Ever have one of your friendly amplifier reps walk in your office to present their new mondo-gazillion-watt beast and point out the damping factor spec of greater than a bazillion?
Why, gee-whiz! That’s, like, 10 times more than the other guy! It must be awesome, right?
Well, as we have seen before, it depends on how you are going to use it.
Let’s start with defining damping factor and see what it means to us.
Amplifier damping factor is defined as “the ratio of the load impedance (loudspeaker plus wire resistance) to the amplifier internal output impedance.” (Glen Ballou, editor, Handbook For Sound Engineers, Third Edition)
This basically indicates the amplifier’s ability to control overshoot of the loudspeaker, i.e, to stop the cone from moving. It is most evident at frequencies below 150 Hz or so, where the size and weight of the cones become significant.
A system where the damping factor of the entire Ioudspeaker/wire/arnplifier circuit is very low will exhibit poor definition in the low-frequency range due to the undamped loudspeaker’s ringing.
Low frequency transients such as kick drum hits will sound “muddy” instead of that crisp “punch” we would ideally want from the system.
The formula for calculating damping factor is:
Very few amplifier spec sheets state the output impedance, but you can generally call the manufacturer for this spec or you can calculate it by dividing the minimum rated load impedance by the damping factor rating.
For example, if we are using amplifier with a damping factor rating of 400 and it requires a minimum load of 2 ohms, then its output impedance would be calculated as being 0.005 ohms.
So let’s look at several examples and figure out what we can control in the design of our system to achieve the best results. Say we have two 8-ohm subwoofers connected to an amplifier with a damping factor of 400 with 100 feet of 12 gauge wire, with a resistance of 0.00159 ohms/ft times 100 feet, gives us a total resistance of.0.159 ohms.
Plugging the numbers into our formula, we get:
In this case, our system damping factor is just 12. Most experts agree that a reasonable minimum target DF for a live sound reinforcement system would be 20, so we need to consider changing something to get this up.
The critical element in this definition is’ the “loudspeaker plus wire resistance” part. In this case, the resistance in 100 feet of 12 gauge wire with a 4-ohm load results in around 0.7 dB of loss, much greater than the maximum target of 0.4 dB of loss, so let’s try bigger wire.
10 gauge wire has a resistance of .000999 ohms/ft times 100 feet equals .0999 ohms and will get us to the 0.4 dB target.
What will it do for DF?
OK, now we’re pretty close to the 20 we were looking for. Notice that the loudspeaker impedance can also give us a big change. The higher the circuit impedance, the less loss we have due to wire resistance.
What if we change our wiring so we have one 8-ohm loudspeaker connected instead of two?
Going back to our 12 gauge wire, we calculate:
Even better! In fact, if you run the numbers a few times, you will see that in a system with some significant length of wire, we will find that damping factor will generally be 20 or higher as long as our total wire loss is 0.4 dB or less.