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Amplifiers - How Much Power Do You Need?

Copyright © 2019, Rod Elliott (ESP)

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Introduction

The question posed above is a truly vexing one, and there are as many answers as there are people asking the question.  The short answer is "it depends", and I readily admit that this probably doesn't qualify as a useful answer for most people.  To make matters worse, the long answer is the same as the short one, so we need to examine the dependencies.  Unfortunately, there are a great many, and they change with the type of music you like, your loudspeakers, your room, and whether you expect to reproduce 'concert level' SPL (sound pressure level) in your listening space.

I'm not going to look at 'pro audio' as used for sound reinforcement in large (or even small) venues, although the basics apply equally regardless of the specific application.  However, there is a short section that might help.  It all starts with the loudspeakers, and is heavily influenced by your expectations.  Depending on your age group, you will have different needs, taste in music, and tolerance for loud music (or a requirement for louder than normal music to compensate for hearing loss).

The last point is critical.  When we were (or are) young, loud music was expected, and in general, the louder the better.  Unfortunately, this means that you will suffer from hearing loss and/ or tinnitus (ringing in the ears) when you get older.  Naturally, young people are psychologically incapable of projecting themselves into the future to understand that what you do when young can stay with you for life.  In case you were wondering, I was no different, and I'm now the unhappy sufferer of tinnitus, which is permanent, never-ending and incurable.  While my hearing threshold is raised (so I can't hear very soft sounds), my tolerance for very loud music (or noise) is reduced.  I'm by no means alone.

It should be self-evident that amps should be used within their limits.  An amplifier that's clipping some (or most) of the time is acceptable only it it's a guitar amp, as the vast majority are used with heavy overdrive.  For hi-fi, this is obviously unacceptable, as you literally 'lose' up to half of the music.  One of the many (and mostly false) claims that you'll see is that when an amp clips it outputs DC.  This is unmitigated drivel!  If an amplifier outputs DC, it has failed, and isn't an amplifier any more.  Clipped AC is still AC, regardless of how heavily it's clipped.  The polarity alternates from positive to negative, so it takes a particularly twisted view of physics to imagine that this somehow equates to DC.  Sometimes you'll see claims of "little bits of DC", which is also drivel and again ignores basic physics.  What actually happens is that the power is at its maximum possible value on a more-or-less permanent basis (while the amp is being abused by heavy clipping).  A 20W amp driven into full clipping may output up to 40W, and much more of that power is delivered to the tweeter than normally will be the case.

Without exception, this article concentrates on amplifiers used within their ratings, providing normal programme material with no more than a very occasional transient being clipped.  This will generally go un-noticed by the majority of listeners.  Provided you listen at 'sensible' levels, which means an average power of only about 1-2W, it doesn't matter if your amp is rated for 50W or 5kW - most of the power will never be used.  Naturally, if you do have a 5kW amp and someone turns it way up, your speakers probably won't survive for more than a few seconds.

While it a most useful form of reference, the dB/W (or just dBw) only enjoyed a very brief spell in the limelight.  By definition, it's an amplifier's output power, referenced to 1W.  For example, a 50W amplifier would have an output level of 17dBw (8 ohms) or perhaps 19.8dBw into 4 ohms.  With this information, you can determine the peak output of any loudspeaker, simply by adding the speaker's sensitivity (dB/W/m) to that of the amplifier.  For the 50W case and the 'reference' 8Ω speaker I've used in this article (86dB/W/m), you get 103dB - the peak level at 1 metre at the onset of clipping.  This is useful, but you must still contend with the room, listening distance and a myriad of other minutiae that all influence the sound level at the listening position.

An orchestra has also been used as a reference, because it's more predictable than a rock concert.  Of course, not every one is 'into' orchestral music, but it remains one one the most demanding in terms of reproduction in the home.  With 'pop/ rock' and other genres, live performance levels depend on the venue size and where you sit/ stand, the type of PA (public address/ sound reinforcement system) and how much power is available (which often exceeds 50,000W - 50kW!), and there is no way to predict the level.  An orchestra at full crescendo will produce around 100dB SPL (average, 110dB SPL peak) at the third row [ 1 ], representing an acoustic power of about 400mW (0.4W, with 4W peak).  From this, we can extrapolate the electrical power required (based on 100dB SPL), provided we have enough information.  This still doesn't mean that there's an exact answer, because there most certainly is not .

Project 191 is specifically designed to let you monitor the peak voltage and current delivered by your amplifier, under normal listening conditions.  It's not something that is common, but if you really want to know how much peak power you are using, then it's well worth building.  It's far easier than trying to use an oscilloscope to monitor the voltage, as it is too easy to miss a transient that causes the amp to clip momentarily.


