Loudspeaker Sensitivity & Impedance Explained

Loudspeaker manufacturers sometimes exaggerate the specifications of their products to make them look better than they really are.  Some are more honest than others in this regard.  The focus of this article is on loudspeaker sensitivity and what to look for in this rating so the consumer can make a more educated purchasing decision when comparing products.

In order to begin, it’s important to clearly define a few terms that will be used throughout this article.

Loudspeaker Sensitivity: a measure of Sound Pressure Level (SPL) at a specified distance for a specified input signal. This is usually specified for a loudspeaker in a non-reverberant environment, in dB SPL and referenced to 1 meter on the reference axis with an input of 2.83 volts RMS, typically at one or more specified frequencies (often 300, 400, 500, 600Hz or the average of these). Sensitivity should always be accompanied by an impedance specification.

Loudspeaker Impedance: is the sum of DC resistance and complex AC reactance comprising inductance and capacitance, the value of which changes with frequency.

Editorial Note about SPL Change:
A 3 dB change in sound level is just nicely noticeable as a change in loudness.  It requires 10dB power change to halve or double perceived loudness at mid/high frequencies and about 6dB at low frequencies. 

Loudspeaker Impedance: 8-Ohm vs 4-Ohm Speakers YouTube Discussion 10/20/19

Why is Loudspeaker Sensitivity Important?

This specification is important because it should give the consumer an accurate, easily compared measure of “how loud” a particular speaker will play when fed with a specific input. If sensitivity is measured in the same way, using the same methodology, then we can compare different speakers and have a good understanding of the relative amount of power they’ll need to achieve a certain output level. Their output is measured in dB SPL (Sound Pressure Level).

Note that the sensitivity measurement is only a relative measurement, done under tightly-controlled test conditions. The sensitivity figure does not necessarily relate directly to how loud a given speaker will play in a given room with a given input level; rather, sensitivity is a precise measurement that allows different speakers to be compared in an apples-to-apples manner. Their ultimate loudness capability in real-world situations depends on many factors, which we will explore later on.

Editorial Note from Andrew Jones, Loudspeaker Designer of Pioneer/TAD about Sensitivity

Whenever sensitivity is quoted, the nominal impedance must also be stated. This will prevent the manufacturer from cheating in cases where the lower impedance speaker is able to draw more current making the speaker appear more efficient.  Of course the efficiency has NOT increased, but the sensitivity has, which is why it is important to include nominal impedance into the spec.  Plus, all speakers are designed to be driven from voltage source amplifiers and have a flat frequency response when so driven. Therefore, sensitivity does give a direct indication of how much louder one speaker will sound on a direct comparison (disregarding the capability of the amplifier to drive a speaker that cheats on impedance).

“Efficiency” is NOT the same thing as “Sensitivity”

Speaker engineers use the term “sensitivity” because it is technically more precise definition of how loud a speaker will play when driven by an input signal of at a specified voltage level. “Efficiency” is usually a more colloquial term used by consumers, to informally describe how much power a speaker needs to achieve a desired loudness level: “Oh, your speakers a real power hogs. They’re not very efficient.” From a technical standpoint, “efficiency” is defined as the sound power output divided by the electrical power input—but that’s not how consumers use the word. So rather than try to turn laypeople into engineers, we’ll just concentrate on sensitivity.

The reason for quoting sensitivity rather than efficiency is that the true efficiency of a speaker varies wildly with frequency because of its impedance variation. The efficiency quote would be fairly meaningless, so loudspeaker engineers measure and refer to “sensitivity” instead.

How do we measure loudspeaker Impedance?

An impedance analyzer is used to measure the loudspeaker’s impedance as it changes with frequency.  The lowest impedance is measured at DC, which is also known as the DC resistance. The IEC method of specifying nominal loudspeaker impedance is set such that minimum impedance must not fall below 80% of nominal, so for an 8 ohm speaker this would be 6.4 ohms minimum, and for 4 ohms would be 3.2 ohms.

