Speaker Impedance

[andreasmaaan]

I think you guys are way overthinking this.

If John Smith has an amp that outputs 50W/8Ohms or 100W/4Ohms he will probably choose 4Ohms speakers to benefit of the additional SPL provided by the added power. He doesn't knows that 8Ohms speakers are more amp-friendly (damping factor, less current) and that THD is better, he cares about power.

I guess it's marketing that dictates this.

I think you're onto something. The majority of the population doesn't even realise that power =/= volume.

 

[briskly]

Extended bass response, cabinet size, and midband efficiency are conflicting parameters. These limitations of moving coil drivers are described by the Thiele-Small parameters. Higher-power and higher-current transistor amplifiers enabled the design of smaller speakers with usable bass response.
To hear Neville Thiele describe it

Twenty five years ago, it seems virtually all speakers were 8R. Today, a larger percentage of speakers, it appears, are 4 or 6 ohm. Why is that?

Is the speaker resistance a function of the length of wire in the voice coil? If that were the case, I would them conclude that manufacturers are simply cutting manufacturing costs by using less copper in the windings resulting in lower impedance speakers.

The Lorentz force generated by a moving coil driver is given by F=B*L*I. For variations of the same model, thinner/higher impedance wires suggest more turns such that the space filled by the coil in the magnetic gap is similar enough. Given that modern amplifiers can handle higher current outputs for a given voltage, a lower nominal impedance suggests a more (voltage) sensitive speaker.
Of course, the nominal rating of the speaker may not correspond to the drivers.

On the other hand, wouldn’t stronger magnets in today‘s speakers cause resistance to rise as they interact with the voice coil?

A fact: Free-field pressure from a radiator is proportionate to its acceleration. In terms of displacement, it is proportionate to the inverse square of the frequency. The displacement to sustain SPL increases by 4 with each decreasing octave.
For a piston in half-space, available on-axis pressure

P = a * Sd * ρ / (2πr) = 2π * f² * Sd * x * ρ / r
ρ is the air density, r is the distance from the driver. SPL in SI units is then:
~94 + 20 log (P)

Newton's laws offer a path to answering the loudspeaker response problem. If the acceleration of the membrane is limited primarily by the mass, then the SPL should remain nearly constant. This behavior will dominate above Fs, the mass-controlled region. With the Lorentz force and Ohm's law, we can recast the SPL response of a moving-coil driver in the mass-controlled zone as

P = U₀ * BL * Sd * ρ / (2πr * Mms * Re)
U₀ being the input voltage.

in which we have assumed self-inductance was negligible.

As a practical matter, the coil of a low-frequency driver will have a great deal of mass not present in the magnet gap. The overhang is needed to ensure some coarse linearity as the driver is forced to accommodate quadratic excursions at lower frequencies. The increased mass without a proportionate increase in BL lowers efficiency/sensitivity above Fs. You could scale up the motor size or increase the magnetic field strength in the gap, but BL also determines the reverse voltage generated from moving a coil in a magnetic field. Considering the loudspeaker as a microphone,

U = BL * v
With Ohm's law and shorted driver terminals,
I = BL * v / Re
Which we insert back in the Lorentz force to get
F = (BL)² * v / Re

(BL)²/Re can be taken as the damping coefficient opposing any motion. It represents the electrical damping of the driver, which drives up the impedance of the coil. The velocity of a driver is maximized near the mass-spring resonance, where damping is the main limit on acoustic output. Taking the damping and inertial forces together, we have
Qes = Mms * Kms * Re / (BL)²
This is the driver damping performed by presenting a driver with a low impedance source, a simple voltage divider. Qes, the damping provided by the Lorentz force, will dominate most loudspeakers, whereas mechanical losses tend to be much smaller. Simply increasing BL would lower Qes, and the damping losses would eventually overtake the increased motor force BLI.

 

[Wombat]

What KEF says: https://www.shop.us.kef.com/blog/a-...ave-better-things-to-do-than-study-impedance/

Simple and good enough for well designed amplifiers and most users.

 

[valerianf]

I do not do car audio competition (4 ohms mandatory) or sonorize some dance parties.
Living in an apartment, I will only buy 6-8 ohms rated speakers.
If I find at the end that the sound level is not high enough, I will buy an additional power amp.
I have some tower speakers with dual woofers in parallel, each unit is measured 16 Ohm to get 8 ohms for the speaker.

