amplifier damping factor, another useless spec.
John Drab
> Is there any general agreement about the effect of power-amplifiers
> damping factor? (or output impedance?) How much it depends on
> speakers?
The damping factor would have to be quite low, on the order
of 1 -> 5 before it began to have a significant effect on measured
loudspeaker performance. Sorry, but you have to look elsewhere if
you want to find a meaningful spec. to describe an amplifier's
sound.
-jd
james kraft
wrote:
the opinion stated above is not widely held and does not hold
water. reducing the output impedance of an amplifier and therby
increasing its damping factor will draw more energy from the
loudspeaker driver as it is oscilating under its own inertial
power. this forces the driver to work into the amplifier's
input conductance and brings the driver under more effective
control of the amplifier.
a damping factor of 5, common for tube amplifiers with output
transformers, GROSSLY changes the time/amplitude envelope of
bass notes, for instance. instead of starting almost instantaneously
and then holding at a sustain volume, the note will start sluggishly
and continue to increase in volume for a considerable amount of time,
perhaps a second and a half. i find this effect disconcerting.
given that the effects of a damping factor of 5 are easy to hear,
i don't think that audible damping factor effects would vanish until
at least a damping factor of 100. for a 4 ohm speaker, this would
require a stated damping specification of 200 into 8 ohms.
vive la difference.
--
james kraft
university of colorado
jkr...@clipr.colorado.udu
Richard D Pierce
>In article <2rqq91$u...@introl.introl.com>, jo...@pelican.hac.com (John Drab)
>wrote:
>
>> kekk...@sun2.oulu.fi (Petri Kekkonen) asks:
>>
>> > Is there any general agreement about the effect of power-amplifiers
>> > damping factor? (or output impedance?) How much it depends on
>> > speakers?
>>
>> The damping factor would have to be quite low, on the order
>> of 1 -> 5 before it began to have a significant effect on measured
>> loudspeaker performance. Sorry, but you have to look elsewhere if
>> you want to find a meaningful spec. to describe an amplifier's
>> sound.
>
>water. reducing the output impedance of an amplifier and therby
>increasing its damping factor will draw more energy from the
>loudspeaker driver as it is oscilating under its own inertial
>power. this forces the driver to work into the amplifier's
>input conductance and brings the driver under more effective
>control of the amplifier.
YOUR opinion, which is, indeed, widely held, does not, in fact, hold
water. I recently posted a detailed analysis, based specifically on the
model you suggest, that effectively debunks the notion of hiogh damping
factor having an audible effect on the response of real speaker systems
at resonance (which is, I suppose, what you mean by "oscilating under its
own intertial power").
>a damping factor of 5, common for tube amplifiers with output
>transformers, GROSSLY changes the time/amplitude envelope of
>bass notes, for instance. instead of starting almost instantaneously
>and then holding at a sustain volume, the note will start sluggishly
>and continue to increase in volume for a considerable amount of time,
>perhaps a second and a half. i find this effect disconcerting.
GROSSLY changes? You have proof of this? I think not. In fact, you
specify a decay time of 1.5 seconds. This is utterly ludicrous, certainly
a number which has no origin other than that you must have pulled it out
of thin air, as it is completely unsupportable by either ANY loudspeaker
theory or ANY measurement. A decay time of 1.5 seconds is comparable to
the reverberation time of large acoustic spaces, and exceeds the decay
time of ANY of the thousands of drivers or systems I have measured by
orders of magnitudes. Such a decay time suggests a system with a Q of
many dozens, far, far above the effects of a change of damping factor of
a factor of 100, say, from 5 to 500, which would change the total Qtc of
a system by a few percent at most.
>given that the effects of a damping factor of 5 are easy to hear,
This is offered as an assertion, and you have not supplied on shred of
proof, either in terms of listening or actual measurements or even a
supporting theory for this or any other of the ridiiculous assertions
you've made here.
>i don't think that audible damping factor effects would vanish until
>at least a damping factor of 100. for a 4 ohm speaker, this would
>require a stated damping specification of 200 into 8 ohms.
You don't THINK so, yet your assertions are made in complete contravention
of ALL available evidence and theory.
You may find the effects you claim disconcerting, but the fact that you
have made specific claims of numbers, such as the 1.5 second decay time
figure, that are complete fabrications with NO supporting evidence, is
something that many of us find far more disconcerting..
