Where your decibels go: loudspeaker motors and thermal compression

Your PA is a space heater that makes sound as a side effect. Here's the physics of why the rig that slammed at soundcheck sounds smaller at midnight, and what you can actually do about it.

It's 11:40 on the second night of a two-day festival. The headliner is four songs in. At soundcheck, seven hours ago, the subs hit you in the sternum hard enough that the promoter walked out to front of house just to stand there and grin. Now the same console, the same snapshot, the same limiter thresholds, and the low end feels like someone put a moving blanket over it. The system tech swears nothing has changed. The meters agree with him. The RTA mostly agrees with him. Your ears have filed a formal complaint.

The new guy on the patch reaches for the sub master. You watch him add three dB and get maybe one back, and the one he got sounds worse, slower and rounder, like the kick drum gained forty pounds during the drum solo. Somewhere in each of those sub cabinets there's a coil of copper wire the size of a soup can running at around the temperature of a pizza oven, and it is quietly renegotiating the terms of the show.

Nobody at front of house is going deaf. The rig is running a fever. This week we're going down into the motor, the actual electromagnetic machine inside every cone driver you've ever pointed at an audience, to figure out where the decibels go. There's a resistor in there that grows when you feed it, a magnet that sulks when it gets warm, and a set of ratings on the datasheet that mean much less than the marketing department hopes you think they mean. By the end you'll know why "just turn it up" is the one move guaranteed not to work, and what to do instead.

One to three percent, and that's the good news

Start with the number that explains everything else: the efficiency of a direct-radiating cone loudspeaker. Not the sensitivity spec, the actual energy conversion, watts of acoustic power out per watt of electrical power in.

For hi-fi speakers it's typically 1 to 2 percent. Big pro-audio woofers do better, sometimes 3 or even 5 percent for a high-sensitivity fifteen on a horn-loaded low end. Read that again if it's new to you. The best case in our industry is a machine that throws away 95 percent of what the amplifier sends it. The rest becomes heat, and nearly all of that heat shows up in one place: the voice coil, a few dozen grams of copper wound on a former, sitting in a magnetic gap with clearances measured in tenths of a millimeter.

You can compute this from the Thiele-Small parameters on any datasheet. The reference efficiency is

η₀ = 9.78 × 10⁻¹⁰ × Vas × Fs³ / Qes

with Vas in liters and Fs in Hz. Take a plausible pro fifteen: Fs of 40 Hz, Vas of 120 liters, Qes of 0.32. That comes out to η₀ ≈ 0.0235, call it 2.3 percent. Convert it to the familiar spec with sensitivity ≈ 112 + 10·log(η₀) and you get about 95.7 dB at 1 W/1 m, which is exactly the neighborhood where real drivers of that description live. The formula and the datasheet agree because they're the same physics wearing different clothes.

Now do the ugly arithmetic. Put 1,000 watts of program into that driver and about 23 watts leave as sound. The other 977 watts have to go somewhere, and where they go is into a coil of wire with the thermal mass of a candy bar. A hair dryer on low runs on less power than what that voice coil is asked to dissipate, and a hair dryer has a fan, a big intake, and a housing designed by people whose whole job was getting rid of heat. The voice coil has an air gap the width of a guitar string and whatever cooling the motor designer could sneak in around the magnets.

This is the original sin of the moving-coil loudspeaker, and it's worth sitting with, because everything else in this piece is a consequence. The compression you hear at midnight, the power ratings that seem made up, the reason line arrays exist in the shape they do, the reason a competent system tech cares about average power and not peak power. All of it comes back to the fact that we chose, a century ago, to make sound with a resistor.

And to be fair to the century: we chose well. The moving-coil driver is cheap, rugged, linear-ish, and manufacturable by the million. Every alternative that beats it on efficiency loses on cost, bandwidth, or the ability to survive a Tuesday load-in. But the bill for that bargain is paid in heat, every show, and the currency is your headroom.

F = BL·i, the whole machine in five characters

Here's the entire motor, no simplifications hiding anything important. A permanent magnet drives flux across an annular gap. In that gap sits a cylindrical coil. Push a current i through the coil and it experiences a force

F = BL·i

where B is the flux density in the gap in teslas and L is the length of wire actually sitting in that flux, in meters. Their product, BL, is the force factor, and it's on the datasheet, usually in tesla-meters or the equivalent newtons per amp. It is, opinion incoming, the single most honest number on a driver spec sheet. You can't cheat BL. It's measurable, it's linear in its units, and it tells you how hard the motor can shove per ampere.

