The majority of high performance amplifiers are solid state and employ global (overall) negative feedback, not least for the unit-to-unit consistency it offers over the wild (eg. +/–50%) tolerances of semiconductor parts. One effect of high global NFB (in conventional topologies) is to make the output source impedance (Zo) very low, potentially 100 times lower than the speaker impedance at the amplifier’s output terminals.

For example, if the amplifier’s output impedance is 40 milliohms, then the nominal damping factor with an 8 ohm speaker will be 200, ie. 40 milliohms (0.04) is 1/200th of 8Ω. This ‘damping factor’ is essential for accurate control of most speakers.

Yet describing an amplifier’s ability to damp a loudspeaker with a single number (called ‘damping factor’) is doubtful. This is true even in active systems where there is no passive crossover with their own energy storage effects, complicating especially dynamic behaviour.

Figure 2.13 again takes a sine-swept impedance of an 8 ohm, 15" driver in a nominal box to show how ‘static’ speaker damping varies. Impedance is 70 ohms at resonance but 5.6 ohms at 450Hz.

Now, at the bottom, is plotted the output impedance of a power amplifier which has high negative feedback, and thus the source impedance looking up (or into) it is very low (6 milliohms at 100Hz), though increasing monotonically above 1kHz.

The traditional, simplistic ‘damping factor’ takes this ideal impedance at a nominal point (say 100Hz), then describes attenuation against an 8 ohm resistor. This gives a damping factor of about 3 orders, ie. 1000, but up to 10,000 at 30Hz. Now look at the middle curve: This is what the amplifier’s damping ability is degraded to, after is has traversed a given speaker cable and passed through an ideal 10,000μF series capacitor, as commonly fitted in many professional cabinets for belt’n’braces DC fault protection.

The rise at 1kHz is due to cable resistance, while cable inductance and the series capacitance cause the high and low-end rises respectively above 100 milliohms.

We can easily read off static damping against frequency: At 30Hz, it’s about x100. At mid frequencies, bout x50, and again, about 100 at 10kHz. However, instantaneous dynamic’ impedance may dip four times lower, while the DC resistance portion of the speaker impedance increases after hard drive, recovering over tens to thousands of milliseconds, depending on whether the drive-unit is a tweeter or a 24" shaker.

Even with high NFB, an amplifier’s output impedance will be higher with fewer output transistors, less global feedback, junction heating (if the transistors doing the muscle work are MOS-FETs) and more resistive or inductive (longer/thinner) cabling. Reducing the series DC protection capacitor value so it becomes a passive crossover filter will considerably increase source impedance – even in the pass band.

The ESR (losses) of any series capacitors and inductors will also increase source impedance, with small, but complex, nested variations with drive, temperature, use patterns and aging. The outcome is that the three curves – and the difference between the upper two that is the map of damping factor writhe unpredictably.

Full reality is still more complex, as all loudspeakers comprise a number of complex energy storage/release/exchange sections, some interacting with the room space, and each with the others. The conclusion is that damping factor has more dimensions than one number can convey.

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