POWER TO THE SPEAKER: THE DAMPING FACTOR
When we speak of audio signals, we usually don't refer to the actual acoustic waves propagating through the air. Instead, we often think of audio as a voltage - with a one volt peak value as the ‘0dBu’ reference, clipping the average analogue ‘line’ signal circuit around +24dBu - measured in volts close to the commonly used balanced power supply of 15v. And when we discuss digital audio, we think of a digital code representing a voltage - with 0dBfs ‘full scale’ representing the maximum peak level.
However, the ultimate goal of an audio system is to produce acoustic waves - which is done by a loudspeaker. Connecting an analogue line signal to a loudspeaker normally doesn’t do much. To move the loudspeaker’s coil power is needed, and a voltage alone doesn’t institute power. We need a current as well, with an amazingly simple relationship: power is voltage times current.
This is where the power amplifier comes in. Analogue circuits in mixers, filters and D/A converters are handled by tiny circuits capable of producing very low currents - measured in milliamps. For a big 15” loudspeaker to move, a current of several amps is needed. Power amplifiers basically amplify the line signal’s voltage by not much, maybe a factor two or so. Their main job is to increase the current available to drive a loudspeaker by a factor of a thousand or more.
The power delivered by a power amplifier to a loudspeaker is divided over the loudspeaker, the speaker cable and connector and also over the output circuits of the power amplifier. The division follows the impedance of the three: the loudspeaker impedance, the impedance of the speaker cable and connector, the output impedance of the power amplifier. Circuits and cables convert power into heat, with the loudspeaker converting the power into heat and coil movement. The lower the impedance (measured in ohms, or Ω) of these parts, the lower the power that the part takes. Here it becomes clear that the impedance of the power amplifier and cables should be as low as possible, so most power goes to the loudspeaker.
The impedance of a speaker cable depends on the length and the thickness of the cable. A 2.5mm cable has an average impedance of around 0.01Ω per metre, so 10 metres of cable adds up to a total of about 2 x 10m x 0,01Ω = 0.2Ω. When used with the most commonly-used loudspeaker impedance of 8Ω, this puts more than 98% power to the loudspeaker - no showstopper there.
Almost all power amplifiers don't specify their output impedance as a value measured in Ω. Instead they specify a ‘damping factor’; the ratio between the amplifier’s output impedance and a nominal 8Ω speaker load. The reason for calling this parameter ‘damping’ is that when a loudspeaker is driven by the amplifier’s output, the inertia of the speaker’s moving parts cause it to keep moving at its resonant frequency, trying to flow back power into the power amplifier - even after the signal has stopped. When this happens, the low output impedance of a power amplifier output shortcuts the loudspeaker, dampening the inertia movement. The lower the power amplifier output impedance, the stronger the damping and the more precise the speaker movement is controlled - which is what we are after in high quality audio systems. This happens especially around the lower resonant frequencies, accounting for a ‘tight bass’ response.
Most power amplifiers on the market specify a damping factor of a few hundred, enough to prevent a ‘sloppy’ bass response when used with short, thick speaker cables. As a rule of thumb, a damping factor of 100 is considered a minimum, representing an output impedance of 0.04Ω. A higher damping factor is better of course, but in relation to the cable impedance it’s not as relevant – remember that the 10 meter cable already constituted a five times higher value. Instead of spending money on a power amplifier with a very high damping factor, it makes more sense to spend it on thicker speaker cables.
The power that reaches the loudspeaker finally gets ‘transduced’ into heat and speaker movement, with the speaker movement generating the acoustic air waves. How much of the electrical power is actually transduced into air waves depends on the loudspeaker’s sensitivity (which is another topic).
To conclude: The design strategy for getting as much power from the amplifier to the speaker and to keep a tight bass response is surprisingly simple: keep cables as short as possible, and as thick as possible.