Best Practice: Amplifier Damping Factor

AUTHOR: HiddenWires

By Peter Aylett, Archimedia Middle East. In both the residential and pro audio camps, professionals are split down the middle with an ...

Peter AylettBy Peter Aylett, Archimedia Middle East. In both the residential and pro audio camps, professionals are split down the middle with an argument that has been raging for as long as the industries have existed: Do speaker cables (or any other cables for that matter) make a difference to sound quality. Whilst we could debate the various merits of cable construction, materials, purity, cryogenic treatment and exotic marketing, there are some unarguable engineering facts that affect how speaker cables govern sound quality. [caption id="attachment_10110" align="alignright" width="266"]A speaker that is bi-wired with a single cable that contains four separate conductors. A speaker that is bi-wired with a single cable that contains four separate conductors.[/caption] One not often talked about calculation is damping factor. Damping factor is calculated by dividing the speaker impedance by the sum of the cable impedance and amplifier output impedance. It is a measure of an amplifier’s ability to help control the movement of the loudspeaker transducer. Even when a sound stops, the inertia of a moving speaker means that the speaker will need to be damped for it to stop moving. If it is not damped, the speaker keeps on making a sound even after the signal has stopped. This is sometimes called ‘ringing’ or ‘smearing’. This damping comes from both the mechanical damping of the speaker’s suspension combined with the air behind the speaker, as well as electrical damping. This electrical damping is caused by the movement of the speaker acting like a microphone and generating a signal itself. This signal is called back EMF (EMF = Electro Motive Force), which travels down the speaker cable, through the amp and then back to the speaker. As this back EMF is opposite in polarity to the movement of the speaker, the more of this back EMF that gets back to the speaker, the more the speaker is damped. So, a combination of low output impedance of an amplifier, combined with low speaker cable resistance combine to create a high damping factor. Here is an example: Speaker nominal impedance = 8 Ohm Amplifier Output Impedance = 0.05 Ohm Speaker cable resistance = 0.20 Ohm Damping factor = 8 / (0.05 + 0.20) = 32 The above calculation is complicated by the fact that speaker impedance changes with frequency. Only if you have an impedance curve from your loudspeaker manufacturer can you accurately calculate damping factor at different frequencies. You will also need to know the resistance of the speaker cable that you are using. This is stated in Ohms per meter or foot. As the back EMF needs to travel to the amplifier and then back again, you will need to double the resistance for a given length of cable. Here are some examples of damping factor (DF) assuming an amplifier with an output impedance of 0.05 Ohms using some different speaker cable gauges:
Cable Length Cable Wire Gauge Cable Resistance (Ohms) DF For 8 Ohm Speaker DF for 4 Ohm Speaker
5m 16AWG




5m 14AWG




5m 12AWG




15m 16AWG




15m 14AWG




15m 12AWG




50m 16AWG




50m 14AWG




50m 12AWG




You can see from the table that it is the gauge of the wire used rather than the amplifier that has the greatest effect on damping factor. There is much debate in the ‘Hi-Fi’ world about how much difference damping factor makes to sound quality. This being said, a figure of below 20 is definitely sub-optimal and will be mostly heard in bass frequencies with a tendency for notes to sound blurred together and ‘loose’. Certainly, running 50m of 16AWG cable to 4Ohm speakers with a resultant DF of around 1.5 will never sound good. Recommendations:
  1. Consider designing the system to put the amplifiers close to the speakers. Signals can travel at line level (specially if they are balanced) with far less loss over greater lengths than speaker cables. This is especially true of amplifiers used to drive subwoofers. One of the reasons that powered subwoofers sound so good is that internally the speaker cable is probably only 10cm long! Always consider the gauge of cable that you are using. Beware of the default choice of always just using 16AWG cable and consider using 14 or even 12 AWG cables for long runs if necessary. Remember, it’s always better and in most cases cheaper to put the amplifier close to the speaker it is driving. Consider using 4-core cable such as 16/4 or 14/4. As well as being more flexible for possible future use, doubling up the wires in the cable will halve the resistance.
  2. One of the reasons that B-Wiring speakers (using separate cables connected to the different frequency terminals on the back of a speaker) works so well is that it both doubles the cables going to a speaker, as well as allowing the back EMF from each drive unit to remain unaffected by the back EMF from the other drive unit(s). If a speaker is bi-wirable try to always use this feature.
  3. Almost as a contradiction to all the above, sometimes an under damped ‘sound’ is agreeable to some people. Valve amplifiers have traditionally had a high output impedance which means they have a low damping factor. This helps give them the ‘warm’ sound that many people like but we are talking about ‘Hi-Fi speakers and short speaker cable runs. However, when discussing installation speakers often installed in ceilings with little or no mechanical damping due to the lack of an acoustically engineered back box, these speakers need all the help they can get to control their bass hence the damping factor should always be maximised.
Conclusion The relationship between an amplifier and the speaker it is driving is a complex one. Damping factor is only one parameter in the total equation that also includes slew rate, current capability and THD. It is, however, the primary reason that installing speakers on the end of long cable runs rarely sounds good. Always try to justify the use of the correct gauge of speaker cable in your projects. As always, using engineering calculations rather than conjecture will ensure that your systems are predictably high performance. Peter Aylett is a world-renowned speaker and lecturer in residential technology, and the Technical Director at Archimedia, a multinational high-end residential integrator in The Middle East. He is also currently Chair of CEDIA’s International Technology Council Applied Content Action Team, and a regular contributor to HiddenWires. www.hometechassoc.com You are welcome to comment on this article below.