87-op-amp-relaxation-oscillator

Relaxation oscillator realized with op-amp is given in figure bellow.
Simulate Op-amp relaxation oscillator.

op-amp-relaxation-oscillator

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:

relax_osc_eq01a

Let’s denote

relax_osc_eq02a

Inverting input is on potential:

relax_osc_eq03

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:

relax_osc_eq05a

After V exceed potential of V+, output voltage goes to -VCC, starting discharging process. Discharging process lasts for:

relax_osc_eq05

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:

relax_osc_eq06

Go to op-amp relaxation oscillator.

External links:

Op-amp Relaxation Oscillator on Wikipedia

Op-amp Relaxation Oscillator on All about circuits

 

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