Relate sensitivity/impedance to speaker efficiency

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

The Dali Helicon 800 is a 4 ohm speaker with a listed sensitivity of 89.5. I see the units shown on the Dali website are 2.83 V/1 m. According to what Almarg is saying this would correspond to a sensitivity of 86.5 for a 1w input - is that right?

Yes, assuming the specs are accurate (which is not always the case).

If the 1w / 1m unit is true for the Adagio, then according to what Almarg is saying, to directly compare these speakers you would have to say the sensitivity of the Dali is 86.5 vs 89 for the Adagio for a 1w input.

Yes, assuming the specs are accurate.

The impedance curve of the Adagio is fairly flat as seen here in the 6moon review.

Looks about as good as it gets, in terms of flatness and avoidance of severe capacitive phase angles. I would expect it to work beautifully on the 4 ohm tap of most medium powered tube amps. Perhaps even with an OTL (output transformerless) amp, with the flatness of the curve possibly overshadowing the low nominal impedance. I would definitely expect it to work well with an OTL with a pair of Zero autoformers connected between amp and speakers.

The impedance curves of the Dali 400 don't look particularly worrisome either, but I would not assume they are similar to those of the 800, as the driver complements are quite different. You may want to search the discussion threads and system descriptions here for the 800, and see what amps people are using with it.

With respect to how much power you would need, obviously that depends on listening distance, room size, volume level, and on the dynamic range of the music you listen to (the difference in volume between the loudest and softest notes, classical symphonic music being one of the most challenging kinds in that respect). For most people, I would expect 50W to 100W to be comfortably adequate with the Adagios, assuming 89db/1W/1m, and perhaps 80W or more for the Dali's. Those numbers can vary widely, though, depending on the variables I listed, since as was mentioned by the others a factor of 10 difference in power (which is 10db) corresponds roughly to just a factor of 2 difference in subjectively perceived volume.

Regards,
-- Al

Nnck, IMO everything in your two posts immediately above is correct, with the very minor exception (which is also irrelevant, based on the response from Acoustic Zen) that in the statement "If that is a measurement at 2.83 volts / 1m, that would mean a sensitivity of 87.5dB (since it is a 6 ohm speaker)" the figure "87.5" should be "87.75." The interpolation between 8 ohms and 4 ohms is not a linear function, since the dB scale is logarithmic, and impedance factors in as a reciprocal.

Best regards,
-- Al

02-11-11: Bifwynne
My question is whether I should think about raising the impedance load in my speaker circuit, perhaps by trying "high(er) impedance" speaker cables (if such things exist).

No, there are many reasons why that is not done and should not be done. For starters:

1)A lot of the amplifier's power capability would be converted into heat in the cables, instead of powering the speakers.
2)Tonal imbalances would result, due to interaction of wire resistance with variations of speaker impedance as a function of frequency.
3)Woofer damping would be severely degraded.

You may be thinking of something called "characteristic impedance," which is not the same thing as "impedance," and which does commonly have fairly high values (sometimes approaching 100 ohms). "Characteristic impedance" is, misleadingly, sometimes referred to as "impedance" for short. "Characteristic impedance" is a different subject altogether, which is primarily relevant at rf frequencies, and does not directly relate to your question.

Do I gain anything by trying the 4 ohm tap?

The only way to tell for sure is to try it. Given that your speakers have a lower impedance in the bass region than at higher frequencies, you may find that the bass is both tighter and stronger (relative to higher frequencies) on the 4 ohm tap. The maximum amount of power that the amp can deliver on the 4 ohm tap, though, will be less compared to what it can deliver into the SAME speakers on the 8 ohm tap.

Will the use of the new KT-120 tube change the impedance/capacitance analysis in any way?

Don't know.

Best regards,
-- Al

Thanks, Ralph. Yes I recall discussing those experiments with you and others in a thread here about a year or so ago. And it certainly does seem conceivable that characteristic impedance could affect the sonic performance of a speaker cable in some systems, due to the effect you mentioned, as well as because of its correlation with inductance, and perhaps because of its relation to antenna and vswr effects.

As you realize, though, my point was simply that it is not relevant to Bif's question about easing the load on the amplifier, in the manner that going to a higher impedance speaker would ease the load.

I'll add, also, that to the extent that characteristic impedance may have audible consequences in some systems, both the anecdotal indications and some technical considerations would seem to suggest that in general lower is better. The technical considerations being the correlation between low characteristic impedance and low inductance, and possibly (although I am dubious) the impedance match with the speaker at high frequencies.

Best regards,
-- Al