RC Phase-Shift Oscillator Frequency

f = 1 / (2π · R · C · √6)

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Result
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Formula

f = 1 / (2π × R × C × √6)

Description

An RC phase-shift oscillator uses three cascaded RC sections to provide the 180° of phase shift needed (together with the inverting amplifier’s 180°) for oscillation. With three equal sections the oscillation frequency includes the √6 factor. The amplifier must make up the network’s loss, which for the three-section case requires a voltage gain of at least 29.

Variables

  • f — Oscillation frequency (Hz)
  • R — Resistance of each section (Ω)
  • C — Capacitance of each section (F)

Practical Notes

The loop attenuation at the oscillation frequency is 1/29, so the amplifier gain must be ≥ 29. More sections lower the required gain but complicate tuning. Best for fixed audio-frequency sine generation.

Related Concepts

All Timing & Oscillators formulas →
555 Timer Astable 555 Timer Monostable Crystal Load Capacitance RC Oscillator Frequency Crystal Frequency Stability PLL Lock Time VCO Tuning Sensitivity Jitter from Phase Noise

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