The table below shows the damping for various wire lengths and gauges for 8, 4 and 2 ohm loudspeakers.
It also shows the SPL loss for the audio signals from the power loses because of the cable resistance. It can be readily seen that the SPL loss is far less important than damping factor in choosing a loudspeaker cable.
For example, on a 4 ohm loudspeaker with 100 length of #14 cable will only reduce the SPL by a minimal 1 dB, but the damping factor is less than 1/2 of what is considered adequate.
Note: The calculations for the table are based on loudspeaker nominal impedances rather than DC resistances. Therefore the values listed in the table for DF and the SPL losses are quite useful but are only approximate values.
An amplifier with a rated damping factor of 1000 at 8 ohms was used for the calculations in the table below. The internal impedance of such an amplifier is 0.008 ohms. Even using an amplifier with a rated damping factor of 100 ohms, the DF numbers change surprising little.
The reason is the output impedance of such an amplifier is 0.08 Ohms, which is still small compared to the cable resistance in most cases. The SPL loss is unaffected by an amplifier’s output impedance.
If you wish to “plug in” some numbers other than those shown, here are the calculations used to make the table:
> Total Cable Resistance = (2 x Cable Length x Wire Resistance per 1000 Feet) / 1000
> SPL Loss = 20 x LOG (Speaker DC Resistance / (Speaker DC Resistance + Total Cable Resistance) [see note below table]
> Damping Factor (DF) = Speaker DC Resistance / (Amplifier Output Impedance + Total Cable Resistance)
Looking At The Table
For short cable lengths the damping factor of the amplifier will have some affect on the numbers, especially for 2-ohm loudspeakers. For cable lengths over 50 feet the cable resistance, rather than the amplifier’s specified DF, will determine the electrical damping factor. For runs over 50 feet (15 m) at 2 ohms, 100 feet (30 m) at 4 ohms, and 200 feet (60 m) at 8 ohms it is not practical to maintain a damping factor of 20 and still use a practical wire gauges.
Figure 2: Wire lengths and gauges for 8, 4 and 2 ohm loudspeakers and SPL loss for the audio signals from the power loses due to cable resistance.