It is the speaker manufacturer that needs to make an effort to keep the impedance high enough in the low frequencies range.
It is not the end user that needs to have headaches to find a suitable amplifier.
I remember Amir testing a speaker and its powerful McIntosh amplifier was going to protection mode.
Bad design of the speaker.

 

[voodooless]

I remember Amir testing a speaker and its powerful McIntosh amplifier was going to protection mode.
Bad design of the speaker.

Not necessarily, it's can just as well be bad amplifier design! If you claim to build a build a modern amplifier, better make sure that it can handle lower impedance speakers. It's really not that hard.. Almost any sub €$ 50,- Chinese Class D amp can pull it off pretty well. Of course there are limits to how low should be acceptable nowadays and I don't know the specific example, but in general I think amps should handle the occasional excursion into the 3 Ohm (with the accompanying worst case phase) regions just fine IMHO.

@briskly Thanks for your insights. You might know this: were there, apart from the absence of amplifier available, historically any technological hurdles in speaker driver design that prevented low impedance products?

 

[Rock Rabbit]

Imagine you have certain 8 ohm model LS and the same LS has a 4 ohm version.
They use same magnetic circuit (motor), same cone, coil form diameter and same spider (compliance, the corrugated thing behind speaker cone), as you can guess now they try to make the 4 ohm version identical even same power.
Savings in copper?: the force factor for LS is B•l, at 4 ohms you have 1.4 times more current (same power) so it needs 1.4 times wire section and 0.7•l wire length at 4 ohms impedance (less value in real driver), 40% more copper mass (no savings at low impedance). The force B•l•I still constant at 4 ohms.
Both LS versions have similar TS (Thiele, Small) parameters, specially same Qes and efficiency.
Qes~ Re/(B•l)^2 for the 8 ohm or 4 ohm version (with Re/2 and 0.7•l).
In short, as you see we still can make even 16 ohm speakers with same parameters.
TS parameters are still the same all this years...and we still use cheap ceramic magnets.
P.S.: the magnetic motor gap works by magnetic flux (B•(pole piece area)), it's all about concentrating magnetic flux in a small area. With a humble 3,000 Gauss ceramic magnet the pole pieces can work over 1.2 Teslas.

 

[RealityCheck18]

Cost and style...the manufacturers have to do all sorts of odd things to sell speakers,

For example, say you have the typical cones and domes 5" or 6" woofer bookshelf speaker and you know it will be purchased at Best Buy (or whatever audio shoppe') Say your speaker in the market driven size, frequency response or whatever punches out 85dB 1w/1m and it is 8 ohms. I'm talking a "real" 8 ohms in that it does not drop below 6.2 ohms--like it used to mean. OK, now you have another company and they build the same cones and domes speaker in the same size--however, they know that if it is "louder" than you, it will "sound better" because that is how human hearing works. Say they claim it is 6 ohms but it dips down to 4 ohms in the bass region and, because physics and Hoffman's Iron Law demands it...the efficiency is 85dB 1w/1m the same as the solid 8 ohm speaker. However, in reality the other brands is sitting at 4 ohms in the bass region and the Best Buy comparison box is just a bunch of switches.

The speaker efficiency is the same with both speakers, 85dB at 1w/1m but the sensitivity is actually 85dB for the 8 ohm speaker and in reality, the sensitivity for the 6 ohm speaker that is really 4 ohms is higher at 88dB. Yep, the 4 ohm speaker will be louder when flipping the switches because of the lower impedance--not improved efficiency. Since louder sounds "better" because of human hearing, the higher sensitivity speaker will sound "better" and make the sale! They can also go with strict 4 ohms to drive it harder and use that ability to make it go slightly louder and/or slightly deeper in bass response--for the win! Look at the Elac UniFi thing--the sensitivity is 85dB 1w/1m at 2.83V but it is a 4 ohm speaker. It's actual efficiency would be 82dB 1w/1m which is horrible--that won't sell! It does produce decent enough bass and the same "loudness" when compared to the 8 ohm speakers but has deeper bass response--for the win! It sounds just as loud at Best Buy but has deeper bass..cha-ching!

That makes a lot of sense on the showroom floor--they don't make speakers for fun after all. Sure, it will pull some serious current from an AVR because it is ineffiient AND has low impedance but that is YOUR problem because you are clueless how they work. Sucks to be you!

