Necessity of 75 ohm cable?

Question

(NB: I feel this is better here than super-user because it is hardware based)

Trying to connect my laptop's S/PDIF output to some headphones. Setup is: Laptop -> 3.5mm to RCA cable -> Co-ax to Toslink converter -> toslink optical cable -> headphone decoder box -> headphones

Everything from the Co-ax to toslink converter works fine from an alternate source RCA S/PDIF connector on my desktop's motherboard.

Using a random 3.5mm mono jack to RCA cable works but it is very quiet (as in laptop volume settings maxed out, and headphone volume control (active (yes they need their own power supply!)) also maxed out and I can barely hear the sound above the noise.

Would a genuine 75\$\Omega\$ cable (eg. this) sort out the attenuation issue?

I am thinking that the laptop lacks the impedance matching output system my desktop has, so the laptop is setup for:

spdif ----
        |
      ----
      |  | 75 ohm
      |  |
      |  |
      ----
        |
      ---- GND

hence provides \$I=\frac{V}{R}=\frac{0.5}{75}\simeq6.7\mbox{ mA}\$

but because of my random cable (which multimeter measured at ~2\$\Omega\$) sees:

spdif ----
        |
       ----
       |  | 2 ohm
       |  |
       |  |
       ----
        |
       ---- GND

hence the voltage across the load (the converter box) is \$V=IR=13\mbox{ mV}\$ instead of the \$0.5\mbox{ V}\$ it should be.

Is this anywhere near correct? And is a proper 75\$\Omega\$ cable the solution?

Answer 1

'75ohm cable' refers to a reactive load - it's the capacitance and inductance of the cable, not the resistance end to end

spdif is a digital thing - 2 ohms from one end to the other of a digital cable sounds high if anything but shouldn't be an issue - because it's a digital signal loss will cause noise, not loss of volume