Calculation - cable length and cable capacity cutoff frequency microphone - sengpielaudio
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Calculation: Cable Length, Cable Capacitance,
and
Treble Loss (Attenuation, Cutoff Frequency) •

mic cable
Cable and treble damping
treble cut filter (low pass)
Simplified principle
C = Cspec ·
d
RC-pad = cable

A frequently asked question is at which cutoff frequency has the microphone cable a
treble loss of (−) 3 dB?

Cables are characterized by the capacity of the cable between the leaders, the
resistance, inductance of the cable along the leader, and the current crowding, which
boost the resistance at high frequencies. The
microphone cable usually has a
capacitance from wire to wire of about 100 pF per meter.
The line resistance, and the inductance is usually negligible in practice. Each wire has
an unavoidable cable capacitance, that leads to the damping of high frequencies
(
cable loss). Because the input resistance (load) is large against the small output
resistance (source), the load can be neglected.

Calculating the treble cutoff frequency of a cable

Source impedance Zout   ohms
Capacitance C per m   pF/m
Cable length d   meters
                        
Cutoff frequency fc   Hz
Zout = Output impedance of microphone, source impedance
Cspec = Specific capacitance of the cable in pF per m cable lenghth
d = Length of the cable in m            C = Cspec · d


Formula for the cutoff frequency of the treble damping:
Cable cutoff frequency - sengpielaudio

Another frequently asked question is of how long can the microphone cable be,
without having treble loss?

Calculation of the length of a cable at 3 dB treble attenuation

Source impedance Zout   ohms
Capacitance C per m   pF/m
Cutoff frequency fc   Hz
                        
Cable length d   meters
Formula for the length of the cable for a given cutoff frequency:
Cable length - sengpielaudio
fc = Cutoff frequency at (−)3 dB treble loss
Zout = Output impedance of microphone, source impedance
Cspec = Capacitance in pF per m cable lenghth     C = Cspec · d

If you want to know how long the cable can be and permit a level damping
of only 1 dB, you need to enter the double value of the cutoff frequency.

Cable characteristic impedance is a cable characteristics which is only
valid for high frequency signals. Multimeters use DC current for resistance
measurements, so you cannot measure the cable impedance using your
multimeter or other simple measurement equipments.

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