Damping factor

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

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 loudspeaker impedance is used. The amplifier output impedance is also assumed to be totally resistive. The source impedance (that seen by loudspeaker) includes the connecting cable impedance. The load impedance Zload (input impedance) and the source impedance Zsource (output impedance) are shown in the diagram.

Image:Source and load circuit Z.png

The damping factor DF is:

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

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[edit] Explanation

In loudspeaker systems, the value of the damping factor between a particular loudspeaker and 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 electro-dynamic drivers which use a magnetic motor to generate the forces which move the diaphragm.

Speaker diaphragms have mass, and their surrounds have stiffness. Together these form a resonant system and the mechanical cone resonance may be excited by electrical signals (eg, pulses) at audio frequencies. But a driver with a voice coil is also a current generator since it has a coil attached to cone and suspension and that coil is immersed in a magnetic field. For every motion the coil makes, it will generate a current which 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 so resistance. And finally, passive crossovers (made of relatively large inductors, capacitors, and resistances) 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 Ω (ohms), and, from the point of view of the driver voice coil, is a near short-circuit.

The loudspeaker's load impedance (input impedance) of Zload is usually around 4 to 8 Ω although other impedance speakers are available, sometimes as low as 2Ω.

Solving for Zsource:

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

[edit] 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
  • 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 larger (say between 4 and 8 ohms typically) than any other resistance in the output circuitry of an Output TransformerLess amplifier.

[edit] 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. The effect is small.

This is called voltage bridging. Zload >> Zsource. The loudspeaker's load impedance (input impedance) of Zload is usually around 4 to 8 Ω although other impedance speakers are available.

Solving for Zsource:

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

[edit] 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 even so. Given the controversy that has long surrounded the use of feedback, some extend their distaste for negative feedback 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 which 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 negative feedback at all.

[edit] In practice

Transient oscillations in electric circuits are normally reduced (damped) by inserting resistance into the circuit. Or reactance which increases in the frequency region requiring damping.

This technique cannot be used with loudspeakers because increasing the mechanical resistance to cone movement would make the speaker less efficient requiring larger amplifiers. For high fidelity use, such speakers will be less capable of responding properly quickly to musical or speech transients. Instead, the generator effect in voice coil drivers is used to damp oscillations electrically.

Damping factor describes the ability of the amplifier to control unintended movement of the speaker cone near the resonant frequency of the driver. All other things being equal, a high damping factor indicates that an amplifier will have greater control over the movement of the driver cone, particularly in the bass region near the resonant frequency of the driver.

The higher the resistance of the speaker cables or the output impedance of the amplifier, the lower the damping factor since the resistance seen by the voice coil will increase. The damping factor is affected to a small extent by the resistance of the speaker cables and for most amplifiers to small changes in the output impedance of the amplifier.

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