Literature about matching power amps and speakers

looking for some recommendations for good literature that addresses optimizing power amp/speaker combinations.  I feel like I've read/heard various conflicting ideas over the years, but never from very reputable sources.  At it's most basic I'm wondering about how to match the max power output of an amp to the power handling specs of a speaker, but I'm interested in a more in depth treatment of that and other related issues.  anyone have some good sources?  Thanks.

For what application? While the general rules still hold.

Loudspeakers have two or more constraints... Long term average power (voice coil heat dissipation). In the extreme the voice coil can fuse, before that you can experience "power compression". As the voice coil heats up the DCr increases due to temp coefficient of the VC wire, so same voltage makes less power. It you turn up the signal to maintain output the VC heats even more, until it releases it's smoke.

  Other dominant limitation is speaker peak or maximum excursion (travel in/out).  Loudspeakers are not linear (voltage = literal motion) but voltage inputs create acceleration in/out so excursion vs voltage is not a simple peak voltage equation, but that can be close enough for government work.

Loudspeakers can handle more short term power than the long term average power, and the genre of music matters too... very dense bass heavy music is more stressful than sparse classical music.

Loudspeaker drivers can have two or three different power handling specs depending on which aspect you are talking about.

In live sound reinforcement there are some rules of thumb like the amp can be 2x the continuous power of the speaker, but YMMV and operators can melt speakers even with underpowered amps. Note: a sine wave driven into hard clipping so bad that it turns into a square wave, will put out 2x the power of a clean sine wave. So how the operator drives the system matters a bunch,

It is possible to craft a DSP based protection circuit with intimate knowledge of the design and drivers used inside a speaker. For years I have been advocating for powered speakers, because actual speaker design engineers match the amps to the drivers, instead of consumers with incomplete information. Even better a smart powered speaker should be hard to kill.

JR

http://www.bennettprescott.com/downloads/LoudspeakerFundamentals.pdf

https://soundforums.net/threads/9953-matching-amp-with-speakers

http://forums.prosoundweb.com/index.php/topic,154017.msg1412814.html#msg1412814

There are probably a hundred threads on sound forums asking amp/speaker matching questions.

There is an old JBL paper (from old HIFI days floating around that is not accurate wrt modern amps and speakers but like a bad penny it keeps popping up in such discussions.

It's a quite complex subject, enough to justify several books..

The main causes of loudspeaker failure (apart from your 5-year old poking knives in the cone) are:
Excessive heat
Excessive excursion

Heat depends on the amount of energy the voice coil receives; energy is power x time. A speaker rated at 100W may very well withstand peaks of 1kW if they are really short.
LS mfgrs generally publish AES power rating; it's the power that the loudspeaker may handle for 100 hours continuously.
The behaviour is actually close to that of a fuse, that can withstand about 10 times the nominal current in order to cope with surges.
About 95-99% of the energy is turned into heat, but ventilation can reduce the temperature increase.
A bass-reflex system has almost zero excursion at the box tuning frequency, so there's a risk of overheating there that may not exist with a closed-box design.

Overexcursion is not difficult to understand; that's when the voice-coil or the cone hits the pole pieces. Again excursion varies vs. frequency in different ways according to the type of box (closed, BR, passive radiator, 4th & 6th-order, labyrinth...).
But overexcursion problems do not necessarily involve brutal collision.
Fatigue is the 2nd most common cause of failure after overheating.
It is extremely difficult to put in equations because there are extreme threshold effects.

Indeed, the life expectancy of a speaker depends very much on the type of program it receives, much more than on the actual power of the amp it is used with.

Multiway speakers present another peculiarity; the power handling of the tweeter is typically about 1/5th of the speaker rating, 10W for a 50W speaker. In order to play safe, one should use a 10W amp.
The dilemma is that the power limit that would ensure total safety is too low in many cases.

I suggest you familiarize yourself with the basics of Thiele & Small parameters and you play with a good simulation software. I recommend WinISD. You can watch the excursion graphs for the different alignments and simulate the energy.

A number of manufacturers of hi-power PA systems use activeprotection systems that simulate the thermal and mechanical stress and apply preventative signal processing. As a result, the systems can be operated closer to their limits with uninterrupted service, at the cost of increased fatigue that imposes preventative maintenance and frequent replacement of drivers.

http://www.eminence.com/d-fend/

For an interesting approach Eminence makes a driver protection device that mounts in series with the driver and steals power from the audio. They use a clever PWM duty cycle to reduce the voltage/power the driver receives when they detect too much.

