Why you can't improve your hi-fi system by upgrading the mains cable
It's almost impossible to believe, if you have even the most rudimentary
understanding of electronics, but you can actually spend more than
£400 on a mains cable for your hi-fi system. It's not clear to
me whether the people who manufacturer and sell these products genuinely
think they offer the benefits they claim, or whether it's all just
a cynical ruse to part the gullible from their cash. Are they
sitting around in their offices,
giggling behind their hands at the gullibility of purchasers?
Or do their claims stand
up to any kind of scientific scrutiny at all?
Resistance
The most common claim for the efficacy of premium mains cables is that they have conductors with exceptionally low electrical resistance. Could this be possible?
Well, yes. Electrical resistance can be decreased in a number of ways, most obviously by making the conductors thicker. Resistance per unit length is (at mains frequencies) inversely proportional to the conductor area -- double the area, halve the resistance. It's also possible to use exotic materials: silver is more conductive than copper, gold more conductive still. To the best of my knowledge nobody makes entire cables out of gold (yet) -- it would be fabulously expensive even by ridiculous standards we're considering here. Still, increasing conductor area is a straightforward way to reduce electrical resistance.
So a thicker, heavier, and thus more expensive, cable could have a lower electrical resistance than a cheap one. Here's the problem, though -- we generally don't power our hi-fi systems with a power station in the same rack (yet). The mains cable plugs into a domestic electrical socket which connects to a fuse box which connects to an area transformer which connects to a regional transformer which connects to... well, it hardly matters.
What actually matters is how the electrical resistance of the mains cable compares with that of the electrical supply as a whole. We can't easily measure the supply resistance (although there is specialist equipment that can), but in the UK it's usually taken to be between 0.1 and 0.5 ohms at the subscriber's switchboard. If we assume that there is 20m of mains cabling between the switchboard and the electrical outlet, that will add about 0.4 ohms to the total resistance at the outlet. So the total supply resistance at the electrical outlet can be taken to be 0.5-0.9 ohms. The electrical resistance of one metre of perfectly standard mains flex is about 0.02 ohms. So the mains cable from the outlet to the hi-fi equipment contributes at maximum 0.02/(0.02+0.4+0.1) = 4% of the overall resistance, and at minimum 0.02/(0.02+0.4+0.5) = 2%.
If a premium cable had -- and let's be generous here -- one quarter the resistance of the regular cable, then it would contribute about 0.5% -1% of the overall resistance of the electrical supply to the equipment. Another way of looking at this is to see that that overall electrical resistance of the system can only be reduced by 0.02 ohms at best because that's what would be achieved by a super-conducting cable -- one with no resistance at all.
Still, a reduction in electrical resistance of the order 2% or so, although small, is still a reduction. We could measure that, if we had sensitive enough equipment. But is there any reason to think this will have any effect on sound quality?
Frankly, it's not easy to see how. The reason for this is that power amplifiers -- the components usually claimed to benefit most from improved mains cables -- are unaffected by mains supply resistance. Let's see why.
The amplifier is driving two speakers (perhaps more) with a nominal resistance of 8 ohms. That popular "8 ohm" figure is an impedance, really, not a resistance -- speakers are essentially conductors at DC. Still, that distinction is a technicality here. The amplifier is driving an overall load resistance of 4 ohms (two 8 ohm speakers effectively in parallel) with a source resistance of about 1 ohm. That's like filling up a gardener's watering can with a fire hose. A one percent, or even a ten percent, improvement in the flow in the fire hose isn't going to make any appreciable difference.
It's fair to say that, in certain conditions, the effective resistance of the speakers drops dramatically. This is particularly true for very low-frequency transients (the pluck of a bass guitar, for example). The resistance of the speakers in that situation might be as low as 1 ohm. In that situation the supply of power to the amplifier becomes critically important, but there are two reasons why it's not affected by the mains cable.
First, in a situation like this, a fractional change in the cable resistance will have no appreciable benefit -- there simply isn't enough energy in the system even if the mains cable were a superconductor.
Second, amplifier designers are aware of this problem -- they've had at least seventy years to work on it. The typical solution is to fit the amplifier with enormous capacitors to store energy that can be discharged into the speakers when there are transients. These capacitors are the specific solution to the problem of insufficient energy supply and, if they are inadequate, the deficiency will not be made good by a miniscule change in supply resistance.
In short, reduced resistance as an explanation for the efficacy of premium mains cables is busted.
Electrical interference
Premium mains cables are usually provided with conductive shielding around the power conductors. This shielding may or may not be connected to some kind of ground -- perhaps the earth terminal of the plug. The 'faraday cage' effect does not rely on grounding for its reduction in magnetic coupling; but straightforward capacitive coupling -- if it even exists in a mains cable -- might be affected by grounding.
Here is what one manufacturer has to say about the product:
"The main benefit is the shielding which helps to ensure that other low level signal cables are not affected by the close proximity of the [...] mains cable - induced RF interference has been one of the biggest bug-bears of high quality audio and video reproduction [...]
There are two effects that need to be considered here, and at a range of different frequencies. First, we need to think about noise being coupled into the equipment that has been induced into the mains cable. Second, there's the question whether the mains cable can itself induce noise into nearby equipment.
There's no question that a domestic electrical outlet is electrically noisy, at a huge range of frequencies. At the low end of the spectrum is the 50Hz frequency of the mains itself. In the middle of the range we have electromagnetic signals from radio, television, etc. Then at the top of the band there are microwave signals from mobile phones and wifi equipment. This noise is on the mains conductors, because it is on every piece of material that is capable of carrying an electrical current. For better or worse, that's the world we now live in.
