# Speaker efficiency vs sensitivity



## Doctor X (Apr 3, 2007)

Hi Guys,

Not sure if this is the correct forum to be posting this. So I was having this discussion concerning efficiency and sensitivity and some of the guys were lumping the terms together as if they were exchangeable. 

The one EE I discussed this with said both terms vary in the same way and there is a direct relationship between the two terms. He then went on to say that doubling the efficiency would net a 3 dB increase in sensitivity. 

I don't agree that it's simply semantic word play. Efficiency is power out/power in. Sensitivity is power out/voltage in. Now in my mind, power and voltage are certainly not the same thing. Clearly, impedance is a factor.

I mean, if you have two speakers with equal sensitivities of 90dB/2.83V and one has a 4 ohm impedance and the other has an 8 ohm impedance, the latter speaker will have a higher efficiency, since the 2.83V will represent half the number of watts. So clearly you can't lump the two terms together. They don't correlate with one another.

What do you guys think ? I'm no EE, but I've been told that efficiency/sensitivity is just hair splitting. I don't agree but I would like to know from the more experienced guys here. Thanks.


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## Anthony (Oct 5, 2006)

Ah, I see the disconnect.

Sensitivity is usually spec'd for specific conditions, all of which must be considered. A good speaker or driver will post exactly how they came to that. For example: [email protected]/1m. That Watt, though was made by driving the speaker at a certain voltage decided by the impedance. A 4Ω speaker develops more power for the same voltage (P=V^2/R), so to keep the 1W constant, they have to lower the voltage.

So you are right, for [email protected], the 4Ω and 8Ω speakers are completely different. In this case the 4Ω speaker was actually tested at 2W and the 8Ω speaker at 1W, so the 4Ω speaker is 3dB _less_ efficient.

So the terms are interchangeable, if you have all the test data. Sadly, many spec's lack this or handwave it by using voltage instead of wattage (hoping you don't realize that 86dB was at 2W of power on the 4Ω speaker and not 1W when comparing speakers/drivers).

Clear as mud?


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## Doctor X (Apr 3, 2007)

Is it true that doubling the efficiency nets a 3 db sensitivity or is that just 'in a perfect world' ? Because the EE basically told me that with sensitivty and efficiency there is a direct relationship (without mentioning any other variables). Isn't that a blanket claim ?


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## Doctor X (Apr 3, 2007)

Also, if sensitivity is power out/voltage in and efficiency is power out/power in, I don't see how the relationship could be interchangeable since voltage and power are different.

I mean, can you say that a speaker that is more efficient is more sensitive ? I'm sure you could, but on it's own it's just a blanket claim. Take that example I mentioned with the 4 ohm and 8 ohm speaker. Assuming identical efficiencies, the 8 ohm speaker would be -3 dB's less sensitive. So it's not a scalable metric. 

As I understand it, when you add in several real world variables the differences between sensitivity and efficiency become more apparent I think. I'm not good with equations which is what the EE was flashing around, but he didn't seem to understand why there would be big differences between the two.


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## Anthony (Oct 5, 2006)

I think what he meant was.

Pout=Pin*efficiency

assume Pin is constant

Pout_new/ Pout_original = (Pin * eff_new)/(Pin * eff_orig) = eff_new/eff_orig

in dB terms this is 10 log (eff_new / eff_orig) = dB so in this case 3 = 10 log (eff_new/eff_orig). Solve for eff_new/eff_orig and we get 2. Put it all together and 

Pout_new / Pout_original = 2

A lot of algebra there, but basically in a base 10 dB scale, 3dB represents a doubling or halving (depending on the sign) of whatever value you are measuring.


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## Anthony (Oct 5, 2006)

Vaughan100 said:


> Also, if sensitivity is power out/voltage in and efficiency is power out/power in, I don't see how the relationship could be interchangeable since voltage and power are different.
> 
> I mean, can you say that a speaker that is more efficient is more sensitive ? I'm sure you could, but on it's own it's just a blanket claim. Take that example I mentioned with the 4 ohm and 8 ohm speaker. Assuming identical efficiencies, the 8 ohm speaker would be -3 dB's less sensitive. So it's not a scalable metric.
> 
> As I understand it, when you add in several real world variables the differences between sensitivity and efficiency become more apparent I think. I'm not good with equations which is what the EE was flashing around, but he didn't seem to understand why there would be big differences between the two.



I think the real issue is that you are using sensitivity to mean "voltage sensitivity", while others use it to mean power sensitivity. In your example, the 4 and 8 Ω speakers are not the same speaker, so it reasons that they would have different sensitivities even if the stated voltage sensitivity is the same (since the same voltage on 1 is double the power on the other).

I see your point, and I think we are pretty close in agreement: you have to have all the details to exchange one for the other. Otherwise, that might be a bad assumption. It is not a difference between them, since most drivers fall into the 4Ω or 8Ω category and the results are easy to standardize.


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## Doctor X (Apr 3, 2007)

Yes, the 4 ohm and 8 ohm speaker are not the same, but only have different impedance. So clearly the impedance will change the efficiency or sensitivity. 

