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Discussion Starter #1
I had trouble previously grasping how the sensitivity could be lower or higher in some frequency ranges, but still maintain a flat frequency response. Those two concepts seemed in opposition.

Voltage Drive, Impedance Determines Watts
Then I finally wrapped my brain around how (for today's solid state amps, not tubes) the volume level sets the voltage level, which is constant for the source signal and no matter what the power draw is. The impedance of the speaker, which is a varying curve through the frequency response, determines the power drawn from the amp in watts.

Questions

Impedance Curve is Almost Inverse of Sensitivity Curve?
So you wouldn't power a speaker with 1w and get a flat curve. I imagine that if you could keep it at 1w you'd have a frequency response that varied as impedance does?

Speakers are Easy, Even with Big Dips?
Now I'm having trouble understanding how speaker reviews that measured impedance and acknowledge a dip to 3 or 4 ohms in mid-bass, but the average impedance is over 7 ohm, say "This speaker is easy to drive with an average receiver."

Take this Stereophile review of the Klipsch RB-15: http://www.stereophile.com/content/klipsch-rb-15-loudspeaker-measurements.
"It drops to around 4 ohms in just two regions—around 80Hz, the port tuning frequency; and in the lower midrange—and though the electrical phase angle is quite high at times, this is always when the impedance magnitude is high, mitigating any negative effects. The speaker will therefore be well-suited to being driven by inexpensive amplifiers and receivers."​
I do not see how it's easy to drive, if between 200 and 300Hz it's 4ohms, so we could say the sensitivity is 3dB less than the measured 90dB, so 87dB. It takes all of 100w get get to reference level from 12 feet, and that's with the more generous 3dB loss double-distance and figuring in-room. That seems to be on the ragged edge of a typical receiver. So why is this speaker well-suited to cheap receivers (which I imagine to be realistically 50wpc)?

Phase Angle
Here's a Stereophile review of the Klipsch Palladium P-17B that's more damning because of the phase angle: http://www.stereophile.com/content/klipsch-palladium-p-17b-loudspeaker-measurements
"[Impedance] drops below 3 ohms between 128 and 265Hz, with a minimum value of 2.6 ohms at 170Hz. There is also an amplifier-frightening combination of 4.5 ohms and –50° electrical phase at 104Hz, a frequency where music has high energy levels. So while the Klipsch will play loud with a low-powered amplifier, that amplifier will still need to be able to deliver goodly amounts of current."

How could one determine by phase angle and impedance what the watts drawn will be?
 

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Impedance Curve is Almost Inverse of Sensitivity Curve?
So you wouldn't power a speaker with 1w and get a flat curve. I imagine that if you could keep it at 1w you'd have a frequency response that varied as impedance does?
I think this would be more accurately written as:
Impedance curve is almost inverse of efficiency curve.

In my opinion this all comes back to the way manufacturers and enthusiasts carelessly use "sensitivity" and "efficiency" interchangeably. It would be less confusing if everybody would agree to quote sensitivity numbers in something like dB/V(1m) instead of dB/W(1m). Some do, though I've also seen some call it "cheating".
 

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I imagine that if you could keep it at 1w you'd have a frequency response that varied as impedance does?
You would if you could keep the power constant, but you can't. Frequency response is voltage derived, and the voltage delivery of an amp remains constant into any load. Current, and therefore power, does change as the load impedance changes, but that has no effect on the speaker output or frequency response.
I think this would be more accurately written as:
Impedance curve is almost inverse of efficiency curve.
To be completely accurate current draw is inversely proportional to impedance. Power is not, as power varies with the square root of the impedance load. That's why 1 watt into 8 ohms is 2.83v, while 1 watt into 4 ohms is 2v, not 1.41v.
Efficiency is expressed as a percentage figure, acoustical watts output versus electrical watts input, and is never properly expressed in decibels.
 

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I had trouble previously grasping how the sensitivity could be lower or higher in some frequency ranges, but still maintain a flat frequency response. Those two concepts seemed in opposition.

Voltage Drive, Impedance Determines Watts
Then I finally wrapped my brain around how (for today's solid state amps, not tubes) the volume level sets the voltage level, which is constant for the source signal and no matter what the power draw is. The impedance of the speaker, which is a varying curve through the frequency response, determines the power drawn from the amp in watts.

Questions

Impedance Curve is Almost Inverse of Sensitivity Curve?
So you wouldn't power a speaker with 1w and get a flat curve. I imagine that if you could keep it at 1w you'd have a frequency response that varied as impedance does?