Infinity P363 8 Ohm Rated Speaker Failing IEC Specification

RBH Sound SX-8300/R 4 Ohm Rated Speaker Passing IEC Specification

As you can see in the above impedance graphs, the Infinity speaker measured well below the 6.4 ohm minimum to be classified as an  8 ohm speaker by the IEC method.  In fact, it's off by a great margin. This speaker purposely utilizes a 4 ohm tweeter to boost sensitivity which affects its overall impedance value.  The RBH Sound speaker truly is a 4 ohm speaker as specified by the manufacturer. In fact, as you can see by the dotted red line, the impedance stays well above the minimum 3.2 ohm mark to be classified as such by IEC method.

Comparing the Sensitivity of Speakers with Different Impedances

If the amplifier is set to 2.83V, the 4 ohm speaker will draw 2 watts of power from the amplifier while an 8 ohm speaker draws 1 watt.  (Power = Voltage²/resistance. So, 2.83² = 8. 8/8ohms = 1 watt.) This potentially gives the 4 ohm speaker a +3dB SPL advantage over the 8 ohm speaker for a given input level. This seems to be unfair. Therefore, some engineers and reviewers adjust the input voltage so that it equates to 1 watt at the impedance of the input frequency (or band of frequencies) of the speaker under test.

The other viewpoint is that in the real world, a speaker’s impedance is what it is, and the amplifier puts out its voltage as it does. Assuming the amp is muscular enough to drive low impedances, then if a speaker has a lower impedance, it will play louder for the same voltage input from the amp and this is information the consumer should have. In other words, the speaker’s sensitivity rating should not be “penalized” because it’s a 4-ohm instead of an 8-ohm speaker.

There is an international standard that defines sensitivity, and it specifies that sensitivity be referred to SPL @ 1m for 2.83V input. The actual measurement can be made at any distance and input level, but must be calculated back to 1m and 2.83V equivalent. A 4-ohm speaker will under these conditions appear to have an advantage, and many manufacturers take unfair advantage of this. This is why it is also required to quote nominal impedance, so that one can see that if the nominal impedance is low then the speaker will in fact be drawing more power from the amplifier and hence the amplifier will have to be able to deliver this. Not all manufacturers follow the industry standards in every instance of published specifications, so the consumer needs to pay close attention and read the fine print.

Andrew Jones adds:

Because a speaker is a voltage-driven device, we would be much better off to move away from amplifier power to amplifier voltage, specified in dB relative to 2.83 volts. At the same time, the minimum impedance of the load that the amplifier can maintain at this maximum voltage should be quoted. Using this, we could directly calculate how loud the speaker could go. An example will illustrate this: suppose we take a conventional 100W amp into an 8 ohm load. 100W is 28.3Vrms, which is +20dB relative to 2.83V. If the speaker is 90dB sensitivity, then max SPL is 90+20= 110dB.  So, we quote the amp as a +20dB amp. That’s it...we now know how loud it will play with any sensitivity speaker. Easy!

Note: Of course this doesn't factor in loudspeaker compression or distortion which will vary in degree depending on the quality of drivers and crossover components of each particular speaker.

Now, what happens about impedance...well, we specify minimum impedance that the amplifier will drive at full output. If we quote 6.4 ohms, then we know if it will provide +20dB into an 8 ohm speaker, but not a four ohm speaker. If we quote 3.2 ohms, then it will drive both an 8 ohm and a 4 ohm speaker to full level.

Hypothetical Discussion on Loudspeaker Sensitivity: Engineering vs Marketing

Here is an interesting take on the matter with engineering folks at Atlantic Technology and Andrew Jones from Pioneer/TAD, with us playing the devil’s advocate as the Worthless Marketing Slug.

image courtesy of: xkcd: Spinal Tap Amps

Question from Worthless Marketing Slug: But if you use 2.83V, then isn't a "4-ohm" speaker getting 2 watts, and therefore, won't its sensitivity come out "higher" than an 8-ohm speaker?

• Answer from Atlantic Technology Engineer: "Regarding sensitivity: I once thought using 2.83V was unfair to 8 ohm speakers. Unless you look more closely at watts. A watt is not an accurate unit in this case (1w 1 meter). A watt is a measure of work done in heat loss. That’s it.
  
  So, it is much more relevant to compare a speaker using the same voltage source, in this case 2.83V, as any amplifier can provide at least this much stimulation. It just so happens a 4 ohm speaker is more able to translate that 2.83V into SPL. Bottom line is I tend to use 2.83 volts whenever possible.
• Answer from Andrew Jones: Yes, but this is why we quote impedance!

