THE MYTH OF THE WATT

by Andre Jute

 

HOW MUCH POWER DOES YOUR AMP REALLY NEED?

We all know that it the simplicity of valve gear that makes them sound so good. We also all know that a lot of transistor gear is vastly overpowered for no good purpose. But what is less commonly admitted is that good many valve amplifiers are also overpowered.

 

Another way of putting this is that push-pull pentodes are for most of our applications as music lovers quite unnecessary.

 

The problem is that most people shy away from the complication of calculating how much power they actually need, and simply accept the always-generous >recommended power rating< given out by loudspeaker manufacturers.

 

The perceived complication is mistaken. You can discover how many watts your intended amp should put out with your preferred speakers in your own room with nothing more involved in the line of electronics than a voltmeter, which is of course part of any multimeter.

 

Even if you don't have a multimeter, all the required math is so simple and approximate that mental arithmetic will do the job fine. Or the simplest of calculators, which can multipy, divide and find square roots, if you want to work with those irrelevant decimal fractions. You do not need a set of log-tables.

 

PRINCIPLES

How loud your amp will drive your speakers depends on how much power it puts out, the sensitivity of your speakers, how far from your speakers you listen, and the size, shape and furnishings of the room.

 

Taking these factors from the back, the room is a given. We will assume an average size of room; it really doesn't make all that much difference. The shape of the room can be finetuned with baffles and the furniture changed or moved around to alter reflexivity/absorption.

 

The sensitivity of speakers are normally specified as so many decibels (dB) output for each watt input, measured at one meter; the >at one meter< is often left out and but is always assumed. One meter is 39 inches. It will do no harm to think of it as one yard or three feet.

 

If you find a specification that reads >xdB at one meter for 2.83V< that's just 1W across an 8ohm speaker impedance. We'll come to the importance of the speaker impedance in a moment.

 

An 80dB speaker is insensitive, one of 90dB or better is sensitive.

 

A good rule of thumb is that a symphony orchestra playing full fortissimo in an acoustically sound hall will reach a punter in a good seat (say about four to six rows back, directly or nearly directly behind the conductor) at 90dB. In a theater with drapes on the walls and other soft furnishings, the sound pressure will be less. The purpose of high fidelity is the nearest approach to the concert hall. We can thus say that a lover of orchestral music who wants to reproduce the concert hall experience requires 90dB acoustic level at his ears, regardless of where he sits. That 90db will then take care of any possible peak in the sound; for most of the time the acoustic level will be much lower.

 

The physics of sound are simple and depend on the volume required and the distance from the speaker. It is said that the smallest change in volume that everyone can hear is three decibels; some can detect a change of one decibel. All this is at around 1000 cycles, with hearing acuity and discrimination increasing towards the higher frequencies, but you needn't worry about that. Working in three decibel steps gives you a small margin of safety.

 

Every additional three decibels requires double the power. Thus, if a speaker has a sensitivity of 81dB, to hear 90dB at the same one meter from the speaker, an additional 9dB must be powered, so the power required is 1x2x2x2 or 8W.

 

Every doubling of the distance (over one meter) requires an additional 6dB or quadruple the power to maintain the same acoustic sound level. So, taking our 81dB speaker above, we require 8W to hear 90dB at one meter and 8x4 or 32W to hear the same 90dB at two meters.

 

That, in a nutshell, is the argument for sensitive speakers.

 

It is also only theory. In a normal room reflections reduce the amount of power required to give the same sound level at double the distance, and beyond double the distance the sound pressure level does not fall much unless the room is abnormally large or very differently furnished from the rooms normal people live in.

 

As a rule of thumb, you can reduce the requirement of the extreme case we have now reached--to drive a truly insensitive speaker at peak orchestral levels at a distance of two meters or 7ft8in--by at least a quarter to allow for reverberative effects. So now we are down to 32-8 = 24W.

 

Next, consider that this pressure level, unless you are into monaural sound, is for two speakers. So each channel of the amp (or monobloc) requires only half: 24/2 = 12W.

 

However, this gives no safety margin for overload (or for rock fanatics) so let's double it to 24W or even treble it to 36W.

 

All of this is still only theory but it does prove that if you choose your speakers stupidly, you will have to build or buy a stupid amp to drive them. On the other hand, if you keep your head, you don't have to go in for the masochism of monstrous horns, divorces etc.

