Audio interconnect cables explained
- Electrical equivalent circuit
- The most important factor: line driver output impedance
- Frequency response of a 10 meter long cable
- Table: maximum cable length vs. output resistance and attenuation at 20 kHz
- Some notes on nonlinear distortion, phase-shift and group delay
The subject of this analysis is unbalanced line level signal transmission. Interconnect cables that used for line level signal transmission shouldn't be confused with S/PDIF digital interconnects or analog video cables. All use the same RCA type connector, but composite video and S/PDIF require '75 Ohm' coaxial cables.
Last edited: Feb. 28, 2019
Audio interconnect cables (sometimes called RCA cables) are still an important part of many audio systems. As with speaker cables, there are a lot of myths and pseudo-science in their marketing. According to these claims some expensive and exotic cables sound better than those cheap ones that you can find in an 'average' electronics or AV store.
Interconnect cables connect the 'line out' or the 'headphone out' of the signal source to the 'line in' of the amplifier. Connectors can be RCA, XLR or headphone plugs (also known as TRS or tip-ring-sleeve). Interconnects transmit max. 2 Volt amplitude voltages and the load is more simple than a loudspeaker.
The longest and heaviest 'interconnects' on Earth lie deep in the oceans: the transatlantic telecommunication cables and trans-pacific cables. The telephone cables between Europe and North America were in operation until the mid-1990s (today data travels in optical cables) and an average cable had a full bandwidth of 400 kHz (!). The goal was speech intelligibility with as many simultaneous connections as possible and not audio fidelity. I just mentioned these cables, because some folks believe that science can't explain a two meter long audio cable...
For a detailed analysis of interconnect cables we need a relevant electrical model of the full system (equivalent circuit, RC model). If we are interested in our cable's response up to 100 kHz (which is five times the frequency range of the human hearing!), this simple RC model is perfectly valid up to 200 meters (model is valid for '75 Ohm' coaxial cables up to 400 meters). I think that's enough, this length is far beyond any room size. As we can see the propagation of the electromagnetic wave is negligible in interconnect cables with normal room length.
Line out, line in and the interconnect cable (unbalanced system, grounding not shown)
In the model, the voltage source Ug and the Rg series resistance represent the line out or headphone output. Rin is the input resistance of the amplifier, Uin is the voltage on the input resistor (which will be amplified by the amplifier). Rs is the total resistance of the conductor and the shield, Cp is the capacitance between the conductor and shield. Due to the high input resistance (minimum 600 Ohm), the effect of inductance is negligible, the resistance of the cable does not affect the amplitude response up to a few hundred meters and the skin effect is not significant in audio cables. So we can ignore these in further analysis.
A typical line out has an output impedance from 100 to 600 Ohms, with lower values being more common in newer equipment. Output resistance of headphone connections ranges from 30 to 200 Ohms (although values higher than 100 Ohm are quite rare nowadays). The input resistance falls within 10 kOhm and 100 kOhm. The distributed capacitance of interconnect cables varies between 120-300 pF/m (picofarad per meter). For more information about line in and line out, see the related Wikipedia article.
Line level circuits use the impedance bridging principle, in which a low impedance output drives a high impedance input. In this scenario the dominant parameters are the capacitance of the cable and the output resistance of the source. The output resistance of the signal source (line driver) and the capacitance of the cable forms a low-pass filter. The higher the capacitance of the cable (the longer the cable) and the higher the output resistance of the source, the lower the cut-off frequency. Thus, the frequency response of the cable (and any electronic device) "on its own" is meaningless. Attributing characters like dynamics or soundstage to an interconnect cable is just fantasy.
The graph above shows the low-pass response of a ten meter (32.8 ft) long interconnect cable (TINA simulation). The cable is driven by a voltage source that has a 600 Ohm output resistance. The input resistance is 10 kOhms, the cable's distributed capacitance is 300 pF/m (so 3000 pF is the total). This is essentially a "worst-case" simulation, as both the 300 pF/meter and the 600 Ohm output resistance can be taken as an upper limit. The difference from the linear response at 20 kHz is 0.21 dB only!
