Relate sensitivity/impedance to speaker efficiency


Can you help me relate speaker sensitivity and impedance to how efficient speakers are relative to one another?

What I mean is, given 2 speakers with the same or similar sensitivity (say 89 or 90), if one has a nominal impedance of 4 and another has a nominal impedance of 6, would the higher impedance speaker be easier to drive? Would the higher impedance speaker perhaps offer more flexibility in amplification (perhaps allowing the use of tubes?

What matters more for ease of amplification - a speaker with higher sensitivity or a speaker with a higher nominal impedance? (i.e. given similar nominal impedance, going from a speaker with a sensitivity of 87/88 to one with a sensitivity of 90/91; or given a similar sensitivity, going from a speaker with a nominal impedance of 4 to one with a nominal impedance of 6 or 8?)

I realize the answer to these questions is probably more complex, but are there some general rules to use as guidelines before actually trying the speakers out?
nnck
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.
Thanks for all the info. It's all good to know and I feel that I'm learning a lot.

To get into some specifics as Mmike84 suggested - A couple specific speakers I am considering are the Dali Helicon 800 and Acoustic Zen Adagio.

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?

The Adagio is a 6 ohm speaker and the website lists the sensitivity as simply 89 dB SPL @ 1 meter (doesnt indicate 1w or 2.83 volts). I noticed a couple of other websites reviewing the speaker list it as 89 dB / 1w / 1 meter. But I have sent an email directly to Acoustic Zen to ask them to clarify.

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.

Also, the impedance curve of the Adagio is fairly flat as seen here in the 6moon review: Adagio curve

Unfortunately I cant find the same curves for the Helicon 800. The closest I can find is the Helicon 400 from the stereophile review and it drifts a bit more: Helicon 400 curve

Anyway, the ability to use tube amplification successfully is one important criteria for me in choosing the right speaker. Of course, there are several other things I am considering (room size, placement, price, etc). But if anyone has any opinions about how these speakers might perform with tubes relative to one another, I'd like to hear more. Thanks again.
Meiwan, see if this helps:
at 8 ohms on 87db speakers, at 1 meter in front of them
1 watt = 87db
2 watts = 90db
4 watts = 93db
8 watts = 96db
16 watts = 99db
32 watts = 102db
64 watts = 105db
128 watts = 108db
It takes double the wattage to gain 3db.
You have to gain 10db to hear a "perceived" doubling of volume. No one is going to be able to tell the difference between an 87db speaker and a 90db speaker unless your amp is only 3 watts(2A3 tube amp).
However, impedance is another issue. Most solid state amps will double power output with halving of impedance. Some only give a 50% or so gain. Most tube amps will not give any increase in output.

For Nnck-are we talking stereo or theater. Almost any 2 channel amp will handle 4 ohms. Many theater receivers have issues driving five 4 ohm speakers. Be careful there. Do the math when looking but most theaters require 110db to 112db continuous output for THX or Ultra THX.
Elevick-
I am mainly concerned with 2-channel stereo right now. And I am mainly looking for help in comparing speakers relative to one another with respect to how well they might perform with tube amplification.

Specifically, I would love to hear what anyone has to say about Dali Helcion 800 vs Acoustic Zen Adagio given the info on sensitivity and impedance charts I provided in my post previous to yours. Thanks again everyone.
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
There are a couple of other things to consider, in addition to the points that Al makes. some are here:

http://www.atma-sphere.com/papers/paradigm_paper2.html

As I understand it though, both speakers are friendly to tubes. However impedance plays a couple of other roles. Output transformers in tube amps tend to be more efficient when driving higher impedances. Certainly speaker cables become less critical as the impedance of the speaker is increased. The result of this is that (all other things being equal) as you raise the speaker impedance it will appear to become smoother and more detailed, regardless of the amplifier used.

While 4 db may not seem to be much, that is more than doubling the amplifier power to make the same sound pressure. That can be a significant cost! So it should not be ignored.
Thanks for the additional info. Its all quite interesting I think.

And I'm still waiting for a response from Acoustic Zen to verify whether their sensitivity rating of 89 for the Adagio floorstanders is for an input of 1W or an input of 2.83 volts.
Nnck, First lets look at the two options as if they are both on the Power Paradigm (efficiency, 1 watt 1 meter).

Under this model the Acoustic Zen is 90/91db. The other speaker is 84/85db if it is also 4 ohms. If you want a tube amp the latter is going to be hard to live with unless you are near-field.

