Emulating capacitance and resistance of long cable lengths.

[Chris935]

I am building an automated mic cable tester. It drives a conductor high one one end, then reads the status of each pin on the other end. One limiting factor in how fast this can be done is the time constant created by the resistance and capacitance of the cable, and the output impedance of the source.

Say I want this to work on up to 1KM of cable, but I would like to be able to test this without having that much cable coiled up beside me, how do I do this? I can easily create something that has the same total capacitance and resistance but I'm not sure if this is applicable, as the capacitance and resistance is distributed evenly along the length. Am I correct in my assumption that the current charging the first metre of capacitance only flows in the first metre of cable? ie The first metre's capacitance only has 2 metres worth of resistance between it and the source whereas the last metres same capacitance has 2 kilometres worth of resistance?

Mic cable has about 0.085 Ohms and 50pf per metre.

Thanks.

[Ian.M]

You could probably do well enough with  a lumped element model of a transmission line.   1.7 ohms and 1nf for every 20m, so cascade 50 pairs of series resistors and shunt capacitors to ground for a 1KM cable equivalent.   Build it with SMD parts directly soldered to a copper strip for the ground then slide it into a copper tube for screening.

You can easily model a lumped line in LTspice^*, so try it out and see if it does what you expect of the real cable.

* Here's a sim I prepared earlier you can hack about with till it matches your cable

[PTR_1275]

Eevblog 756 has a cable simulator in it. Not sure if it’s similar to what you are wanting or if it would work, but might be useful to watch nonetheless.

[Zero999]

I am building an automated mic cable tester. It drives a conductor high one one end, then reads the status of each pin on the other end. One limiting factor in how fast this can be done is the time constant created by the resistance and capacitance of the cable, and the output impedance of the source.

Say I want this to work on up to 1KM of cable, but I would like to be able to test this without having that much cable coiled up beside me, how do I do this? I can easily create something that has the same total capacitance and resistance but I'm not sure if this is applicable, as the capacitance and resistance is distributed evenly along the length. Am I correct in my assumption that the current charging the first metre of capacitance only flows in the first metre of cable? ie The first metre's capacitance only has 2 metres worth of resistance between it and the source whereas the last metres same capacitance has 2 kilometres worth of resistance?

Mic cable has about 0.085 Ohms and 50pf per metre.

Thanks.

At low frequencies, when the cable has a load impedance far greater than its characteristic impedance, then it can simply be modelled as its parasitic capacitance, in series with its resistance.

Your assumption is incorrect. If the current flows down the entire length of cable, through the resistance and charging up the capacitance.

If the end of cable is short circuited, it can then be treated as an inductor, at low frequencies.

At much higher frequencies, the cable needs to be treated as a transmission line, because it takes a finite amount of time for changes in voltage and current to travel down the cable and get to the other end.

Assuming the signal propagates down the length of the cable, at half the speed of light, the wavelength of the upper audio band at 20kHz is:
Lambada =  (0.5*299.792458*10⁶)/20*10³ = 14.99*10³m

Transmission line effects become significant when the length of the cable is significant, compared to the wavelength of the signal and 1km is about ¹/₁₅ of a wavelength, so you're probably around the limit here.

Another potential issue is the impedance of the microphone being too high to drive the cable, which will happen before you reach the above figure. If the cable's capacitance is 50nF and the impedance of the mic. is 500R, then the lower cut-off frequency will become:

FC = 1 / (2pi * 50*10^-9 * 500) = 6.4kHz.

You should consider installing a pre-amplifier, as close to the mic. as possible.