1 - Maximum SPL Vs. Time

There are many charts and guidelines, but the following is a pretty good estimation of the likelihood of hearing damage (from any source - not just loud music).  Many hi-fi systems (and especially headphones) are able to create sound levels capable of causing permanent hearing loss, so you must be very careful to avoid damaging levels.  While we do have two ears, one is not a spare!

Continuous dB SPLMaximum Exposure Time
858 hours
884 hours
912 hours
941 hour
9730 minutes
10015 minutes
1037.5 minutes
106< 4 minutes
109< 2minutes
112~ 1 minute
115~ 30 seconds
Table 1 - Maximum Exposure to SPL (0dB SPL = 20µ Pascals)

Note that the exposure time is for any 24 hour period, and is halved for each 3dB SPL above 85dB. The above shows the accepted standards for recommended permissible exposure time for continuous time weighted average noise, according to NIOSH (National Institute for Occupational Safety and Health) and CDC (Centres for Disease Control) [ 2 ]. Although these standards are US based, they apply pretty much equally in most countries - hearing loss is not affected by national boundaries.

You need to be aware that if your ears 'ring' after a concert or even a loud listening session at home, that indicates the you have done permanent, irreparable damage to your hearing.  Yes, it will pass after a few hours or days, but if you keep doing it, it eventually becomes permanent, and is called tinnitus [ 3 ].  As a sufferer, I can assure readers that it's not something to aspire to.  Home listening will rarely be loud enough to cause problems, especially for people who live in apartments - the neighbours will let you know (in no uncertain terms) when you've reached their limits.  Concerts (and of course, industrial (work related or otherwise) noise) are prime causes of hearing damage.

This is not intended to scare anyone - sensible levels are ... sensible, and it's often easier than you imagine to drive a hi-fi system to get loud enough for long enough to cause problems.  This information is provided because it's relevant to how we listen, and therefore how much power we really need for a home hi-fi system.  The 'reference' level (used to calibrate sound level meters) is 1 Pascal, which is 94dB SPL.  The calibration process involves producing exactly 94dB SPL at 1kHz, usually in a small chamber into which the meter's microphone is inserted.  You don't need to know this, but it's provided as 'background' information that might come in handy one day.


2 - Loudspeaker Sensitivity

Sensitivity (or efficiency) is the first thing that needs to be assessed.  The range is fairly wide, depending on the driver(s) themselves, and how they are configured (e.g. horn loaded, direct radiating, etc.).  The listening space also plays a significant role, in particular whether it is reverberant or highly damped.  Most home listening spaces are somewhere in between, and the level of room treatment (if used), furnishings, floor covering, etc., influences the amount of reverberation experienced.  Some people go to great lengths to treat their listening space for the best reproduction, while others allow fashion to dictate the space.  While these things all matter when it comes to the quality of reproduction, the effects on SPL are less certain.

The distance between your listening position and the loudspeakers makes a big difference, so 'near field' listening (where the speakers are no more than around 1 metre from you) requires less power than if the speakers are at one end of a large room and you listen from the other end.  This is generally not considered to be a good idea, but this article is about how much power you need, rather than optimum speaker and listener placement.  The latter is a topic unto itself, and there are probably as many opinions as there are listening spaces, although there really are many sensible guidelines.

If a typical domestic hi-fi (or even 'lo-fi') speaker system has a sensitivity of (say) 86dB/W/m, that means that with an input of 1W, the SPL will be 86dB at a distance of 1 metre from the speaker.  Sensitivity isn't always specified correctly, with some manufacturers using a 'reference' voltage of 2.83V RMS regardless of the actual impedance (2.83V gives 1W into 8 ohms).  If the speakers are 4 ohms, that's 2W, not 1W, a difference of +3dB.

For much of this discussion, 86dB/W/m will be assumed, as it's representative of many systems.  Higher sensitivity is better, but that often compromises other parameters (such as box size for the required low frequency cutoff point).  The design of loudspeaker drivers involves many compromises, and efficiency is one of the first parameters that suffers in order to get good low frequency response.  Before we go too much further, I suggest that you read Power Vs. Efficiency, which examines the power handling capacity of loudspeaker drivers.  Sine even a high efficiency loudspeaker will be lucky to exceed 5% efficiency, the vast majority of the remaining power is dissipated as heat in the voicecoil.  There are losses in the suspension and even the magnetic circuit, but these don't amount to very much in the majority of drivers.

The hypothetical speaker described here (86dB/W/m) has an efficiency of around 0.2%, meaning that for every Watt of input, only 0.2W emerges as acoustic energy (sound).  The remaining 99.8% of the input power is converted into heat.  If one were to find a driver that measured 112.1dB/W/m, it would be 100% efficient, with no losses at all.  Needless to say, this driver does not exist.  Even horn compression drivers have a theoretical maximum efficiency of 50% (measured using a plane-wave tube), and most will only manage around 24-30% in real life.  These are the most efficient (conventional) drivers that exist, and expecting anything to be 100% efficient is unrealistic.  You can calculate the efficiency easily with the following formula ...

