Damping Factor

Definition:

DF = Z_speaker / Z_output_amplifier

Output impedance from spec:

Z_output = Z_speaker / DF_rated

System damping factor (including wire resistance):

DF_system = Z_speaker / (Z_output + R_wire)

Worked example:

Amplifier: DF = 500, speaker = 4Ω

Z_output = 4 / 500 = 0.008Ω

16 AWG speaker wire, 12-foot run (24 feet round trip):

R_wire = (4.016 Ω/1000ft) × 24 = 0.096Ω

DF_system = 4 / (0.008 + 0.096) = 4 / 0.104 = 38

Amplifier rated DF of 500 reduced to 38 by speaker wire alone. This is why speaker wire gauge matters even for passive systems. Upgrading to 12 AWG:

R_wire = (1.588/1000) × 24 = 0.038Ω
DF_system = 4 / (0.008 + 0.038) = 87

Still far below amplifier's rated DF — wire dominates.