How Loudness Relates to Amplifier Power

Pretty much everyone who has been playing in the A/V game for more than a few minutes is aware how important amplifier power is … or at least or how important marketing departments tell us it is. It is rather obvious that a 110 watt amplifier is better than a 100 watt model and a 200 watt model is just the bee’s knees and will play much louder than that measly 100 watt model.

That’s just plain logic isn’t it?

Well, it turns out that this isn’t the case at all.

Apart from the fact that rated power outputs are subject to rather a lot of interpretation, some come with ratings so blatantly false that they should be reported to the authorities (this will be a subject of another article).

It turns out that how we actually hear doesn’t follow the logic marketers would like us to believe.

Loudness, or volume, is measured in Decibels SPL (Sound Pressure Level). The pressure part refers to Pascals, as in the same type of pressure you use in your car tyres, except in our case this pressure alternates between a positive and negative pressure. The decibel (dB) is derived from the Bell, with one dB equal to one tenth of a Bell, so 10 dB = 1 Bell, 20 dB = 2 Bell, etc.

Hold on to your hat now, as here comes the most important bit of this article.

An increase of 10 dB (or 1 Bell) is perceived as being twice as loud. 70 dB will sound twice as loud as 60 dB and 80 dB will sound four times louder than 60 dB. It’s a simple logarithmic scale.

Let’s move onto amplifiers and speakers, and see how this begins to relate to the above.

To keep the maths simple I’m going to assume that we have an 8 Ohm speaker that is rated to deliver 90 dB of sound with 1 watt input and with a maximum power rating of 200 watts.

According to what I’ve said above, if you want to hear your music twice as loud, your speakers will need to play at 100 dB.

Our false logic tells us that if we double the volume of our amplifier we will get to 100 dB, so we need 2 watts of amplifier power to get to 100 dB.

In reality though, doubling of amplifier power equates to a barely perceptible increase of only 3 dB. To get our doubling of volume we need TEN times the amplifier power. In our example this means we need 10 watts to get to 100 dB. If we now wish to double the level again, we now need 100 watts. Should you now want to start moving into rock concert type levels and 110 dB, you now need 1000 watts.

The maths now follows that if you really want to rock like you were at the concert and get to 120 dB, you would need a 10 000 watt amplifier. Of course if you were trying to pump a real 10 000 watts (or around 283 volts RMS) into your domestic loudspeaker, it would probably catch fire.

Looking into the reality of audio life we see that the difference in maximum levels between the 100 watt and 110 watt amplifier will be virtually undetectable, while the  theoretical level difference between the 100 and 200 watt amplifiers will be a just audible 3 dB.

If we add in another audio reality called ‘speaker power compression’, things start to look a little bleaker.

What happens in a loudspeaker is that as we put more power into it, voice coils and crossover components heat up and increase resistance. This creates a vicious cycle where to play louder we need more power, which heats up the speakers … meaning we need more power. The result is more and more amplifier power being wasted as heat. As power increases we also start getting close to the physical limitations of the speakers’ suspension. At some point the suspension of the drivers will simply stop them from moving any more. Voice coil and speaker gap geometry will also lead to compression.

This all means that our speakers become less and less linear as we increase amplifier power, so doubling the amplifier power won’t necessarily lead to a 3 dB increase in output. If our test speaker was properly rated, it would probably only start suffering from power compression at 20 to 30 watts. At 60 watts it would possibly only increase output by around 2.5 dB and with 120 watts being fed into it, output may increase by only 2 dB. Adding more power may only lead to hotter voice coils, particularly if the drivers have already reached their mechanical limit.

These are some of the reasons why Pro Audio speaker systems use lots of drivers — to spread the power around and keep temperature in check — and why they are often horn-loaded for greater efficiency.

You should hopefully by now have noted that small power differences between amplifiers will make almost no difference to the maximum volume you will hear. Double the power rating will make small differences and ten times the power will (so long as your speakers can handle all the power) will only yield a perception of twice as loud.

What is far more important than the absolute power rating of an amplifier is what it sounds like and how the power ratings were derived.

If you want to play your music or movies at concert levels you need efficient speakers that can handle power and decent amplification. And to get these you typically need deep pockets.

Joel Kopping