Speaker's efficiency, sensitivity and impedance

Hi folks, this has been discussed earlier but could you please explain once more in a rather simple manner what the relation is between a speaker's efficiency, sensitivity and it's impedance? Does a low impedance loudspeaker also have low efficiency? In reversal: does a low efficiency speaker have low sensitivity and low impedance? Thank you in advance.

A speaker's(or speaker system's) efficiency/sensitivity rating is determined by it's SPL output in DB with a 1 Watt(or 2.83v) input, measured on axis at a distance of 1 meter(in an anechoic chamber). The speaker's impedance is not relevant in this measurement.
Looks like you've got an impedance obsession disorder!

Would you buy a car based on the sole parameter of engine displacement? If I told you one vehicle had a 6.2 liter engine and another had a 7.8 liter one, would you be tempted to say which one is the fastest?

The displacement number alone tells you nothing. It is a lot more useful to know the smaller engine goes in a Corvette and the larger one is a diesel from an Isuzu delivery truck.

A speaker's efficiency is due to many factors. Magnet type & strength, precision of voice coil gap, the number of turns on the coil winding, the voice coil gauge, diameter & other physical attributes, cone, spider & suspension materials and design, size, crossover design and cabinet design and more are involved in the performance of a speaker.

I'm curious as to why you are so intent to reduce such a complex issue to such a limited, simplistic view.
I feel for you, it appears as if you are hung up on amps lately. I assume for your sound labs- forgive me if I am wrong.

Sensitivity=efficiency= how much power(watt) for how much sound(spl)-typically measured in db/w {decibels(perceived loudness) per watt(measure of power)}.

Impedance is AC (alternating current) resistance and is not related directly to sensitivity. Impedance pertains to the load characteristics of the speaker. A watt is voltage x current and ideally the amplifiers output impedance should match the speakers input impedance for proper power transfer between the two. Sort of like being in the correct gear in a vehicle in so that the motor is in the correct rpm range. Extra horsepower (kph) can overcome being in the wrong gear somewhat, but usually at the expense of "nimbleness"- engine lugging. Ultimately this becomes complex quickly as impedance often varies with frequency. If there were an easy answer someone would have capitalized on it by now. Contrary to what we read in the magazines, there really are very few "new developments" in audio. One of the reasons Western Electric gear is so sought after is they had the budget and the market for doing a lot of R&D. Way mor so than any company since. Often what we see are a rehash of their's and other's experimentations, or that manufacturing technology has advanced in so that their research is affordable to produce for a marketable product. The best amp I know of was never made for consumer use, but as a piece of test equipment not related to audio (and no, I'll not tell what or my friends will hang me for letting the cat out of the bag!). If you are still looking for an amp for your Sound Labs you really ought to give the JC-1's a go. Better yet, Pass Labs if you can afford it. I know you think they are mid fi, and maybe they are. However they offer a lot for the money and are not "clunky" or as you have put it "mechanical".
Read Robert Harley's "Complete Guide to High End Audio" available from Amazon.

Excellent explanation in the book.
Well, my answer is a little bit different - so I guess you get to take your pick!

Unfortunately the relevant terms get used inconsistently or imprecisely, leading many people to think that efficiency and sensitivity are the same thing.

Here is the convention that I follow. Some manufacturers also follow this, but not all.

As commonly used in consumer audio, "efficiency" is the 1 meter on-axis broadband anechoic SPL that a speaker delivers with a 1 watt input. Some manufacturers use a non-anechoic measurement (including room contribution), and some use a peak somewhere in the response curve instead of using a broadband average - so comparing two manufacturer's numbers may not really be apples-to-apples.

"Sensitivity" is the 1 meter SPL the speaker delivers from a 2.83 volt input. Sometimes called "voltage sentitivity" to make that clear. The same opportunities for optimistic specs enter the picture - namely, using non-anechoic conditions and/or taking the measurement at a peak rather than using a broadband average.

So, to recap: Efficiency is related to Watts, and Sensitivity is related to Volts.

(Some manufacturers use these terms interchangeably or backwards from this convention, so it's up to you to read carefully and figure out what they're really saying. Look and see whether they are talking about 1 watt input, or 2.83 volts input.)