 

MEASURING EXACTLY--THE PLUTOCRAT WAY

A way of measuring precisely how many watts an amp you want to buy or build should put out is to use whatever amp you have to hand and measure with a true RMS multimeter how many volts it puts into a speaker when driven so hard that your ears hurt.

 

This level, say 96dB, if constantly used, will reduce your hearing to frequencies below 4000Hz before you are forty. It is negligibly below the 97dB level of an automatic rivetter at 35ft: would you want that outside your window all day? 96dB also represents four times the power required to listen to a realistic reproduction of a full symphony orchestra playing at its lusty loudest. With that much to spare, there will always be overload provision and your amps, if properly designed, will be able to work forever only in the strictly linearpart of their curve.

 

Unfortunately a true RMS meter is an expensive item more likely to be found in the toolbox of a professional than of most amateurs. (But see the Velleman K7105 Handheld Oscilloscope Kit which has an inbuilt RMS meter and costs only only $229 from Old Colony; it is also a storage oscilloscope complete with software to download waveforms to your computer and manipulate them, it measures frequency, AC peak to peak and DC voltage.)

 

A MORE PRACTICAL WAY FOR HOBBYISTS

For this exercise you need a voltmeter. Anything that measures whole volts up to about 50V will do.

 

A brief diversion on meters, inspired by some comments from Glen Pitt-Pladdy, to whom I am grateful for this as for much other assistance. To measure what you use at civilized levels, you would use a milli volt meter to show that your amps hardly ever put out more than a volt, which comes to less than a watt, but here we want to go into deliberate antisocial overdrive. If you have access to a millivoltmeter with a range of say 20V or 30V, that will give a better result than your standard multimeter because the standard DMM is optimized for 50 or 60 cycle working and therefore does not give a wholly accurate picture at 1000 cycles, never mind 20,000. But don't sweat it; this is rough work and almost any meter will do. Best of all, if you can borrow one, is a wattmeter, also called a power meter, from which you can read the wattage directly without doing any mental arithmetic at all.

 

Attach the leads to speaker outputs of the amp, with the speaker also attached. WEALTH WARNING: DON'T OPERATE VALVE AMPS WITHOUT SPEAKERS OR DUMMY LOADS OF THE SAME IMPEDANCE ATTACHED TO THE OUTPUTS.

 

Now turn the speakers up as loud as you can bear and note how many volts are being put on the speakers by the amp at the peaks.

 

Here is all the math you will require. You probably already know that watts out equals voltage squared divided by resistance:

 

Watts out = (V x V)/R

 

but note that here we are talking about the power on the speaker side of the output transformer (in the case of a valve amp). Textbooks normally use this formula for the power before the transformer and ask you to calculate further losses in the transformer. We have made that allowance already by measuring beyond the transformer; a shortcut. The V is for the measured volts and is multiplied by itself to save the bother of measuring current consumed as well. The R stands for resistance but is here the speaker impedance which is usually 4, 6 (many KEFs), 8 or 16 ohms for modern speakers.

 

You don't need to know the sensitivity of speakers you have in your possession to run this test.

 

Let's see how it works in practice. I have bought a pair of QUAD ESL63 but it will be a while before they reach here. Meanwhile I want to build a single-ended tube amp to drive the ESL63, which have a sensitivity of 86dB for 2.83V, i.e. for one watt input to the speakers over their 8ohm nominal impedance I should measure sound output of 86dB at one meter. I want to know how powerful my amp should be to drive my new speakers.

 

The speakers I do have here include a single first series QUAD ESL (correct name, no digits) with a nominal impedance of 16ohms, and a pair of Bang & Olufsen Beovox S25 with a nominal impedance of 4ohms. The sensitivity of the ESL63 will almost certainly fall between these two, so their power requirements will define upper and lower limits for the ESL63. The amps in my study, where I am running the test, are QUAD II rated at 15W. I sit five feet from my speakers, but for the test moved to two meters; that gives yet another safety margin.

