Damping factor

Damping factor is one of the most mis-understood parameters used when talking about speakers and amplifiers. It exists a lot of misconceptions around this item and many people deliberatly misunderstand or mix up the effects damping factor can have on the performance of a amplifier speaker combination. Amplifiers are advertised as having a damping factor of 100 or even 1000 and people are led to believe that the higher damping factor the better the speakers will dampened.

Definition of Damping factor

Damping factor is defined as the quote between the nominal speaker impedance Zs and the amplifier output impedance Za, as an example if we have a speaker with nominal impedance 8 ohm and an amplifier with an output impedance of 0.5 ohm the damping factor would be 8/0.5 = 16.

Suggested effect of damping factor as defined above

An electrodynamic speaker consist of a coil moving in the field of a magnet. A speaker can convert electric current to movement, (the coil and the attached membrane will move when a voltage is applied to the coil), but also a voltage will be generated in the coil when the the membrane is moved physically for instance by hand. If a transient voltage is applied to a speaker the speaker membrane will try to move in accordance with the transient voltage and then stop, but because of the mass of the membrane it will continue to move after that the applied voltage is removed, a voltage is then generated by this movement.

The theory about the need for high damping factor is that if this generated voltage would be short circuited by an amplifier with low output impedance, (high damping factor) the transient response of the speaker will be improved as the effect of short circuiting the voltage would generate a high current in the coil and that would generate a physical force that would stop the speaker membrane moving. If however the amplifier had high output impedance, (bad damping factor) the voltage would not be dampened completely and the speaker would continue ringing after a transient was applied.

Unfortunately the amplifier output impedance has not so much effect on the transient response of a speaker. It is true that the effect described above exist, it is easy to check this by comparing how a speaker element reacts wether the terminals is open or short circuited. Try this on a woofer element and tap the membrane with a finger, if the terminals is shortcircuited the sound is more dull then when the terminals are open, indicating that the effect of controlling the membrane exists.

Real effect of amplifier damping factor on speaker transient response

So the effect of transient damping exists so why is damping factor a very misunderstood concept?
One factor is deliberatly forgotten in the description above i.e. speaker internal resistance Rs. A normal electrodynamic speaker has a internal resistance that is usually ~Zs/1.2 so an 8 ohm speaker have an internal resistance of ~6.7 ohm. Even if the speaker is completely short circuited externally it will still have the internal resistance that will determine how well it is dampened!

Alternative way of describing damping factor

By including the speaker internal resistance in the formula for damping factor we can see what effect differences in amplifier output impedance will on real damping factor and on transient response.

Advertised damping factor Amplifier output impedance Za + 6.7 Real damping factor Zs/(Za + 6.7) Amplifier type
100 0.08 6.78 1.18 typical solid state amp
20 0.4 7.1 1.13 Push-pull tube amp
5.3 1.5 8.2 0.98 OTL amp
2.67 3.0 9.7 0.82 typical SE amp

Relationship between conventional damping factor and real effect on speaker damping.

As can be seen from the above table the amplifier output impedance have a very small effect on the real damping on a speaker, what is not included is the effect of finite resistance of speaker cable which willeffect the result for the solid state amplifier.

Real effect of finite damping factor

I have now showed that the so called damping factor have very small influence on the transient response or damping of the speaker but there exists other effects that depends on the value of damping factor.

A speaker have not constant impedance over its frequency range, normal is that there exist some high peaks at low frequencies at the resonance frequencies of the speaker itself and also that the speaker impedance increases with higher frequencies.

This is the impedance characteristics of a a Lowther PM6A element in a Fidelio cabinet, from the page of Bart Oostergeel, Bart Oostergeel homepage

As can be seen there are two high peaks at low frequencies, the highest of 33.8 ohm at 75Hz and the speaker impedance increases at high frequencies reaching ~22 ohm at 20 kHz.

This is not in anyway an extreme examples and there exist other speakers which has a impedance curve that creates even more problems than in this case.

Effect of damping factor on frequency response of a real speaker

If an amplifier with finite damping factor is connected to a speaker with non constant impedance across its frequency range the frequency response will be affected in some non ideal way, the following table give the effect for the same amplifiers as in the example above when connected to the Lowther Fidelio cabinet.

Amplifier output impedance Response at 75 Hz, (Zs = 33.8 ohm) Response at 20 kHz, (Zs = 22 ohm) impedance dip of 4 ohm
0.08 + 0.08 dB + 0.05 dB - 0.09 dB
0.4 + 0.38 dB + 0.27 dB - 0.4 dB
1.5 + 1.3 dB + 0.9 dB -1.3 dB
3.0 + 2.4 dB + 1.7 dB - 2.1 dB

As can be seen by the above table the frequency response can be affected quite much if the damping factor is low, in these examples it is easy to imagine that the effect of + 2.4 dB rise at 75 Hz will affect the sound of the speaker and give a muffled bas note. It is important to realise that the bassy and therefore often muddled bass that can be heard sometimes when using a SE amplifier without global feedback is not because of "low damping" per see but because of the effect the high output resistance have on the frequency response.

How to counter the effect of high amplifier output impedance on frequency response

With small means it is quite easy to improve the frequency response of a speaker and lessening the effects of high amplifier output impedance.

Connecting parallel resistance over the speaker terminals

By connecting a 30 ohm resistor of god quality in parallel with the speaker terminals some people say it is easy to improve the frequency response of speakers like the Lowther Fidelio in the above example, is it really so?

The impedance at 75 Hz will be 19.9 ohm, the impedance at 20 kHz will be 12.1 ohm and the mid frequency impedance will be 6.2 ohm.

Amplifier output impedance Response at 75 Hz, (Zs = 19.9 ohm) Response at 20 kHz, (Zs = 12.1 ohm)
0.08 + 0.08 dB + 0.05 dB
0.4 + 0.37 dB + 0.26 dB
1.5 + 1.2 dB + 0.9 dB
3.0 + 2.2 dB + 1.5 dB

As can be seen from this table the effects are very small, just 0.2 dB even for the SET amplifier with high output impedance so this is not at all a good way to counter the problem.

Real solution to the problem

A better solution to counter the problems with affected frequency response due to high output impedance is to use frequency dependent networks consisting of inductors, capacitors and resistor between the amplifier and the speaker. When I was using my SET amplifier together with my Lowther Fidelio horns I used a network consisting of a resistor and capacitor connected in series, i.e. a Zobel network, this was then connected in parallel with the speaker terminals. This network has a good effect on compensating the rising impedance at high frequencies but has little or no effect on bass frequencies. With this network connected the resulting impedance never go below 7.4 ohm neither above 9 ohm and the frequency response even with a SET amplifier is practically unaffected compared to using a solid state amplifier.

In order to compensate for the impedance peaks at low frequencies resonant circuits can be used, it is possible to use one somewhat more complicated circuit to compensate for both low frequency impedance peaks of the Fidelio.

Created on ... februari 18, 2001