Go learn about how loudspeakers and amplifiers REALLY work, then try again.
Vive le difference for sure, but death to wild eyed, strident,
unsupportable claims.
--
| Dick Pierce |
| Loudspeaker and Software Consulting |
| 17 Sartelle Street Pepperell, MA 01463 |
| (508) 433-9183 (Voice and FAX) |
james kraft
and to suppose that one has exhausted the
possible audible effects of a change in damping
factor when analyzing these effects on paper
or even with instruments is conceit masquerading
as science.
the data are what is audible, not what is measurable.
if you lose sight of that, you are merely discussing
theoretical matters.
John Drab
jkr...@clipr.colorado.edu (james kraft) wrote:
;the data are what is audible, not what is measurable.
;if you lose sight of that, you are merely discussing
;theoretical matters.
I agree that there are many areas in audio reproduction
where we do yet not know how to correlate measurement with
emotional impact. Your assertation was that a damping factor
of 5 would result in an envelope rise time approaching 1.5 seconds.
Such an effect would be quite easy to analyze or measure, but
analysis and measurements do not support your assertation.
Your claim along with Dick Pierce's comment "A decay time
of 1.5 seconds is comparable to the reverberation time of large
acoustic spaces" brings to mind the pipe organ recording "Recitial"
by James Welch from Wilson Audio. While I find this recording musically
uninvolving, I do like the effect of the eigenmode reinforcement in the low
frequencies. Organ petal tones start, then maybe a second later, when
the reflected wave from the back of the concert hall makes it back to
the microphone position and interferes with the direct wave, the amplitude
dramatically increases. Pretty easy to see on a 'scope, too.
- Audio and science can and do coexist.
-jd
Ian Hin Yun Chan
down the equations for the electrical and magnetic interactions between
coil and magnet). Is there any text out there that will help me with
"real world" considerations (eg what real magnet and coil designs look like,
how the damping term of a driver depends on frequency)?
All this has probably been worked out, but I'd like to learn it for myself.
BTW, I'm a physics major, so some "translation" from engineering jargon
would be appreciated.
Thanks!
- Ian
John Drab
;>
;>In article <2rqq91$u...@introl.introl.com>, jo...@pelican.hac.com (John Drab)
;>wrote:
;>
;> The damping factor would have to be quite low, on the order
;> of 1 -> 5 before it began to have a significant effect on measured
;> loudspeaker performance. Sorry, but you have to look elsewhere if
;> you want to find a meaningful spec. to describe an amplifier's
; sound.
;> -jd
;>
;the opinion stated above is not widely held and does not hold
;water.
I fully acknowledge that a large number of equipment users believe that
the damping factor of an amplifier should be high, but find that analysis
and measurement will not support that position.
;a damping factor of 5, common for tube amplifiers with output
;transformers, GROSSLY changes the time/amplitude envelope of
;bass notes, for instance. instead of starting almost instantaneously
;and then holding at a sustain volume, the note will start sluggishly
;and continue to increase in volume for a considerable amount of time,
;perhaps a second and a half. i find this effect disconcerting.
I presume I would also find such an effect disconcerting.
If you can support your assertation that envelope rise times of 1.5 seconds
either with analysis or measurements, please present your data/analysis.
All of the analysis/measurements I have done or seen show a envelope
rise time *several* orders of magnitude faster, limited mostly by the rise
time of the test waveform i.e. ~62->112mS for 20hz packet, 8ohm, DF=5.
(this means that amplitude of the second or third cycle in the packet is
equal to the steady state amplitude ) I admit to having problems with
room reflections on this type of measurement even though I measure in
the near field, I no longer have access to an anechoidal chamber.
You might also look at the analysis Dick Pierce posted yesterday which
is mostly in agreement with my work.
-jd
Richard D Pierce
Effects On System Response
Dick Pierce
INTRODUCTION
Much ballyhoo surrounds the concept of "damping factor." it's been
suggested that it accounts for the alleged "dramatic differences"
in sound between tube and solid state amplifiers. The claim is made
(and partially cloaked in some physical reality) that a low source
resistance aids in controlling the motion of the cone at resonance
and elsewhere, for example(1):
"reducing the output impedance of an amplifier and therby
increasing its damping factor will draw more energy from
the loudspeaker driver as it is oscilating under its own
inertial power."