Now lets look at it as if both are under the Voltage Paradigm, (sensitivity, 2.83V 1 meter). Since the Zen is 6-8 ohms, and if the other speaker is 4, in this particular case the difference in sensitivity is about 3-4 db, which might make things easier to live with. But you should note that the reason the sensitivity spec exists is to accommodate amplifiers that can double power as the speaker impedance is cut if half. Tubes won't do that! Tube power is also expensive and while 3 db does not seem like a lot, it would be a mistake to think that you won't hear it.
It does seem to be "common knowledge" that 10 db sounds twice as loud.
However, what does that mean? Try listening to some music at a normal volume. Note the setting (this assumes you have a db scale to refer to).
then close your eyes, press and hold the Volume Up button until the sound is twice as loud to you. Then open your eyes & see how many db it took. It sure isn't 10 db for me.
Atmasphere: I use an ARC VS 115 tube amp in my rig. Its rated output is about 115 watts driven into an 8 ohm load. My speakers are nominally rated at 8 ohms, but as mentioned above, their impedance curve drops in the lower frequencies and their impedance is more capacitive in the low frequencies. The amp/speaker combo subjectively sounds ok to me and plays quite loud, but maybe I'm not listening critically enough.

You mention that "[o]utput transformers in tube amps tend to be more efficient when driving higher impedances. Certainly speaker cables become less critical as the impedance of the speaker is increased. The result of this is that (all other things being equal) as you raise the speaker impedance it will appear to become smoother and more detailed, regardless of the amplifier used."

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). I think I'm using Kimber speaker cables -- don't remeber which type. I also run my speaker cables off the 8 ohm taps. Do I gain anything by trying the 4 ohm tap?

Oh . . . one more factor to consider. ARC is replacing the SED "Winged C" 6550C power tube with the new Tung Sol KT-120 tube. I understand that the KT-120 tube will increase the power output of the VS 115 by about 10%. I also understand that the new KT-120 tube sounds better than the SED 6550C tube. Will the use of the new KT-120 tube change the impedance/capacitance analysis in any way? That is will my speakers sound "smoother and more detailed"?
Nnck, First lets look at the two options as if they are both on the Power Paradigm (efficiency, 1 watt 1 meter).

Under this model the Acoustic Zen is 90/91db. The other speaker is 84/85db if it is also 4 ohms. If you want a tube amp the latter is going to be hard to live with unless you are near-field.

I lost you just a bit here. Seem like under the Power Paradigm, if the Adagio is listed as 89dB efficient, despite it being a 6ohm speaker, it's efficiency is still just 89dB, not 90/91 (that is, if the efficiency was measured in units of 1w / 1m, it wouldnt matter that the impedance is 6 ohms, and not 8).

Is still havent heard back from Acoustic Zen, but the Dali Helicon 800 is very clearly labeled on the manufacturers website with a sensitivity rating of 89.5dB at 2.83 V/1 m. Which means it must be 86.5dB at 1w / 1m (since it is a 4 ohm speaker).

Acoustic Zen lists the Adagio with an Avg. Efficiency (not 'Sensitivity' if that is at all meaningful) of 89dB SPL @ 1 meter. 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). But if the measurement was at 1 w / 1 m (as some websites note), then the efficiency is simply 89dB, as stated.

Of course, I am new to this. So I dont know if I have it all right.
Still hoping for some explanation of the comments I made directly above.

But I did hear back from Acoustic Zen this afternoon and they verified that the efficiency of the Adagio floorstanding loudspeaker is about 89dB and the measurement is for 1w / 1m.

So it looks like I am comparing 2 speakers: the Adagio (6 ohm speaker) is 89 dB at 1w / 1m vs. the Dali Helicon (4 ohm speaker) which is 89.5dB but at 2.83 volts / 1m.
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 Al and Atmasphere: I experimented with the 4 Ohm taps. Although I can not offer a technical explanation, I can only say that my speakers sounded terrible across the board when played off the 4 Ohm taps: way less efficient, rolled off treble and muddy bass. By contrast, everything was great on the 8 Ohm taps. As I mentioned above, the speakers are nominally rated at 8 Ohms, so I guess that's the way the manufacturer intended them to be played.

I plan to switch out the 6550C power tubes for the KT 120 tubes in a month or two. There's an outfit that breaks the tubes in for 72 hours and matches the tubes using three criteria. The cost is less than half of what ARC charges. I may try them out. When I do, I'll report back. Hifigeek1 is an ARC buff, so he may be interested. Thanks again.
Hi Al, I was involved in a rather ambitious speaker cable project about 25 years ago, wherein we used a time delay reflectometer to analyze a variety of cable geometries. What we found is that characteristic impedance does indeed play a role (not nearly so important as it does at RF frequencies though) in the performance of the cable.

If the load is highly reactive, then the characteristic impedance can be important if the amplifier is otherwise unstable with the back EMF. Just a side note- obviously I am way OT here.

Nnck, my apologies- you were correct and it was me that was getting confused with all the conjecture. But as it has turned out, the less efficient speaker is on the Voltage Paradigm and the more efficient one is on the Power Paradigm, so now we find that it is true that one is about 4 db more efficient than the other, despite the sensitivity of them being almost the same.
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
Agreed!