Question from Worthless Marketing Slug: What do you say to those people who say that a 4-ohm speaker should be given a 2V input, so it ends up with the same 1 watt input that an 8 ohm speaker gets with 2.83V?

• Answer from Andrew Jones: This would be confusing as it is trying to get back to the old idea of constant power input in order to measure power and efficiency, something that has no practical value with a loudspeaker whose impedance varies wildly with frequency

Question from Worthless Marketing Slug: Now, impedance varies all the heck over the map.  What--if any--is the frequency spectrum or single frequency point where sensitivity is measured? If, say, it's 'industry standard' (is there such a thing for sensitivity measurements?) to measure at 1000 Hz, then shouldn't the speaker under tests be measured for impedance at 1000 Hz, then the input voltage adjusted so it comes out to be 1 watt? So if it's 6 ohms, then the input voltage is 2.44V, if it's 8 ohms, it's 2.83, if it's 5 ohms, it's 2.23, etc. Shouldn't we hold the input wattage constant so we're comparing apples to apples all the time?

• Answer from Andrew Jones: It’s the varying impedance issue which is responsible for moving away from “efficiency” towards “sensitivity.” 1000Hz has no special significance as a frequency for making the calculation, so we instead ignore this, use sensitivity, and average this over a range of frequencies.

Question from Worthless Marketing Slug: How does THX (they're real sticklers for accuracy and consistency) say you should measure for sensitivity?

• Answer from Andrew Jones: THX gets it right...partly because Laurie Fincham rewrote the specs when he took over, in light of the work that he had done on the international standards committee that defined sensitivity and impedance. THX requires sensitivity to be specified exactly as the international standard, and they also require that the speaker meets the true 4-ohm impedance as defined by the standard (3.2 ohms minimum). There are then no surprises!

• Answer from Atlantic Engineer: Like I said, watts are probably the wrong way to look at things in this situation, when we’re evaluating loudspeaker sensitivity. The power amplifier is delivering 2 watts to the 4 ohm speaker, and some portion of those 2 watts is being turned into heat, and some part of those 2 watts is being turned into sound by the speaker. Now, let’s look at the amplifier, First of all, it needs to be able to deliver current, to not limit the current it delivers into a low-impedance loudspeaker. That’s what allows low impedance loudspeakers to receive more input power, and to play at higher sound levels than higher impedance units.
  
  An amp is a voltage source in your listening room. That voltage source is capable (for instance) of 0 to 10 volts. Now, a more efficient speaker will make better use of that voltage source than a less efficient speaker. So, changing the voltage source unfairly “evens” the playing field. We’re assuming for this conversation that the amp is “gutsy,” and has no meaningful current limitations.
  
  Think of a lab. In the lab you test things. Do you constantly change your test settings so everything tests fairly? Or do you maintain as many settings as possible so you can compare the absolute performance/output/measurement? If THX, as an example, were to set up tests so everything passed, why bother having them test anything? Same goes for UL and CE. The DUT [Device Under Test] is the variable. Your test settings should not be the variable.
  
  Generally, impedance is stated totally incorrectly. Kind of like most companies saying they have “200 watt” speakers. If you put a multi-meter on a speaker, and read it as 4 ohms, we rate it as 4 ohms. This is not the impedance. This is the DCR, or DC resistance. Impedance is resistance that fluctuates with frequency. Generally DCR is as low as it will ever go. If you rate a speaker using DCR, you are usually safe in that consumers will team up the speaker with an amp capable of driving a similar load. That is why we do that. I think AR published detailed impedance curves back in the '60's, as they were the first company to publish and educate the consumer about most technical information about speakers. It was important to match up your speaker and amp in the old days, especially if you used tube amplification, with their “4 ohm,” “8 ohm,” and “16 ohm” taps. Not so much anymore. As long as the amplifier is capable of driving a 4-ohm load, it’s ok to connect a nominal “4 ohm” speaker to it.
  
  I measure the input voltage at 1000hz. Because impedance varies with frequency I adjust my input so I have 2.83 volts at 1000hz.
  
