Cable capacitance

A lot of mystery attached to cables and the impact on sound in systems. So some basics to keep the myths going….!

We all (?) know every cable has a capacitance value valued in picofarads per meter. This is the relationship of the dielectric of cable sleeve and conductors. It is like a capacitor in parallel between signal and ground. This capacitance acts as a low pass filter (rolls off tremble notes at 3db slope (3db per octave)). This is easy to calculate as below. The ruling factors are the total capacitance and source impedance. Total capacitance will be higher the longer the cable length. One just takes the specified picofarads per meter and multiply by length of cable used to get total capacitance.

Now…Cable manufactures tend to keep the value secret so as to entertain, I suppose, the mystical side of things. Professional cables are obliged to indicate these as they are providing pro audio users that will run very, very very…, long lengths of cable on set or in studio, meaning 100’s of meters.

Anyway to the basics and if you follow the maths below you get for a source impedance of say 100ohms and 2 meter cable with a very high capacitance (300pf/mtr) a roll-off of treble at…..2 652 582 hertz.

Or source 20ohms and 10 metres of 200pf cable : 3 978 874 hertz

Now 200pf or 300pf is huge! Typical cables will be under 30pf/mtr so in real life the roll off will be at an even higher frequency!…..

With our short lengths at home we should be okay I guess! Although perhaps my speakers and ears are not that good, meaning I cannot hear of feel that roll off at ultra high frequency.

You need some totally lousy cables and very high output impedance to get a roll off within hearing range….

Just as a reminder :

The higher the cable capacitance the lower the low pass frequency
The higher the output impedance the lower the low pass frequency

So you can run your calculations :

fc = Cutoff frequency at (−)3 dB treble loss in Hz
Zout = Output impedance of microphone, source impedance
Cspec = Specific capacitance of the cable in pF per m cable length
d = Cable length of the cable in m C = Cspec × d
1 pF (Picofarad) = 10−12 F (Farad)

Formula for the cutoff frequency fc of the (−)3 dB treble damping:

20140421-175706.jpg

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