This is picture of big dog 300V unit, IIRC they also make a smaller PCB version that mounts to the back of a driver.

JR

many valid points given already, here an other one for your consideration:

listen.

your ear is able to tell how much you are pushing it. of course this is much easier if you have muchos muchos more (peak) power then the max specified so that you hear the driver, not amp clipping. this is by the way the 'better' approach for an educated listener. for the volume addicted it's a sure kill.... 

if you need to limit power make sure your limiter (whatever portion of the signal chain is kindly doing that for you) is playing along nicely. so if it is the amp going into hard clipping, it will be harsh, unpleasant, and probably deadly for your tweeter. if it is a softclipping limiter, it might get you a big safety margin. it it is a fancy digital limiter, you might be able to tune it to allow for quite some headroom before your distortion becomes very unpleasant. this might be welcome for an unattended PA you dry hire to a costumer.

I recall using a peveay CS800 featuring a switch-able softclipper - a revelation at the time, 20 years ago.... nowdays I prefer having large amount of power at hand and a tech that can listen.

the long term power handling is much more difficult to set up (band limiting in the x-over). you can go by numbers but to have a faithful setting you might have to run a few hours to simulate real conditions. think of a multi hours / days running rave with lots of low end... might check with the manufacturer for a peak voltage allowed.

- michael

audiomixer said:

I recall using a peveay CS800 featuring a switch-able softclipper - a revelation at the time, 20 years ago.... nowdays I prefer having large amount of power at hand and a tech that can listen.



- michael

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DDT Peavey's "clip limiter" was actually a fast attack/fast release (hard) limiter that detected amplifier clipping and momentarily reduced the gain, then quickly restored it. The fast attack/fast release dynamic characteristic was fairly benign sounding, while effectively protecting amps and speakers from inexperienced operators. (within reason Peavey customers could still blow up stuff when they tried hard enough).

Best practice for experienced operators is indeed using a larger amp, and being careful about how hard you drive the speakers. For the rest, powered speakers are getting smarter as DSP gets cheaper.

JR

thanks for the responses.  very helpful.  If you have any books to recommend on the subject, let me know.

mostly I'm thinking about this in terms of guitar and bass  speaker cabinets, to some extent PA setups, but I guess I'm hoping for information that is general/theoretical enough that it will inform other types of setups as well.  This also makes it hard to "listen" as Michael recommends, because the average guitar signal I deal with is often distorted on purpose, making it harder to detect distortion in the driver itself.

abbey road d enfer said:

It's a quite complex subject, enough to justify several books..

Click to expand...

yeah, this is why I am not satisfied with scouring the web for random forum posts starting with "my general rule of thumb is..."

another tangent issue that I'm hoping to read about somewhere is the logic behind an amp using an array of several speakers in parallel or series/parallel - is it based on volume, power handling, tone differences compared to one more powerful speaker, etc.  Lots of details that I'm curious about.

Matt C said:

thanks for the responses.  very helpful.  If you have any books to recommend on the subject, let me know.

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Like many areas there is good general knowledge in textbooks, but specific answers to your question are not as widely available.

mostly I'm thinking about this in terms of guitar and bass  speaker cabinets, to some extent PA setups, but I guess I'm hoping for information that is general/theoretical enough that it will inform other types of setups as well.  This also makes it hard to "listen" as Michael recommends, because the average guitar signal I deal with is often distorted on purpose, making it harder to detect distortion in the driver itself.

Click to expand...

Designing guitar amps is a whole 'nuther topic.... In fact lead guitar is different that bass.

Regarding speaker distortion, many lead guitar speakers are designed to intentionally distort with the cone exhibiting break-up modes to create a distinctive sound. Further amp front ends are often over-driven to intentionally compress the signal, so this waveform will exhibit high average wrt peak as compared to typical music waveforms.

Bass guitar OTOH is more conventional with less intentional driver break up, and often sealed or ported cabinets vs the open back common with lead guitar amps.

I have worked with guys who designed those  amps as their day job. I don't recall seeing any specialized text books.  Loudspeaker manufacturers my offer some general characterizations of dedicated (lead) guitar amp speakers. I never bought one so don't know.

abbey road d enfer said:

It's a quite complex subject, enough to justify several books..