  When I test THX speakers I take the SPL of each data point from about 500hz to 8khz and then average it. This is an extreme and time-consuming process. And not really all that necessary. Note that even LMS does not measure true impedance. It measures a composite made up of the real part and modulus. The formula is ridiculously complicated so I don’t perform the calculation, although THX uses a device to separate the two.”

Statement from Worthless Marketing Slug: Most people think of "watts" as an independent, absolute "thing" on its own. But it's not.  It's voltage squared over impedance.

• Andrew Jones corrects the Marketing Slug: Not quite. This is a derived equation. Simply stated, watts are the complex product of voltage applied to the load and current drawn.

• Answer from another Atlantic engineer: I agree that you can go around a few times about 4 vs. 8 ohms, 2.83 vs. 2 volts, etc., and the morality of that advertising/marketing game.  I'm staying out of that discussion.
  
  I suspect that what's important to a user is how loud it will play when compared to another speaker, and that most folks don't really care about the impedance as long as their receiver will drive it well enough to not break, sound bad, or trip the relay out.
  
  These days, it's fairly easy to make amps which will drive 4 ohm loads cleanly (this is actually short money), even if they can't take the thermal loading (heatsinks and big transformers are where the money goes, as you know).
  
  Having said that, as you suspect, the THX boys take a slightly different tack.  They measure sensitivity at "2.83V drive signal", applied over a specific frequency band (depending on what type speaker - LCR, surround, subwoofer, etc.).  Separately, they specify requirements for minimum impedance (Ultra2 satellites: minimum modulus (complex impedance) 3.2 at any frequency; real part (DC res) 2.4 at any frequency).
  
  In other words, they don't care if it's 30 ohms, it's gotta play 89dB at 1 meter when driven with 2.83V.  Lastly, they require that freestanding models be tested at 4pi, and wall mounted ones at 2pi.”

Under What Conditions is Loudspeaker Sensitivity Measured?

The sensitivity as internationally specified should be measured in a defined environment, and that environment should be quoted along with the measurement.

Drive units are measured in one of three environments:

1. 2pi - measured in an infinite baffle, or in practice a large wall
2. 4pi test box IEC dimensions
3. 4pi test box Japan test standard dimensions

Systems are measured typically either in 2pi if they are intended for 2pi operation --think In-Wall speakers--or otherwise in 4pi if they are intended to be used away from the wall.

Actually, a speaker measured in the wrong environment will not measure with a different sensitivity, just a different bass frequency response. Most typical size speakers will self-baffle above a few hundred Hz (the wavelengths become small enough that the speaker’s baffle provides the 2pi environment) and therefore will be radiating only into 2pi anyway, so if you calculated sensitivity using frequencies above around 300Hz then the answer you get will not change significantly from a 2pi to a 4pi environment.

Then, of course, there is the question of where to measure sensitivity. Should it be measured at one standardized frequency, say 1000 Hz, or over a range of frequencies? If a range, what range?

Back in the ‘70’s, High Fidelity magazine used to feed a speaker with pink noise at a set input level over a spectrum of 200-2000 Hz and measure the speaker’s SPL output at 1 meter. Their rationale was that this range constituted the “midrange,” and it was therefore realistically indicative of how loud a given speaker would be perceived to play with a constant input level that could be repeated from speaker to speaker. The 200-2000 Hz range was a range that any speaker with “hi fi’ pretensions could easily reproduce, and it eliminated the variances between speakers with wildly differing capabilities at the frequency extremes.

It was a valid and scientifically-defensible approach that produced results that could be reliably compared from speaker to speaker, irrespective of size, design approach or price.

The validity of High Fidelity’s approach can be seen by the fact that today the highly-respected NRC (National Research Council) of Canada uses a very similar method. As noted on the goodsound.com website:

“Second, you can’t just measure a speaker’s sensitivity at one frequency and say that’s that. Unlike amplifiers, speakers always have substantial fluctuations in their frequency response -- as much as +/-3dB, or even more, depending on the frequencies being measured. Therefore, the best way to do this is the way the NRC does it -- by averaging a broad range of frequencies so the fluctuations iron themselves out. The NRC averages readings taken between 300Hz and 3kHz.”

