The inverting comparator with hysteresis requires a three-resistor network that is referenced to the comparator supply voltage (V_CC), as shown below.

Figure 6-3 Inverting Configuration With Hysteresis

The equivalent resistor networks when the output is high and low are shown below.

Figure 6-4 Inverting Configuration Resistor Equivalent Networks

When V_IN is less than V_A, the output voltage is high (for simplicity, assume V_O switches as high as V_CC). The three network resistors can be represented as R1 || R3 in series with R2, as shown above on the left.

The equation below defines the high-to-low trip voltage (V_A1).

Equation 1.

When V_IN is greater than V_A, the output voltage is low. In this case, the three network resistors can be presented as R2 || R3 in series with R1, as shown above on the right.

Use the equation below to define the low to high trip voltage (V_A2).

Equation 2.

The equation below defines the total hysteresis provided by the network.

Equation 3.