HiFi Formulae - Calculations for your sound system - Don't lose power in thin speaker cables
POWER - Watts
Example: My amplifier is rated at 100W output, my speakers are 8 Ohms, what size cable should I use?
Cable size is dependant on the CURRENT carried. Hence from (2) above W=IxIxR
Before selecting a cable, we need to know the length of the speaker cable from amplifier to speaker in meters (m). Say you have a large room and the length is 25m. In this case the sound current starts (say) at the +Ve terminal of your amplifier and travels through the +Ve conductor of your speaker cable to the speaker +Ve terminal. Inside the speaker, this current then goes around the speaker coil (causing the speaker cone to move) and comes out on the speaker -Ve terminal. Back down the -Ve speaker wire and into the amplifier -Ve terminal thus completing the circuit.
So the sound current has travelled 25m to the speaker and 25m back, or 50m in total. If the cable has any loss (resistance) then we start to lose some of the original power. For example:
Suppose you use cheap bell wire which has a CSA of 0.25mm. This typically has a resistance of 0.0667 Ohms/m, or 3.335 Ohms for our speaker run. Our 100W amplifier therefore drives an 8 Ohm speaker plus a 3.335 Ohm cable, or a total load of 11.335 Ohms. If you do the maths again, you will quickly realise that almost a THIRD the available power (29W) is wasted (lost) in the speaker cable as heat! Quadrupling the cable size to 1mm CSA gives a loss of almost 10W, and even if you use 10mm CSA (ie really heavy cooker grade wire) you still lose 1W! AND these calculations are at steady state power levels - you need to DOUBLE the losses for instantaneous power delivery.
So the lessons are:
Sub Bass Speakers Are likely to be driven by very powerful amplifiers (250W++) and can have a minimum quoted impedance (ac resistance) of 6 Ohms or less. Be aware that cable losses can be huge from the above formulae and that lessons 1, 2 and 3 are Absolutely Critical.