Damping factor


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 includes the connecting cable impedance.
The load impedance and the source impedance are shown in the diagram.
The damping factor is:
Solving for :

Explanation

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 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 amp'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 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. It is generally 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 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 is generally smaller than 0.1 ohm, and from the point of view of the driver voice coil, is a near short-circuit.
The loudspeaker's nominal load impedance of is usually around 4 to 8Ω, although other impedance speakers are available, sometimes as low as 1Ω.

The damping circuit

The voltage generated by the moving voice coil forces current through three resistances:
This is key factor in limiting the amount of damping that can be achieved electrically, because its value is larger than any other resistance in the output circuitry of an amplifier that does not use an output transformer.
A loudspeaker's flyback current is not only dissipated through the amplifier output circuit, but also through the internal resistance of the loudspeaker itself. Therefore the choice of different loudspeakers will lead to different damping factors when coupled with the same amplifier.

Effect of cable resistance

The damping factor is affected to some extent by the resistance of the speaker cables. The higher the resistance of the speaker cables, the lower the damping factor. When the effect is small, it is called voltage bridging. >>.

Amplifier output impedance

Modern solid state amplifiers, which use relatively high levels of negative feedback to control distortion, have extremely low output impedances—one of the many consequences of using feedback—and small changes in an already low value change overall damping factor by only a small, and therefore negligible, amount.
Thus, high damping factor values do not, by themselves, say very much about the quality of a system; most modern amplifiers have them, but vary in quality nonetheless.
Tube amplifiers typically have much lower feedback ratios, and in any case almost always have output transformers that limit how low the output impedance can be. Their lower damping factors are one of the reasons many audiophiles prefer tube amplifiers. Taken even further, some tube amplifiers are designed to have no NFB at all.

In practice

Typical modern solid-state amplifiers with negative feedback tend to have high damping factors, above 50 and sometimes above 150. High damping factors tend to reduce the extent to which a loudspeaker "rings", but the extent to which damping factors higher than about 20 help in this respect is easily overstated; there will be significant effective internal resistance, as well as some resistance and reactance in cross-over networks and speaker cables. Older amplifiers, plus modern triode and even solid-state amplifiers with low negative feedback will tend to have damping factors closer to unity, or even less than 1.
Large amounts of damping of the loudspeaker is not necessarily better, for example a mere 0.35 dB difference in real-life results between a high and medium Damping Factor. Some engineers, including Nelson Pass claim loudspeakers can sound better with lower electrical damping. A lower damping factor helps to enhance the bass response of the loudspeaker by several decibels, which is useful if only a single speaker is used for the entire audio range. Therefore, some amplifiers, in particular vintage amplifiers from the 1950s, '60s and '70s, feature controls for varying the damping factor. While such bass "enhancement" may be pleasing to some enthusiasts, it nonetheless represents a distortion of the input signal.
One example of a vintage amplifier with a damping control is the Accuphase E-202, which has a three-position switch described by the following excerpt from its owner's manual:
By contrast, in modern high fidelity amplification, the trend is to separate the bass signal and amplify it with a dedicated amplifier. Often, amplifiers for bass are integrated with the speaker cabinet, a configuration known as the powered subwoofer. In a topology that includes a dedicated amplifier for bass, the damping factor of the main amplifier is not relevant, and that of the bass amplifier is also irrelevant if that amplifier is integrated with the speaker and cabinet as a unit, since all those components are designed together and optimized for the reproduction of bass.
Damping is also a concern in guitar amplifiers and low damping can be better. Numerous guitar amplifiers have damping controls, and the trend to include this feature has been increasing since the 1990s. For instance the Marshall Valvestate 8008 rack-mounted stereo amplifier has a switch between "linear" and "Valvestate" mode:
This is actually a damping control based on negative current feedback, which is evident from the schematic, where the same switch is labeled as "Output Power Mode: Current/Voltage". The "Valvestate" mode introduces negative current feedback which raises the output impedance, lowers the damping factor, and alters the frequency response, similarly to what occurs in a tube amplifier.

Footnotes