ICEinLAVA's Domain

Damping Factor may not be the most obvious topic to use as a way to address amplifier-to-speaker connections, but this often overlooked spec is a good way to check the quality of materials and electrical performance, plus look at how they affect overall audio fidelity. Consider this my roundabout way of getting on my soapbox regarding the use of good cabling and short-as-possible cable runs.

Damping Factor is traditionally a way of defining the ratio of load impedance to source impedance. A larger number means a speaker cone is well-controlled, permitting “tight” sounding bass notes, instead of “flabby” sounds that remind you of plucking a taut rubber band. The term “damping” refers to a power amplifier’s ability to control the motion of the loudspeaker cone when tracking the signal. The best definition I have found was on the reference page of the Rane Web site (www.rane.com—an excellent reference).

“This term describes the action where, after the signal stops, the speaker cone continues moving, causing the voice coil to move through the magnetic field (now acting like a microphone), creating a new voltage that tries to drive the cable back to the power amplifier’s output. If the loudspeaker is allowed to do this, the cone flops around like a dying fish. It does not sound good. The only way to stop back-EMF (electromotive force, literally “back voltage”) is to make the loudspeaker see a dead short, i.e., zero ohms looking backward, or as close to it as possible.”

Take the damping factor of an amp and divide the nominal impedance load by that number and you will get the output impedance of the amp. Since we are trying to get an output impedande close to zero, the higher the damping factor, the better. For example, the QSC RMX4050HD has a listed damping factor of greater than 250 at eight ohms, which makes the output impedance in the neighborhood of .032 ohms—pretty close to zero. Most solid-state audio power amplifiers made for live sound have damping factor specs of hundreds or higher, and many have lab specs more than 1,000, and for live use, this is plenty to overkill.

A Reality Check

In the real world, there are plenty of other source impedance aspects that need to be accounted for in the damping factor computation. Actually, every piece of hardware between the amp and the speaker contributes to the final damping factor. For example, if the amplifier output jack, speaker cable, cable connectors, speaker input jack and speaker cabinet wiring add a half-ohm of source impedance in series to that 8-ohm load and the amplifier output impedance of .032, then the system damping factor is reduced to about 15.

There is good news and bad news in these computations. The good news is that we humans generally can only detect flabbiness if the damping factor gets below 10. Some golden-eared studio rats claim detection up to a damping factor of 20. So shooting for a higher-than-20 system goal is reasonable in choosing speaker cable types and factoring connector losses. The 10 to 20 range of damping factor results in a millisecond or two of damping time constant. With a typical 100Hz bass note extending its cycle over 10 milliseconds, you can get a feel for how much acoustic waveform control you have.

Another reality check is that historically, we have been brought up with amplifier-speaker combinations that have had horrible damping factors per the definition. Tube power amplifiers typically have output transformer windings with 10% or more of the load impedance expressed in the speaker-side transformer winding, giving damping factors in the two to 10 range without other aspects taken into account. Most live sound and just about all hi-fi speakers include passive crossover networks with inductors in the low-frequency driver path. These inductors block high frequency audio content, but also add many hundreds of milliohms into the signal path, further degrading the damping factor.

The final insult to most golden-eared sound engineers is that if you considered voice coil parasitics, also known as the non-contributing impedances to speaker operation, the Damping Factor would never get above one. About 80% of the voice coil impedance is the wire winding resistance that does nothing but produce heat. The remaining voice coil inductance does the work of moving the cone by storing energy in the magnetic circuit and working against the permanent magnet motor of the speaker basket. For example, a typical 4-ohm low frequency driver has about 3.2 ohms of winding resistance. The remaining impedance is the voice coil inductor containing an inductance (reactive impedance) plus back-EMF voltage that the amplifier must dissipate through its low impedance circuit paths for tight bass response. By moving the 3.2 ohms from load impedance to source impedance, you see that we live in a poorly damped speaker reality. However, by keeping our wiring and connection losses low, we give every chance to control the speaker effectively.

Pull Out the Scientific Abacus

Ignoring the dismal news of voice coil resistive losses, let’s run the numbers on a common example for an amplifier-speaker connection. Using a typical Crown Macro-Tech 10 milliohm output impedance driving a 50-foot length of a 12-gauge Speakon patch cable to a 4-ohm sub-woofer speaker cabinet, we can compute a nominal Damping Factor. The first item is to find all the resistive losses between the amplifier circuits and the voice coil. Some will be readily available, some will be by heuristics (guess your best). NL4 Speakon jack-to-plug connections are rated by Neutrik to be about three milliohms per connection fresh from the factory. I like to round these up to 10 milliohms per connection to take into account wire/socket oxidation, and connector contact oxidation. With two interconnects, we get another 20 milliohms. Next, look at Table One for 12-gauge wire and note the 1.650 milliohms per foot specification. Since a 50-foot patch cable has to complete the circuit using two 12-gauge wires, a total of 100 feet, or 165 milliohms, is tallied into the source impedance.

Adding the source impedance milliohms gives us 10+20+165, or 185 milliohms. Tacking on another five milliohms for inside the speaker cabinet wiring totals to 190 milliohms, or 0.19 ohms estimated source impedance. Given the nominal load impedance of four ohms, the computed Damping Factor is 4/0.19, or about 21. Now if we force a nasty situation by substituting 16-gauge cable for the 12-gauge cable (in other words, getting cheap), 100 feet of 16-gauge is 417.2 milliohms. Taking this value and adding the 35 milliohms of other source impedance losses gives us a new damping factor of about 8.8. This value is below the 10 criteria, and swapping cables would likely be detected in blind A/B tests.

Another aspect of interconnect choices is the resistive losses that begin to be sizable power losses, especially in professional live sound reinforcement using kilowatt level power amplifiers. In the above example, the 50 feet of 12-gauge speaker cable would provide about a 4% drop of power into a 4-ohm speaker load. If that load is powered by a 2,100-watt amplifier, more than 80 watts are lost as heat in the copper wire. In the 16-gauge example, about a 10% loss is expected and about 220 watts of the 2,100 watts peak signal is left in the copper wires. While these losses may not be easily heard as a loudness loss, the change in damping factor and slight cable warmth may be detected.

It needs to be repeated that short lengths of speaker cables with high current capable interconnects is your best bet to not “hear” your cabling. While I listed example numbers on near perfect condition, all it takes is a little bit of contact corrosion or a loose connector termination to make things sound terrible. If possible, choose Speakons or EP connections over banana and phone connector options to minimize contact resistive losses (count those milliohms). Also invest the time and materials to wipe the connector contacts with a light coating of contact cleaner. I use cotton swabs and the CAIG Labs two-step process of “DeoxIT” and “PreserveIT” on cabling periodically. Old soundmen will know these chemicals as Cramolin red and blue, and they have been around since the birth of the vacuum tube.