Look at "tower" speakers, the going style is a pile of woofers, 5 and 6 inchers be they two or three of them. Say you make a single 6" bookshelf speaker at a solid 8 ohms or higher. Now you make a "tower" with two of those 6" woofers and the impedance drips down to around 5 ohms....hmmmm, throw THREE of the same woofers in there and your impedance now dips around 3 ohms---but it is more efficient and louder! Winning! Think of the cost savings by not making 8 ohm, 16 ohm, 24 ohm woofers....same parts, different speaker and all is well. Keep pushing those things, if you have those 3 woofer towers it is your fault because you need a better amp because the speakers are so good! Don't forget to make them piano black finish or something really shiny and claim they make great home theater speakers also....because everyone should have shiny speakers to reflect the light from the screen....makes perfect sense to me.

Look at the impedance measurements and specs on a lot of the slender towers--don't matter if they come from Revel or whomever--you will notice the impedance falls with the towers. Are the manufacturers being cheap and saving cash at your expense? Yes! Does it matter? Well, all depends on how hot your AVR or amps run at 3 or 4 ohms. Granted, the lower the impedance the hotter the amps run which HDMI chips love the heat so... that is fine, should make it past the warranty. I love the smell of hot electronics in the morning...smells like upgrade time.

The lowest impedance dip my speakers make is around 6 ohms as they are a solid 8 ohms or higher. My AVR is 4 ohm capable but runs very cool with my speakers which is a win for me. I'm not saying using low impedance, low efficiency speakers on a 9 or 11 channel AVR is not a good idea--I wouldn't do it but feel free. I do know that my AVR will drive people out of the room without getting hot, clipping or going into protection mode but that is my standard. My center channel uses two 8" 16 ohm woofers and together they give a very easy load and exceed 98dB 1w/1m so no worries. Those speakers replaced speakers at 92dB 1w/1m at "8 ohms" and my AVR ran hotter even at low volumes. There was probably an impedance dip down in the 4 ohm range which makes sense.

Ya see, they used to have a standard that at 8 ohm speaker would not drop below 6.2 ohms, at 6 ohm speaker would not drop below 4.8 ohms and a 4 ohm speaker would not drop below 3.2 ohms (basically would not dip more than 20 to 25% of the rated impedance) Kiss that goodbye! I've seen 8 ohm speakers with 3.2 ohm dips in frequency response--they used to call those speakers "4 ohms". I think B&W has a "8 ohm" speaker that dips down to 2.9 ohms! B&W, Revel, KEF and those "real" brands are full of crap...that is find because their consumers are clueless? Not sure why they can't make a speaker that has accurate impedance specs--too expensive? Because all the other companies are doing it and it has to be as loud as the others at Best Buy? Beats me! Then again, I don't care because I don't buy that stuff--I'm content with what I have.

Imagine if they sold professional PA speakers rated at 8 ohms and it dipped down to 3.2 ohms. Quite common to run a pair of PA speakers on each channel depending on what your configuration is... think how well that would sell knowing the amp is getting hammered at 1.6 ohms instead of 4 ohms implied by the rating. Quite common in the PA world to have a single woofer 8 ohm speaker and the dual woofer model rated at 4 ohms. I'm talking a "real" 8 or 4 ohm speaker as very low impedance dips will shut down PA amps, shut down the gig and you don't get paid. If your speaker is a current pig and causes amplifier issues--most people will avoid those because reliability is key at high power/SPL levels.

Ever see the impedance sweep of car audio subs? Most of the time, they don't go below their rated impedance--ever. Quite common for 4 ohm subs to stay above 5 ohms and so on. The reason for this is obvious! Their customers tend to buy amps and run them at their minimum impedance be it 4/2/1 ohm so if you wire four 12" subwoofers together at "1 ohm" it had better be 1 ohm or higher because it will kill the amplifier.

What I have learned is consumer speakers have bogus specs--pro gear and even automotive is more accurate at least with impedance. Now more than ever you NEED to look at the impedance sweep testing on any speaker, consumer speakers really demand that as the specs are bull shit. The sensitivity/impedance/power handling specs or frequency response with -10dB or -6dB non-standard measurements are now common--even from the great messiah like Andrew or whatever. Funny, they can get the specs right with pro gear but consumer stuff is pure marketing.

So, now is the time to really learn, understand and apply all those charts/graphs that Amir generates and make an informed/educated purchase. Maybe in the future with the increasing power, efficiency and current capabilities of chip amps will allow AVRs to easily push 3 ohm dips all day without overheating, current limiting or cooking the processors--but for now we are stuck with A/B for the most part so paying attention to the impedance can allow your gear to make it past warranty.