Put numbers on it. A serious pro woofer might spec BL at 20 T·m. Drive 5 amps through it, which is about 200 watts into a 8-ohm nominal coil, and the motor produces 100 newtons of force. That's the same force as hanging a 10 kg weight, applied to a moving assembly, cone plus coil plus former plus half the surround and spider, that weighs maybe 150 grams. Do the division and the cone sees an acceleration of about 667 m/s², or 68 g. Your cone accelerates harder than anything at the theme park, thousands of times a second, all night. When people ask why drivers cost what they cost, that number is a decent start on the answer.

The two ways to grow BL are more B and more L. More B means more magnet or a better magnetic circuit: bigger ferrite donuts, or neodymium, which packs several times the energy product into a fraction of the weight and is why modern line array boxes don't require a chiropractor on the rider. More L means more wire in the gap, and here the designer walks into a lovely trap: more wire means more mass, which eats efficiency (mass shows up squared in the denominator of the efficiency math); it also means more resistance, which makes more heat; and if you make the wire longer by winding the coil taller, most of the extra winding hangs outside the gap where B is weak, contributing resistance and mass while doing almost no work.

So every motor is a negotiated settlement between force, mass, heat, and cost, and the negotiation happens in a space about the size of your fist. The gap itself wants to be narrow, because flux density is roughly inversely proportional to gap volume for a given magnet; but a narrow gap can't carry cooling air and will scrape the coil the first time a stagehand drops the cabinet off the truck lip. The pole piece wants to be fat for flux, but a fat pole steals room from the coil. Nothing in there is an accident. When you buy a good driver you are mostly buying ten thousand hours of someone else's arguments about half-millimeters.

Hold onto BL. It comes back twice more: once when heat attacks the magnet that makes B, and once when the coil physically leaves the gap and BL collapses with excursion. Both are compression. Only one of them shows up on a thermometer.

Copper charges interest: 0.4 percent per degree

Copper is a wonderful conductor with one clause in its contract that ruins evenings: its resistance rises with temperature, at roughly 0.4 percent per degree Celsius. Aluminum, the other common coil material, behaves almost identically. This isn't a defect of cheap drivers. It's the material physics of every metal you'd actually wind a coil from; the alloys with flat temperature response, manganin and friends, have resistivities so high they'd make hopeless voice coils.

Follow the chain. You push the system harder. More average power lands in the coil. The coil gets hotter. Its resistance rises. And now three separate bad things happen at once.

First, the obvious one: with an amplifier that behaves as a voltage source, which is essentially every amplifier you've ever used, current is what the resistance allows. Resistance up, current down, and force is BL times current, so force falls, so output falls. Keith Howard measured and wrote this up years ago in a piece that should be required reading: heat a copper coil from 20 °C to 200 °C, a temperature real pro drivers reach and are built to survive, and its resistance rises by a factor of about 1.7. Sensitivity falls correspondingly, in the region where the coil's resistance dominates the impedance, by nearly 5 dB. Five. You could double the size of the amp racks and get 3.

It's worth being precise about the bookkeeping here because the industry isn't. When a manufacturer specs "power compression," they typically mean SPL loss versus input power, measured after some prescribed cooking period at −10 dB, −3 dB, and full rated power; those figures come out smaller, a few dB at rated power for a good driver, because power delivered into a hotter coil also falls, and the two effects partially net out on paper. Both descriptions are true. The one your audience experiences is the simpler one: the amps are doing what they always did, and the rig is quieter.

Second, the sneaky one: damping. The electrical damping of a driver, the thing that grabs the cone at resonance and stops it flapping, depends on the resistance in the loop. Qes is proportional to Re, so a coil that's picked up 40 percent more resistance drags the whole box alignment with it. Your neat maximally-flat reflex tuning drifts toward underdamped: fatter around tuning, slower to settle, boomy. This is why hot subs don't just get quieter, they get worse. The kick that was a punch at soundcheck is a shove by the encore. You can hear compression as a level problem and reach for gain, but this part isn't a level problem, and gain makes it more of itself.

Third, the one passive boxes suffer alone: crossover drift. A passive network is a filter terminated by the driver's impedance. Design it against 6.3 ohms of cold coil, then let the coil climb to 9 or 10 ohms, and the filter isn't the filter anymore; crossover points slide, response wrinkles appear, and the tweeter's padding changes relative to a woofer that's compressing on its own schedule. Fully-processed active rigs are immune to this specific failure, one of the quietly enormous arguments for them, though they compress thermally like everything else.

