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HiFi Formulae - Calculations for your sound system - Don't lose power in thin speaker cables

POWER - Watts

  1. Watts = Voltage x Current .....W=VI...where V = Volts and I = Amps
  2. Watts = Current x Current x Resistance....W = I x I x R
  3. Watts = (Voltage x Voltage) / Resistance....W = (V x V) / R
  4. Voltage = Current x Resistance....V = I x R
  5. Current = Votage / Resistance....I = V / R
  6. Resistance = Voltage / Current....R = V / I

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
Transpose to give IxI=W/R. W=100, R=8, hence IxI = 100/8, I = 3.54A.
However 3.54A is the RMS or steady state current. Peak current will be higher than this by a factor of X 1.4 and if we add an overhead for instantaneous power, then it is reasonable to suggest our current requirement will be 2 x 3.54A or 7A maximum. So we need to choose a cable capable of delivering 7A to the speaker with no (minimal) losses.

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:

  1. Keep all speaker cables as short as possible - critical
  2. Make sure that the connections between amplifier / cable and cable / speaker are as good as can be made - critical
  3. Use thick (large CSA) good quality cable with the lowest resistance per unit length available - important
  4. Plated cables will help - small diference
  5. Other cable parameters - Inductance and capacitance are less important than resistance - very small (if any) difference
  6. Use Oxygen Free Cable - You might possibly hear a difference given studio grade equipment if listening in a special environment! - miniscule & esoteric - spend your money on better speakers or equipment!
Remember that ANY loss inbetween amplifier and speaker WILL change the sound output quality relative to the signal actually produced by the amplifier and WILL degrade the amplifier ability to properly control the speaker cone dynamics.

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.

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