6 Loudspeaker cabinets
6.10 Efficiency and sensitivity
Loudspeakers are very inefficient devices. Nearly all input power is converted to heat, and only a very small portion (2-5% typically for live sound drivers) is converted to acoustic energy. This is inherent to the working principle of a loudspeaker. However, modern computer aided design and the use of high tech plastics as well as Neodymium magnets have made it possible to increase efficiency considerably in the past 10 years, sometimes up to 20%.
Trade-off
If a speaker is optimized for efficiency, it will have less low frequency response and/or need a large cabinet. In bass speaker design, one of the most important trade-offs is the "efficiency vs. size vs. low end" trade-off. You can't have all three. If you want flat response down to 20 Hz, you'll end up with either a very large cabinet or an inefficient one. If you want high efficiency, you won't have a small cabinet or a good low frequency response. If you want a small cabinet, you'll have to settle for low efficiency or poor low end. You can jiggle the equation, but with the current state of technology, you can't simply have a small, efficient, deep sounding cabinet.
Efficiency
Efficiency, also known as "reference efficiency", symbol η0, is the theoretical fraction of electrical input power that is converted to acoustic output power with the driver mounted in an infinite baffle. It's a calculated specification, that serves mainly as an approximation of what a driver is capable of, and as an easy way to match driver units in a multi way speaker cabinet. In other words: it's a design tool.
Efficiency is heavily dependent on the free-air resonance frequency Fs of the loudspeaker, in such a way that when Fs doubles, efficiency increases by a factor of eight (with all else equal). It's also dependent on the equivalent air volume Vas, and, to a lesser degree, on the electrical Q factor Qes. In algebraic form it looks like this:
| η0 = 9.64 · 10-10 · Fs3 · Vas / Qes | Vas in liters |
| η0 = 2.73 · 10-8 · Fs3 · Vas / Qes | Vas in cubic feet |
The result of this equation is a fraction. Multiply by 100 to get percents. Or apply the following equation to convert to dB(SPL):
| 112.2 + 10 · 10log (η0) |
Reference efficiency is not tied to a specific frequency range.
Sensitivity
Sensitivity is the real-world efficiency, and is a measured specification. It's different from the reference efficiency in that it takes a lot of real-world influences into account; most importantly the cabinet, but also impedance variations, by assuming that amplifiers are voltage sources, not power sources. Because of this, sensitivity is specified at an input voltage level, unlike efficiency, which is specified at an input power level. External factors are ruled out as much as possible by performing the measurements in an anechoic space. It is, as such, a much more useful specification. In most cases, a cabinet's sensitivity is higher than the separate drivers' reference efficiency. For multi driver cabinets like 4x10s the mutual coupling 
effect of the drivers greatly contributes to this.
When specifying sensitivity, it is good custom to include the measurement voltage and distance to avoid confusion. For instance:
| sens = 96 dB(SPL) (2.83 V, 1 m) |
However, most manufacturers rate their cabinets are a power level of 1 Watt. While not entirely correct, it prevents confusion, because what is really meant is "1 Watt at the cabinet's nominal impedance". Specifying a 4 Ω cabinet at 2.83 V would translate to 2 Watts, increasing the rating by 3 dB, making comparison with an 8 Ω cabinet confusing.
Sensitivity is usually specified as an average sound pressure level over the cabinet's intended frequency range.
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© Joris van den Heuvel 2001-2009