A relaxation oscillator is a circuit that combine Schmitt trigger with slow negative feedback realized with RC circuit. Output voltage oscillate from rail to rail (from VCC to -VCC). Change of the output voltage level automatically trigger capacitor C charging or discharging process.
Let assume that initially output voltage was high (+VCC). Via voltage divider R2-R3, non-inverting input is on electrical potential of:
Inverting input is on potential:
Positive voltage on Rf start to charge capacitor C with time constant τ=CRf. Voltage on capacitor increases from -VCC·β tending to reach +VCC. However, once when capacitor voltage exceeds potential of +VCC·β, inverting input is higher then non-inverting, and output of op-amp goes to -VCC. This charging process takes time of:
After V– exceed potential of V+, output voltage goes to -VCC, starting discharging process. Discharging process lasts for:
Obviously, for symmetrical power supply of op-amp (±VCC), T1=T2, so duty cycle is always 50%, independently of R3 over R2 ratio. R3 over R2 ratio affect frequency, but as logarithmic function. Frequency of generated signal is:
Go to op-amp relaxation oscillator.