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.

## No comments:

## Post a Comment