Add it up and thermal compression isn't one artifact, it's a syndrome: less level, worse damping, shifted response, all arriving together, all growing with the average power of the last several minutes rather than with anything you can see on a peak meter. Which is exactly why it fools people. The meters at front of house are showing you volts. The compression is living in degrees.

Where the heat actually goes

So the coil makes heat. What happens next is a plumbing problem, and it's worth understanding because every mitigation a manufacturer brags about is plumbing.

Model it the way driver engineers do, as a thermal circuit. Heat flows from the coil to the pole piece and top plate across the air gap; that path has a thermal resistance, call it a couple of degrees per watt for a big woofer. From the magnet structure, heat flows to the outside air through a second, slower resistance. Each stage also has a thermal capacitance, its ability to soak heat before its temperature rises. The coil's is tiny, tens of grams of copper, so its time constant is a few seconds. The magnet assembly is kilograms of iron and ceramic, so its time constant runs from tens of seconds into minutes. Klippel's group has published the whole nonlinear treatment, including the fun wrinkle that cooling improves with excursion because the coil pumps air through the gap like a piston.

The two time constants are the practical takeaway. The coil rides the last few seconds of program: one sustained bass drop and it's up hundreds of degrees, one quiet verse and it sheds most of that into the metal around it. But the metal doesn't forget. Over a set, the whole motor structure climbs, and the coil's excursions now start from a higher floor. This is why the rig sounds fine for the opener, decent for the support act, and congested for the headliner: you're listening to the integral of the whole evening, not the current song. It's also why a fifteen-minute changeover genuinely helps, and why the difference between night one and night two of a festival, same rig, same weather, can be the residual heat of night one if the crew struck the covers late.

Do one honest worked example. Say the long-term thermal resistance, coil to ambient, totals 2 °C per watt, a reasonable order of magnitude for a large woofer. Your amp is peaking at 800 watts, and the music has a crest factor of 9 dB, so the average power is about 100 watts, and roughly 97 of those become heat. Steady state: about 195 degrees of rise. On a 25 °C summer night the coil is sitting near 220 °C, adhesives are at their rated limits, resistance is up around 80 percent, and you've lost about 5 dB of the sensitivity you paid for. Nothing has failed. This is the machine working as designed.

Everything the industry does about it is an attack on one of those resistances. Bigger coil diameters put more copper surface near more metal. Thick top plates and finned housings move the coil's heat outward faster. Vented pole pieces and ventilated gap designs let the cone's pumping actually exchange air instead of churning it. Ferrofluid in the gap, common in tweeters, conducts heat across the gap far better than air. And DSP-era systems increasingly model coil temperature in real time and limit or compensate accordingly, which is honest engineering, even if it means the system is now protecting itself by doing gently and deliberately what physics would otherwise do rudely.

The magnet, meanwhile, has its own grievances. Magnet materials weaken as they warm; ferrite loses roughly 0.2 percent of flux per degree, recovered on cooling. Heat soak from the coil therefore trims B, and with it BL, which is more compression through a second door. With ferrite this stays reversible in normal use. Neodymium is the interesting case: standard grades tolerate only about 80 °C before losses start becoming permanent, so pro drivers use high-temperature neo grades and layouts that keep the magnet out of the worst heat. Get that engineering wrong, or buy from someone who did, and a hard season doesn't just compress the driver, it permanently retunes it: BL down, sensitivity down, Qes up, forever. Cheap neo drivers that "wore out" usually didn't wear out. They cooked.

The other ceiling: BL(x) and the honest millimeter

Thermal compression has a colder cousin that arrives instantly and leaves instantly, and confusingly, we often just call it compression too. It lives in geometry.

BL assumed the coil sits in the gap's flux. But the coil moves; moving is its job. In the common overhung design, the winding is taller than the gap: picture a 19 mm tall winding centered in a 9 mm deep gap. Near rest, the same amount of wire is always immersed, and BL is constant. Displace the cone far enough, though, and winding starts leaving the flux on one end without being replaced on the other. BL(x), the force factor as a function of excursion, rolls off. Force per amp falls exactly when the program is demanding the most, the motor squeezes the waveform's extremes, and you get level compression plus a bouquet of odd-order distortion.

The classical spec for this is Xmax, and the classical formula is pure geometry: winding height minus gap depth, over two. Our example driver: (19 − 9)/2 = 5 mm of one-way excursion before the coil's edge reaches the gap's edge. Simple, but it flattered everyone, since BL doesn't fall off a cliff at that point, it slopes, and slopes differ. So the modern definition, from Klippel's work and adopted in AES recommendations, is behavioral: Xmax is the excursion where BL has fallen to 82 percent of its rest value, which corresponds to roughly 10 percent motor distortion; for subwoofers, where the ear forgives more, the threshold is commonly relaxed to 70 percent. When two datasheets disagree wildly about Xmax on similar hardware, this definitional fork is usually why, and the AES-style number is the one that means something.