Would I be correct in assuming that if one increased sensitivity between two speakers and the impedance curve was identical in both, that the efficiency would also increase ? Two identically, linear impedance curves. 

But that's the thing. Speakers don't have identical impedance curves so then claiming that the higher the efficiency, the higher the sensitivity doesn't have any basis in truth in the real world because there are several variables that come into play.

I take it that the doubling of efficiency = 3dB increase in sensitivity is an equation that doesn't include any other real world variables. It's just a theoretical number. 

I'm just trying to understand this because it's difficult for me to understand it. I thought the definitions for sensitivity and efficiency were not up for debate re voltage and power. Other EE's I've spoken with have told me sensitivity concerns itself with voltage...efficiency with power....but when you introduce impedance to the equation both terms don't scale in a linear fashion.

Sorry for the rant, I'm just talking to myself.


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## Doctor X (Apr 3, 2007)

Let me post something from the EE to give you an idea :

"_Yes, it is obviously clear (as I also stated) that sensitivity and efficiency are calculated in different ways; the one is after all given in dB and the other as a ratio! But both is dependant on the varying impedance - both are average values integrated over a frequency band, both vary in the same manner, and when talking about relative differences between loudspeakers, they indicate the same tendencies: doubling the efficiency gives a 3dB rise in sensitivity and vice versa. You mention mathematics; perhaps one could cut qualitative statements short by looking at the simple conversion factor between the two:

Sensitivity(dB) = 112 + 10*log(efficiency)

That is a direct relationship without other variables._"

That's his post but he doesn't believe that there are big differences between both terms. I've been led to believe that both terms are not interchangeable and there are several sources that also claim that people erroneously make the mistake of confusing both for the same thing.


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## fbov (Aug 28, 2008)

When two quantities are related by single-valued mathematical relationships, they can be used interchangably. 

There is a seconary issue in that speaker sensitivity is sometimes expressed at constant voltage, instead of constant power. That doesn't change the interchangeability, it just adds impedence to the relationship. More complex, but perhaps better for comparison in some cases. 

Have fun,
Frank


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## Ricci (May 23, 2007)

Right. Sensitivity is measured by voltage but only in so far as the voltage applied equates to 1w of power into the nominal load. Many people don't understand this and marketing/manufacturers will take advantage of that by posting sensitivities measured with 2w or even 3w.


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## Doctor X (Apr 3, 2007)

> When two quantities are related by single-valued mathematical relationships, they can be used interchangably.


So then in the real world these relationships have zero merit ? Is that what you are suggesting ? Also, based on what the EE said, is that correct ? Because if not, I want to kick his . 

Speakers aren't perfectly linear devices with perfect impedance curves. So if one says that efficiency and sensitivity correlates in mathematical terms based on a set variable then that doesn't mean it correlates in the real world with multiple changing variables does it ? If you increase sensitivity that is no guarantee of increasing efficiency. That's what I'm trying to get across. It's like using room mode calculators using code designed to work in rectangular rooms but leaves out all other room shapes. 

So what I'm saying is that one can't use the terms efficiency and sensitivity interchangeably in real world terms because there are variables at play. If you play around with 1 variable then you could probably make a case for the terms having a connection in mathematics, but in reality, impedance changes, on and off-axis dispersions I believe also have a role to play etc..etc. Efficiency is just a maths equation that leaves out a bunch of other variables. So if that is true, then it's really useless to us in the real world ?


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## Anthony (Oct 5, 2006)

I think the real problem is that there is no "standard" in the industry.

Case and point is my Magnepan speakers. They are listed as [email protected]/1m So you are thinking, oh, they only need twice the power of my 89dB speakers I'm replacing for the same volume. Wrong!  You need 4x the power, because those 89dB speakers were 8Ω and the Maggies were 4Ω. Just a case of marketing, b/c [email protected]/1m doesn't look too good 

And I wouldn't say they are useless. You just need to make sure you know what stat you are reading and if they just say "90dB efficient" you know they aren't giving you all the stats.


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## Doctor X (Apr 3, 2007)

Just to bring in more info since I've recently been talking to an individual that actually designs transducers, he said that _only_ time sensitivity and efficiency can be used interchangeably is when the driver acts as a point source which you can never have in a system that uses physically separated drivers to produce different frequency ranges.


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## fbov (Aug 28, 2008)

Vaughan100 said:


> So then in the real world these relationships have zero merit ? ... Efficiency is just a maths equation that leaves out a bunch of other variables. So if that is true, then it's really useless to us in the real world ?


If "efficiency" is the ratio of the input (electrical) power to the output (acoustic) power, how does it differ from something expressed as dB/watt? (Remember, dB are measure of acoustic power and watts, electrical power). They are the same concept. I don't have a problem with that. Those who are technically competent in the field will use the metric that suits their needs. 