Can the shielding prevent mains-born interference being electromagnetically coupled to nearby equipment? Well, yes, probably. But it's too late -- the noise has been coupled into the equipment directly on the mains cable: induced noise is irrelevant when that happens. No amount of shielding will change this -- it's like locking the axe-murderer in the house with you, rather than outside.
So can the shielding prevent interference being coupled into the mains cable? Well, again, yes; but it's worth asking what difference that will make, if the supply is itself polluted.
The solution to the problem of RF interference in hi-fi equipment -- if there is a problem at all -- is mains filtration. That is, the provision of high-frequency filters right in the mains conductors, and as close to the equipment as possible. But wait -- the equipment designers have already thought of that -- this kind of filtration is perfectly common-place in the power supply circuits of decent hi-fi equipment. If yours doesn't have it, you can buy an inline supply filter for about £10.
Now, in the interests of fairness, I should point out that RF induction is a strange phenomenon. It isn't always easy to predict how it will behave in practical set-ups. It's impossible to say for certain that shielding your mains cable won't have some effect. However, the unpredictability of RF behaviour is such that the effect, if there is one, is just as likely to be negative as positive. If you really do have a problem with RF interference, it's unlikely that shielding your mains cable is going to help. But don't take my word for it -- you can wrap your existing mains cable with aluminum foils -- which is a decent conductor -- for a minimal sum and try it for yourself.
Oxygen-free copper (and similar)
A common claim of premium cables -- not specifically mains cables, but all kinds of cables -- is that they are made of oxygen-free copper (OFC) or some other extraordinary material. OFC materials do not have a substantially different overall conductivity than ordering copper at audio frequencies so, if they have any benefit, it doesn't arise from the ordinary bulk properties of the material. One proponent says:
"Copper purity affects its crystal structure and the accuracy of phase transmission, which is not dependent on tiny differences in conductivity, meaning resistance."
I'm not at all sure what the 'accuracy of phase transmission' is, but it clearly has something to do with the propagation of a signal. I'm sceptical about the benefits of OFC and similar substances in a signal path, but that's irrelevant here because the mains cable carries no signal.
Oxygen-free copper: busted (at least in mains cables).
Length. Length??
One product has as its main selling point it's length. It's specifically 1.65m long, because:
"Listening tests showed consistently that the best sound quality was obtain (sic) from cables cut to a length of 1.65m [...] This aligns very closely with the quarter wavelength of the 50 Hz mains frequency of 1.7m"Well, leaving aside the question of why the 50Hz mains frequency is relevant, it's worth asking what exactly has a quarter wavelength of 1.7m at 50Hz. It's certainly not an electro-magnetic wave in an electrical cable. In general
wavelength (metres) = speed of propagation (metres/sec) / frequency (Hz)
The speed of propagation of an electromagnetic wave in cable is of the order 2x108 m/sec. It's not quite the speed of light, because the propagation is affected by the dielectric properties of the cable, but it's in that region. So the wavelength at 50Hz is 4,200 km. Yes, that's kilometres. What does have a quarter wavelength of 1.7m at 50Hz is a sound wave, propagating in air. The speed of propagation is about 343 m/sec, so 343/50/4 = 1.715 metres.
But so what? No actual sound travels (we hope) in the mains cable; and, even if it did, the propagation velocity would not be the same as in air. And even if it were, it's not remotely clear how the wavelength would be relevant, at any frequency, let alone 50Hz.
The manufacturer seems to want us to believe that somehow the mains electrical energy has to be coupled into the hi-fi equipment by a process of impedance matching, as happens in radio-frequency antenna circuits. But, even if that were true -- and of course it isn't -- the wavelengths are completely wrong -- wrong by factors of a thousand or more, for the length of 1.7m to be relevant.
Of all the claims that are made for mains cables, this one is just so utterly absurd that I can't believe it was ever seriously made.
What's really going on here?
None of the mechanisms claimed by manufacturers for the efficacy of premium mains cables stands up to any rigorous analysis. If these products work, the explanation is in the same class as that for homeopathy -- sympathetic magic, or its contemporary equivalent, the placebo effect.
I've known many people -- a number that surprises me -- who claim that their cars run better when they are clean and shiny. There really isn't any scientific explanation for this, either but, presumably, the effect is there, because it's an effect on a person's perception. In the end, this is personal enjoyment we're talking about, not a Mars mission.
There's an intriguing story in Robert Pirsig's Zen and the Art of Motorcycle Maintenance about the owner of a brand new bike who found that the handlebars were loose in the yokes. This made the machine difficult to ride and, presumably, less enjoyable. The author's proposed solution was to cut a beer can into strips, and bolt the strips under the handlebar mounts. This, it seems, was something that the frustrated biker was not prepared to do with his shiny new motorcycle. Instead, he purchased a set of branded handlebar shims from a specialist supplier at, we presume, considerable expense. In the end, the branded shims were made of exactly the same material as the beer cans, and both would have been invisible when installed.
I don't know if this story is true, but it certainly sounds plausible. We develop attachments to our possessions, and the pleasure we take in them is only loosely related to the function they fulfil. I own many things which have no discernible function at all -- probably we all do. Part of the pleasure of owning a top-shelf hi-fi system is the knowledge that everything about it is as perfect as it can possibly be. We can't easily change the distance of our houses from the power station, but we can do what little we can by fitting a better mains cable.
More cynically, I suspect that if you spend a lot of money on a premium mains cable you have to hear a difference in the sound. If you don't, it's hard to avoid having to conclude that you're a fool.
