Quarter wavelength

[Vincent Kars]

A proper SPDIF cable should have an impedance of 75 Ohm and terminated with 75 Ohm (BNC) plugs.
In practice it is often RCA so no 75 Ohm termination at all.
Qne can also use an "analog" cable, whatever its impedance might be.
There is a rule of the thumb called the quarter wavelength rule. As long as the cable is shorter than 1/4 of the wavelength, is will work fine.

My problem is calculating the wavelength.
The SPDIF part is straight forward.

Sample rate	44,1​
bit	32​	1411,2​
channel	2​	2822,4​
Bi-phase encoded	2​	5644,8​	Mhz
Frequency		5644800​	Hz

Speed is simple too
Divide speed by the frequency of the signal

Speed vacuum	299.792.500​
Propagation in coax	0,7​
Speed cable		209854750​	m/s
Wave length		37,18​	m
Quarter Wavelength	4​	9,29​	m

Much longer than I expected.
However, in this article http://hinton-instruments.co.uk/reference/audio/digiprimer/pg02.htm the author says wavelength is about sine waves hence we should not use the frequency of the signal but the 7th order. Doing so:

Sample rate	44,1​
bit	32​	1411,2​
channel	2​	2822,4​
Bi-phase encoded	2​	5644,8​	Mhz
Freqency		5644800​	Hz
7 th harmonic	7​	39513600​	Hz
Speed vacuum	299.792.500​
Propagation	0,7​
Speed cable		209854750​	m/s
Wave length		5,31​	m
Quarter Wavelength	4​	1,33​	m

Now I end up with 1,33
What is the right value?

 

[Speedskater]

Only when the cable length is a significant fraction of the signal wave length does the cable's Radio Frequency Characteristic Impedance become important. In the case of SPDIF that length is greater than 30 feet. For shorter cables, a coax with a 50 to 125 Ohm impedance will do just fine. The connector impedance will never matter with SPDIF.

 

[wwenze]

The calculations seem right and I can't really say if either is wrong... It's more of a feeling thing

Below picture is taken from a supposedly open termination (yellow) vs good-terminated (red)

Between two peaks in the ringing, the reflecting signal has traveled 4 times the length of the cable. And it looks like it rang about 6 times in a half-period of the fundamental.

So basically how many harmonics / what length you want to use depends on how much ringing you can tolerate.

Complete impedance mismatch causes the most ringing, so with typical scenarios even with a small mismatch the situation is much better. The amplitude is less even if the duration is the same.

 

[radix]

If you look at IEC60958-1, the AES standard, they have different requirements for different interfaces. For unbalanced, it is simply a 75-ohm cable. No special terminators.

A frame is 2 sub-frames (L+R), so "frame rate" is sample rate * 32 bits.

The standard unbalanced connector is "8.6 of Table IV of IEC 60268-11:1987", but I don't happen to have that so do not know if that means BNC or RCA.

The receiver is supposed to present the correct termination

Also, your frequency calculations are not quite right. AES does not try to send a square wave. A "UI" is the timing interval for a given sample rate.

 

[Blumlein 88]

I suppose another approach is to record results using a DAC fed by 1 meter and by 15 meters or more. See how the results differ. Doesn't tell you about reflections in the cable, but tells you the effect upon the analog output.