Oscillators

Oscillators generate repeating signals — the heartbeat of every digital system and radio. Learn the Barkhausen criterion, RC phase-shift and Wien-bridge oscillators, LC Colpitts/Hartley, crystal oscillators and their stability, relaxation oscillators and the 555 timer, VCOs and PLLs.

Every microcontroller needs a clock, every radio needs a local oscillator, and every PWM needs a timebase. Oscillators use positive feedback (or a charging/discharging cycle) to sustain oscillation at a frequency set by R, C, L or a quartz crystal.

An analogy

An oscillator is like a child on a swing: timely small pushes (positive feedback) keep the swing going at its natural frequency.

How oscillation starts

Noise contains all frequencies; the frequency-selective network passes one frequency with 0° (360°) total loop phase. If loop gain > 1 there, it grows until amplitude limiting (non-linearity or AGC) reduces gain to exactly 1.

RC and LC oscillators

RC types (phase-shift, Wien) suit audio frequencies; LC types (Colpitts, Hartley, Clapp) suit RF from ≈ 100 kHz to GHz. The Wien bridge needs gain 3 with amplitude stabilisation (lamp, diodes, JFET).

Crystal oscillators

Quartz crystals resonate mechanically with Q of 10⁴–10⁶, giving ±10–50 ppm accuracy (TCXO ±0.5 ppm, OCXO ±0.01 ppm). MCUs use a Pierce oscillator with two load capacitors; 32.768 kHz crystals keep real-time clocks.

Relaxation oscillators, VCOs and PLLs

Relaxation oscillators (555, Schmitt + RC) charge and discharge a capacitor. VCOs change frequency with voltage (varactors). PLLs lock a VCO to a reference, multiplying frequency — used to generate CPU clocks and RF carriers. Phase noise and jitter are key specs.

Formulas

• RC phase shift (3 sections): f₀ = 1/(2πRC√6), gain ≥ 29
• Wien bridge: f₀ = 1/(2πRC), gain = 3
• Colpitts: f₀ = 1/(2π√(L C_eq)), C_eq = C₁C₂/(C₁ + C₂)
• 555 astable: f = 1.44/((R₁ + 2R₂)C), D = (R₁ + R₂)/(R₁ + 2R₂)

Worked example: Wien and phase-shift

Given: R = 10 kΩ, C = 10 nF

Find: Frequencies.

• Wien: 1/(2π × 10⁴ × 10⁻⁸) = 1.59 kHz
• Phase-shift: 1.59 kHz/√6 = 650 Hz

Answer: 1.59 kHz (gain 3) and 650 Hz (gain 29)

Worked example: Colpitts

Given: L = 10 µH, C₁ = C₂ = 1 nF

Find: f₀.

• C_eq = 0.5 nF
• f₀ = 1/(2π√(10⁻⁵ × 5 × 10⁻¹⁰)) = 2.25 MHz

Answer: 2.25 MHz

Common mistakes

• Wrong: Wrong crystal load capacitors. — Right: C_load = C₁C₂/(C₁ + C₂) + stray ≈ crystal spec.
• Wrong: Too much loop gain in a Wien bridge. — Right: Stabilise amplitude or the sine clips.

Applications

• MCU clocks: Crystal and RC oscillators, PLL multiplication.
• Radio: Local oscillators and frequency synthesisers.
• Timers & tone generators: 555 and RC relaxation circuits.

Key takeaways

• Positive feedback + frequency selection.
• Wien 1/(2πRC), phase shift ÷√6.
• LC for RF, crystals for accuracy.
• 555: f = 1.44/((R₁ + 2R₂)C).

Going further

• Phase noise: Spectral purity of oscillators.
• Fractional-N PLLs: Fine frequency synthesis.
• MEMS oscillators: Silicon replacements for quartz.