How much amplifier power do you need

Before the amplifier power recommendation was made, quite a few listening tests were performed in typical living conditions. Most of the listeners preferred the music at these tests at the average listening level of 80 to 84 dB. Tests proved that listening at this spl does not feel tiring even at prolonged listening and does not cause any psychological discomfort. 

The main deciding factor on spl is Nmin (minimal spl in room), which is equal to Nnoise (background noise) plus the dynamics (D). 

Nmax  =   Nmin   +    D

In the city, where the houses or flats are near the roads, railways, construction sites, the background noise is on average 40 to 50 dB. This, at the average Nmax 80 to 84 dB allows the dynamic range of the music for 30 to 40 dB. 

If you want more dynamics, you have to raise the spl, which leads to irritation of your spouse, and neighbors, and even you being tired. 

What should be the wattage of the amplifier recommended for normal listening level? Because high quality amplifier needs to handle peaks without the distortion, and music is full of short peaks, transients, the Nmax was raised to 94 dB. 

Acoustic power can be calculated using equation:

P  =  wcoA / 4

where w is level of acoustic energy (J/m3)

co is speed of sound (340 m/s)

A is absorbing surface (m2)

Absorption can be calculated as:

N  =  10log  w/wo

where wo is threshold of hearing (3.1E-15 J/m3)

w  = wo * 10N/10

Then we can calculate the required electric power  from acoustic power Pa  and efficiency of the speakers (Eff):

P  =  Pa /  Eff

For the size of three typical rooms (42, 54 and 82 m3), typical sound delay of 0.35, 0.40 and 0.50 s, and assuming speaker efficiency Eff ~ 1%, we get the required amplifier electric power as 4.92 watts, 5.68 watts and for third largest room 8.57 watts. Yes, less than 10 watts. 

For highly efficient horn loudspeakers, with Eff ~10%, required amplifier power is 10x lower, yes, less than 1 watt. 

  

  

subwoofers and satellites

This post is my justification for selecting 150Hz crossover point to split the frequency range for subwoofers and satellites.  

Audio chain consists of three parts. First: signal sources, that is your cd player, record player, FM tuner, cassette deck or reel to reel player, mp3 player, streaming device and so on. Second: signal amplification, this includes all the signal manipulation like preamplifier, equalizer, active crossover, all the way to power amplifier. Third: speakers. 

Speakers are the last part of electroacoustic chain. Speakers have a very difficult task of converting the electric signal from the amplifier into the sound image as closely as possible to the original sound in the recording. 

No single speaker is capable of reproducing full range of frequencies in concert hall. Life like reproduction of low frequencies, like organ, base, tympany, big drums, and so on, requires the speaker with large membrane area moving lots of air. Just like the instruments generating the low frequency sounds. This speaker, on the other hand, has large membrane mass, and can not radiate high frequencies effectively and with proper directionality. Lack of pistonic behavior, cone breakups and beaming limits the upper range of large membrane woofer. 

Effective radiation of high frequencies requires small membrane speaker, with light membrane, which on the other hand, can not produce mid or low frequencies. Therefore, it is more practical to split the frequency range into bands. Small 2-way bookshelf speakers are quite common. Midbass driver is accompanied with tweeter. Such speakers can sound good, but they lack low frequency extension. Big floorstanding speakers with woofers, midrange drivers and tweeters are next step up, and can be very good sounding. This is classic approach. However, other approach, where one builds separate woofers enclosure, one or two, cross it low enough so that it can not be localized, and uses smaller bookshelf speakers to reproduce the rest of the frequencies above the subwoofer. 

The point here is to cross the subwoofer low enough, such that our ears can no longer localize its position. Whether one uses just one or two or more subwoofers, or places them under the bookshelf or some place else is the main reason to call these woofer boxes subwoofers. Unlike in classic 3-ways speakers, crossover point between woofer and midrange driver does not allow separating the woofer enclosure far from mid and tweeter. 

Lets discuss optimum crossover frequency for subwoofer. As is shown in the Figure 1 below, authors suggested fd1, the crossover point between the subwoofer and the bookshelves, also called satellites, to be between 70 and 200 Hz. 

Our ears allow us to recognize the directionality of sound source. This is rather complex process based on binaural hearing. Signal source coming from the left side reaches left ear sooner and with higher sound intensity, as sound to the right ear. This is true for most of the frequencies. 

Our ears are horizontally placed on our head with the goal to be able to localize the sound as precisely as possible on the horizon for survival reasons. When our ancestors roamed flats of Africa, they needed to listen carefully where the predators are hiding. The sounds from top or bottom where less important. Therefore horizontal behavior of speakers is of utmost importance. Minor vertical irregularities can be easily tolerated. 

Let's return back to the discussion to the ideal subwoofer crossover point. As shown on the Figure 3 below, there is a difference in phase of arriving audio signal between the left and right ear when signal comes from the side. This phase difference is increasing with increasing frequency. The phase difference at low frequencies is negligible. This is because wavelength is much bigger than the distance between ears. 

Similarly with the phase difference between left and right ear, the sound intensity depends on frequency too. Our head presents much bigger barrier for higher frequencies, as shown in Figure 4 below. Please note that the sound level is identical between the left and right ear below certain frequency. This means we can not localize the sound below 200Hz. Wait a minute, you say, when you set your subwoofer at 200Hz, you clearly heard where it was placed. Well, this is because there was still significant signal above 200Hz, since every crossover has some slope. If you would use brick wall filter, the result would be different. Other reason for being able to localize the subwoofer may be its poor quality. Distortion is basically the generation of upper harmonics. Distorting subwoofer is producing higher frequencies above its crossover point. 

So we have arrived at the point, where if the subwoofer is executed well, that is low distortion without any chuffing, we can state that ideal crossover frequency would be anywhere between 70 and 200Hz. To be on the safe side, I decided on the 150Hz for a long time ago, so all my active crossovers are built this way. Most of the woofers I worked with have no problem covering from Fs to 200Hz, behaving pistonicaly. Some people argue that subwoofers crossover point should be set very low, like 40Hz or lower, just to extent the range of main speakers, hence the name 'sub', but I disagree with that. You should build your classic 3-way tower properly, so it does not need subwoofers. I am not discussing the needs of HT and explosions, I do not care about that crap.  

There are countless ways to make crossovers, passive or active. Two examples, one for active, one for passive, is shown below. 

One can do completely passive crossover for subwoofer, but the inductors are substantial. If one insists on using just one amplifier, there is no other way around. 

I prefer active. Active crossover brings little more complexity, but offers lot more flexibility. While if you are using passive crossover, you need to use amplifier capable of driving woofers, as well as bookshelves. However, if you have active crossover, you can use big classAB on the woofers, but small tube or solid state classA amp on satellites. Much less power is required for the frequencies above 200Hz. Depending on the efficiency of midrange and tweeter, even few watts may be plenty. Other advantage of active crossover is no need to match efficiencies between woofers and bookshelves. There are other advantages too, if you are speaker builder. Building bookshelves is lot easier that building big classic 3-way speaker every time you want to try new mids or tweeters. 

Happy listening!