Speaker sensitivity ratings and amplifier power

10 * log (power) = decibel

10 ^ (decibel / 10) = power

10db increase (10x the power) is perceived as twice as loud

Most desktop-size speakers are in the mid 80s db/W @ 1m sensitivity wise. We’ll call it 85db for the sake of calculating stuff. The sensitivity rating means that with one watt of power, you’ll get 85db of sound at one meter away. For reference, 80db is pretty loud. It’s about the level of a running garbage disposal or an alarm clock. You can listen at 85db for eight hours before you start risking hearing loss; this is also the sound level at which OSHA will fuck your shit up.

For nearfield listening, there may be less than a meter between you and the speakers. If you halve the distance, you can add 6db to the sensitivity rating. Now with the same speakers you’re getting 91db at half a meter with one watt of power. You should probably turn it down a touch to protect your hearing (2 hours at 91db is the maximum recommended duration). Every halving of the power deducts 3db, so one quarter of the power (0.25W) gets you back down 6db to a non-litigious 85db. If you want to listen at 80db (which is comfortably loud, believe me) you only need around 100mW.

Aren’t decibels fun?

This goes to say that you do not need a whole bunch of power for nearfield listening, even if the speakers have a low sensitivity rating. And if you have high sensitivity speakers in your “main rig”, a single-ended low wattage amplifier works there, too. Say you have speakers rated at 95 db/W @ 1m and like to listen around 80db. If you listen at one meter, you only need 32mW. If you listen at two meters, you need just 125mW of power.

The above discussion of power and decibels does not take into account dynamic headroom. It’s always good to have some power in reserve for music dynamics. Or for cranking it when OSHA isn’t paying attention. I try to have at least 10db to spare (10x the power) over what I expect my average listening levels to be. If you didn’t fall asleep while I fapped around with decibels and logarithmic math, you noticed that average, safe listening levels (80-85db) need only a fraction of a watt with average sensitivity speakers nearfield or high sensitivity speakers at a regular distance.  Ten times more power is just a couple watts and will often get you pretty comfortable listening levels with headroom to spare.

Just make them some high quality watts.

Back at it finally!  This is an excerpt from the first speaker amp write-up I’m doing for the site.  Happy Cinco de Mayo!

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Coming soon to a workbench near you…

In a world where near-field and headphone listening has become an unstoppable force. Where every DIY builder is bored to death of rational and safe two-stage, single-ended triode designs. Where power supplies have become an afterthought and parts values are just plugged and chugged. Prepare your butt for a new madness. Prepare it for La Luciérnaga…

the-big-sheet

Note db scale for the predicted frequency response graph: +/- 1 dB from 40-20khz. If that’s not good enough, I’ll show you how to make it even better. There’s mucho tube math coming your way, amigo.

Here’s the worksheet I used to create the above:

two-stage-set