 

When the single QUAD ESL was driven to unbearable levels in my room with me sitting two meters from it, the voltmeter never read more than 10V. At this level I could stand it for no more than seconds at a time and feared my classic speaker would break up. Ten volts represents a driving force of (10V x 10V)/16ohms or 6.25 watts. Even 12V represents only 9.0W. Remember, we have here a built-in over-power and sound level factor of four times and then a bit. (We shall return to the importance of this apparently huge discrepancy below.) For a pair of these speakers, each amp, in order to keep up the same sound pressure level, would have to put out only half the power required for a single speaker. That works out to a sensible lower range of 3.25W and an absolute, insane, maximum of 4.5W.

 

Repeat the experiment with the B&O speakers. They require 6V for a sound pressure level that has to be shut down after only seconds because we want to use our ears for the rest of our lives. Once we saw 8.5V but I stopped that by pulling the plug because it was further from the speakers than the pre-amp was. 6V across 4ohm impedance represents 9W as above and the outrageous 8.5V works out to 18W. In this case it is per side, because we had two speakers running on the test.

 

At no time did my nominally 15W QUAD II amps sound distressed, nor the speakers. With quality gear your ears provide the limit of endurance.

 

I repeated the test with Quad and Bang & Olufsen transistor amps, as well as with custom KT88 and trannie amps but the results were the same. That is what one would expect, because it is the speakers' requirement for power we are measuring; nothing to do with the amps. Tests on other odd speakers here revealed how economical of power drivers properly designed for PA duty can be but that is another story.

 

WHY WE NEED AT LEAST FOUR TIMES OVERAGE WITH A COMMON CHEAP DMM

 What we just did, measuring with an averaging non-RMS cheap digital multimeter, makes electrical engineers uneasy.

 

Here is a list, by George R. Gonzalez, of a few things wrong with our cheap meter method:

 

>Speakers can't be modeled as X ohm resistors. They vary up to 600% depending on frequency. They're also inductive or capacitive as heck. W equals E squared over R just doesn't apply when R is extremely variable and has inductive or capacitive components. 8 ohms for a voice-coil speaker is a ballpark figure, usually measured for some midrange frequency. It could go up to over 100 ohms at bass resonance point and at over 10kHz.<

 

>Voltmeters of under $400 or so measure average AC voltage, not RMS which is the basis for power. They read correctly for a sine-wave, but music isn't a sine wave.<

 

>Non-RMS voltmeters also average the power over a fraction of a second. Music has peaks of up to 20 times the average power. So a voltmeter will read a long way below the peak voltage.<

 

>If you have more people in the room, or a window open, or add a rug, you'll need a lot more power.<

 

>Music with lots of bass requires much more power than music with more normal balance. AHA may sound good at X watts, but hip-hop may need 5X watts to sound equally loud.<

 

>All these little points can add up to a very large error in estimating power.<

 

Absolutely. What all this comes down to is that if you don't have specialist knowledge and measuring instruments, you'd better allow very large margins. We have overcome these problems to the maximum extent possible without expensive equipment by:

 

a) measuring with the speakers attached (instead of with a fixed dummy load attached to the speaker output terminals, as professionals use), so that their impedance variations are taken into account

 

b) measuring at a minimum of 6db over a symphony orchestra going full fortissimo, which allows a basic minimum of 400% margin (generally much more) for transients

 

c) measuring at hurtful volumes with your favourite music rather than with "neutral" signals, and calculating for antisocial automatic rivetter volumes

 

d) using another method (calculating from the speakers' nominal impedance) as a double check

 

e) adding an arbitrary 200-300% margin, so that our visible mimimum margin is 9 to 12db over a rather loud 90db (if you commonly play your music at 102dB you will soon be deaf!) which is ample headroom

 

f) arriving at results long hallowed by actual practice (well, actually, our results are higher than traditionally accepted tube practice and a lot higher than modern single-ended afficionados commonly find satisfactory)

 

We don't want to pretend this is precision engineering! But still, tube amps and speakers aren't rocket science. Near enough--as long as it is near enough on the high side--is more than good enough.

 

SPECIFYING AN AMP FOR ABSENT SPEAKERS

So how many watts should my projected amp produce to drive the ESL63 when they arrive? Well, the Quad literature supplies the interesting information that the speakers are not intended to run at more than 10Vrms continuous, that distortion sets in at 40Vrms, and that the maximum permitted peak is 50Vrms. But we know that Quad's own tranny amps have output limiters at 20V when they are used with the ESL63!