This is absolutely true, to a point. But many of the claims made,
especially for the need for triple-digit damping factors, are not
based in any reality, be it theoretical, engineering, or
acoustical. This same person even suggested:
"a damping factor of 5, ..., GROSSLY changes the
time/amplitude envelope of bass notes, for instance. ...
the note will start sluggishly and continue to increase in
volume for a considerable amount of time, perhaps a second
and a half."
DAMPING FACTOR: A SUMMARY
What is damping factor? Simply stated, it is the ratio between the
nominal load impedance (typically 8 ohms) and the source impedance
of the amplifier. Note that all modern amplifiers (with some
extremely rare exceptions) are, essentially, voltage sources, whose
output impedance is very low. That means their output voltage is
independent, over a wide range, of load impedance.
Many manufacturers trumpet their high damping factors (some claim
figures in the hundreds or thousands) as a figure of some
importance, hinting strongly that those amplifiers with lower
damping factors are decidedly inferior as a result. Historically,
this started in the late '60's and early '70's with the widespread
availability of solid state output stages in amplifiers, where the
effects of high plate resistance and output transformer windings
traditionally found in tube amplifiers could be avoided.
Is damping factor important? Maybe. We'll set out to do an analysis
of what effect damping factor has on what most proponents claim is
the most significant property: controlling the motion of the
speaker where it is at its highest, resonance.
The subject of damping factor and its effects on loudspeaker
response is not some black art or magic science, or even
excessively complex as to prevent its grasp by anyone with a
reasonable grasp of high-school level math. It has been
exhaustively dealt with by Thiele(2) and Small(3) and many others
decades ago.
SYSTEM Q AND DAMPING FACTOR
The definitive measurement of such motion is a concept called Q.
Technically, it is the ratio of the motional impedance to losses at
resonance. It is a figure of merit that is intimately connected to
the response of the system in both the frequency and the time do-
mains. A loudspeaker system's response at cutoff is determined by
the system's total Q, designated Qtc, and represents the total
resistive losses in the system. Two loss components make up Qtc:
the combined mechanical and acoustical losses, designated by Qmc,
and the electrical losses, designated by Qec. The total Qtc is
related to each of these components as follows:
Qmc Qec
Qtc = --------- [1]
Qmc + Qec
Qmc is determined by the losses in the driver suspension,
absorption losses in the enclosure, leakage losses, and so on. Qec
is determined by the combination of the electrical resistance from
the DC resistance of the voice coil winding, lead resistance,
crossover components, and amplifier source resistance. Thus, it is
the electrical Q, Qec, that is affected by the amplifier source
resistance, and thus damping factor.
The effect of source resistance on Qec is simple and
straightforward. From Small(3):
Re + Rs
Qec' = Qec ------- [2]
Re
where Qec' is the new electrical Q with the effect of source
resistance, Qec is the electrical Q assuming 0 source resistance
(infinite damping factor), Re is the voice coil DC resistance, and
Rs is the combined source resistance.
It's very important at this point to note two points. First, in
nearly every loudspeaker system, and certainly in every loudspeaker
system that has nay pretenses of high-fidelity, the majority of the
losses are electrical in nature, usually by a factor of 3 to 1 or
greater. Secondly, of those electrical losses, the largest part, by
far, is the DC resistance of the voice coil.
Now, once we know the new Qec' due to non-zero source resistances,
we can then recalculate the total system Q as needed using eq. 2,
above.
The effect of the total Q on response at resonance is also fairly
straightforward. Again, from Small, we find:
4
Qtc 1/2
Gh(max) = (-----------) [3]
2
Qtc - 0.25
This is valid for Qtc values greater than 0.707. Below that, the
system response is overdamped.
We can also calculated how long it takes for the system to damp
itself out under these various conditions. The scope of this
article precludes a detailed description of the method, but the
figures we'll look at later on are based on both simulations and
measurements of real systems, and the resulting decay times are
based on well-established principles of the audibility of
reverberation times at the frequencies of interest.
PRACTICAL EFFECTS OF DAMPING FACTOR ON SYSTEM RESPONSE
With this information in hand, we can now set out to examine what
the exact effect of source resistance and damping factor are on
real loudspeaker systems. Let's take an example of a closed-box,
acoustic suspension system, once that has been optimized for an
amplifier with an infinite damping factor. This system, let's say,
has a system resonance of 40 Hz and a system Qtc of 0.707 which
leads to a maximally flat response with no peak at system
resonance. The mechanical Qmc of such a system is typically about
3, we'll take that for our model. Rearranging eq. 1 to derive the
electrical Q of the system, we find that the electrical Q of the
system, with an infinite damping factor, is 0.925. The DC
resistance of the voice coil is typical at about 6.5 ohms.