Speakers are Easy, Even with Big Dips?
Now I'm having trouble understanding how speaker reviews that measured impedance and acknowledge a dip to 3 or 4 ohms in mid-bass, but the average impedance is over 7 ohm, say "This speaker is easy to drive with an average receiver."

Take this Stereophile review of the Klipsch RB-15: http://www.stereophile.com/content/klipsch-rb-15-loudspeaker-measurements.
"It drops to around 4 ohms in just two regions—around 80Hz, the port tuning frequency; and in the lower midrange—and though the electrical phase angle is quite high at times, this is always when the impedance magnitude is high, mitigating any negative effects. The speaker will therefore be well-suited to being driven by inexpensive amplifiers and receivers."​
I do not see how it's easy to drive, if between 200 and 300Hz it's 4ohms, so we could say the sensitivity is 3dB less than the measured 90dB, so 87dB. It takes all of 100w get get to reference level from 12 feet, and that's with the more generous 3dB loss double-distance and figuring in-room. That seems to be on the ragged edge of a typical receiver. So why is this speaker well-suited to cheap receivers (which I imagine to be realistically 50wpc)?

Phase Angle
Here's a Stereophile review of the Klipsch Palladium P-17B that's more damning because of the phase angle: http://www.stereophile.com/content/klipsch-palladium-p-17b-loudspeaker-measurements
"[Impedance] drops below 3 ohms between 128 and 265Hz, with a minimum value of 2.6 ohms at 170Hz. There is also an amplifier-frightening combination of 4.5 ohms and –50° electrical phase at 104Hz, a frequency where music has high energy levels. So while the Klipsch will play loud with a low-powered amplifier, that amplifier will still need to be able to deliver goodly amounts of current."

How could one determine by phase angle and impedance what the watts drawn will be?

The big problem with a speaker that has a highly inductive or highly capacitive characteristic at certain frequencies (large phase angle), is that many amplifiers are not designed well enough to remain in stable operation with that kind of load and they will distort badly.

Cheap amplifiers like the large majority of AVRs have will almost invariably sound like crap when trying to drive this kind of nasty load because they distort so badly.

That is why really high-quality amplifiers have such huge reserves of capacitance in their power supplies; to supply the out-of-phase current peaks that these difficult speakers need, with minimal distortion. That is one reason why a more expensive amplifier may not be rated at a lot more power than another, yet sound a lot better.
 

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You may be working too hard at this. It's a matter of convention, of specsmanship.

Sensitivity has come to mean the spl at one meter with 2.83 volts input, regardless of impedance. An 8-ohm load is assumed for the sake of this number, even if the speaker is 16, 8, 4, 2 or any other actual impedance.

The reason for this has to do with the comparative loudness experienced when speakers from different manufacturers are compared in a showroom with a simple switch. The more sensitive speaker will be louder (not necessarily more efficient). The amplifier, as has been pointed out, will maintain a constant voltage regardless of the load.

This does give an apparent advantage to the lower-impedance loudspeakers, but users will usually be aware/advised of the limitations vis-a-vis their chosen amplifier.
 

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Discussion Starter #6 (Edited)
It would be less confusing if everybody would agree to quote sensitivity numbers in something like dB/V(1m) instead of dB/W(1m). Some do, though I've also seen some call it "cheating".
I suspect some manufacturers' goals include: They want to sell more speakers by hiding their warts. User confusion and mis-assumption helps them.
Customers' goals include: Compare speakers. Learn whether the speaker will do the job they want it to do. Learn how that will affect the rest of the system (e.g. the amp).

If a manufacturer wants to accommodate the customers' goals, impedance and sensitivity should be made comparable. One should realistically be able to tell what one can get out of the speaker. And how one's amp will work with that speaker. And how the speaker will work in their room (different topic of providing polars).

Showing sensitivity from 1w relates the finite amount of power to what the speaker can do. If the amp can provide honestly provide 50w, and if I see the speaker will require 100w for my desired SPL, there's a problem, and I can make decisions.

Do we really care what voltage level the amp was turned up to? Isn't it amps and watts that are in finite supply?

You may be working too hard at this. It's a matter of convention, of specsmanship..
It's specmanship until one sees graphs of frequency response and impedance.
"8 ohm compatible" means very little. Is it, "Your amp probably won't shut down with this speaker as long as you keep it below 40w sustained."? They're telling us what amp can be used.
"8 ohm nominal" means the speaker is supposedly 8 ohm nominal, but that also might mean very little.
I like the method used in Germany DIN and I think an IEC document that says minimum impedance should be 80% of nominal. The tells the customer something!