Now, here is how the two are related: 2.83 volts into 8 ohms is one watt; 2.83 volts into 4 ohms is 2 watts; and 2.83 volts into 16 ohms is one-half watt.

So if you have a 4-ohm, 91-dB/2.83 volt sensitive speaker, it's an 88-dB/1 watt efficient speaker. If you have a 16-ohm, 85 dB/2.83 volt speaker, it is also an 88 dB/1 watt efficient speaker. I prefer to convert back to watts, because you can usually figure out the amplifier's maximum wattage output into a given load more easily than you can figure out its maximum voltage output (which may or may not vary with load, depending on the amplifier), and because if you are interested in power handling then you want to know the wattage going into the speaker.

Hope this helps.

That was quite elaborative Duke, thanks. So in fact sensitivity is closely related to efficiency and in fact they are expressions of the same thing but differs from one to the other in approach? Mlsst: instead of picking on me and telling me that I have an impedance obsession disorder (in fact I'm a bit neurotic, but that's another story :) ) it is better to explain things the way Duke did. I do appreciate your precious input though because I know you are a very knowledgeable person.

Efficiency is related to Watts, and Sensitivity is related to Volts.
To supplement Duke, if I may,here are some semantics. Basically,
* efficiency is a measure of how much electrical energy the spkr converts into acoustic energy (very little). It can be expressed in %: this speaker's efficiency is 5% (that high!)

* Sensitivity relates to how much acoustic energy a spkr produces given a specific amount of electrical (potential) energy.

I.e. for a "sensitive" spkr: you give it a little bit of electricity and, being very sensitive, it starts singing

So, the more sensitive it is, the more efficient it will be in the long run. I.e., if it is "sensitive" and plays very loud with very few volts, it is more "efficient" converting electricity into sound.

As you know, impedance is the resistance the spkr "system" has at 1kHz usually.(the actual res changes with frequency, hence the name "impedance" rather than "resistance"). Paraphrasing Duke above, and as a rough rule of the thumb, the lower the impedance quoted, the less "efficient" the speaker.
Check out Musical Fidelity's excellent explanation of "Why amplifier power is important"

musicalfidelity (dot) com/about/amplifier (dot) html
Chris, my ribbing was meant to be good naturedly humorous, but I think my underlying point was serious. You've spent a lot of energy trying to reduce a rather complex issue to a single parameter. Impedance is only meaningful when it is considered in combination with all the other factors.

Simply put, there is no one "audiophile" impedance that people should shoot for. It is only one of many factors to be juggled depending on the overall design goals for the speaker in question.
Chris, thanks - hope that was somewhat helpful.

Gregm, you are of course correct - the proper expression of efficiency would be a percentage, and then we could probably do apples-to-apples comparisons! I've only seen percentages given in prosound, though. Note that I used the wording "as commonly used in consumer audio" so that I could go back and weasel my way out if necessary, and I'm invoking that weasel clause now.

So, what would be easier to drive?
A speaker with 90DB and 4 ohms or a speaker with 88DB and 8 ohms?
YES- semantic gymnastics seems the most popular sport in the audio industry, and these forums. You can see by the definition for "sensitivity/efficiency" given by a company some of you MAY be familiar with(after all the years they've been manufacturing for the sound industry), that even JBL considers the two terms synonymous- second question on this site: (http://www.jbl.com/home/product_support/JBL_contactus.aspx). The difference between the two terms lies in the input being measured in volts for sensitivity, and watts for efficiency(as mentioned), and that depends on the semantic application that the manufacturer or rater chooses to observe. Another professional view: (http://www.projectsunlimited.com/audioProducts/MovieClips/TechNotes/Glossary.asp?articalID=29) This site offers a caveat regarding the use of 2.83v as a reference, and how the result's affected by a system's impedance: (http://www.transcendentsound.com/amp_input_sensitivity_and_gain.htm) So much obfuscation found in here!

06-26-08: Jeffjarvis
So, what would be easier to drive?
A speaker with 90DB and 4 ohms or a speaker with 88DB and 8 ohms?

The two speakers in your example don't differ a great deal assuming their impedance curves are similar. If one has a flatter impedance curve, then that one would be more successfully driven by a larger selection of amplifiers.

The 90dB speaker would require slightly less power to produce the same output level as the 88dB speaker in the same room.

