DF: why it isn't so important, but still has meaning (long!).

"Robert Morein" <nowhere@xxxxxxxxxxx> said:


>> >Tell us why damping factor is an important specification.


>> Do you want an answer from Robert per se or can I give it? :-)

>Tell him, Sander. Perhaps Mikey will accept enlightenment if it comes from
>another source.


I'll try to explain this in as simple terms as possible.
( I'm sure Mike knows most of this already).

Damping factor, as the single number that is usually provided, is in
itself pretty meaningless.
Only when it is measured at different frequencies and with varying
loads and signal levels, we can draw some conclusions from it.

DF is always explained as the quotient of Rload/Ri of an amplifier's
output.
In general, the number is > 1 even with modest tube amps, and with
modern solid state amps, the number may well be above 100 or more.

What does this tell us? That with a load of 8 ohms and a DF of 100,
the Ri seems to be 0.08 ohms.
Following the usual Kirchhoff notation, we have an ideal voltage
source with a Ri in series, to which we connect the load.
The voltage divider that is created thusly, only loses 1/100th part of
the actual source EMF over Ri.
Nothing to worry about, one would think, so what are those silly
audiophiles acting so neurotical about?

This: such a low Ri is physically impossible without using large
amounts of negative loop feedback.
That is not a bad thing per se, but depending on the design of the
amp, it may in some cases lead to problems, of which some are outlined
below.

Let's assume an amplifier stage with BJTs in class AB such as we find
in most common products of today.
We remove the feedback loop for a moment, thereby creating an amp with
open loop amplification factor "Aol".
What are the consequences?
When we drive the input with a sine sweep signal, and connect an 8
ohms dummyload at the output, we can observe that not all frequencies
are equally amplified, and that the distortion of the signal is pretty
significant.
Due to the push-pull topology of the output stage, even order
harmonics are supressed, so the remainder of the distortion will have
an odd harmonics character.
The frequency response looks a bit like an inverted bath tub, meaning
the lowest and highest frequencies are lower in amplitude than the
middle frequencies. Such is the nature of non-ideal components.

Suppose we have an amplification factor "Aol" for 1 kHz (which
happens to be the, usually unspecified, frequency at which the DF of
commercial products is measured).
At say 10 Hz and 10 kHz, the factor "Aol" is then a lower number.
Because the feedback loop provides an equalizing and lowering function
on the amplification, distortion and Ri , one will observe that the
frequency range is extended and has become nearly flat over the entire
range, be it at a lower amplification factor that we'll call simply
"A".
The distortion is lowered by the same factor of feedback, as is the Ri
at the output of the amp.

Good, negative loop feedback linearizes the amplifier's properties, so
applying ever more and more of it should make for an even better
amplifier, no?

No.

First of all, we must realize that negative loop feedback can't be
increased indefinitely.
Why not? Well, because we must then start off with an amplifier with
huge amounts of Aol, since we want to keep a reasonable amplification
factor.
With opamps, we can get away with it because as a rule, they don't
have to supply as much current (= power) as an output stage in an
audio amplifier.
The other side of the coin is that in an amp stage with high gain, the
bandwidth goes down.
So, high gain equals low bandwidth.

The second reason why we can't increase negative feedback indefinitely
is that, because of inevitable physical effects like phase shifting
inside one or more stage(s), self-oscillation may and will probably
occur.
We want an amplifier, not an oscillator.

OK, so we settle for a reasonable amount of negative loop feedback.
(I'll use the acronym GNFB from now on, I'm having blue fingers
already!)
But there's no gain without pain (pun intended).
At the frequency extremes, Aol was lower than at 1 kHz.
This means, the loop feedback factor is decreased there.
This means that, compared to 1 kHz, at the frequency extremes, the
distortion and Ri are higher than at 1 kHz.

Again no problem, as long as we keep the GNFB factor as high as
possible without getting into problems with oscillation, our
distortion will still be well under the audible threshold at those
frequency extremes.

