Colpitts Oscillator Frequency
f = 1 / (2π√(L · Cs)), Cs = C1·C2/(C1+C2)
Quick answer
This calculator solves f = 1 / (2π√(L × Cs)), Cs = C1·C2 / (C1 + C2) for Frequency. With Inductance 100 µH, Capacitor C1 100 nF, Capacitor C2 0.22 µF, the result is 60.7 kHz. It solves in 4 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
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.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| f | Frequency | MHz | Hz, kHz, MHz, GHz |
| L | Inductance | µH | nH, µH, mH, H |
| C1 | Capacitor C1 | nF | pF, nF, µF, mF, F |
| C2 | Capacitor C2 | nF | pF, nF, µF, mF, F |
Step by step
- 1. What you know: Inductance 100 µH, Capacitor C1 100 nF, Capacitor C2 0.22 µF
- 2. The relation: f = 1 / (2π√(L × Cs)), Cs = C1·C2 / (C1 + C2)
- 3. Substitute: L = 100 µH, C1 = 100 nF, C2 = 0.22 µF
- 4. Result: Frequency = 60.7 kHz
Worked examples
Minimum range
Given: Inductance 100 nH, Capacitor C1 100 pF, Capacitor C2 0.22 nF
Result: Frequency = 60.7 MHz
Low range
Given: Inductance 1 µH, Capacitor C1 1 nF, Capacitor C2 2.2 nF
Result: Frequency = 6.07 MHz
Typical
Given: Inductance 100 µH, Capacitor C1 100 nF, Capacitor C2 0.22 µF
Result: Frequency = 60.7 kHz
High range
Given: Inductance 0.47 mH, Capacitor C1 1 µF, Capacitor C2 2.2 µF
Result: Frequency = 8.854 kHz
Maximum range
Given: Inductance 4.7 mH, Capacitor C1 10 µF, Capacitor C2 22 µF
Result: Frequency = 0.8854 kHz
Solving for each variable
Solve for Frequency
Inductance 100 nH, Capacitor C1 100 pF, Capacitor C2 0.22 nF → 60.7 MHz
Solve for Inductance
Frequency 100 kHz, Capacitor C1 100 pF, Capacitor C2 0.22 nF → 36.84 mH
Solve for Capacitor C1
Frequency 100 kHz, Inductance 100 nH, Capacitor C2 0.22 nF → -0.22 nF
Solve for Capacitor C2
Frequency 100 kHz, Inductance 100 nH, Capacitor C1 100 pF → -100 pF
How Frequency changes with Inductance
| Inductance (input) | Frequency (result) |
|---|---|
| 10 µH | 0.1919 MHz |
| 25 µH | 121.4 kHz |
| 50 µH | 85.84 kHz |
| 75 µH | 70.09 kHz |
| 100 µH | 60.7 kHz |
| 150 µH | 49.56 kHz |
| 0.2 mH | 42.92 kHz |
| 0.4 mH | 30.35 kHz |
| 0.7 mH | 22.94 kHz |
| 1 mH | 19.19 kHz |
The same result in other units
| Unit | Value |
|---|---|
| Hz | 60700 |
| kHz | 60.7 |
| MHz | 0.0607 |
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<p><a href="https://vbatpower.com/formulas/colpitts-oscillator/">Colpitts Oscillator Frequency</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Colpitts Oscillator Frequency?
Use f = 1 / (2π√(L × Cs)), Cs = C1·C2 / (C1 + C2). With Inductance 100 µH, Capacitor C1 100 nF, Capacitor C2 0.22 µF, Frequency works out to 60.7 kHz.
What is the formula for Colpitts Oscillator Frequency?
The formula is f = 1 / (2π√(L × Cs)), Cs = C1·C2 / (C1 + C2). 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.
How do you find Inductance when you know the other values?
Rearrange for Inductance: with Frequency 100 kHz, Capacitor C1 100 pF, Capacitor C2 0.22 nF, Inductance is 36.84 mH.
How do you find Capacitor C1 when you know the other values?
Rearrange for Capacitor C1: with Frequency 100 kHz, Inductance 100 nH, Capacitor C2 0.22 nF, Capacitor C1 is -0.22 nF.
What units does Colpitts Oscillator Frequency use?
Frequency is shown in Hz, kHz, MHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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