Colpitts Oscillator Frequency

f = 1 / (2π√(L · Cs)), Cs = C1·C2/(C1+C2)

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Formula

f = 1 / (2π√(L × Cs)), Cs = C1·C2 / (C1 + C2)

Description

The Colpitts oscillator sets its frequency with an LC tank in which the capacitance is a series combination of two capacitors whose junction provides the feedback tap. The series capacitance Cs resonates with the tank inductor. Colpitts oscillators are prized for clean output and good high-frequency stability, making them common in RF signal sources and crystal oscillators.

Variables

  • f — Oscillation frequency (Hz)
  • L — Tank inductance (H)
  • C1, C2 — The two tank capacitors (F)
  • Cs — Series combination C1·C2/(C1+C2)

Practical Notes

The capacitive divider C1/C2 also sets the feedback ratio. Replacing the inductor with a crystal makes a Colpitts crystal oscillator (Pierce-type), the most common microcontroller clock circuit.

Related Concepts

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