Audio Cable High-Frequency Rolloff
f_3dB = 1 / (2πRC)
Quick answer
This calculator solves f_3dB = 1 / (2πRC) for Rolloff Frequency. With Source Impedance 0.47 kΩ, Cable Capacitance 100 pF, the result is 3.386 MHz. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Long audio cables form a low-pass RC filter between the source output impedance and the cable capacitance, causing high-frequency rolloff that dulls the sound. This is particularly problematic for high-impedance sources like passive guitar pickups (5-15 kΩ) and some microphone circuits. The -3 dB point is where the signal is attenuated by half power. Cable capacitance typically ranges from 30-100 pF per foot, so a 20-foot guitar cable can have 2000 pF or more of capacitance.
Variables
- f — -3 dB rolloff frequency (Hz)
- R — Source output impedance (Ω)
- C — Total cable capacitance (F)
Practical Notes
A passive guitar pickup with 8 kΩ impedance driving a 20-foot cable at 80 pF/ft (1600 pF total) rolls off at about 12.4 kHz, audibly dulling the high end. Buffer pedals and active pickups solve this by presenting a low source impedance (typically < 1 kΩ). For professional audio, keep cable runs short or use balanced low-impedance connections (150Ω mic level or 600Ω line level).
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| f | Rolloff Frequency | Hz | Hz, kHz, MHz, GHz |
| R | Source Impedance | Ω | mΩ, Ω, kΩ, MΩ |
| C | Cable Capacitance | pF | pF, nF, µF, mF, F |
Step by step
- 1. What you know: Source Impedance 0.47 kΩ, Cable Capacitance 100 pF
- 2. The relation: f_3dB = 1 / (2πRC)
- 3. Substitute: R = 0.47 kΩ, C = 100 pF
- 4. Result: Rolloff Frequency = 3.386 MHz
Worked examples
Minimum range
Given: Source Impedance 1 Ω, Cable Capacitance 1 pF
Result: Rolloff Frequency = 159.2 GHz
Low range
Given: Source Impedance 10 Ω, Cable Capacitance 10 pF
Result: Rolloff Frequency = 1.592 GHz
Typical
Given: Source Impedance 0.47 kΩ, Cable Capacitance 100 pF
Result: Rolloff Frequency = 3.386 MHz
High range
Given: Source Impedance 4.7 kΩ, Cable Capacitance 1 nF
Result: Rolloff Frequency = 33.86 kHz
Maximum range
Given: Source Impedance 47 kΩ, Cable Capacitance 10 nF
Result: Rolloff Frequency = 0.3386 kHz
Solving for each variable
Solve for Rolloff Frequency
Source Impedance 1 Ω, Cable Capacitance 1 pF → 159.2 GHz
Solve for Source Impedance
Rolloff Frequency 5 Hz, Cable Capacitance 1 pF → 31830 MΩ
Solve for Cable Capacitance
Rolloff Frequency 5 Hz, Source Impedance 1 Ω → 31.83 mF
How Rolloff Frequency changes with Source Impedance
| Source Impedance (input) | Rolloff Frequency (result) |
|---|---|
| 47 Ω | 33.86 MHz |
| 117.5 Ω | 13.55 MHz |
| 0.235 kΩ | 6.773 MHz |
| 0.3525 kΩ | 4.515 MHz |
| 0.47 kΩ | 3.386 MHz |
| 0.705 kΩ | 2.258 MHz |
| 0.94 kΩ | 1.693 MHz |
| 1.88 kΩ | 0.8466 MHz |
| 3.29 kΩ | 0.4838 MHz |
| 4.7 kΩ | 0.3386 MHz |
The same result in other units
| Unit | Value |
|---|---|
| Hz | 3386000 |
| kHz | 3386 |
| MHz | 3.386 |
| GHz | 0.003386 |
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<p><a href="https://vbatpower.com/formulas/audio-cable-rolloff/">Audio Cable High-Frequency Rolloff</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Audio Cable High-Frequency Rolloff?
Use f_3dB = 1 / (2πRC). With Source Impedance 0.47 kΩ, Cable Capacitance 100 pF, Rolloff Frequency works out to 3.386 MHz.
What is the formula for Audio Cable High-Frequency Rolloff?
The formula is f_3dB = 1 / (2πRC). Long audio cables form a low-pass RC filter between the source output impedance and the cable capacitance, causing high-frequency rolloff that dulls the sound.
How do you find Source Impedance when you know the other values?
Rearrange for Source Impedance: with Rolloff Frequency 5 Hz, Cable Capacitance 1 pF, Source Impedance is 31830 MΩ.
How do you find Cable Capacitance when you know the other values?
Rearrange for Cable Capacitance: with Rolloff Frequency 5 Hz, Source Impedance 1 Ω, Cable Capacitance is 31.83 mF.
What units does Audio Cable High-Frequency Rolloff use?
Rolloff Frequency is shown in Hz, kHz, MHz, GHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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