Efficiency = 10 ^(( dB SPL - 112.1) / 10) × 100

For our speaker, that calculates to an efficiency of only 0.209% - hardly something to crow about.  While efficiency is important for a large auditorium or other spacious venue, it's pretty much a non-issue for home listening.  Certainly, there are people who love their high-efficiency horn loaded systems driven by a couple of watts from a tiny valve (vacuum tube) amplifier, but that's not something most listeners want.  Horn loading is a wonderful concept, but for low frequency performance, the horn has to be large (both in length and mouth area).  This rarely sits well in most home environments.

The speaker sensitivity itself doesn't really tell us very much, other than how loud it will be at a distance of one metre and with one Watt of input power.  This isn't the average listener's primary criterion, because we want to know how loud it will be at the listening position.  Almost all systems will be stereo, so there are two sources, driven by two amplifiers.  If each is driven with 1W, the acoustic power into the listening space is doubled (+3dB).  This falls at 6dB for each doubling of distance in free field (the inverse square law).  This is almost never the case in reality, because few (if any) home speakers are operated in free field (i.e. open space without 'significant' boundaries). At some point in the room, one enters the 'reverberant field', where the level is relatively unchanged by distance.  The point where this occurs is known as the 'critical distance'.  It's highly dependent on the room geometry, room treatment and directionality of the loudspeakers.

Part of the difficulty of analysing and understanding loudspeaker efficiency ratings is that we are rarely told how the measurement was taken.  The microphone will usually be on axis of the speaker (or the mid-point where multiple drivers are used), and it's location can be any distance from the source, 'normalised' to the level at 1 metre.  What we generally are not told is whether the measurement was in 'free space' (no significant boundaries), half space (on an infinite baffle, with no other significant boundaries), or using some other (perhaps proprietary) method.  A speaker's directionality also comes into play, so a driver with a horn or a waveguide may show a significant improvement in sensitivity, because it's directional.  Even if a speaker appears to indicate that its sensitivity is greater than the theoretical maximum of 112.1dB/W/m, that doesn't mean the supplier is lying (not that this would ever happen in audio of course ), because if it's highly directional that improves the apparent efficiency.

Omnidirectional speakers (equal radiation in all directions) are preferred by some, along with other arrangements such as bi-polar (figure 8 radiation pattern).  These can generally be expected to show reduced sensitivity compared to a 'normal' forward radiating design, but the way the sensitivity is measured can sometimes be misleading.  Not too many people have access to calibrated microphones or sound level meters, but you can often get a passable estimate using nothing more than a smartphone app.  These are far from precision devices (even the best of them), largely due to the microphone and the acoustically large (at high frequencies) case of the phone itself.  However, it's better than nothing, and great precision isn't necessary because music is so varied.


3 - The Room

The listening room plays a very significant role in the reproduction of music of any genre.  Many hi-fi enthusiasts will have a well damped listening room, with absorption panels to limit the amount of reverberation, and diffusers to ensure that the remaining reverb is scattered.  Bass traps (absorbers) may also be used to limit standing waves.  Soft furnishings, rugs or carpet, heavy curtains and bookshelves (preferably filled with books) all help to create a diffuse sound field, so the sound directly from the loudspeakers is by far the most dominant.  This diffuse field with a minimum of reverberation (and especially so-called 'slap' echoes, because they are very distinct) ultimately reduces the overall level you hear.

You can almost always get a good idea of a very reverberant space in a bathroom, which will have tiled floor and walls, and minimum (if any) sound absorbing material except maybe a bath mat and a couple of towels.  If your listening room is similar, then it's unrealistic to expect good clear sound, because the reverb will muddy everything.  In some cases, the listening environment is dictated by 'fashion', which at the moment seems to mean minimalist, with hard floors, lots of glass (but no heavy drapes/ curtains), and few (if any) rugs.  In many cases, a hi-fi or home theatre layout and furnishings may be dictated by 'SWMBO' (s/he who must be obeyed), and there's little that can be done to appease one's partner and get a satisfactory listening space.

A reverberant room usually needs very little power before the entire performance turns into mush - with all the details obscured by echoes of varying durations.  While this is far from ideal, for many people there is simply no choice, other than to use headphones for personal listening, or to set up a 'man/ woman cave' where things can be arranged to get a reasonably acoustically dead listening environment.  The latter may not be possible either, unless one's domicile has an extra room that can be dedicated and shut off from the rest of the house.