Inverse Square Law Courtesy of Hyperphysics

Some people want to include the bass range in speaker sensitivity measurements, so the user can get a realistic idea of how loud the speaker will play on wide-range material, for a given input. However, if you try to specify sensitivity lower than 200 Hz, you start to get into the 2pi vs. 4pi complication. As the speaker approaches the room boundaries to the point where the speaker is closer than a half-wavelength away, the acoustic environment will start to transition from 4pi to 2pi, depending on the distance and frequency. So if the frequency range you’re using for sensitivity includes some location/boundary-dependent frequencies on the low end, your sensitivity measurement will be invalid, because part of the speaker’s output will result from a 2pi (higher reading) environment, and part will result from a 4pi environment. This is an argument in favor of measuring all speakers in a 2pi setting, as it will give you directly-comparable readings from one speaker to another over the full frequency range—as long as the speaker under test is all forward-firing, with no woofers, ports, radiators, etc. on its side or rear. Not always the case, unfortunately.

Another problem with sensitivity measurements is that they depend on different speakers having an essentially flat frequency response through the midrange, in order to allow their sensitivities to be directly compared. If you are using an averaged 200-2000 Hz range or 300-1000 Hz, or whatever, if speaker A has a 4 dB peak at 850 Hz but speaker B is flat, then their apparent comparative sensitivities will be thrown off. Even if A and B have similar 100-500 Hz and 3000-8000 Hz levels, A’s 850 Hz peak will result in a sensitivity measurement “advantage” that is not indicative of their actual real-world “how loud does it play with a given input” performance. This is not always accidental. Sometimes a manufacturer will “juice up” a particular frequency range knowing that they’ll get a “better” sensitivity rating as a result.

Although these days most loudspeaker manufacturers are scrupulous, in days past you had to look carefully to make sure that the sensitivity measurement distance was the same from manufacturer to manufacturer. With the inverse square law stipulating a 6 dB change for the halving or doubling of distance, a less-than-honest speaker manufacturer might have been tempted to use a “.5 meter” measurement distance in order to obtain a 6 dB higher sensitivity reading. This doesn’t really happen these days, but similar deception can take the form of whether the manufacturer specifies if the speaker was measured in a non-reverberant (anechoic) environment, or in a “normal listening room with average reflective characteristics.” And remember, the inverse square law applies to anechoic environments. In a live listening room, it’s usually much less than 6dB. Obviously, for the same speaker measured in the two different environments, the anechoic reading will be much lower, perhaps in excess of 10dB. The point is, the reader must pay attention to the test conditions and parameters, and be sure the comparisons are valid.

Editorial Note about Inverse Square Law & Real Rooms

We’ve all heard the -6dB inverse square law of SPL reduction for every doubling of distance but in reality that pertains to free space, or an anechoic chamber – which is a room without echoes.  Real world listening rooms will see more along the lines of 3-4dB of loss for every doubling of distance.  But for arguments sake, we stick to the common -6dB figure for all of our calculations in this article.  Just recognize the real world losses should be much less, unless of course you live in an anechoic chamber or are listening to your speakers outdoor in free space. 

And speaker companies are pretty sharp, too. They know how to make the laws of physics operate in their favor. Here’s probably the best example: Remember the Advent Loudspeaker and the Smaller Advent Loudspeaker? They were two of the best-selling speakers on the market during the heyday of the stereo boom of the early 1970’s. The Advent (commonly called the “Large Advent”) was a full-sized 2-way bookshelf speaker with a very fetching tonal balance—not too bright and harsh, not too reticent and polite. It sounded just right to many people on all kinds of music. The Advent’s crowning glory, however, was its bass response—full and solid down into the low-40 Hz range. Considerably deeper and stronger bass than competitive speakers of similar size and price.

Advent wanted to follow the Large Advent with a smaller, less expensive model. But they wanted to retain that extraordinary bass response, especially in the Smaller Advent, because a compact model that had low-40 Hz bass would really have a competitive edge in the market.

However, there is this inconvenient truth about loudspeaker design called “Hoffman’s Iron Law.” Named after Anthony Hoffman (the “H” of KLH), this rule identifies the tradeoffs inherent in speaker design. There are three main characteristics of bass response:

• Frequency extension
• Enclosure size
• System efficiency

The Law goes like this: Pick any two at the expense of the third. In the case of the Smaller Advent, they wanted deep bass extension and a compact size, so they had to give up system efficiency. The Small Advent, as we stated at the top of this article, was a real power hog.

