How Much Power Do You Need?

While discussing amplifier design with a British amplifier manufacturer I was a little surprised when he said that they needed to produce amplifiers of 500 watts or more 'for the American market'. A survey carried out on this website showed that only a small minority of those responding were interested in even a 100 watt version of my amplifier, and some even wanted a lower power version!

To put this question in perspective, consider how much actual acoustic sound power is needed to provide an adequately high peak level. A peak sound pressure level of 100dB (relative to 0.0002 micro-bar) seems a reasonable aim. Prolonged exposure to this level would cause significant hearing loss, and few listeners would feel comfortable listening to music at a much higher level. So how much power do we need to produce this level? A sound level of 100dB corresponds to a power density of a millionth of a watt per square cm. Put in more familiar terms, a power source of 1 watt will give this sound level at a distance of 3 metres. This is a fairly typical listening distance from a loudspeaker in domestic use, and so we require a maximum acoustic sound power of only 1 watt from our loudspeakers. Even this figure is an over estimate because it assumes free air conditions and a single non-directional source. Real speakers are directional, usually used in pairs, and also in an enclosed room the reverberant conditions add to the sound level, so somewhere around 300mW per channel is actually all we need.

Looking at acoustic power levels from musical instruments we find similarly small values, for example a clarinet produces a peak level of 50 mW, and a piano 400 mW. (Sivian, Dunn & White, Jour. Amer. Soc. Acoust, Vol.2, p330, 1931).

So why should anyone want to use a 500 watt power amplifier? Part of the reason is that many loudspeakers have such a poor efficiency. Less than 1 % efficiency is not unusual, and of course if only 1 watt out of every 100 ends up as sound while the rest is converted directly into heat, then 100 watt plus amplifiers start to seem more reasonable.

There are some very good reasons for not being entirely happy with this high power low efficiency approach. Apart from the high cost of both amplifier and speakers capable of handling such power levels, there are good reasons why the resulting sound quality will be poorer than a low power high efficiency alternative. The big question is what happens to those hundreds of wasted watts? The answer is that most is converted to heat in the voice coils of the speaker units. This has one important effect, which is to increase the temperature and consequently the resistance of the voice coil. There are reports of resistance values doubling at high power levels. This will produce a reduction in sound level, and so loud passages of the music will be reproduced at a reduced level. This effect is known as compression.
Another effect is a result of the frequency range usually being split between two or more drive units, which in general will not change their resistances in the same proportion, and so the acoustic output levels will fall to a different degree over different frequency ranges, and so the frequency response will change at different sound levels.
Using heavy gauge speaker cables to ensure a good damping factor at the bass resonant frequency seems to be a good idea, but the power dissipation from the first few seconds of music may add more resistance to the speakers than a few metres of even the cheapest cable.
One other effect is the modulation of the voice coil resistance by low frequency signals, which would be expected to generate third harmonic distortion, though in practice other sources of low frequency speaker non-linearity are likely to be far greater.

The effects are certainly real, and the variations in voice coil resistances are well known to high power speaker manufacturers ( or at least some of them ). Peter Walker, of Quad fame, mentioned the effect on damping factor as far back as 1974. (Wireless World, May 1974, p148, 'Letters to the Editor', followed up July 1974 p228). He said that even applying 4 watts to a typical speaker for a few seconds would increase its resistance by half an ohm, and that high quality monitor speakers used in recording studios frequently doubled their resistance at high levels. Figures for even a genuine high power unit, the Fane Crescendo 12in bass speaker, rated at 100W (continuous rating!) with a 2 inch diameter voice coil showed a 22% resistance increase even at 21 watts. ( A.E.Falkus, Wireless World Nov 1972 p543-544 ). The effect will of course be greater for some types of music than for others depending on peak to average power ratio, dynamic range, duration of peak levels and so on.

There are many claims to hear differences in sound quality between different speaker cables, which most published tests seem to agree have no measurable harmonic distortion and give only very small difference in frequency response, and yet the much larger effects of high power dissipation are not given a similar level of attention. I can certainly understand the designers of high power amplifiers not wanting to acknowledge the thermal problem. (Though there are well known but inconvenient solutions, such as current drive amplifiers, motional feedback and so on.).

But what is the alternative? I personally use low efficiency speakers with an 85 watt per channel amplifier. My previous system, which I still regret dismantling, used concrete horn loaded speakers, and an active crossover filter and 5 watt class-A amplifiers. In my opinion the sound quality was better than anything else I have heard, and high sound levels were produced effortlessly. The frequency response had some unfortunate resonances which made some types of music sound less pleasing, but most who heard it were impressed by the sound quality. The important feature of this sort of system is the high acoustic efficiency, and figures over 20 % have been claimed for similar speakers. This is not intended as an advert for horn loaded speakers. These are inconveniently large, and not entirely suitable for mass-production. What I am trying to discourage is the assumption that high power is a 'good thing'.

It is instructive to measure the peak power level at whatever sound level you prefer. When I did this myself I was surprised to find that with the amplifier output peaking at only 2 volts it was already fairly loud (equivalent to peak power level 500mW into 8ohms). Sound level is entirely a personal choice, I mention it only in the hope that listeners will check for themselves what amplifier power they need rather than just believe what they are told. Borrow an oscilloscope, if you don't already have one, and set what you believe is a reasonable sound level for domestic listening using speakers of average sensitivity (e.g. 88dB per watt), then check the peak voltage across one of the speakers. You may be surprised at the result.

There is evidence described here that exposure to high sound levels, e.g. 110dB for an hour, causes a temporary shift in the threshold of hearing, typically over 20dB, but over 40dB at 4kHz in some cases, so turning up the volume too far may reduce the audible dynamic range in addition to the thermal compression effects mentioned above. Other effects of high sound levels include permanent hearing loss in the important 3 to 4 kHz range, and temporary ringing, similar to tinnitis, believed to be a result of trauma to the inner ear.

For those of us who just like to relax with some soothing music after a hard day at the office 20 to 30 watt amplifiers should be more than adequate. Those who like their music loud, and don't care if they damage their hearing and annoy their neighbours, can find plenty of more powerful designs on other sites.