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Damping factor

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The term damping factor can also refer to the amount of damping in any oscillatory system

In audio system terminology the damping factor gives the ratio of the rated impedance of the loudspeaker to the source impedance. Only the resistive part of the loudpeaker impedance is used. The amplifier output impedance is also assumed totally resistive. The source impedance includes the connecting cable impedance. The load impedance <math>Z_\mathrm{load}</math> (input impedance) and the source impedance <math>Z_\mathrm{source}</math> (output impedance) are shown in the diagram.

Image:Source and load circuit Z.png

The damping factor <math>DF</math> is:

<math>

DF = \frac{Z_\mathrm{load}}{Z_\mathrm{source}} </math>

Contents

[edit] Explanation

In loudspeaker systems, damping factor describes the ability of the amplifier to control undesirable movement of the speaker cone near the resonant frequency of the speaker system. A speaker diaphragm has mass, and the surround has stiffness. Together these form a resonant system and the cone may resonate in response to short audio pulses.

A high damping factor indicates that an amplifier will have greater control over the movement of the speaker cone, particularly in the bass region where the resonant frequency of the speaker system will lie. This damping gives a "tight bass" sound from the sound system.

For audio power amplifiers this source impedance <math>Z_\mathrm{source}</math> (also: output impedance) is generally smaller than 0.1 Ω (ohms), and can be seen from the point of view of the loudspeaker as a near short-circuit. This low impedance very rapidly damps any unwanted cone movements induced by the mechanical resonance of the speaker, and acts as a very effective 'brake' on the speaker (just as a short circuit across the terminals of a generator will make it very hard to turn).

The loudspeaker's load impedance (input impedance) of <math>Z_\mathrm{load}</math> is usually around 4 to 8 Ω although other impedance speakers are available.

Solving for <math>Z_\mathrm{source}</math>:

<math>

Z_\mathrm{source} = \frac{Z_\mathrm{load}}{DF}</math>

[edit] The damping circuit

The voltage generated by the moving voice coil sends the braking current through three resistances:

  • the resistance of the voice coil itself
  • the resistance of the interconnecting cable
  • the output resistance of the amplifier

[edit] Effect of voice coil resistance

This is the major factor in limiting the amount of damping that can be achieved electrically, because its value is far greater (say between 4 and 8 ohms typically) than any other resistance in a practical damping circuit of a OTL amplifier.

[edit] Effect of cable resistance

The damping factor is affected to a small extent by the resistance of the speaker cables. The higher the resistance of the speaker cables, the lower the damping factor.

For audio power amplifiers this source impedance <math>Z_\mathrm{source}</math> (also: output impedance) is generally smaller than 0.1 Ω (ohms), and can be seen from the point of view of the loudspeaker as a near short-circuit.

This is called voltage bridging. <math>Z_\mathrm{load}</math> >> <math>Z_\mathrm{source}</math>. The loudspeaker's load impedance (input impedance) of <math>Z_\mathrm{load}</math> is usually around 4 to 8 Ω although other impedance speakers are available.

Solving for <math>Z_\mathrm{source}</math>:

<math>

Z_\mathrm{source} = \frac{Z_\mathrm{load}}{DF} </math>

[edit] Amplifier output impedance

Modern amplifiers, employing relatively high levels of negative feedback, generally exhibit extremely low output impedances — one of the many consequences of using feedback - and affect overall damping factor by only a miniscule and therefore negligible amount.

Thus "damping factor" figures in themselves do not say very much about the quality of a system. Given the controversy that has surrounded the topic of feedback for many years, some may see a high damping factor as a mark of poor quality because it implies a high level of NFB in the amplifier.

[edit] In practice

A speaker diaphragm has mass, and the surround has stiffness. Together these form a resonant system and the cone may resonate in response to short pulses or excessively amplify frequencies near the resonance. Transient oscillations in electric circuits are normally reduced (damped) by inserting resistance into the circuit. This technique cannot be used with loudspeakers because increasing the mechanical resistance to cone movement would make the speaker less efficient. Instead, the generator effect in the loudspeaker can be used to damp the oscillations electrically. Damping factor describes the ability of the amplifier to control undesirable movement of the speaker cone near the resonant frequency of the speaker system.

A high damping factor indicates that an amplifier will have greater control over the movement of the speaker cone, particularly in the bass region where the resonant frequency of the speaker system will lie. This damping gives a "tight bass" sound from the sound system.

The damping factor is affected to a very small extent by the resistance of the speaker cables. The higher the resistance of the speaker cables, the lower the damping factor.

[edit] Zero electrical damping factor

Nelson Pass made a case to be for a loudspeaker system with zero electrical damping. In the case of a speaker in a small sealed box, there is no way to reduce the system resonance below a few hundred Hz (even if the speaker itself has a very low free air resonance) because of the low compliance of the air in the box. However, because of the high system resonance, other losses being equal, the acoustic cone damping will be high. Nelson Pass, amongst others, has shown that all that is needed is then to electrically drive the speaker from an amplifier with a high output impedance (a current source) for a flat cone displacement response all the way down to DC.

One advantage of the system is that whether it is being operated above or below the system resonance, the cone excursion is current controlled and is therefore linear (independent of surround nonlinearities). A problem with this scheme is that the efficiency may be low.

[edit] See also

[edit] References:

[edit] External links

nl:Dempingsfactor

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