Click to expand...

yeah, this is why I am not satisfied with scouring the web for random forum posts starting with "my general rule of thumb is..."

another tangent issue that I'm hoping to read about somewhere is the logic behind an amp using an array of several speakers in parallel or series/parallel - is it based on volume, power handling, tone differences compared to one more powerful speaker, etc.  Lots of details that I'm curious about.

Click to expand...

All of the above.  Loudspeakers in series parallel will handle the combined power of all the drivers. In general the drivers can combine constructively at some frequencies. Not very precise or hifi, but a sound many bass guitar amp players like.

JR

Matt C said:

abbey road d enfer said:

It's a quite complex subject, enough to justify several books..

Click to expand...

yeah, this is why I am not satisfied with scouring the web for random forum posts starting with "my general rule of thumb is..."

Click to expand...

Unfortunately, the litterature is spread over a number of pages, some are AES white papers, others can be found on the sites of measurement systems (check AP, NTI, Clio...), and much of the basic knowledge is in reference books. To my knowledge, no one has succeeded in compiling a neat book for intermediate learners.

another tangent issue that I'm hoping to read about somewhere is the logic behind an amp using an array of several speakers in parallel or series/parallel - is it based on volume, power handling, tone differences compared to one more powerful speaker, etc.  Lots of details that I'm curious about.

Click to expand...

Lots of different motivations.
Anecdote: Leo Fender, after being criticized for his original single-15" equipped Bassman Amp farting out, he opted for a quartet of 10", thinking that the less flappy smaller cones would better behave.
Quite the contrary, to the point that the 4x10 would become a favourite of guitarists and harmonica players.
There are many parameters that govern the choice of multiple speakers.
For the original Marshall 4x12, the reason was the speakers available for guitar applications in the UK at the time were not powerful enough. A typical 12" would be rated at max 30W (the 12" in the AC30 were rated at 15W).
But people discovered that the 4x12 had better projection than most speaker cabinets. The reason is that, as the source becomes larger, the directivity increases, that means the sound goes to the front more than to the sides. There's not more acoustic power, but it is better concentrated.
This concept permeated into the 70's, where the Martin PA system used a wide aspect ratio for providing more  front-directed sound.
And again, there are a number of screwy reasons: one that always make me sigh is when I read in HiFi ads that a speaker uses smaller bass units in order to provide "faster bass", which is a ridiculous notion. The "speed" (let's say rise-time) is almost entirely governed by the cross-over frequency.
Now there is a certain sound that a 18" cannot deliver and a 10" can.
That's why many bass rigs use a combination of 18" and 10". Since the power handling of the 10" is much lower than the 18, multiples are a necessity. In fact, quite often, 3x10" would be a good match for 1x18", but that would pose a problem of impedance and physical arrangement, hence the more common 4x10.

For GUITAR, it is fairly simple.

Find the amplifier claimed output. Today this will be at 5% Sine distortion.

Double that. This is the FULL OVERDRIVE square-wave power output.

Look at GUITAR-rated speakers and find a speaker rated for at least that much power.

Example. I built a hot little amp and measured 13W clean, 16W pretty distorted, Sine. When OVER-driven to total flat-top, I measured 23 Watts of near-pure Square Wave. A guitar-market "25W" speaker would be a good fit. (A "25W" hi-fi or car-sound speaker would not survive.)

Can you use a higher-Watts speaker? Depends. Some players prefer break-up, and the old Magnavox-pattern cones do go into distress with modern coils and big amplifiers. You probably do not want to over-Watt the speaker much past the factory suggested power. OTOH serious transducers like JBL D-130 and E-V MI-series just do not have cone break-up at any sane power level. For the player who likes that tone (break-up the amp, not the speaker), a 300W speaker on a 30W amp is fine. (I did consider an EVM-12L on that 13W/23W amp.)

Bass is different. IMHO the speaker system should be larger than the venue and the genre. This is usually impractical. The bass players I have worked with seem to change systems, often radically, every few years. I recall when an Ampeg B-15 (early series) was go-to for jazz bass. But for upper register fingerings it is sluggish and beamy. The early Bose plastic-box speakers were wonderfully more responsive (and lighter!). But after a few years they sounded bad, and I found the cones just hanging out (over-excursion). Harke had a better plan of more less-small drivers in a larger box. Of course outside jazz, the bass does not do tenor (that's the guitar's job) and the best answer is as many medium-box 18s as will fit in the van, plus a KiloWatt of amp.