 

The literature also claims the ESL63's sensitivity as 86dB for 2.83V but reliable friends have measured it in my room as 85dB, so we shall work with that.

 

Here we go: 1W gives 85dB at one meter, double to 2W for 88dB, double again to 4W for 91dB, which is more than enough for the loudest music I play. So we have 4W at one meter but I sit 5ft away, say 1.5 meters. Let's call it 2 meters and allow the rest for an additional margin, so 4Wx4 is 16W for two speakers, or 8W per speaker. Allow one quarter reduction for the room effects, so the barest minimum is 6W per side. But let's not be mean with our margins. Let's double that, or treble it, as the theory demands. So now we have 12W to 18W, including generous margins. Remember too that this theoretical approach always overestimates the power required.

 

To show you how approximate this all is and how the small bits of margin multiply up, let's not call my 1.5 meters distance from the speakers 2 meters, let's temporarily call it precisely 1.5 meters. Now the calculation above is 4W for 91dB at one meter as before, and then becomes 4W x 2.25 or 9W for 1.5 meters, of which half is 4.5W per speaker, and less 25% for room effects leaves 3.375W absolute minimum. Double for overload is 6.75W and treble 10.125W, down to almost half of what we arrived at by conservatively including a small margin along the way. Okay, let's go back to the `big' round figures, which I remind you were 12W or 18W.

 

By rearranging the formula we already know, we discover that the voltage created by the power source (the amp) across the impedance of the speakers equals the square root of the product of the power in watts and the speaker impedance in ohms. So we cancalculate that across the 8ohm resistance of the ESL63 an amp producing 18W would put 12V on the speakers and that an amp producing 12.5W (slightly higher than the twice-minimum power calculated above) would put 10V on the speakers. Why do these numbers sound so familiar?

 

Now, single-ended 2A3 are obviously best left to the horn-merchants and other masochists. (It is not worth counting the owners of a good pair of first series ESL even if, as seems likely from the serial numbers, there are probably plenty out there; they mostly drive them with QUAD II and have no interest in selling their speakers to wannabee 2A3ers.)

 

But either a single-ended big transmitting valve of the 211/845 class or two 300B in parallel single-ended configuration will give 18W at a walk.

 

As a radical alternative, we could possibly (though no one I know does actually do it) generate 12.5W from a single 300B by putting 400V on the plate with a grid bias of -84V, at which it will draw 80mA plate current, and outputting through a transformer with 2500ohm resistance. That is on the last line of the `Recommended Operating Conditions' as specified by Western Electric for the 300B. A 2.5Kohm single ended output transformer is catalogued by Sowter in the UK (as the SE7-A) and another by Audio Note UK, so we're not talking about custom windings. A small part of the 12.5W will be lost in the transformer (note that we are now back to approved academic electrical engineering practice, taking our power output from the valve before the output transformer) and some more oomph will be unrealized because no-one in his right mind drives a 300B right up to the 5% total harmonic distortion at which WE took their figures, but even incompetently-built amps along these lines, tied to a pair of ESL63, will still have enough welly to damage your ears permanently.

 

So what can we conclude? Surprise, surprise. You don't need horns to enjoy single ended tubes to their fullest, indeed to painful volume levels! And, unless you choose your speakers while operating on auto-pilot, or drive them at psychopathologically anti-social levels, around 8 or 9 watts will do all the business you will ever require. Come to think of it, won't a pair of parallel single-ended 2A3 produce 7W?

 

Naw, let's leave sweaty footprints and go for the full megalomaniac 15 Watts!

 

*****

I want to thank:

 

--Bob Bolton for giving me the rare tube-operated RMS millivoltmeter that I used for doublechecking the end results given as examples in the article

 

--Glen Pitt-Pladdy for a most illuminating discussion of the abilities and limits of professional meters and the shortcomings of cheap multimeters, particularly with reference to their frequency bandwidth

 

--Bill and Declan at Real McCoy Audio for interrupting their teabreak to triplecheck my results with modern professional measuring instruments


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All text and illustration is Copyright © Andre Jute 1995, 1997

and may not be reproduced except in the thread KISS xxx on rec.audio.tubes