Relate sensitivity/impedance to speaker efficiency

The simple answer is the sensitivity is the sound pressure level with 1 watt of amplification at a specific frequency. Given 3db is a perceived doubling of loudness, going from 87 to 90 means the latter will sound twice as loud with the same power input.

Impedance is the resistance load put on the amplifier. A lower impedence puts more load on the amp. So a nominal 4 ohm load puts twice the load on the amp vs. an 8 ohm load. Hence you will see specs saying an amp will put out 50 watts into 8 ohms or 100 watts into 4 ohms - same loudness.

Generally, pretty much any amp will drive an 8 ohm load - sensitivity variances will affect perceived loudness only. A more robust power supply is needed to drive a lower load so that's where you need to be more selective in matching.

Hope this helps.

Actually, I beleive a doubling in perceived loudness corresponds to a 10 dB increase. A 3 dB increase in sensitivity means the speakers need 1/2 the power input to give the same perceived loudness. So, yes, more sensitive speakers are easier to drive to louder levels. Impedence correlates with how much current the amplifier must provide at a given power level. So, an amp with lower current capabilities, such as a tube amp (as a generalization) will find a higher impedence speaker easier to drive.

As you suggest, it is more complicated than that, as nominal impedence of a speaker does tell you whether there is a very low impedence at a particular frequency, or whether phase shifts at some frequencies may require more current capability. I'll leave those details to the real experts.

A point which can be important to keep in mind is whether the speaker sensitivity is defined with respect to an input of 1 watt, or with respect to an input of 2.83 volts.

2.83 volts corresponds to 1 watt into 8 ohms. So for an 8 ohm speaker, the sensitivity number would be the same for both definitions.

However, for a 4 ohm speaker 2.83 volts corresponds to 2 watts, so a sensitivity of 90db for a 2.83V input would be equivalent to only 87db for a 1 watt input.

2.83 volts into 6 ohms corresponds to 1.33 watts, which means that a sensitivity of 90db for a 2.83V input in that case would be equivalent to about 88.75 db for a 1W input.

Although as was indicated above speaker impedance can vary considerably as a function of frequency, so it's all a very inexact science.

What matters more for ease of amplification - a speaker with higher sensitivity or a speaker with a higher nominal impedance?

Sensitivity in itself just relates to how much power is required to produce a given volume. "Ease" of amplification, and versatility with respect to what kinds of amplifiers would be good matches sonically, are dependent on nominal impedance (the higher the better); how constant the impedance is as a function of frequency (the flatter the curve the better); and to what extent the impedance is capacitive, especially at frequencies where the impedance magnitude reaches low values. Capacitive impedances correspond to negative phase angles in impedance plots that you will see in some reviews, especially those in Stereophile.

Regards,
-- Al

No one says it better than Al! the only thing to add, is that many tube amplifiers will sound "better" driving a higher impedance load, which I am sure Al and Atmasphere can provide the technical back-up for. This is reported to be especially true for output transfomerless (OTL) tube amps, which is the reason that some people use impedance multiplying devices like the Speltz boxes between OTLs and lower impedance speakers. Just to show that, generally, you can't generalize, many people report that Sound Lab electro-stats mate very well w OTL amps, and they have a low pretty low impedance at some frequencies.

You could try asking in this forum about specific speaker models as it is likely someone here has empirical knowledge of how they perform with different amps.

However I have been surprised many times by how well some speakers sound when matched with a tube amp that supposedly was way too underpowered. My general rule of thumb is a good sounding amp usually sounds good regardless of the speakers, and you'll never know for sure until you try it.