RC Phase-Shift Oscillator Frequency
f = 1 / (2π · R · C · √6)
Quick answer
This calculator solves f = 1 / (2π × R × C × √6) for Frequency. With Resistance 10 kΩ, Capacitance 100 nF, the result is 64.97 Hz. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
An RC phase-shift oscillator uses three cascaded RC sections to provide the 180° of phase shift needed (together with the inverting amplifier’s 180°) for oscillation. With three equal sections the oscillation frequency includes the √6 factor. The amplifier must make up the network’s loss, which for the three-section case requires a voltage gain of at least 29.
Variables
- f — Oscillation frequency (Hz)
- R — Resistance of each section (Ω)
- C — Capacitance of each section (F)
Practical Notes
The loop attenuation at the oscillation frequency is 1/29, so the amplifier gain must be ≥ 29. More sections lower the required gain but complicate tuning. Best for fixed audio-frequency sine generation.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| f | Frequency | kHz | Hz, kHz, MHz, GHz |
| R | Resistance | kΩ | mΩ, Ω, kΩ, MΩ |
| C | Capacitance | nF | pF, nF, µF, mF, F |
Step by step
- 1. What you know: Resistance 10 kΩ, Capacitance 100 nF
- 2. The relation: f = 1 / (2π × R × C × √6)
- 3. Substitute: R = 10 kΩ, C = 100 nF
- 4. Result: Frequency = 64.97 Hz
Worked examples
Minimum range
Given: Resistance 100 Ω, Capacitance 100 pF
Result: Frequency = 6.497 MHz
Low range
Given: Resistance 1 kΩ, Capacitance 1 nF
Result: Frequency = 64.97 kHz
Typical
Given: Resistance 10 kΩ, Capacitance 100 nF
Result: Frequency = 64.97 Hz
High range
Given: Resistance 100 kΩ, Capacitance 1 µF
Result: Frequency = 0.6497 Hz
Maximum range
Given: Resistance 1 MΩ, Capacitance 10 µF
Result: Frequency = 0.006497 Hz
Solving for each variable
Solve for Frequency
Resistance 100 Ω, Capacitance 100 pF → 6.497 MHz
Solve for Resistance
Frequency 100 Hz, Capacitance 100 pF → 6.497 MΩ
Solve for Capacitance
Frequency 100 Hz, Resistance 100 Ω → 6.497 µF
How Frequency changes with Resistance
| Resistance (input) | Frequency (result) |
|---|---|
| 1 kΩ | 0.6497 kHz |
| 2.5 kΩ | 0.2599 kHz |
| 5 kΩ | 129.9 Hz |
| 7.5 kΩ | 86.63 Hz |
| 10 kΩ | 64.97 Hz |
| 15 kΩ | 43.32 Hz |
| 20 kΩ | 32.49 Hz |
| 40 kΩ | 16.24 Hz |
| 70 kΩ | 9.282 Hz |
| 100 kΩ | 6.497 Hz |
The same result in other units
| Unit | Value |
|---|---|
| Hz | 64.97 |
| kHz | 0.06497 |
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<p><a href="https://vbatpower.com/formulas/rc-phase-shift-oscillator/">RC Phase-Shift Oscillator Frequency</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate RC Phase-Shift Oscillator Frequency?
Use f = 1 / (2π × R × C × √6). With Resistance 10 kΩ, Capacitance 100 nF, Frequency works out to 64.97 Hz.
What is the formula for RC Phase-Shift Oscillator Frequency?
The formula is f = 1 / (2π × R × C × √6). An RC phase-shift oscillator uses three cascaded RC sections to provide the 180° of phase shift needed (together with the inverting amplifier’s 180°) for oscillation.
How do you find Resistance when you know the other values?
Rearrange for Resistance: with Frequency 100 Hz, Capacitance 100 pF, Resistance is 6.497 MΩ.
How do you find Capacitance when you know the other values?
Rearrange for Capacitance: with Frequency 100 Hz, Resistance 100 Ω, Capacitance is 6.497 µF.
What units does RC Phase-Shift Oscillator Frequency use?
Frequency is shown in Hz, kHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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