But best is seeing an impedance graph, but that usually doesn't appear until a review.
What I was asking about above though is, "If an impedance dip suggests needing 3x the power as the 8ohm level, shouldn't that make this speaker NOT a speaker suited for any ol' receiver?" That's not specmanship. That's speaker measured attributes interpretation and application.

Sensitivity has come to mean the spl at one meter with 2.83 volts input, regardless of impedance. An 8-ohm load is assumed for the sake of this number, even if the speaker is 16, 8, 4, 2 or any other actual impedance..
I've seen JTR and JBL speakers give volt input equal to 1w, thus 4ohm speakers' sensitivity is given as 2.0v. This keeps it comparable with 8ohm and 6ohm speakers.
 

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I suspect some manufacturers' goals include: They want to sell more speakers by hiding their warts. User confusion and mis-assumption helps them.
Customers' goals include: Compare speakers. Learn whether the speaker will do the job they want it to do. Learn how that will affect the rest of the system (e.g. the amp).

If a manufacturer wants to accommodate the customers' goals, impedance and sensitivity should be made comparable. One should realistically be able to tell what one can get out of the speaker. And how one's amp will work with that speaker. And how the speaker will work in their room (different topic of providing polars).
I'm sure you're right. The more I learn about speaker design, the more I appreciate how completely inadequate the normal set of measurements given is for describing a speaker's performance. And the less tolerant I become of speaker manufacturers that don't give the proper data to let me make an informed decision. One of the biggest things that has pushed me toward the world of DIY/AIY is the availability and even insistence upon proper measurements. I've pretty much decided for myself that I won't purchase another speaker for which I can't find at least a couple off axis frequency response measurements. If the designer doesn't have them, then he hasn't done his job. If he has them and is choosing not to share them, then he's trying to hide something.

Showing sensitivity from 1w relates the finite amount of power to what the speaker can do. If the amp can provide honestly provide 50w, and if I see the speaker will require 100w for my desired SPL, there's a problem, and I can make decisions.

Do we really care what voltage level the amp was turned up to? Isn't it amps and watts that are in finite supply?
No we really don't care about the gain setting on the amp, provided we maintain plenty of headroom to the rail voltage. But I think it's influenced by the way speakers are designed. Goal #1 of speaker design is flat frequency response i.e. the same output at all frequencies for a given voltage input. If that goal has been met, then a meaningful number can exist for sensitivity. That same flat frequency response does not imply that a single number can represent output per Watt. Output per Watt (I'd been calling it efficiency. Bill pointed out that this probably isn't the ideal name.) would have to be plotted to give a real representation.

Either way we need at least 2 plots to understand what it takes to drive a speaker. That can be a plot of frequency response (either scaled and labelled to show sensitivity or accompanied by a sensitivity number) and an impedance plot. Or it can be a frequency plot and an output per Watt plot. The first option is much easier to measure. And I'd argue that any consumer educated enough to know how to interpret one of the options could probably also comprehend the other.
 

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Discussion Starter #8
In the auto industry, reviewers nowadays provide all sorts of performance metrics for those interested in those aspects of the vehicle in question (turning radius, g forces, 0-60, time to brake, mpg).
Given that, I'd think the manufacturer would provide that info itself as part of marketing. But they don't.

Maybe from the manufacturer's standpoint, if there's a dearth of objective reviews with measurements, they want to provide measurements even LESS than auto manfs?
From a customer's standpoint, of course, objective measurements are even more needed, so we'd welcome the manf data if they'd be willing to provide it.

Drives me nuts when Audioholics or Secrets of HTHF don't do any measurements. They've done it before, they know how.

On a slightly different tangent, it's interesting how the community is now much more cognizant of measurements and the limitations of speakers in terms of SPL and distortion when it comes to subwoofers.
Ikkla and data-bass.com etc. did a lot for that, and CEA-2010 burst tests provides some standard for measuring peak output for transients, which is where the limits are often found.

I guess it's more apparent for subs due to how most subs can't even claim a frequency response down into the the lowest octave of soundtrack content, and the level being 10dB higher puts more of a strain.

I'd like to see that same awareness for output-related limitations make their way to main speakers. For some reason people grasp a subwoofer is limited but they think a speaker is not. I'd say there's some level of awareness or at least interest in amp limitations, judging by people's concern with wpc and using external amps.
 
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