Excursion compression and thermal compression stack, and they take turns being the binding constraint. Down near tuning in a reflex box the port unloads the cone, excursion stays modest, and heat is the limit. An octave higher, excursion demand can peak while the coil is merely warm, and BL(x) takes over. A well-designed limiter structure respects both: a fast peak limiter for the mechanical ceiling and a slow RMS limiter, seconds of attack, tracking the thermal one. If your processor gives you both and you've only set one, you've locked one of two doors.

While we're inside the motor, one more piece of copper deserves its shout-out: the shorting ring, also sold as a Faraday ring or demodulation ring. It fixes yet a third motor sin. The coil's own field magnetizes the iron parts around it, and since the coil moves and the current alternates, the coil's inductance varies with position and drive, Le(x) in the literature. That modulation is a distortion generator and it also lets big low-frequency currents smear the midrange, real intermodulation you can hear on full-range drivers. A ring of aluminum or copper placed in the magnetic circuit behaves as a shorted transformer turn: eddy currents in the ring oppose the flux wiggles, inductance drops and flattens with excursion, the top end of the driver's band extends, and IM distortion falls. When a datasheet mentions a "demodulating ring" it isn't decoration; it's one of the cheapest large improvements in modern driver design, and its absence in a "professional" driver at a suspicious price is telling.

Reading the datasheet like an adult

Now that you know what's inside, the ratings page becomes legible, and mildly funny.

Start with the wattage, since that's the number the marketing department prints largest. A serious manufacturer's power rating traces to a standard test: pink noise, band-limited to the driver's working range, with a stated crest factor, run continuously for a couple of hours. B&C, to name one house that documents this properly, rates nominal power with 6 dB crest factor pink noise for two hours, then defines "continuous program" as double the nominal figure, a nod to the fact that music is spikier than test noise. That's what a power rating is: survival of a specific torture, at a specific spikiness, for a specific time. It is not a promise of proportional loudness, and after the copper section you know it can't be; the last few dB of that rated power are substantially converted to temperature, not level.

Crest factor is the load-bearing idea. The test noise sits 6 dB peak-over-average. Most live music runs 8 to 10 dB or more, so an amp that can swing big peaks spends most of its life delivering far less average power, which is precisely what the thermal path cares about. This is also why heavily "maximized" program, the mastering-war stuff, or a DJ running everything pinned into a brickwall limiter, cooks drivers that handle a live band all summer: push the crest factor down 4 dB and you've roughly two-and-a-halved the heat at the same peak level. When someone tells you their playback set killed a rig that bands never hurt, no mystery remains. Density did it.

Sensitivity has its own small cons. Check whether it's specified at 1 watt or at 2.83 volts, because 2.83 V into 8 ohms is 1 watt but into 4 ohms is 2 watts, a free 3 dB for the brochure. Check the averaging band, since a generous octave choice can harvest a presence peak. And then look for the row that separates grown-up datasheets from brochures: measured power compression at −10 dB, −3 dB, and rated power. A good big woofer shows a few tenths of a dB, then 1-something, then 2-to-4 as you climb to full rating. Those are the honest decibels. A manufacturer who publishes them is telling you, in writing, that the last 3 dB of amplifier you were about to buy will deliver less than half of itself as sound. Respect that candor. It's rarer than it should be.

Read this way, the spec sheet stops being a leaderboard and becomes what it actually is, a map of the compromises someone chose. High BL and low Mms buys sensitivity at low-end extension's expense. Monster Xmax means a tall coil that's mostly outside the gap, so efficiency paid for it. A 4-inch coil handles heat a 2.5-inch never will, and costs and weighs like it. There are no free parameters in there. There never were.

A field guide to a hot rig

You can't see coil temperature from front of house, but the syndrome has fingerprints, and once you know them you'll spot it in the first thirty seconds of walking into somebody else's problem.

The reliable tell is the mismatch between the meters and the room. Output metering on the amps and processor reads normal, or even higher than earlier, because everyone has been nudging faders, while the SPL at the mix position has sagged and the spectral balance has tilted. It tilts in a particular direction: the deep low end thickens and slows as damping degrades, while the octave or two above the subs, the punch region, is where the level loss reads most clearly. People describe it as "the kick disappeared but the boom stayed," and that sentence, verbatim, is thermal compression introducing itself.