Let's generate a table that shows the effects of progressively
lower damping factors on the system performance:
Damping Rs Qec' Qtc' Gh(max) Decay
factor Ohms dB time (sec)
-------------------------------------------------------------
inf 0 0.9252 0.7071 0.0* 0.0396
2000 0.004 0.9257 0.7074 0.0* 0.0396
1000 0.008 0.9263 0.7078 0.0* 0.0396
500 0.016 0.9274 0.7084 0.0001 0.0396
200 0.04 0.9309 0.7104 0.0004 0.0397
100 0.08 0.9366 0.7137 0.0015 0.0400
50 0.16 0.9479 0.7203 0.0058 0.0403
20 0.4 0.9821 0.7399 0.0327 0.0414
10 0.8 1.0390 0.7717 0.1133 0.0432
5 1.6 1.1529 0.8328 0.3523 0.0466
2 4 1.4945 0.9976 1.2352 0.0559
1 8 2.0638 1.2227 2.5411 0.0685
-------------------------------------------------------------
* less than 0.0001 dB
The first column is the damping factor using a nominal 8 ohm load.
The second is the effective amplifier source resistance that yields
that damping factor. The third column is the resulting Qec' caused
by the non-zero source resistance, the fourth is the new total
system Qmc' that results. The fifth column is the resulting peak
that is the direct result of the loss of damping control because of
the non-zero source resistance, and the last column is the decay
time to below audibility in seconds.
ANALYSIS
Several things are apparent from this table. First and foremost,
any notion of severe overhang or extended "time amplitude
envelopes) resulting from low damping factors simple does not
exist. We see, at most, a doubling of decay time (this doubling is
true no matter WHAT criteria is selected for decay time). The
figure we see here of 70 milliseconds is well over an order of
magnitude lower than that suggested by one person, and this
represents what I think we all agree is an absolute worst-case
scenario of a damping factor of 1.
Secondly, the effects of this loss of damping on system frequency
response is non-existent in most cases, and minimal in all but the
worst case scenario. If we select a criteria that 0.1 dB is the
absolute best in terms of the audibility of such a peak (and this
is probably overly optimistic by at least a factor of 2 to 5), then
the data in the table suggests that ANY damping factor over 10 is
going to result in inaudible differences between such a damping
factor and one equal to infinity. It's highly doubtful that a
response peak of 1/3 dB is going to be identifiable reliably, thus
extending the limit another factor of two lower to a damping factor
of 5.
All this is well and good, but the argument suggesting that these
minute changes may be audible suffers from even more fatal flaws.
The differences that we see in Q figures up to the point where the
damping factor is less than 10 are far less than the variations
seen in normal driver-to-driver parameters in single-lot
productions. Even those manufacturers who deliberately sort and
match drivers are not likely to match a Qt figure to better than
5%, and those numbers will swamp any differences in damping factor
greater than 20.
Further, the performance of drivers and systems is dependent upon
temperature, humidity and barometric pressure, and those
environmental variables will introduce performance changes on the
order of those presented by damping factors of 20 or less. And we
have completely ignored the effects presented by the crossover and
lead resistances, which will be a constant in any of these figures,
and further diminish the effects of non-zero source resistance.
CONCLUSIONS
There may be audible differences that are caused by non-zero source
resistance. However, this analysis and any mode of measurement and
listening demonstrates conclusively that it is not due to the
changes in damping the motion of the cone at the point where it's
at it's most uncontrolled: system resonances. We have not looked at
the frequency-dependent attenuative effects of the source
resistance, but that's not what the strident claims are about.
Rather, the people advocating the importance of high damping
factors must look elsewhere for a culprit: motion control at
resonance simply fails utterly to explain the claimed differences.
REFERENCES
(1) James Kraft, reply to "Amplifier Damping Factor, Another
Useless Spec," rec.audio.high-end article
2rcccn$u...@introl.introl.com, 24 May 1994.
(2) A. Neville Thiele, "Loudspeakers in Vented Boxes," Proc. IRE
Australia, 1961 Aug., reprinted J. Audio Eng. Soc., 1971 May
and June.
