Relaxation Oscillator

Generate a square wave by repeatedly charging a capacitor between Schmitt-trigger thresholds.

A1 uses RF = RG = 100 kΩ for a half-output switching threshold. R1 = 10 kΩ charges C1 = 100 nF from the output. The capacitor voltage reaches a threshold, flips the output, and then moves toward the opposite threshold. A 0.1 V capacitor initial condition starts the otherwise symmetric ideal circuit.

$$T=2R_1 C_1\ln\left(\frac{1+\beta}{1-\beta}\right)$$ $$\beta=\frac12,\qquad f\approx\frac{1}{2R_1 C_1\ln3}\approx455\,\mathrm{Hz}$$

Vcap is green, the square-wave output red and load current blue. Capacitor voltage swings near ±6 V with exponential segments. The simulation uses the specified initial condition instead of the DC operating point. Finite amplifier delay shifts frequency slightly.

Read the results. The saved transient chart uses separate voltage and current panels; the table provides numerical samples. The first voltage probe is green and the second red. The first current probe is blue; a second current probe is purple.

Model limits. The three-terminal op-amp model has implicit ±12 V output limits, 200,000 low-frequency gain and 10 MHz gain-bandwidth product. Supply pins are intentionally absent in this functional model. In Schmitt-trigger and relaxation/integrator oscillator examples, the switching amplifier uses a 100 kHz gain-bandwidth setting to resolve transitions cleanly at the saved time step. It omits detailed slew-rate, input common-mode, output-current and thermal limits.

Try it. Set R1 to 20 kΩ; the oscillation period approximately doubles. Restore the original values after comparing the results.