Oscillators

An oscillator generates a periodic signal with no external input — it's a self-sustaining feedback loop. The same feedback that makes amplifiers unstable becomes useful when controlled deliberately. Clock signals, audio tones, RF carriers, PWM timing references — they all originate from oscillators. Choosing the right type is mostly about frequency stability requirements and how much circuitry you want to build.

The Barkhausen Criterion

An oscillator requires two conditions to be met simultaneously at the oscillation frequency:

1. Loop gain ≥ 1    (enough gain to sustain oscillation)
2. Loop phase = 0° (or 360°) exactly  (signal reinforces itself)

At exactly one frequency, both conditions are met → the circuit oscillates at that frequency.
In practice, loop gain starts slightly above 1 and a non-linearity (saturation, AGC) limits amplitude.

Oscillator Types Overview

Type	Frequency range	Stability	Output waveform	Complexity
555 (relaxation)	1 Hz – 1 MHz	Poor (±5–20%)	Square	Minimal — 2 resistors, 1 cap
RC phase-shift	1 Hz – 100 kHz	Moderate	Sine	One op-amp, 3 RC sections
Wien bridge	1 Hz – 1 MHz	Good (with AGC)	Sine (low distortion)	Op-amp + AGC circuit
Colpitts (LC)	100 kHz – 500 MHz	Good	Sine	Transistor + LC tank + biasing
Hartley (LC)	100 kHz – 30 MHz	Good	Sine	Transistor + tapped inductor
Crystal	1 kHz – 300 MHz	Excellent (±20–1 ppm)	Sine/Square	Crystal + 2 caps + inverter
TCXO	Various	Very high (±0.5 ppm)	Sine/Square	Packaged module
OCXO	Various	Exceptional (±0.01 ppm)	Sine/Square	Packaged module with oven
VCO	Wide range	Moderate (tuning-dependent)	Sine or Square	Varactor diode + LC or RC

RC Oscillators

Phase Shift Oscillator

Three RC stages each contributing 60° of phase shift at the oscillation frequency, plus 180° from an inverting amplifier. Total phase around the loop: 360°:

RC phase-shift network topology: three cascaded RC sections shift the output feedback signal before it returns to the inverting amplifier input.

f = 1 / (2πRC√6)

Example: R=10kΩ, C=10nF
f = 1 / (2π × 10,000 × 0.00000001 × 2.449) ≈ 649 Hz

Minimum amplifier gain for oscillation: 29 (28 dB)

Wien Bridge Oscillator

Non-inverting amplifier with Wien network in feedback. Produces a low-distortion sine wave — used in audio test oscillators and function generators:

Wien bridge frequency-setting network: a series RC branch and parallel RC branch feed the non-inverting amplifier input.

f = 1 / (2πRC)

For unity phase at f: the Wien network has voltage ratio = 1/3
Amplifier gain must be exactly 3 for oscillation (R_f = 2×R_g)

AGC (automatic gain control) holds gain at 3:
  Classic: small incandescent lamp in gain network (resistance rises with heat)
  Modern: FET-based or dedicated IC amplitude control

LC Oscillators

An inductor-capacitor tank circuit oscillates at f₀ = 1/(2π√LC). The transistor amplifier compensates for the resistance (energy loss) to sustain the oscillation indefinitely:

Colpitts Oscillator

Colpitts oscillator schematic: a common-base transistor sustains an LC tank, and the C1–C2 capacitive divider feeds a portion of the tank signal back to the emitter.

Frequency: f₀ = 1 / (2π√(L × C_total))
C_total = C1 × C2 / (C1 + C2)  (series)

Feedback ratio: C1/C2 (determines loop gain)
Typical: C2 = 2–10× C1

The Colpitts is the workhorse for RF oscillators — stable, predictable, easily variable with a trimmer capacitor or varactor diode.

Crystal Oscillators

A quartz crystal resonates at a frequency determined by its physical dimensions. The Q factor is 10,000–100,000 (compared to 100–200 for a good LC tank), making the frequency extremely stable:

Simple Pierce crystal oscillator (common in MCU circuits):

Pierce crystal oscillator: an inverter and crystal feedback path use two load capacitors to set the crystal’s specified load capacitance.

Load capacitance = (C1 × C2)/(C1 + C2) + stray
Crystal frequency is trimmed to be correct with the specified load capacitance.

Frequency	Use	Notes
32.768 kHz	Real-time clocks	2^15 = 32768 — 15 binary divisions = 1Hz exactly
4 MHz	Microcontrollers	Classic PIC/AVR clock, often doubled internally
8 MHz	Microcontrollers	ATmega328 (Arduino) external crystal option
16 MHz	Microcontrollers	Standard Arduino clock frequency
20 MHz	Microcontrollers	STM32 common HSE clock
25 MHz	Ethernet PHY, AD9833	Standard reference for many network ICs
10 MHz	Frequency standard	GPSDO / OCXO reference output standard

Relaxation Oscillators — 555 Timer

Astable 555 circuit:

555 astable timing network: RA and RB charge and discharge capacitor C through the timer’s discharge and threshold/trigger pins to set frequency and duty cycle.

f = 1.44 / ((RA + 2×RB) × C)
Duty cycle = (RA + RB) / (RA + 2×RB)

For 50% duty: use RA very small (100Ω) + steering diodes around RB
Or: use a CMOS 555 (TLC555) with equal charge/discharge paths

RA	RB	C	Frequency	Application
1kΩ	1kΩ	100nF	4.8 kHz	Audible tone, buzzer
10kΩ	10kΩ	100nF	480 Hz	Mid-range audio tone
100kΩ	100kΩ	10µF	0.48 Hz	LED blinker (~1s period)
1kΩ	10kΩ	10nF	6.6 kHz	Motor drive PWM

VCO — Voltage-Controlled Oscillator

A VCO's frequency is controlled by a voltage. Increasing voltage increases (or decreases) frequency depending on the design. The critical component in PLLs (phase-locked loops):

Applications of VCO + PLL:
  FM radio demodulation
  Clock synthesis (CPU PLLs multiply a crystal reference)
  Motor speed control
  Frequency modulation (direct FM transmitter)
  Clock recovery from serial data streams

Simple VCO using 555: replace RA or RB with a transistor-based
variable resistance controlled by the input voltage.
Better VCO: CD4046 has a built-in VCO and phase comparators.

References

Horowitz & Hill — The Art of Electronics, 3rd ed. Chapter 7
Razavi — Design of Analog CMOS Integrated Circuits
Electronics-Tutorials — Oscillator Circuits ↗
TI — Oscillator Design Guide (PDF) ↗