Yes, I had an older friend that had a pair of the original Infinity Kappa 9 speakers--the ones that dipped down to 0.8 ohms (complete with delicate ribbons AND foam surrounds!) His Marantz integrated was rated for 4 ohm loads but it would go into protect mode rapidly. He had to purchase an 80 pound block of iron and aluminum just to drive his "4 ohm" speakers and he was PISSED when he figured out he had been had by Infinity and their bogus specs. Shortly after he bought those speakers, Harman bought them out and attempted to get the impedance corrected but... just a bad design with multiple woofers, poorly done crossovers etc. He is probably pissing on Arties grave... the 1980's Marantz could not find a problem with his integrated amp (it was gold baby!) but when they found out his speakers--informed him he needed a very high current amp to make it work. The Marantz was not a POS...it's the speakers.

Just a few ramblings--a few things to think about and ways to sell speakers as the consumer switches speakers around at Best Buy. Just the name of the game in marketing...I'm sure the engineers would prefer to do it right. Keep the shiny side up!

 

[voodooless]

Look at the Elac UniFi thing--the sensitivity is 85dB 1w/1m at 2.83V

That is not how they specify it. You can't have it both ways, it's either at 1W or at 2.83V. They are both valid efficiencies. It all depends on what you find important.

 

[tuga]

Twenty five years ago, it seems virtually all speakers were 8R. Today, a larger percentage of speakers, it appears, are 4 or 6 ohm. Why is that?

Is the speaker resistance a function of the length of wire in the voice coil? If that were the case, I would them conclude that manufacturers are simply cutting manufacturing costs by using less copper in the windings resulting in lower impedance speakers. On the other hand, wouldn’t stronger magnets in today‘s speakers cause resistance to rise as they interact with the voice coil?

What’s really behind this phenomenon?

Small sized boxes and woofers?

 

[Rock Rabbit]

Imagine you have certain 8 ohm model LS and the same LS has a 4 ohm version.
They use same magnetic circuit (motor), same cone, coil form diameter and same spider (compliance, the corrugated thing behind speaker cone), as you can guess now they try to make the 4 ohm version identical even same power.
Savings in copper?: the force factor for LS is B•l, at 4 ohms you have 1.4 times more current (same power) so it needs 1.4 times wire section and 0.7•l wire length at 4 ohms impedance (less value in real driver), 40% more copper mass (no savings at low impedance). The force B•l•I still constant at 4 ohms.
Both LS versions have similar TS (Thiele, Small) parameters, specially same Qes and efficiency.
Qes~ Re/(B•l)^2 for the 8 ohm or 4 ohm version (with Re/2 and 0.7•l).
In short, as you see we still can make even 16 ohm speakers with same parameters.
TS parameters are still the same all this years...and we still use cheap ceramic magnets.
P.S.: the magnetic motor gap works by magnetic flux (B•(pole piece area)), it's all about concentrating magnetic flux in a small area. With a humble 3,000 Gauss ceramic magnet the pole pieces can work over 1.2 Teslas.

Savings in copper?: the force factor for LS is B•l, at 4 ohms you have 1.4 times more current (same power) so it needs 1.4 times wire section and 0.7•l wire length at 4 ohms impedance

Edit: sqr(2) more section and l/sqr (2) gives exactly 4 ohms, same copper volume and mass, no material savings

 

[MrPeabody]

I don't doubt that the complicated elaborations are adding genuine insight into this question. There is always another twist that can be explored.

I will nevertheless point out the obvious. With lower impedance the SPL will be greater, relative to a given voltage seen by the speaker. Current will obviously increase, which means that consumed power will increase, which generally implies an increase in acoustic power. When acoustic power increases according to some given factor, SPL at any given location increases by the square root of that factor (assuming no change in the way acoustic power is spatially distributed).

There are likely multiple potential advantages in obtaining greater SPL relative to the voltage sent to the speaker, although it is debatable how strong or significant they are. If perchance your amplifier is capable of taking the heat (can cope with the current) but is so-so in terms of the +/- DC voltage from the power supply, such that clipping will occur if the volume control is turned up very far, then this can be mitigated by using a speaker with lower nominal impedance.

This would seem to be the most obvious answer. I point it out not because it is necessarily the true answer, but only because it is the most obvious answer.

 

[bigguyca]

That is not how they specify it. You can't have it both ways, it's either at 1W or at 2.83V. They are both valid efficiencies. It all depends on what you find important.

Not efficiencies, the efficiency of a typical home loudspeaker is in the range of 1% or less. The correct term is sensitivity, power or voltage as the case may be. .