That's partly right.
Now we're getting at the interesting part of DF: until now, the
speaker load was presumed to be constant and resistive.
Sadly, with almost all speakers, it isn't
The impedance (AC- "resistance") isn't constant over the audio range,
it varies, sometimes wildly, from e.g. 4 to 40 ohms for a speaker that
is said to have "8 ohms" .
Even worse, since a speaker+crossover filter is actually a
combination of coils, capacitors and resistors, it will show phase
shifts as well.
This means that, where in a resistor current and voltage are in phase,
with a speaker they are not.
At one moment the voltage can be at a maximum, while the current can
be at minimum, and vice versa and all possibilities inbetween.
That means that an amplifier not only delivers current into a speaker
load, it has to sink current as well.
(This is one of the reasons why I prefer class A amps, they're better
able to cope with phase-shifting loads, ie. current sinking. Also, the
output impedance in OL is more constant. Enough).

Then we have the physical limitations of the power supply.
An amplifier is just a modulated power supply.
When the supply voltages are say plus and minus 40 V, we can't get an
output signal that is 100 V (top-to-top).
The theoretical maximum output swing would then be 80 Vtt ,
practically it is lower since output devices and other components take
some for themselves.

Since power is described as V^2/R (for DC), there is a relation
between supply voltage and speaker load.
For AC, the average output power is Vtt^2/8R.
In this example, for 8 ohms, the max. avg. output power would be 100
watts.
However, at the resonance frequency of the speaker, at say 40 ohms,
the avg. power is only 20 watts, and at the lowest impedance dip, say
4 ohms, avg. power is 200 watts.

And this is where the debate is all about: at half the load, the
output power (meaning current, the voltage stays the same) is doubled.
THIS IS ONLY POSSIBLE WHEN THE POWER SUPPLY CAN DELIVER ENOUGH CURRENT
WHILE THE VOLTAGE DOESN'T DROP.

So why the long story about GNFB, and what is the relationship with
DF?
Well, GNFB seems to make the Ri of an amp lower, but when the power
supply reaches its limits, the amp will clip at either the nominal
supply voltage, or it will "current-clip" at a lower supply voltage
because the supply voltage drops due to the demanded current.
The latter term isn't entirely correct, because the clipping is still
voltage-clipping, but it is caused by a weak power supply, not able to
deliver the current.

The GNFB will try to correct the error signals that occur because of
the (near) clipping, but the amp can't follow because the power supply
has run out of steam.
At that moment, THD reaches incredibly high levels.
To make things worse, the output devices can enter a condition called
"saturation", in which they keep passing their maximum current,
despite the fact that the driving signal has already disappeared.
With power BJTs, this effect can hold on for several hundreds of
microseconds.
In that condition, the GNFB loop doesn't work, so the amp is
essentially working under open loop conditions, which aren't that
good, as we saw earlier.
As soon as the output devices are turned off, they slowly return to
their normal operating conditions, thereby forcing the feedback loop
to still send error signals into the input stage, * where no reason
for correction exists anymore*, let alone that said error signals have
any relationship to the actual input signal at that moment.
Clipping can also occur under far more unlikely conditions, like in
the input- or driver stages, and that can also happen way under the
max. output voltages of the power stage.
Then there is thermal distortion, which I have discussed many times
here in the past.

I should write a book (in fact, I'm busy doing so, but it will be in
Dutch).

And all this can, to a degree, be determined from the damping factor,
provided that figures are given at various frequencies, with various
loads, and preferably, at various levels.

The only way to obtain those figures, is to measure them yourself.
Manufacturers never provide such detailed information.


And for those of you who know better: I know that there are ways to
design around these problems, and I know that there are amplifiers on
the market that are correctly designed, but I also happen to know that
many are not.
The reason they still sell is because most people never reach the
limits of their amp, and therefor won't notice, or they don't care
about it, as long as it plays LOUD.

PMPO is around for a reason.

--

"Audio as a serious hobby is going down the tubes."
- Howard Ferstler, 25/4/2005
.

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