The oscillation frequency is determined by the resistor and capacitor values. The following calculation provides details of the steps.

Figure 9-10 Square-Wave Oscillator Timing Thresholds

First consider the output of Figure Figure 9-9 as high, which indicates the inverted input V_C is lower than the noninverting input (V_A). This causes the C₁ to be charged through R₄, and the voltage V_C increases until it is equal to the noninverting input. The value of V_A at the point is calculated by Equation 7.

Equation 7.

if R₁ = R₂= R₃, then V_A1 = 2 V_CC/ 3

At this time the comparator output trips pulling down the output to the negative rail. The value of V_Aat this point is calculated by Equation 8.

Equation 8.

if R₁ = R₂ = R₃, then V_A2 = V_CC/3

The C₁ now discharges though the R₄, and the voltage V_CC decreases until it reaches V_A2. At this point, the output switches back to the starting state. The oscillation period equals to the time duration from for C₁ from 2V_CC/3 to V_CC / 3 then back to 2V_CC/3, which is given by R₄C₁ × ln 2 for each trip. Therefore, the total time duration is calculated as 2 R₄C₁ × ln 2.

The oscillation frequency can be obtained by Equation 9:

Equation 9.