Thursday, July 29, 2021

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.