With apartment living now becoming much more common than it once was, there will be definite limits to the level you can produce, lest the wrath of the neighbours descend upon you with great force.  Bass is especially troublesome, because it can penetrate concrete walls, floors and ceilings if loud enough.  Bass also has the ability to travel great distances without significant attenuation by the atmosphere.  Most people have to deal with what they have, and when you have close neighbours it's quite surprising just how little power can be used before someone starts hammering on your door.

There are countless articles on the Net about room treatment, and if that's something you wish to examine in detail I suggest a search.  Beware of snake oil - many vendors sell 'products' that achieve exactly nothing (other than in the mind), and these are usually easily identified.  Bags of coloured rocks (no, I'm not joking), small stick-on patches, 'holographic' images and the like cannot change a room's acoustic properties, and are fraudulent.  Many people claim that a room can be 'equalised', but this is also false.  The effects of reverberation and/ or echoes are time related, and you cannot correct time with amplitude (which is all an equaliser can alter).  Unfortunately, the home theatre industry seems to have convinced people otherwise, which is shameful IMO.  However, in some instances the use of EQ can compensate for speakers that are 'inadequate' at frequency extremes, or have pronounced peaks at some frequencies (for example).  However, it must always be understood that ...

You Cannot Correct Time With Amplitude

Equalisers affect only amplitude and phase (the latter is 'incidental', and occurs when any filter is applied), and there is no amount of equalisation that can genuinely 'fix' a bad room.  The frequency response at the listening position can be 'corrected' to some degree, but that only means that it will be far worse elsewhere in the listening space.  This has become one of the greatest myths around, with respected manufacturers providing (often 'automatic') 'room correction' features on equipment, because that's what the buyers want.  Such 'room correction' uses a microphone, and these cannot (and do not) 'hear' the same way that we do.  A great deal of our hearing is in the brain, not our ears, something that cannot be replicated by current systems.


4 - Dynamic Range

The next issue is dynamic range.  An orchestra has a (theoretical) dynamic range of perhaps 70-80dB, with up to 85dB being possible, but not necessarily achievable in real life.  Much depends on the venue, how much audience noise is present, and the ambient noise in the venue itself.  With other music genres, the range is from perhaps 60-70dB down to almost zero (i.e. the music starts loud, and is loud throughout the performance).  The only break may be between songs, so the effective dynamic range can be as low as 6dB (a power ratio of 4:1).

Recordings are often much the same.  Some have good dynamics, and include soft bits and loud bits as required, but many 'post-production' facilities have engaged in the 'loudness war' [ 6, 7 ] that have been with us in earnest since the 1970s or so (it actually started in the 1940s!), where every recording made tries to be louder than anything that came before it.  That this is a travesty is not disputed by many, others don't seem to mind that a solo acoustic instrument is just as loud as the whole band/ orchestra (etc.) playing at full crescendo.  Unfortunately, the idea of pp (pianissimo - very soft) and ff (fortimisso - very loud) [ 4 ] seems to have been lost in many recordings.  ppp (softer than very soft) and fff (louder than very loud!) are gone - to some producers, everything has to be fff or people will presumably not like it.

Almost without exception, recordings use varying amounts of compression to limit the dynamic range.  Some take it to extremes, so there is little or no variation of loudness, leading to flat, lifeless recordings that might be alright in the noisy interior of a car, but that sound dreadful when heard on a good system in the home.  The available dynamic range also depends on the ambient noise in the listening space, and unless you are blessed with a rural location far from the madding crowd, you can generally consider yourself lucky if the background noise level is below around 30dB SPL.  Traffic noise, planes, trains and neighbours all conspire against getting much better than this, other than late at night.  Few of us have the luxury of a dedicated soundproofed listening room.  Note that in almost all cases, ambient noise is measured using A-Weighting (see A-Weighting (Sound Level Measurements & Reality) for my take on this).

Although we can hear things that are below the noise floor, we can't expect to hear them clearly.  In general, that means that we'll probably have the TV set for a level approximately the same as 'normal speech' (typically around 60dB SPL), perhaps a little more depending on the programme material (and to compensate for hearing loss - especially for older people).  This is also a realistic level for background music, but if we are having a listening 'session' that may increase somewhat.

Remember that our reference speaker has a sensitivity of 86dB/W/m, so to get an average (and comfortable) level of 75dB SPL, we probably won't need more than 100mW/channel (average, and assuming a reasonable listening space).  However, audio isn't about averages, because there are dynamics involved.  We must also consider the peak to average ratio, i.e. how much power is needed to reproduce peak levels for the average output level of interest.  Consensus is hard to find on this, and it can vary from 20dB down to as little as 6dB, depending on the material itself, and how much post-processing (predominantly compression) has been applied.  An average figure of 10dB is, well, average.  There are also some potentially confusing references to 'crest factor', which is ostensibly the same thing, but is sometimes used in unexpected ways.  For example, a pure sinewave has a crest factor of 3dB, meaning that the ratio of the peak to RMS voltage is 1.414 (√2).