The second tell is time. Nonlinearity from over-excursion arrives instantly and leaves instantly; it lives on the peaks of this bar of music. Thermal compression has memory, minutes of it. If the rig sounds noticeably better after the acoustic set, or after a changeover, and worse twenty minutes into anything dense, you're watching the thermal time constants breathe. Clipping doesn't heal during a ballad. Copper does, partially.

If you have access and inclination, you can measure it. Modern amp platforms report load impedance per channel; watch the reported impedance of a sub channel climb over a set and you are literally reading the coil's temperature in ohms, 0.4 percent per degree, in real time. No fancy platform? The classic crew check still works: the back of a hard-run cabinet's magnet structure will be unmistakably hot to the hand, and while your palm is not a calibrated instrument, "can't hold it there" on the outside of the motor means the coil inside spent the evening far hotter. And the before-and-after test settles arguments: play the same reference track at the same drive level at load-in and after the show, measure both, and the difference, typically a couple of dB on a hard-worked rig, is the tax the evening collected.

One caution while diagnosing: hot and clipped can coexist and feed each other. An operator who chases thermal sag with gain eventually runs the amps out of voltage, and now peak limiting and thermal compression are stacked, which reads as a rig that is simultaneously dull and harsh. Fix the order of operations. Get the average power down first, let the coils shed a hundred degrees, and only then judge what the system actually has left.

What you can take back to the desk

The physics is fixed, but almost everything about how you spend it is a choice. Here's what we'd actually change on the next gig.

Stop chasing the fade. When the rig compresses, the level you add mostly becomes heat, which becomes more compression; you're paying a tax to raise the tax. If the show got quieter over two hours and the meters didn't, the honest fixes are average power and time: trim the low-end density, let the limiters do their slow work, use the changeover. The fader is the one tool guaranteed to make tomorrow night worse too, because the magnet remembers.

Mix with crest factor in mind. The single biggest thermal lever you own is how dense the last twenty minutes were. A mix with dynamics left in it runs the coils cooler at the same perceived size. Buss compression pushed 4 dB deeper into the reds isn't "glue" from the driver's point of view; it's wattage with the sound removed.

Set both limiters like you mean it. Peak limiting protects Xmax; only a slow RMS stage, seconds, not milliseconds, tracks the thermal reality. If your drive processor offers a proper thermal or RMS limiter and you've left it at defaults from a different box, that's the first hour of homework after reading this.

Buy sensitivity and count boxes, not watts. Three dB of sensitivity equals a doubling of amplifier power that never happens, with no heat bill attached. And four boxes at quarter power make the same SPL as one box at full power while each coil runs dramatically cooler and further from BL(x) trouble; a good chunk of why big-format arrays sound effortless is exactly this, distributed dissipation, compression that never gets a foothold.

Tune for the second hour, not the first. Your soundcheck happens on the coldest, best-damped, most sensitive version of the system you will hear all day. If the low end is perfectly voiced at 5 PM on a cold rig, it's slightly over-ripe at 11. Experienced system techs voice a hair lean and let the evening thicken the rig into place. It always does.

And when you spec or buy: look for vented gaps, big coils, demodulating rings, published compression figures, and high-temperature neo grades, and treat a suspiciously light, suspiciously cheap neo driver as the liability it is. The heat is coming either way. The only question is whether somebody designed for it.

The moving-coil driver has been converting most of our amplifier power into warmth since before any of us were mixing, and it will keep doing it long after. It's not a scandal, it's a settlement, and the terms are printed on every honest datasheet in tenths of a dB. Know the terms, spend your average power like the scarce currency it is, and the rig that slammed at soundcheck can still be slamming when the encore hits.

Above the Fader

Sauce

• Keith Howard, "Hot Stuff: Loudspeaker Voice-Coil Temperatures," Stereophile
• Wolfgang Klippel, "Nonlinear Modeling of the Heat Transfer in Loudspeakers" (Klippel GmbH)
• Wolfgang Klippel, "Assessment of Voice Coil Peak Displacement Xmax" (Klippel GmbH)
• Klippel Know-How: Voice Coil Temperature measurement
• B&C Speakers, "Power Handling" (test methodology and program power definitions)
• Rod Elliott (ESP), "Measuring Loudspeaker Driver Parameters" (Thiele-Small and efficiency)
• speakerwizard.co.uk, "η₀ (Eta Zero) – Reference Efficiency"
• Wikipedia, "Power compression"
• AE Speakers, "Designing for Low Distortion: Lambda 001 Motor" (shorting rings and Le(x))

Featured photo by Jonathan Phillips on Unsplash.