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Cable Capacitance High-Frequency Rolloff

Calculate the high-frequency rolloff (-3 dB point) caused by cable capacitance interacting with source impedance.

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Formula

f_c = 1 / (2π × Z_s × C_total)

Z_s— Source impedance (Ω)
C_total— Total cable capacitance (F)

How It Works

Unbalanced audio cables (guitar cables, RCA cables, TS patch cables) have significant capacitance per metre — typically 80–150 pF/m. This cable capacitance, combined with the high source impedance of passive instruments (guitar pickups: 100 kΩ–1 MΩ, passive bass pickups: 50–500 kΩ), forms a simple RC low-pass filter. The −3 dB cutoff frequency is f_c = 1 / (2π × Z_source × C_total), where C_total = capacitance_per_metre × length. Above f_c, treble and presence frequencies are attenuated at −20 dB/decade (first-order rolloff), reducing the bright, airy quality of the instrument signal. Long cables with high-capacitance conductors can roll off at 5–10 kHz, noticeably dulling the tone. Balanced cables and buffer preamps (active pickups, guitar buffers) have low source impedance and are essentially immune to this effect.

Worked Example

Guitar pickup source impedance: 250 kΩ. Cable: 100 pF/m, 5 m long. Total capacitance: C_total = 100 × 5 = 500 pF = 500 × 10⁻¹² F Cutoff frequency: f_c = 1 / (2π × 250,000 × 500 × 10⁻¹²) = 1 / (2π × 1.25 × 10⁻⁴) = 1 / (7.85 × 10⁻⁴) = 1273 Hz Rolloff at 20 kHz: ΔdB = −20·log₁₀(√(1 + (f/f_c)²)) at 20 kHz = −20·log₁₀(√(1 + (20000/1273)²)) ≈ −23.9 dB At 1273 Hz the signal is already 3 dB down, and 20 kHz is severely rolled off. Switching to a low-capacitance cable (60 pF/m) with 5 m gives C = 300 pF and f_c = 2122 Hz — still significant rolloff for a passive guitar.

Practical Tips

  • ✓Use a guitar buffer pedal (unity-gain JFET or op-amp buffer with 1 MΩ input, <1 kΩ output impedance) at the instrument end of the cable. This reduces effective source impedance to near zero, making cable capacitance irrelevant.
  • ✓Capacitance specs in cable datasheets are given as pF/m (or pF/ft). Look for values below 75 pF/m for guitar applications — this doubles the cutoff frequency compared to a 150 pF/m cable at the same source impedance.
  • ✓The 'presence peak' at the resonant frequency of pickup inductance and cable capacitance is a deliberate tonal characteristic of many electric guitars. Some players use cable capacitance intentionally to shape their tone — changing cable length or capacitance changes the resonant frequency.

Common Mistakes

  • ✗Assuming the problem is only with long cables — even a 3 m cable with 100 pF/m = 300 pF combined with a 500 kΩ pickup source has f_c ≈ 1060 Hz. Short cables still cause significant rolloff with high-impedance passive sources.
  • ✗Ignoring the guitar tone pot — the tone control capacitor (usually 22–47 nF) is already intentionally rolling off treble. The cable capacitance adds to this. At low tone settings, cable capacitance effect is masked; at maximum tone (bright), it is fully audible.
  • ✗Thinking balanced cables are capacitance-free — balanced cables also have capacitance (typically 30–100 pF/m), but because they operate at low source impedance (150–600 Ω), the resulting f_c is in the MHz range and completely inaudible.

Frequently Asked Questions

Instrument-level inputs on audio interfaces typically have input impedance of 1 MΩ or higher, and the cable run is very short (or via a direct connection). This preserves more high-frequency content than a long cable run to an amplifier with a 1 MΩ input. The interface impedance combined with cable capacitance still forms an RC filter, just at a much higher cutoff frequency.
Negligibly. Microphone outputs have source impedances of 50–200 Ω. Even 50 m of cable at 100 pF/m = 5000 pF gives f_c = 1 / (2π × 150 × 5×10⁻⁹) ≈ 212 kHz — far above the audio band. Balanced cable capacitance only matters for digital audio interfaces (AES/EBU) at megahertz signalling rates.
Active pickups (EMG, Fishman) include a built-in preamp with output impedance of 10–100 Ω, lowering the source impedance by 1000–10,000×. This pushes the cable capacitance rolloff frequency into the megahertz range, making it completely inaudible regardless of cable length.

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