Some amplifiers (e.g. B&O Icepower modules, and based on the datasheet for the ASX series)) are designed for a peak to average ratio of 8:1 (18dB), and if operated at close to full power with material having a lower dynamic range, the amp will shut down due to over-temperature.  Rest assured that many other manufacturers will take a similar approach.  Ultimately, it's all about heatsinking, and keeping it to a minimum consistent with normal programme material.  Heatsinks are bulky and expensive, so minimising them reduces costs.  If you build your own gear these's no limit to the heatsink that can be used, but ultimately cost has to be considered.

Essentially, the goal is to determine just how much power is needed from an amplifier to provide a satisfactory level in the listening space, without clipping, and without causing the amplifier to overheat.  If we take 85dB SPL as our basic target level, this is not unreasonable, and as shown in the table above, our ears can handle that for 8 hours without causing damage.  If we now assume a peak to average ratio of 10dB, that means that we need 10W to reproduce the peaks.  In theory then, a 10W/ channel amplifier will do just fine.  Or will it?

A mere 10W/ channel actually will be alright, but it's very limiting.  You'll be able to listen to (most) music at up to 85dB SPL, but if you try turning it up for a track you particularly like (or because there is more background noise than normal), you'll run out of power and the amplifier will clip the transients and higher level peaks.  Equally, some music has a wider peak/average ratio, with anything up to 20dB being common with well engineered material.  Some (small) amount of clipping can go un-noticed, and to save you the trouble, some CDs are produced with the material pre-clipped, saving you the all the bother of over-driving your amplifier.  This is (of course) an appalling state of affairs and should never happen, but it does.

We mustn't forget about the well reported claims that underpowered amplifiers cause speaker failure (tweeters in particular).  While it can be argued that this is a myth, there is a modicum of truth behind it, which makes it harder to dispel.  The problem is not the underpowered amplifier, it's the user pushing up the volume until the amp is in heavy clipping.  What this does is limit the dynamic range, which may fall below 3dB.  Imagine a 50W power amp, which can deliver up to 5W average power before the peaks start to clip.  Now increase the volume until it's clipping badly (around 50% of the time).  The 'normal' peak to average ratio is reduced from around 10dB to as little as 3dB, so the average power is now closer to 50W, and not the 5W normally expected.  In particular, the HF energy is increased disproportionately, due to a combination of extreme compression and additional harmonics.

The idea of using a larger amplifier to provide 'headroom' can only work if the additional power remains unused.  In other words, you can avoid speaker damage by using a bigger amplifier, but not if the user increases the volume so that all the power is used again.  When a speaker (driver or system) is rated for (say) 100W, that doesn't mean that it can handle the full power at any frequency, it means that if used sensibly (without excessive clipping) it can handle the output from a 100W amplifier with normal programme material.  As a specific example, a tweeter rated for 100W will die almost instantly if you actually apply 100W to it - the rating is for system power only.  In normal use, that same tweeter will only get around 10W, and that's close to its maximum power handling capacity.  In general, it's not unreasonable to use a 150-200W amplifier with speakers rated for 100W, but only if the amp is never driven into clipping!

Speakers also need headroom.  If a driver is operated at (or near) its maximum rating for long periods, the voicecoil will get hot, and its resistance increases.  This raises the speaker's impedance, so less power can be delivered for a given voltage.  Power compression isn't a common problem with home hi-fi, but it's of considerable concern for high power systems.  If your drivers have no headroom, they will not be able to respond to crescendos in the music.  The power may increase by (say) 15dB, but the speaker might only manage 10dB, so you lose dynamics.  At worst, this turns the music to mush - detail is lost, and the music sound compressed and lifeless.

All of this brings us back to the original question ... How much power do you need?  As should now be apparent, the question might seem simple, but the answers are not.


5 - How Much Power Do You Need?

For most systems these days, it seems to be the accepted norm that somewhere between 50W and 150W/ channel is 'about right'.  Even with low efficiency drivers, this lets you get to an average level of between 5 to 15W, with peaks taking up the remainder.  That lets you get to a listening level of perhaps 92dB SPL (room and distance dependent of course), and up to 97dB SPL with a 150W amp - assuming the speakers can handle the power of course.

If we assume that the peak to average ratio is somewhere around 4:1 (12dB), then our 50W amplifier can deliver peak levels (transients) of around 102dB, with the average level being about 90dB SPL.  However, nothing is 'cast in stone', because the type of music you listen to makes a very big difference to the overall experience.  Some music may present much greater peak to average ratios than the 4:1 quoted, and it's extremely difficult to get reliable information on this unless you perform your own measurements.  Material with a wide dynamic range (say 40dB or more) may leave soft passages down around 50dB SPL, which is fairly soft.  It's unrealistic to expect that a home hi-fi can handle the full dynamic range of an orchestra, while keeping the softest passages above the ('typical') noise floor of 30dB SPL.  That would require that the system reproduce up to 100dB SPL average, meaning that peaks may reach 112dB SPL.