So to offset that, Advent’s engineers intentionally made the Smaller Advent a 4-ohm system, whereas the Large Advent was an 8-ohm system. Now you can see as we’ve laid out in the preceding discussion, a lower-impedance speaker will draw more power from an amplifier at a given volume control (voltage) setting, thus appearing to have a higher sensitivity than it would if it were an 8-ohm system. The Smaller Advent actually required more power than the Large Advent, but for a given setting of the receiver’s volume control, they seemed to be of comparable “efficiency,” due to the Smaller Advent’s lower impedance.

How Sensitivity Translates into Real-World Loudness Capability

A sensitivity specification is one thing, and we hope that speakers from different manufacturers are tested and spec’d for sensitivity using the same methodology. If they are, then we can compare them and get a pretty good idea of how that spec translates into loudness and power requirements in an actual living room.

Here’s a very good example of how a spec-sheet sensitivity rating translates into real-world information:

Let’s say you have a speaker with a sensitivity rating of 86dB 1m on-axis with a 2.83V input. Some might consider 86 dB to be on the “low” side for sensitivity.

But 86dB is really a pretty healthy level, much more than background listening. It may not be loud enough in a dealer showroom, but in your quiet listening room, you’d have to turn it down to answer the phone.

Now, you’ve got two speakers, so there’s some addition to the 86dB SPL figure because of that. You are also about 8-10 feet away from the two speakers (and somewhat off axis, to boot), so there’s some reduction because of that (the inverse square law, which says that SPL reduces by -6 dB as the distance doubles). Throw in your room’s absorptive characteristics, any open walls that lead to the next room, etc, and what you’re left with is that the raw sensitivity figure for one speaker is a pretty decent number to work with as to how loud two speakers will sound from your listening position with a 2.83V (1 watt) input. There are a LOT of variables, obviously, but 86dB for 1 watt for a pair of speakers from your listening chair is not a bad estimate.

Every doubling of power is another 3dB of increased SPL, So:

• 2 w = 89 dB
• 4 w = 92 dB
• 8 w = 95 dB
• 16 w = 98 dB
• 32 w = 101 dB
• 64 w = 104 dB
• 128 w = 107 dB
• 256 w = 110 dB

So you can see that most amps have the muscle to power even low sensitivity speakers to healthy levels. It’s those peaks that are 10-20 dB louder than the average program level where you really need the power.

This is valid only if Speaker Company A and Speaker Company B test and measure for sensitivity the same way. If they do, great. We’re in the money. If they don’t—if one company is fudging the truth or rigging their tests—then we can’t do a proper direct comparison, and all bets are off.

Conclusion

Probably the best thing would be if every speaker company followed IEC Document 268 to the letter, giving all of us one very specific, agreed-upon, universally-recognized way of measuring and stating sensitivity. If all speaker companies did this, then consumers would have a reliable, transparent way to compare sensitivity ratings from different manufacturers, and reviewers would have a concrete benchmark against which to verify their test result findings against the manufacturer’s claims. But, alas, not everyone does—so caveat emptor! 

Bottom Line: Just make sure when your comparing loudspeaker sensitivity numbers between products from competing manufacturers that you can clearly identify how they have specified this metric by knowing the following:

• Measurement Method:  (In-room, anechoic, groundplane, etc) - anechoic is preferred if measurement isn't bandwidth limited
  
• Measurement Distance:  (1 meter, 2 meter, other) - scaled to 1 meter is preferred
• Signal Type: (Full bandwidth, limited bandwidth, etc) - 300Hz to 3kHz bandwidth is preferred
• Signal Strength:  (2.83V, 1 watt, etc) - 2.83V is preferred
• Specified Impedance: (Static # or Impedance curve) - Average impedance over the sensitivity test bandwidth and an impedance curve is preferred.  

Acknowledgements

• Steve Feinstein, Audio Industry Consultant
• Andrew Jones, Chief Engineer of Pioneer/TAD
  
• Dr. Floyd Toole, Former VP of Acoustical Engineering of Harman; published author of "Sound Reproduction, The Acoustics and Psychoacoustics of Loudspeakers and Rooms", Focal Press, 2008.
• Ed Mullen, SVS Sound