Circuit building blocks

Oscillators

Circuits that make their own steady wave from a DC supply. Each one is an amplifier whose output is fed back to its input through a network that only lets one frequency come back in step; noise at that frequency grows until the amplifier limits it.

Think of it as: A microphone held near its own speaker: the howl picks one note and stays loud.

The variants

RC phase-shift

An inverting amplifier turns the wave upside down (180°). Three RC stages shift it by another 180° at exactly one frequency, so that frequency comes back in step. Cheap, but the amplifier needs a gain of 29.

Frequency: 1 / (2π·R·C·√6) = 650 Hz for 10 kΩ, 10 nF · Gain needed: 29

Wien bridge

A series RC and a parallel RC form a filter that passes one frequency with no phase shift and one third of the size. A non-inverting amplifier with a gain of exactly 3 makes up the loss. The classic low-distortion sine source for audio test gear.

Frequency: 1 / (2π·R·C) = 995 Hz for 10 kΩ, 16 nF · Gain needed: 3 (RF = 2 × RG)

LC (Colpitts)

An inductor and two capacitors make a tank that rings at one frequency, like a bell. The split capacitor feeds part of the ringing back to the amplifier. Used for radio frequencies, usually with a single transistor as the amplifier.

Frequency: 1 / (2π√(L·C1C2/(C1+C2))) = 2.25 MHz for 10 µH, 1 nF + 1 nF · Range: About 100 kHz to a few hundred MHz

Crystal (Pierce)

One inverter, two small capacitors and a crystal. The quartz acts like an LC tank that is thousands of times sharper, so the frequency hardly drifts. Every microcontroller clock is built this way.

Frequency: Set by the crystal: 32.768 kHz, 8 MHz, 16 MHz … · Accuracy: ±10 to ±50 ppm

The oscillators side by side

Type	Sets the frequency	Range	Stability	Typical use
RC phase-shift	Three RC stages	Hz to ~100 kHz	Fair	Simple tone generators
Wien bridge	RC bridge, gain 3	Hz to ~1 MHz	Good, very clean sine	Audio test oscillators
LC (Colpitts)	L and C tank	~100 kHz to hundreds of MHz	Fair (drifts with temperature)	Radio, RF signal sources
Crystal	Quartz crystal	32 kHz to ~50 MHz	Excellent (ppm)	Microcontroller and clock chips
555 / RC relaxation	R and C charge time	mHz to ~500 kHz	Poor to fair	Blinkers, PWM, square waves

The rule every oscillator follows

Round the loop, the signal must come back in step (a total phase shift of 0° or 360°) and at least as big as it left (loop gain of 1 or more). This is called the Barkhausen criterion. The astable multivibrator and the 555 are oscillators too, of a different kind: they snap between two levels instead of making a sine.

Where you’ll use it

Clocks for every microcontroller and computer (crystal).
Radio transmitters and receivers (LC).
Audio test tones and function generators (Wien bridge).
Blinkers, buzzers and PWM (relaxation oscillators like the 555).

Common mistakes

Wrong load capacitors on a crystal. It starts slowly, runs slightly off frequency or not at all.
Too much loop gain in a sine oscillator: the output clips into a square-ish wave.
Long PCB traces to the crystal, which pick up noise and add stray capacitance.
Accidental oscillators: an amplifier with long wires or no decoupling capacitor can start oscillating on its own.

Lessons that use it

The RC time constant (2.2) and op-amp gain (3.3) are the two ingredients of the RC oscillators here.

Go deeper

|A\,\beta| \ge 1,\qquad \angle A\beta = 0^\circ \;(\text{or } 360^\circ)

Barkhausen criterion: loop gain of at least one and the signal back in step.

f = \dfrac{1}{2\pi R C \sqrt{6}},\quad A = -29

Three-stage RC phase-shift oscillator.

f = \dfrac{1}{2\pi R C},\quad A = 1 + \dfrac{R_F}{R_G} = 3

Wien bridge oscillator.

f = \dfrac{1}{2\pi\sqrt{L\,\tfrac{C_1 C_2}{C_1 + C_2}}}

Colpitts LC oscillator: the two capacitors act in series.