To examine this issue, we need to look at amp power again.  We know that as a rough guide we'll get around 86dB SPL with 1W (stereo of course), so to get another 26dB above that to accommodate peaks/ transients, we need a bit over 400W of amplifier power for each speaker.  The average power during loud passages will be a little over 31W.  While these may not look too outlandish at first glance, very, very few home speaker systems will tolerate 500W peak power without serious distortion.  If this power is maintained for any length of time, driver failure will be the inevitable result.

One respected manufacturer (Klipsch [ 5 ]) used a fully horn loaded system to get around this.  The systems were primarily designed with wide dynamic range material in mind, and used a folded corner horn with a horn loaded compression driver for the top end.  This was never an approach taken lightly, and while a great many found their way into domestic environments, the actual number would be tiny compared to more conventional (or perhaps less unconventional) loudspeakers.

For the vast majority of listeners, an amplifier capable of delivering around 50 - 150W will be more than sufficient, but another approach helps squeeze every last Watt from a system - biamping or triamping.  This topic is covered in some detail in the article that started the ESP website - Biamping - Not Quite Magic (But Close).  By splitting the audio signal prior to the main power amplifiers there are some real gains to be had in terms of SPL, but there are other benefits as well.  Of these, the flexibility of an electronic crossover can't be matched by any passive design, but as with everything, there are limits.  One of the biggest is that it becomes extremely difficult to swap speakers around, because the external crossover network means that they can't just be connected to any amplifier you like, because you need two (or three) stereo amplifiers, rather than just one.

Average dB SPLAverage Power (W)Peak Power (W)Peak Power (W) ¹
561m10m32m
6610m100m320m
76100m11.2
861 (reference)1032
9610100320
1061001,0003,200
1161,000 (1k)10k (!)32k (!!)
Table 2 - SPL Vs. Power (86dB/W/m Reference)

Every 10dB requires that the power is multiplied (or divided) by a factor of ten.  If we allow for 15dB peaks (indicated in the last column ¹), this is increased to a factor of 32.  From this you can see that at more-or-less typical listening levels (which I'd place at around 75dB SPL, ±10dB) you only average about 100mW, and peaks won't go much beyond 1W (3.2W 'worst case').  If we were to choose 86dB (which is actually quite loud), that increases to 1W and 10W for peaks.  Note however that the 10:1 ratio is far from an exact science, and it can vary by up to +10dB.  Some instruments are also capable of large amounts of asymmetry (muted trumpet is one of the most extreme I've seen), so the peaks are predominantly of one polarity.  In some cases, this may increase the required voltage swing further than expected.

It may not seem right, but doubling the power (a 3dB increase) is not 'twice as loud'.  To obtain the subjective effect of 'twice as loud' means that the power must be increased by 10dB - 10 times as much.  In fact, an increase of 3dB is audible, but not readily so, and the smallest increase (or decrease) that we are able to discern is 1dB.  Indeed, the very definition of the decibel is based on the smallest increment that's normally audible, but in a subjective test, listening levels should be matched to within 0.1dB.  Our hearing tricks us in many unexpected ways, and a system that's 1dB louder than another will usually be declared as sounding 'better' (assuming both have equivalent frequency response, directivity, etc.).

Bass heavy material can be far more demanding than other programme material, with a much higher than expected peak to average ratio.  This is an area where biamping (and up to full 4-way active) systems will outperform almost any system using passive crossovers.  The subwoofer can require far more power than expected, depending on the topology.  For example, mine uses an equalised sealed box, and while it can get to 20Hz easily enough, it needs 400W to do so at 'realistic' sound levels.  That's more power just for the sub than I have available in the rest of the system combined (which is 3-way active, not counting the sub).  I seriously doubt that I have ever clipped the main amplifiers.

At this point, we've come close to a full circle.  All of the aspects have been examined, and the answer is still "it depends".  However, if you know the speaker sensitivity and your preferred listening level, you can get a reasonable estimate.  It also turns out that somewhere between 50 and 150W really is 'about right', with the higher power generally needed only if you listen at higher levels than normal, have particularly inefficient speakers, or listen to material with a much greater dynamic range than most 'modern' recordings (whether analogue (vinyl) or digital).