One reason no one talks in terms of speaker efficiency is that the efficiency is so incredibly low. My MTMs are [email protected]@1m sensitivity, but only 0.56% efficient (no the decimal point is not misplaced). It's also hard to translate acoustic watts to hearing sensation, while dB has that built in. Anything that's expressed in terms of "dB/[email protected]" can be expressed in efficiency. You may be confused because efficiency is usually expressed as a total, but the function that's integrated contains all the stuff you claim is missing.

I'm also going to make the wilda$$ guess that you're not an engineer... my money's on law, if only by the way you argue.

Have fun,
Frank

PS Actually, there is one thing that's not in efficiency - distance. Efficiency looks at the power transfer, only. Sound perception varies by the distance initially, then the distance squared. Efficiency integrates over the full 4pi space, so distance doesn't matter. Different metric for different applications

PPS all drivers are point sources at wavelengths that are long compared with the size of the radiating surface. Look at any on-axis vs off-axis FR curves and you can tell where the drivers cross by the points where the on-and off-axis curves coincide.


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## Doctor X (Apr 3, 2007)

fbov said:


> I'm also going to make the wild guess that you're not an engineer... my money's on law, if only by the way you argue.


Have you been keeping tabs on me ? Interesting that you would assume I am a officer of the law as I don't believe I've flexed my argumentation muscles at all here and certainly haven't provided sufficient evidence in support of that allegation. : ) Unless you are referring to other forums, like AVSforum. 

No, _not all all_, I'm no engineer but I find these subjects fascinating. I work within the AV industry. I have learned something new from a transducer engineer though. Sensitivity concerns itself with axial sensitivity (on-axis) and efficiency concerns itself with power out, at _all_ angles. 

I still think it's misleading to call a more sensitive speaker efficient, or vice-versa, as the efficiency metric could be influenced by a number of things. Just as sensitivity could be influenced by dispersion, power compression, frequency response etc. He told me that in the perfect world, with a perfect speaker, efficiency and sensitivity would scale perfectly, but obviously speakers aren't linear devices. Well, linear, up to a point anyway.

So, I'm curious where you read my posts from. Do tell... 

PS I just noticed you covered the 4pi and on-axis/off-axis comments. Thanks.


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## fbov (Aug 28, 2008)

My comments were mainly due to a tendency to reduce to complex issues to black and white, and a reliance on information from others rather than your own understanding. To my knowledge, this is the only thread where we've interacted. And I do appreicate your kind reply. 

I'm also one to try to find the commonality in things, the basic principles that govern matter. In that sense, sensitivity and efficiency are the same concept. At the same time, I know that specialized metric are very valuable, and thus see why speaker designers talk in terms of sensitivity. 

When trying to understand a complex system, I find it useful to think like the smallest unit available, in this case electrons. They flow in a coil, creating a magnetic field. That field interacts with the motor magnet causing the coil to move (electrons interact with the motor magnet, too). The coil transmits the force to the cone which moves air. Now, start speeding things up from the initial DC thought process to one where the coil's oscillating, faster and faster as frequency increases through coil resonance and to the point where things are happening so fast that "extras" start to appear, reflections and resonances in the mechanical system... and that's just what's happening on the driver, much less the air around it. 

Mental models aren't easy, but they gave us Quantum Mechanics, so they have their applications. To be honest, this is how I try to think about all physical systems...

Frank


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## Doctor X (Apr 3, 2007)

fbov said:


> My comments were mainly due to a tendency to reduce to complex issues to black and white, and a reliance on information from others rather than your own understanding. To my knowledge, this is the only thread where we've interacted. And I do appreicate your kind reply.


No problem. I'm usually very passive in these kinds of discussions because on one hand I believe my understanding isn't too far off but I'm bouncing ideas on top of everyone else, so I try not to be overly assertive. Sometimes I just need reassurance that I'm on the right track.

Speaking of the right track, the transducer engineer who gave me a helping hand posts on Audioholics and due to his field is probably the most qualified when speaking on this subject. One of my problems is that I tend to over-analyze _very_ quickly which leads me to asking the same questions over and over again.


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## lsiberian (Mar 24, 2009)

Vaughan100 said:


> No problem. I'm usually very passive in these kinds of discussions because on one hand I believe my understanding isn't too far off but I'm bouncing ideas on top of everyone else, so I try not to be overly assertive. Sometimes I just need reassurance that I'm on the right track.
> 
> Speaking of the right track, the transducer engineer who gave me a helping hand posts on Audioholics and due to his field is probably the most qualified when speaking on this subject. One of my problems is that I tend to over-analyze _very_ quickly which leads me to asking the same questions over and over again.


I don't know of this transducer engineer he must be keeping his identity secret. Nonetheless I think that the driver efficiency when accurately listed is a helpful parameter to any loudspeaker engineer needing a more efficient speaker. There may not always be a one to one correspondence between transducer efficiency and loudspeaker sensitivity, but it is reasonable to conclude that a more efficient transducer will lead to a more sensitive speaker. Of course a model will give you a better comparison, but modeling costs time which is the greatest cost in engineering.


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## Yad (Oct 19, 2009)

offtopic: Hi everybody. A was not here very long))) I was in business. Now i'm here too.


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