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Part 2:

The full theory is higher electronics engineering and there are courses and text books for that. The essential facts needed to be known are these:

Any electrical cable has to be used correctly as a transmission line when the length exceeds a quarter wavelength of the frequency of the signal.

The "wavelength" is found by dividing the speed of light (299,792,500m/s) by the signal frequency. For a 48kHz stereo AES/EBU or S/PDIF signal the bit rate is 3.072MHz, but it is bi-phase encoded so 7.144MHz is present too. As that is a square wave and the theory is for a sinewave let's consider the 7th harmonic, this would have a wavelength of almost 7m making a quarter wavelength 1.75m. Thus any cable over 6 feet long should be of the correct type and termination to prevent unwanted side effects.

Originally the highest sample rate was 48kHz, but this has been doubled and doubled again. Consequently the wavelength is halved. This is why cables that work at one rate become problematic when used for higher rates.

Looking at it another way, the quarter wavelength for 20kHz is over 12,000 feet which is why this phenomena may be ignored in analogue audio cabling.

Cables have to be the correct characteristic impedance.

This is in the domain of Electric Field theory. Most people can visualise magnetic fields going between north and south poles, electric fields can be considered similar going between conductors at different voltages. An electric field exists between a cable conductors and the impedance is given by a formula based on the dimensions of the cable conductors and the dielectric constants of the materials inbetween. Although impedance has units of Ohms it is not the same as the dc resistance measured with an multimeter because it is frequency dependent. Digital twisted pair cable has a typical impedance of 110 ohms and this can be controlled by the twist weave and the material used for the insulation. Coaxial cable is often 50 ohms or 75 ohms and this is determined by the inner conductor and screen diameters and the insulation. This is why ordinary audio twisted pair cable is not suitable for AES/EBU and ordinary screened cable is unsuitable for S/PDIF, although you may get away with using it in lengths shorter than the quarter wavelength.

Cables have to be terminated with the characteristic impedance at each end.

When an electrical signal travels along a transmission line it can get "reflected" by any impedance mismatch. If a pulse signal hits the end of a cable that is either unconnected (impedance = infinity) or shorted (impedance = zero) then all of it gets bounced back. This effect is nulled when the cable has an impedance connected across it that is equal to the characteristic impedance of the cable, usually this is a simple 75 ohm or 110 ohm resistor. At any other termination impedance a corresponding proportion of the signal gets reflected.

Reflections will also occur at any impedance mismatch along the cable length e.g. joins and connectors. A BNC connector is specifically designed to preserve 50 ohms or 75 ohms impedance through a mated plug and socket. (Yes, there are two types and they should not be mixed!) The impedance is controlled by the shape of the pin and insulator. Also crimped types should be used with the proper tooling, it should be obvious now that stripping the screen on a cable and soldering it to a connector constitutes an impedance mismatch.

If a reflection does occur at any point the signal will bounce back and corrupt itself. An analogue example would be a ghost image on a television picture, note this is always to the right because it is a delay. When a digital signal bounces back the data just gets garbled and will cause the receiving circuitry to reject it and an audio signal will become intermittent like analogue gating effects.

Cabling arrangements have to preserve the transmission line.

This means a linear topology with termination at each end. There should be no terminators along the cable run and no branches going off to other devices.

Ideally there should be a single cable run between two two pieces of equipment with internal termination. AES/EBU devices do not usually have switchable termination. Coaxial devices may have a switch on the panel close to input connector and it is possible to daisy chain such devices. The usual method is to have BNC T-pieces on each equipment socket with BNC cables between each and a BNC coaxial terminator on either extreme.

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Last updated: 28 September 2014