This doesn't mean that a higher power amp is necessarily 'wasted'.  If your passion is classical music, it can have a large dynamic range (but only if well recorded of course).  Other recordings can also have a greater than 'normal' dynamic range, and if your speakers can handle short bursts of up to 200W or more, then a bigger than average amplifier may well be warranted.  Bear in mind that when most 'typical' home hi-fi speakers are driven to their limits, loudspeaker driver distortion can quickly become a serious problem.  Consider that a mid-bass driver may normally show an excursion of perhaps 2-5mm with bass, and an excessively powerful amp may push/ pull the voicecoil well outside the magnetic gap.  This leads to high levels of amplitude modulation of higher frequencies, which in turn causes excessive intermodulation distortion products and greatly reduced performance overall.  Everything has its limits!

One of the easiest ways to get more SPL is to use more efficient speakers.  I've used 86dB/W/m for the examples here, but if you have speakers that are rated for (say) 89dB/W/m, the power needed for a given SPL is halved.  It's unusual for hi-fi speakers to exceed 90dB/W/m, because the requirement for 'decent' bass response demands a low resonance driver, and this is not possible while maintaining high efficiency.

Small cabinet, High efficiency, Bass response ... Pick any two !  This is often called 'Hoffman's Iron Law'.

Basically , it means that you can have good bass in a small enclosure, but efficiency will be low.  Likewise, high efficiency and good bass are possible, but perhaps not in an enclosure that will fit through the doorway.  For most people, this means modestly sized enclosures (often bookshelf or small 'free standing' types), and expecting lots of dB/ watt is unrealistic.  Also, consider that smaller drivers have less thermal mass, and since up to 99% of the power delivered to the speaker ends up as heat, power handling is always a compromise.  You can't expect a 200mm diameter driver to handle a continuous average power of more than 50W or so, although the peak power can be considerably higher.


6 - Public Address & Instrument Amplifiers

While the primary focus of this article is home hi-fi, similar principles apply to live sound systems and instrument amplifiers (e.g. guitar amps and the like).  The differences are considerable, usually because large spaces have to be filled with enough sound to keep the punters happy.  For instrument amps, the traditional 100W guitar amplifier is generally huge overkill, because most guitar speakers are far more efficient than any home system.  100dB/W/m is not uncommon, so with a fairly typical amount of 'overdrive' (i.e. distortion) a 100W amp can easily deliver over 125W on a fairly continuous basis.  Even with a single driver, that will produce up to 120 dB SPL at 1 metre.  That's seriously loud, with a maximum exposure time of about 10 seconds in any 24 hour period!

Most modern sound reinforcement systems use line arrays (which I dislike intensely, but that's another story).  Many are not particularly efficient, but that's more than compensated by using multiple amplifiers, each capable of up to 2kW, and sometimes more.  Interestingly, one brochure I looked at claimed that the mid-high section was capable of 114dB/W/m - almost 2dB greater than the theoretical maximum of 112.1dB/W/m (100% efficient).  While this might seem impossible (or at least highly improbable), it comes down to directionality.  If all of the acoustic radiation is concentrated in one direction (rather than 'free field' (in all directions at once - omnidirectional) then the figures can indeed appear to be greater than those indicated by the formula shown in Section 2.  By their very nature, line arrays are directional, and the longer the line (physically), the more directional it becomes.  All directional speaker systems will show (sometimes unexpectedly) higher sensitivity than a normal home hi-fi speaker, but that doesn't always mean that they are actually as efficient as claimed.

Large venues need a lot of amplification, and unfortunately, few venues are designed for optimum sound quality.  The 'modern' approach seems to be that the sound contractor is tasked with providing sound at a reasonable level to every seat in the house.  No-one seems to care much if the sound is crap, provided everyone gets more-or-less the same crap and at more-or-less the same SPL.  It helps if the sound is intelligible, but that may (or may not) be a requirement.  No-one expects high fidelity, and that is certainly not what they get (despite a multiplicity of 'specifications' that say otherwise).  Modern concerts (of the rock/ pop genre) are about 'bums on seats' - the more people you can assault with high-level sound, the greater the profits.  Call me cynical (which is fair and reasonable), but I'd much rather get good sound, where I can actually hear the nuances of the performance, rather than making my tinnitus worse than it is already.

It is possible to get good sound, but not when it has to be served up to 60,000 people in a stadium designed for watching football matches.  I used to run PA systems for a living, mixing the band, and ensuring that the punters got the best sound I could provide.  Despite all the technological advances, it seems that many systems today can't manage to do as well as we achieved 30-odd years ago.  This is another topic altogether of course, and no more electrons will be used up to even try to cover it here.  There is more info in the article Public Address Systems for Music Applications.

One example does warrant a paragraph though.  Guitar speakers are normally very efficient, with around 100dB/W/m being typical.  That means that when driven at full power (usually with some clipping), the SPL can easily reach a long term average of well over 100dB SPL.  Given that guitarists are often very close to the speakers (within 2 metres or so), it should come as no surprise that a great many of the 'old rockers' are as deaf as posts.  Audience members who get as close to the stage (or the PA system) as possible are not much better off, and many of them will be similarly afflicted in later years, if not already.


