Damping factor

This article covers the physical term. The term is also used in the PageRank algorithm.

In the case of an analog interface between two electrical devices, the damping factor indicates the ratio of input resistance to output resistance . Resistance means an alternating current resistance, which is called impedance . ${\displaystyle D_{\text{F}}}$

Basics

The damping factor is the quotient of the input resistance and the output resistance . ${\displaystyle D_{\text{F}}}$ ${\displaystyle R_{\text{a}}}$ ${\displaystyle R_{\text{i}}}$

${\displaystyle D_{\text{F}}={\frac {R_{\text{a}}}{R_{\text{i}}}}}$

Designation of the impedances:

Output resistance = = internal resistance = source resistance ${\displaystyle R_{\text{i}}}$

Input resistance = = external resistance = load resistance = terminating resistance ${\displaystyle R_{\text{a}}}$

The A ußenwiderstand or A bschlusswiderstand may not use the A usgangswiderstand be confused what for the same initial letter A is easily possible. ${\displaystyle R_{\text{a}}}$ ${\displaystyle R_{\text{i}}}$

As a result of the adaptation , the output resistance of the source and the input resistance of the load form adaptation damping at each interface . The important damping factor for the adaptation damping at the interface from the power amplifier to the loudspeaker must be observed in particular .

Meaning of R _a and R _i in loudspeakers

Since alternating current flows through the loudspeaker , the frequency-dependent impedance must be taken into account. If the amplifier has too high an output resistance, it is less loaded at the resonance frequency of the loudspeaker and emits a higher voltage. This leads to an increase in the frequency response at this point. If the output resistance is low, the amplifier attenuates the speaker's resonance.

The amplifier not only drives the loudspeaker by its current generating the diaphragm movement (stroke), it also has to ensure that the swinging movement of the diaphragm is slowed down if there is no voltage at the end of a pulse. This is particularly important with bass. At this moment the voice coil acts as an electrical generator and generates electricity (induction effect ).

If the internal resistance of the amplifier is sufficiently small (usually much less than 0.5 ohms), the loudspeaker will be short-circuited by the amplifier during the decay and the vibration energy is converted into heat in the voice coil. So if is, it's called voltage matching because the amplifier dictates the voltage across the voice coil terminals. ${\displaystyle R_{\text{i}}\ll R_{\text{a}}}$

Since the total damping resistance is the sum of the internal resistance (amplifier) ​​and external resistance (voice coil with typically 6.5 Ω DC resistance), it cannot be smaller than the coil resistance, no matter how small the internal resistance is. This places limits on electrical damping. It is therefore sufficient if the damping factor is greater than approximately 20. A further increase does not lead to any relevant improvements. Almost all modern transistor amplifiers achieve damping factors well above 20, so that the damping factor is usually not a relevant decision criterion when choosing an amplifier. ${\displaystyle {\tfrac {R_{\text{a}}}{R_{\text{i}}}}}$

Strictly speaking, the vibration behavior depends on the optimal quality factor of the loudspeaker and housing system. The optimum sum of mechanical and electrical damping to which the loudspeaker housing is matched is always decisive for the respective application.

By changing the above formula, the internal resistance of loudspeaker power amplifiers can be determined, which is rarely given in data sheets.

${\displaystyle R_{\text{i}}={\frac {R_{\text{a}}}{D_{\text{F}}}}}$

The damping factor is the ratio of to and ${\displaystyle D_{F}}$ ${\displaystyle R_{a}}$ ${\displaystyle R_{i}}$ ${\displaystyle R_{i}=R_{a}/D_{F}}$

The damping factor is also a substitute for the specification of the internal resistance of loudspeaker power amplifiers in the technical data. For example, at and is the calculated internal resistance . ${\displaystyle D_{F}=100}$ ${\displaystyle R_{a}=8\,\mathrm {\Omega } }$ ${\displaystyle R_{i}=0{,}08\,\mathrm {\Omega } }$

More precisely, the damping factor represents the ratio of the nominal impedance of the loudspeaker voice coil to the rest of the entire electrical circuit. The uncontrolled oscillation of the loudspeaker induces an electrical voltage in the voice coil, which is short-circuited via the output stage. The generated counterforce shortens the decay time of the membrane.

The common idea among laypeople that an 8-ohm amplifier should be used with an 8-ohm loudspeaker is wrong. There is no 8 ohm amplifier. An amplifier output resistance that is much smaller than 0.5 ohms is common.

See also

• List of audio terms

Individual evidence

1. ^ Floyd E. Toole: Damping, Damping Factor, and Damn Nonsense . In: AudioScene Canada . February 1975, p. 16-17 ( diyaudioprojects.com [PDF]).
2. ^ George L. Augspurger: The Damping Factor Debate . In: Electronics World . Ziff-Davis Publishing Company, January 1967 ( cieri.net [PDF]).

literature

• Heinz Sahm: HIFI loudspeakers. Basics of electrodynamic loudspeakers in an infinite baffle and in the housing . 2nd improved edition. Franzis-Verlag GmbH, Munich 1982, ISBN 3-7723-6522-1
• Thomas Görne: Sound engineering . Fachbuchverlag Leipzig in Carl Hanser Verlag, Munich et al. 2006, ISBN 3-446-40198-9

Web links

• Damping Factor: Effects On System Response (English; PDF; 142 kB)
• Adjustment for two devices and the damping factor
• Calculation of the damping factor and the adaptation damping
• The fairy tale of performance adjustment (PDF; 204 kB)
• About the correct adjustment of speakers and headphones (PDF; 27 kB)
• About the actual influence of the cross-section of speaker cables on the attenuation factor
• 8 ohm output and 200 ohm input - what is it?