In an audio system, the damping factor gives the ratio of the rated impedance of the loudspeaker to the source impedance. Only the resistive part of the loudspeaker impedance is used. The amplifier output impedance is also assumed to be totally resistive. The source impedance (that seen by the loudspeaker) includes the connecting cable impedance. The load impedance Zload (input impedance) and the source impedance Zsource (output impedance) are shown in the following relationship.
The damping factor DF is:
DF = Zload/Zsource
In loudspeaker systems, the value of the damping factor between a particular loudspeaker and a particular amplifier describes the ability of the amplifier to control undesirable movement of the speaker cone near the resonant frequency of the speaker system. It is usually used in the context of low-frequency driver behavior, and especially so in the case of electrodynamic drivers, which use a magnetic motor to generate the forces which move the diaphragm.
Speaker diaphragms have mass, and their surroundings have stiffness. Together, these form a resonant system, and the mechanical cone resonance may be excited by electrical signals (e.g., pulses) at audio frequencies. But a driver with a voice coil is also a current generator, since it has a coil attached to the cone and suspension, and that coil is immersed in a magnetic field. For every motion the coil makes, it will generate a current that will be seen by any electrically attached equipment, such as an amplifier. In fact, the amplifier's output circuitry will be the main electrical load on the "voice coil current generator". If that load has low resistance, the current will be larger and the voice coil will be more strongly forced to decelerate. A high damping factor (which requires low output impedance at the amplifier output) very rapidly damps unwanted cone movements induced by the mechanical resonance of the speaker, acting as the equivalent of a "brake" on the voice coil motion (just as a short circuit across the terminals of a rotary electrical generator will make it very hard to turn). It is generally (though not universally) thought that tighter control of voice coil motion is desirable, as it is believed to contribute to better-quality sound.
A high damping factor indicates that an amplifier will have greater control over the movement of the speaker cone, particularly in the bass region near the resonant frequency of the driver's mechanical resonance. However, the damping factor at any particular frequency will vary, since driver voice coils are complex impedances whose values vary with frequency. In addition, the electrical characteristics of every voice coil will change with temperature; high power levels will increase coil temperature, and thus resistance. And finally, passive crossovers (made of relatively large inductors, capacitors, and resistors) are between the amplifier and speaker drivers and also affect the damping factor, again in a way that varies with frequency.
For audio power amplifiers, this source impedance Zsource (also: output impedance) is generally smaller than 0.1 Ohm (Ω), and from the point of view of the driver voice coil, is a near short-circuit.
The loudspeaker's nominal load impedance (input impedance) of Zload is usually around 4 to 8Ω, although other impedance loudspeakers are available, sometimes as low as 1Ω.