The insulation between the shield and the conductor has a great influence on the distributed capacitance. The two most common materials for wire insulation are polyvinyl chloride (PVC) and polyethylene (PE). The outer jacket is PVC in almost every cable. Typically, cheapest cables have very thin (dia. 1 mm) PVC insulation around the conductor. These cables have a distributed capacitance of 300 pF/m. With polyethylene wire insulation the most common values are 150 pF/m.
The following table is a summary of the maximum cable length values for various output resistances and attenuation parameters. The distributed capacitance is 300 pF/m and the decibel value is the deviation from linear response at 20 kHz. E.g. a 600 Ohm line out with a seven meter long '300 pF/m' cable has 0.1 dB attenuation at 20 kHz.
|Max. cable lengths in meters|
|Output resistance||for 300 pF/m cables|
|[Ohm]||0.1 dB||0.3 dB||0.5 dB|
The above table refers to cables with a distributed capacitance of 300 pF/m, which is valid for the 'cheapest' cables. In the case of cables with polyethylene wire insulation (150 pF/m) the length values can be doubled!
There is a small noise filter capacitor (100 pF - 330 pF) at the input of every amplifier, and its role is to prevent radio frequency noise getting into the amp. This capacitance is added to the capacitance of the cable, but it pale into insignificance in the audio range. If we want to be accurate, we can subtract one meter from a 300 pF/m cable (and two meters from a 150 pF/m cable after doubling the values).
With a 600 Ohm line out the full audio frequency band can be transmitted within 0.1 dB error up to 14 meters (46 feet) with a 'better' cable and up to 7 meters (23 feet) with a cheapest, high capacitance cable. If we take into account, that modern equipments have much lower output resistance (100 - 200 Ohms), transmitting audio frequency signals in a home audio system shouldn't be a problem.
Nonlinear distortion is simply non-existent in audio cables. There is no need to deal with nonlinear effects, because if we don't exceed the 0.5 dB limit at 20 kHz (which requires a long cable), the capacitance and resistance of the insulation (dielectric) will have so tiny effect on the overall response, that even the possibility of the distortion doesn't exist. The leakage current (dielectric loss) is only significant above 1 MHz even with the worst dielectric (PVC).
We don't have to be afraid of phase shift (or time smearing) either. Phase shift doesn't mean anything in itself, what is important is the change in the group delay: the varying time delay in frequency. Even for a 'large' 0.5 dB relative attenuation at 20 kHz the time shift between 20 Hz and 20 kHz is only 300 nanosec (which is 20 deg phase shift). This is 1000 times lower than the lowest group delay difference that a human ear can resolve in the most sensitive range (at 2 kHz).
The audibility of group delay 'distortion' with the interaural time delay (ITD) are often confused. ITD is important for binaural hearing and localization, the audibility of group delay 'distortion' is about how humans can hear transient smearing.
Dispersion at audio frequencies is only a problem with very long cables - cables which are at least several kilometers long. But in this case the amplitude response will be bad too, not just the phase and - what is interesting - correcting the amplitude response simply cures phase and timing problems.
Audio cables that carry low level signals require protection against EMI (Electromagnetic Interference). RFI (Radio Frequency Interference) is only a concern at those frequencies where the cable becomes an antenna. Therefore interconnect cables are shielded and - in the vast majority of cables - the shield acts as a signal return too. Audio cables have spiral wrapped shield and despite being the simplest and cheapest shielding method, it is enough for audio applications. In order to lower RFI, amplifiers have low pass filters at their input (effective above 1 MHz).
There are few problems with interconnect cables, e.g. in cheaper cables sometimes the wires break close to the connector (this may happen due to the regular cleaning of DVD player, stereo receiver). In this case the solution is a cable with a higher quality strain relief. On the other hand wasting a lot of money for exotic, hi-end interconnect cables is unnecessary.