Hysteresis refers to the nonlinear behavior of a system where the output response does not directly correspond to the same input values but depends on the history of input changes, including both the direction and magnitude of the input.
This nonlinear behavior is often represented by a hysteresis loop, which describes the relationship between the input and output of the system. In the context of digital control in electronics, hysteresis can be modeled using a simple two-state machine with thresholds for state transitions, such as Vth_high and Vth_low. The hysteresis behavior is often visualized through a loop (often called hysteresis loop)that represents the relationship between the system's input and output states. For example, when the input voltage goes above Vth_high, the system transitions to state 1, and when the input voltage falls below Vth_low, the system transitions to state 0.
The plot above shows the complete hysteresis loop in a digital control system, capturing both the increasing and decreasing input voltage:
The x-axis represents the input voltage, initially going from 0 to 2V and then returning back to 0V.
The y-axis represents the output state, which can be either 0 or 1.
High Voltage Threshold (Vth_high): When the input voltage rises above 1.4V (indicated by the red dashed line), the system transitions from state 0 to state 1.
Low Voltage Threshold (Vth_low): When the input voltage falls below 0.7V (indicated by the green dashed line), the system transitions back to state 0 from state 1.
Complete Hysteresis Loop: This loop shows the complete hysteresis behavior as the input voltage first increases and then decreases. The system's current state depends not just on the current input but also on its past, which provides a buffer against rapid state changes.
Practical Applications in Digital Systems
Temperature Control of a Thermostat: In temperature control systems, hysteresis is commonly employed to maintain a desired temperature range. For instance, in a room with a target temperature of 70 degrees, the thermostat's control state machine turns on the HVAC system when the room temperature falls below 68 degrees and turns it off when the temperature rises above 72 degrees. This temperature buffer region helps avoid rapid switching of the HVAC system, improving energy efficiency and the overall lifespan of the HVAC and control circuits.
Hysteresis Loop: The loop formed by the HVAC state as the room temperature varies shows the hysteresis behavior. This design prevents the HVAC system from rapidly turning on and off, thus improving energy efficiency and the overall lifespan of both the HVAC system and control circuits.
Digital Circuit Input Logic Trigger (e.g., Schmitt Trigger): Hysteresis is used in digital circuits to prevent false state transitions caused by noise or small disturbances in the input signal. For example, a digital circuit may store a logic bit 1 when the input voltage is above 1.4 V and store a logic bit 0 when the input voltage is below 0.7 V. The control state machine transitions to Logic 1 state when the input exceeds 1.4 V and transitions to Logic 0 state when the input falls below 0.7 V. The inclusion of hysteresis in the threshold values allows for a noise margin of 0.7 V, reducing the chances of false positive state transitions.
Hysteresis Loop: The loop formed by the output state as the input voltage varies shows the hysteresis behavior. The system's current state depends not just on the current input but also on its past, creating a buffer against rapid state changes. Plot below demonstrate this in action.
A graph comparing a simple comparator (output A) and Schmitt comparator (Ouput B) from input (U). The dashlines in U are the tresholds. Image source(wikipedia: https://en.wikipedia.org/wiki/Schmitt_trigger#/media/File:Smitt_hysteresis_graph.svg)
Hysteresis provides robustness and stability to systems, ensuring that changes in input variables do not immediately trigger undesired or erratic responses. By introducing thresholds and memory of previous states, hysteresis allows for more reliable operation and noise immunity in various applications.