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Analog Electronics

Relaxation Oscillator (Astable)

Add an RC feedback path to a Schmitt trigger and the circuit oscillates on its own: while the output is high, C charges through R toward the upper threshold; on reaching it, the output flips and C now discharges toward the lower threshold.

The period depends on where the thresholds sit: with an equal-resistor divider (β=0.5), T = 2·RC·ln(3) ≈ 2.2·RC. You see an exponential charging curve at the capacitor node and a square wave at the output.

This structure is the foundation of timers, LED flashers, and PWM carrier generators. The astable mode of the 555 timer works on the same principle.

Formulas

T = 2·RC·ln((1+β)/(1−β))
β = R1/(R1+R2) = 0.5 → T ≈ 2.2·RC
f = 1/T

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Test Yourself

For R=100k, C=100n, β=0.5, what is the approximate frequency?
Answer: 45 Hz — T ≈ 2.2·RC = 2.2·10ms = 22 ms → f ≈ 45 Hz.
What is the waveform at the capacitor node?
Answer: Exponential charge/discharge (triangle-like) — C charges/discharges between the thresholds along the RC exponential curve.
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