(3) Richard H. Small, "Closed-Box Loudspeaker Systems," J. Audio
Eng. Soc., Part I: "Analysis," 1972 Dec, Part II, "Synthesis,"
1973 Jan/Feb.
Copyright 1994 Dick Pierce
Permission given for one-time no-charge electronic
distribution via rec.audio.high-end with subsequent followups. All
other rights reserved.
Richard D Pierce
> Am I interpreting this correctly when I infer that this "decay time to below
> audibility" is the time it takes the "peak" to come back down to + or - 0.1dB
> referenced to a nominal 0 dB level?
No, it's based on a lot of studies having to do with reverberation time
audibilities, the sensitivity of the ear to changes in levels at low
frequencies, and so on. Reverberation time in the midband is taken as the
time it takes for the extrapolated decay rate to drop the level 60 dB. At
lower frequencies, the criteria is less stringent, requiring less of a drop.
> Something else bothers me too. A cycle of 40Hz is 25 milliseconds long (thats
> 0.025 seconds). If the decay time is 0.0396 seconds, then this system is
> underdamped for 40Hz even with infinite damping factor in the amp.
> Is that true or am I misinterpreting or is this implied by the Qec' = 0.9252?
> Or does Qtc' = 0.707 still imply a well damped system(maximally flat)?
This is a valid objection, one which also bothers me as well as the first
person to use the criteria, A. Neville Thiele. The problem is (and in
complete contradiction to the ridiculous 1.5 second envelope assertion)
is that the decay time for the energy envelope for the Q's typically
found in loudspeakers is proximal to the period of the frequency at
cutoff. Thus, inorder to get ANY meaningful sense of decay time, the best
that one can do is to interpolate an envelope and derive a time-energy
plot. The problem is that at low Q's, the decay is so quick. Even looking
at simulations with a Qtc = 2.0, the decay envelope encompasses only
about 3 cycles for oscillation before the level of the envelope has dropped
~40 dB.
The point is, we are NOT seeing envelopes that are up to 100 cycles long
due to low damping factors. We are seeing envelopes that they are 1 or 2
cycles long, at the most.
Brock Hannibal
As a preface to my questions let me thank Dick for this article. I like it
and feel it should become part of a FAQ.
[much good stuff deleted]
Am I interpreting this correctly when I infer that this "decay time to below
audibility" is the time it takes the "peak" to come back down to + or - 0.1dB
referenced to a nominal 0 dB level?
Something else bothers me too. A cycle of 40Hz is 25 milliseconds long (thats
0.025 seconds). If the decay time is 0.0396 seconds, then this system is
underdamped for 40Hz even with infinite damping factor in the amp.
Is that true or am I misinterpreting or is this implied by the Qec' = 0.9252?
Or does Qtc' = 0.707 still imply a well damped system(maximally flat)?
Brock Hannibal
Design Engineer
Tektronix, Inc.
Philip Witham
for audible perfection, what about the midrange? I'm wondering, since
the open loop gain of a typical amp drops with frequency, and thus the DF
is worse as frequency goes up, does the effect actually turn out to be
more important in the midrange or treble than in the bass? Especially in
the case of a highly reactive crossover/driver network. A worst case
ballpark calc:
Assume a nominal impedance of 8 Ohms. Say, impedance rises to 20 Ohms at a
frequency of around 2Khz (bad, but possible speaker design). What
damping factor gives us a .1dB (surely inaudible) blip in the response?
(tap tap tatap scribble scribble tap...)
I get about a DF of about 52 for a .1 dB change at this frequency. Many
transistor amps with a damping factor of 500 at 100 Hz would drop to this
level at 2KHz.
Perhaps much more useful than a D.F. spec would be a plot of amp output
impedance-vs-frequency.
- Philip
Mithat Konar
>Perhaps much more useful than a D.F. spec would be a plot of amp output
>impedance-vs-frequency.
>
Give that man a medal! It has always irked me that someone, somewhere thought
it was a good idea to express output impedance, which for many modern designs
can change quite a lot over the the audio range, in terms of a single number.
Maybe it made sense in the days when tube amps had high-ish output
impedances and fairly constant open loop gain through the audio frequencies,
but for a modern spec it's worthless.
___________________________________________________________________________
Mithat Konar, Engineer
Korg Research and Development
1629A South Main Street
Milpitas, CA 95035
USA
___________________________________________________________________________