If the 4 ohm speaker had a flat impedance curve, it could be driven successfully by a good PP tube amp (balance meaning an even frequency output from bass through treble without one are being more prominent than the other). If the 8 ohm speaker had a flat impedance curve, it'd be a better candidate for a tube amp. If the impedance curves have large dips and peaks, the speakers will be more successfully driven by a solid state amp that doubles power output as impedance is halved.

Frequency imbalance as a result of large, varying impedance curves combined with the wrong amplifier is a primary cause of speakers sounding "tipped up" with high frequencies sounding more prominent than bass frequencies.

So, the answer to which of the two speakers is easier to drive depends on several factors: impedance curve, room size, type of amplifier being used.

Jeff- View the last site(URL) in my last post. There's a brief treatise on how impedance, amp output and sensitivity affect a system's SPL(just past the halfway point of the article).
I'll admit, I only completed freshman college calculus and I'm no math wizard, but I can't follow the author's math. I wish he'd explain how he arrives at the following:

Let’s say the loudspeaker has an efficiency of 90 dB for one watt at one meter and the desired maximum sound pressure level during peaks is 110 dB (that’s really loud). This will require 100 watts. If the signal source is 1 volt maximum, how much amp gain is required?

100 watts into 8 ohms requires 28 volts. So the amp needs to provide a voltage gain of 28 times which is 29 dB.
Tvad- Read Robert Harley's "Complete Guide to High End Audio" available from Amazon=8>) The sections on "How Much Power Do I Need?" and "The dBW Power Rating" may lend some clarity. The only aspect Mr Harley leaves out is converting volts to dBW.(pages 159 through 162 in the Third Edition) I had skipped over the part you sited, and concentrated on the section right after when reading the Transcendent article. The writer forgot to say, "Trust me!"
Audiokinesis Duke, Thank you for the first complete explanation of this commonly misleading conundrum, I’ve heard..

Happy Listening!
Is it safe to conclude that the impedance of a speaker gives an indication of the current demand on the amp? It seems that as impedance falls there would be more current drawn to keep the equation in balance. If the amp is not able to supply the current we get clipping.
Is it safe to conclude that the impedance of a speaker gives an indication of the current demand on the amp
That would be very safe! That IS what the impedance actually tells you. It just doesn't tell you the whole story -- but it's a good part of the story!
At the risk of being an idiot could you tell me which speaker would play louder given the same signal
a 88dB/2.83V/M 4ohm speaker. Or a 88dB/1W/M 6ohm speaker.
Be gentle,i'm old and tired
thanks all
Which plays louder?
...a 88dB/2.83V/M 4ohm speaker. Or a 88dB/1W/M 6ohm speaker.

Here's the math.

2.83 volts into a 4 ohm speaker is 2 watts of power. So it takes 2 watts to get to 86 dB. At 1 watt the loudness would be 83 dB.

At 1 watt the 6 ohm speaker you note is more efficient.

However, there are a lot of caveats that need to be considered.

First of all, many speaker manufacturers are rather "imaginative" when it comes to specs. Even when they are relatively honest, variances in test protocol can make direct comparison of the numbers difficult.

Second, the 4 and 6 ohm impedance numbers you noted are "nominal" figures. Speaker impedances vary quite a bit with the frequency involved. Even speakers considered to have a well behaved, benign impedance will vary quite a bit, especially at crossover frequencies and in the bass.

This trait combines with the fact that no speaker is completely flat across the frequency spectrum. Human hearing is also not flat and tends to be more sensitive in the midrange. As such, one can sometimes get deceptive results with a less efficient speaker appearing to sound louder than a more efficient one.

Finally, amplifiers vary in performance with low impedance speakers. Some solid state amps will double in power with a 4 ohm load compared to a 8 ohm one. Other solid state amps may actually misbehave at low impedance and sound worse. Tube amps tend to deliver the same power output at difference impedances but are dependent on output transformer design.

The important thing is that you listen to each speaker with the type of music you enjoy, played the way you want to play it. If you normally listen at low to moderate volume and your room isn't overly large, efficiency may not be a very important consideration for you. If you are a rocker who likes high volume, you'll probably find that neither speaker you mentioned above will be satisfactory.

Good luck with your audition.