input direction and magnitude change.

The nonlinear behavior of the system is characterized by a hysteresis loop. In the context of electronics employing digital control, the system behavior can be modeled as a simple two state machine with two states 1 or 0 with two different state transition thresholds, Vth_high, Vth_low.( I.e state -> 0 when input voltage falls below Vth_low, stage -> 1, when input voltage goes above Vth_high)

• • Note: The difference between Vth_high and Vth_low creates a noise immunity zone where the states will not change due to small disburbance input signal within this zone.

See here for a picture of Hysteresis loop.

Applications:

• Temperature Control of A Thermal stat

  • For example, maintain the room temperature at 70 degrees

  • Control state machine:

    • Turn on the HVAC system when the room temperature falls below 68 degrees

    • Turn off the HVA system when room temperature rise above 72 degrees

  • Analysis

    • There is a 4 degrees temperature buffer region before thermal stat responses. This practical design reduces rapid switch on and off actions of thermal stat in the case of using single temperature threshold. As a result, operating power efficiency improves as well as long term operability of HVAC and control circuits is achieved.

• Digital circuit Input logic trigger

  • For example, digital circuit stores a logic bit 1 when its input voltage is above 1.4 V and store a logical bit 0 when its input value is below 0.7 V.

  • Control state machine

    • Enter Logic 1 state when input > 1.4V

    • Enter Logic 0 state when input < 0.7V

  • Analysis

    • There is a 0.7 of noise margin allowed in this circuit before a false positive state transition occurs.

Reference and Further Reading

"Hysteresis", https://en.wikipedia.org/wiki/Hysteresis