# 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 (that seen by the loudspeaker) includes the connecting cable impedance. The load impedance ${\displaystyle Z_{\mathrm {load} }}$ (input impedance) and the source impedance ${\displaystyle Z_{\mathrm {source} }}$ (output impedance) are shown in the diagram.

The damping factor ${\displaystyle DF}$ is:

${\displaystyle DF={\frac {Z_{\mathrm {load} }}{Z_{\mathrm {source} }}}\,}$

Solving for ${\displaystyle Z_{\mathrm {source} }}$:

${\displaystyle Z_{\mathrm {source} }={\frac {Z_{\mathrm {load} }}{DF}}\,}$

## 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 (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 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 (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 ${\displaystyle Z_{\mathrm {source} }}$ (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 ${\displaystyle Z_{\mathrm {load} }}$ 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:

• the resistance of the voice coil itself;
• the resistance of the interconnecting cable; and
• the output resistance of the amplifier.

### Effect of voice coil resistance

This is key factor in limiting the amount of damping that can be achieved electrically, because its value is larger (say between 4 and 8Ω typically) than any other resistance in the output circuitry of an amplifier that does not use an output transformer (nearly every solid-state amplifier on the mass market).

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. ${\displaystyle Z_{\mathrm {load} }}$ >> ${\displaystyle Z_{\mathrm {source} }}$.

### 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. Given the controversy that has long surrounded the use of feedback,[citation needed] some[who?] extend their distaste for negative feedback (NFB) amplifier designs (and so a high damping factor) as a mark of poor quality. For them, such high values imply a high level of NFB in the amplifier.

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" (undergoes unwanted short-term oscillation after an impulse of power is applied), 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 an 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 (very low damping factor/high output impedance amplifiers approximate current sources).

Large amounts of damping of the loudspeaker is not necessarily better,[1] for example a mere 0.35 dB difference in real-life results between a high (100) and medium (20) Damping Factor.[2] Some engineers, including Nelson Pass claim loudspeakers can sound better with lower electrical damping.[3] A lower damping factor helps to enhance the bass response of the loudspeaker by several decibels (where the impedance of the speaker would be at its maximum), which is useful if only a single amplifier 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:[4]

"Speaker Damping Control enhances characteristic tonal qualities of speakers. The damping factor of solid state amplifiers is generally very large and ideal for damping the speakers. However, some speakers require an amplifier with a low damping factor to reproduce rich, full-bodied sound. The E-202 has a Speaker Damping Control which permits choice of three damping factors and induces maximum potential performance from any speaker. Damping factor with an 8 ohm load becomes more than 50 when this control is set to NORMAL. Likewise, it is 5 at MEDIUM position, and 1 at SOFT position. It enables choosing the speaker sound that one prefers."

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 (an application in which distortion is desirable) 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[5] has a switch between "linear" and "Valvestate" mode:

"Linear/Vstate selector. Slide to select linear or Valvestate performance. The Valvestate mode gives extra warm harmonics plus the richness of tone, which is unique to the Valvestate power stage. Linear mode produces a highly defined hi-fi tone that gives a totally different character to the sound and suits certain modern "metal" styles, or PA applications."

This is actually a damping control based on negative current feedback, which is evident from the schematic,[6] 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. (Contrary to the claim in the handbook, this circuit topology has appeared in numerous solid-state guitar amplifiers since the 1970s.)