7 - Power Compression

As noted earlier, this is a topic well known to professional audio people, but it gets nary a mention (not even in passing) for hi-fi.  It's a very real phenomenon, and is caused by the loudspeaker driver's voicecoil getting hot under sustained power.  Voicecoils are usually made from copper or aluminium, and like all metals they have what's called a 'thermal coefficient of resistance'.  This means that if the voicecoil gets hot, its resistance rises, and the speaker's overall impedance increases.

Without getting into too much detail here, this demonstrates that if the temperature of an 8Ω voicecoil (typically having ~6Ω DC resistance) rises by 100°C, its resistance will increase by around 2.4Ω, so the '8 ohm' speaker now has an impedance of about 11.2Ω.  This does two things - it reduces the power being delivered to the speaker for a given voltage, and therefore make the speaker less efficient.  The other thing that happens is that the crossover frequency and response changes, because it is no longer loaded with the design impedance.

Because the vast majority of hi-fi speakers use a passive crossover, that means that the tonal balance is affected, and invariably not in a good way.  The more power you use into a speaker, the worse the problem becomes, and if you go beyond the limits of the speaker it will be damaged.  With professional loudspeakers, many manufacturers go to extreme lengths to minimise power compression, but consider that a figure of 6dB is considered about average.  When driven at full rated power (actually voltage), the output level is half the 'nominal' value.  A 98dB/W/m driver has been reduced to 92dB/W/m, equivalent to reducing the amp power by a factor of four!  A 1kW amp is delivering only 250W because the impedance has doubled.

This is a very good reason not to push your speakers too hard, so if you need more SPL, then you'll be better off using more efficient speakers than a bigger amplifier.  Power compression affects all drivers at all power levels, but provided you stay with the maker's recommendations it's not likely to be noticed by most listeners.  Naturally, the less power you use, the smaller the effects (to the point where they are virtually inaudible).  Speaker efficiency is always quoted when you purchase individual drivers, but often not for complete systems.  It is an important parameter, but the ramifications aren't something that many people understand fully (if at all).

I don't recommend that you ask any hi-fi salesperson about power compression, because 99% of them will have no idea what you're talking about.


Conclusions

This article was prompted by tests I did on a small bench amplifier I'd just built, which can deliver about 25W into 8 ohms.  When I cranked it up (with the oscilloscope monitoring the output), just below the onset of clipping I thought that it was surprisingly loud, certainly louder than I expected, and all this through a fairly average 2-way vented box with a 125mm (5" in the old measurements) woofer.  Admittedly, the programme material was from FM radio and compressed to within an inch of its life, so the comparison (to a hi-fi system) isn't exactly fair, but so much modern material already has similar amounts of compression that it's not too far off the mark either.

Since then, I've used some fairly dynamic material from a demo CD a friend put together some years ago, and for the majority of the time I thought that at just below clipping, it was too loud to be comfortable for any length of time.  The system is also only mono (stereo in my workshop is impractical for a variety of reasons), so it didn't have the benefit of another channel with the same power helping things along.  While listening, I also monitored the peak (via the oscilloscope) and RMS voltages, and the ratio of 4:1 was passably consistent (statistically speaking).  Some material (such as a drum solo) exceeded that ratio by a good margin, but the peak level is still set by the CD player, so keeping the amp below clipping wasn't difficult.

I found that around 80dB SPL was about as loud as I was comfortable with.  This was achieved quite easily at my workbench, which is around 2.5 metres from the speaker.  The difference between speaker level at 1 metre and 2.5 metres was only 2dB, largely due to the construction of that part of the workshop.  My main workshop speaker system is 3-way active, horn loaded mids and highs, and a dual 300mm vented box for the bottom end.  That easily outclasses the little speaker and amp I was testing, but I still tend to listen at no more than 70dB SPL (and usually much less).

To assist people who really want to know the peak voltage and current they use during listening sessions, a project has been published (see Project 191) that describes a peak detector.  It can capture and hold the peak levels of both voltage and current, and you can read the maximum voltage and current with a DMM (digital multimeter) after the event.  If either reaches your amplifier's maximum capabilities, you know there is a problem.  Another project that's a bit more advanced calculates the actual power in real time (if used with an oscilloscope). This is described in (see Project 192).  For most purposes, Project 191 is the better choice, as it tells you the peak voltage and current, the two parameters that let you decide easily whether your amp is big enough or not.  Usage is described in the article.


References
1   Amplifier Power: How Much is Enough? - Stereophile
2   Noise Dose - NoiseHelp
3   Hearing Loss, Tinnitus - EarScience
4   Dynamics (Music) - Wikipedia
5   Kilpshorn History
6   Loudness War - Wikipedia
7   The Loudness Wars - Why Music Sounds Worse - NPR

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