Damping Factor: A Technical Analysis
Richard D Pierce
A TECHNICAL ANALYSIS
Dick Pierce
Professional Audio Development
1 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:
"reducing the output impedance of an amplifier and
thereby increasing its damping factor will draw more
energy from the loudspeaker driver as it is oscillating
under its own inertial power." [1]
This is certainly 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."
Instead of unbridled hyperbole, there have been attempts at a
reasoned justification for damping factor. Witness a recent
rec.audio.tech post:
"Since the amplifier source impedance is indeed much
smaller than the speaker impedance, the latter is almost
insignificant. In fact, an amplifier with a damping factor
of 50 will sink twice the current of one with a damping
factor of 25, and therefore dissipate four times the
resonant energy." [2]
As intuitive as this analysis might seem, it is quite flawed since,
as we will see, it simply ignores the one major loss factor in the
entire system, throwing it out the window as if the single most
important controlling element over cone motion had no real
relevance.
2 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 unserstanding by anyone with a reasonable
grasp of high-school level math. It has been exhaustively dealt with
by Thiele [3], Small [4] and many others decades ago.
3 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. Another, completely equivalent view is that Q is the
ratio between the amount of energy stored in the system vs the
energy dissipated by losses.
It is a figure of merit that is intimately connected to the response
of the system in both the frequency and the time domains. A loud-
speaker 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 = --------- [Eq 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.
Qec itself is a measure of, simply, the ratio of the energy stored
in the moving system to the energy dissipated electrically by the
losses in the system, that is, in the resistances in the system. The
energy stored in the moving system, the kinetic energy, is dependent
upon the amount of mass and the velocity.
In the context of a speaker, the Qe is (from Small[4]):
2 2
Qec = 2 pi Fc Mmc Re / B l [Eq 2]
where Fc is the resonant frequency of the system, Mac is the
equivalent moving mass of the system, and Re is the DC resistance of
the voice coil (and this assumes 0 source impedance or "infinite"
damping factor). Further, B represents the magnetic flux density in
the gap and l the length of wire in the magnetic field. (We will
assume that we are using the same driver for all considerations
here, thus, Fc, Mmc B and l remain the same as well.)
The effect of source resistance on Qec is simple and straight-
forward. From Small again [4]:
Re + Rs
Qec' = Qec --------- [Eq 3]
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.
The factor
Re + Rs
--------- [Eq 4]
Re
comes from the fact that Re is built into the original derivation
for Qec includes Re in it. The correction simply calculates the
incremental increase in Qe with the incremental increase in the
total electrical resistance. Reconciling [Eq 4] with [Eq 2], we see
that:
2 2
Qec = 2 pi Fc Mmc (Re+Rs) / B l [Eq 6]
Thus it becomes obvious that the electrical Q of the speaker or,
more generally, the electrical damping of the speaker, is NOT
dependent upon the source resistance Rs alone (as the proponents of
damping factor erroneously claim), but on the TOTAL series
resistance seen by the driver, including the DC resistance of the
voice coil, Re. This mistake, as commonly as it is made, the the
fatal flaw in the entire damping factor argument.
It's very important at this juncture to note two points. First, in
nearly every loudspeaker system, and certainly in every loudspeaker
system that has any 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 3],
above.
The effect of the total Q on response at resonance is also fairly
straightforward. Again, from Small [4], we find:
4
Qtc
Gh(max) = sqrt(-------------) [Eq 7]
2
Qtc - 0.25
This is valid for Qtc values greater than 0.707. Below that, the
system response is overdamped and there is no response peak.
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.
4 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 (i.e. the mechanical contributions to system losses
and thus damping) 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:
Qtc * Qmc
Qec = --------- [Eq 8]
Qtc - Qmc
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 time
--------------------------------------------------------
inf. 0 ohms 0.925 0.707 0.0 dB 0.04 sec
2000 0.004 0.926 0.707 0.0 0.04
1000 0.008 0.926 0.708 0.0 0.04
500 0.016 0.927 0.708 0.0001 0.04
200 0.04 0.931 0.71 0.0004 0.04
100 0.08 0.936 0.714 0.0015 0.04
50 0.16 0.948 0.72 0.0058 0.04
20 0.4 0.982 0.74 0.033 0.041
10 0.8 1.04 0.77 0.11 0.043
5 1.6 1.15 0.83 0.35 0.047
2 4 1.49 0.99 1.24 0.056
1 8 2.06 1.22 2.54 0.069
--------------------------------------------------------
Table 1
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 Qtc' 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.
5 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.
Further, we simply do not observe the "factor-of-four" increase in
energy dissipation with a factor of two reduction in source
resistance as claimed in [2]. The statement that it's all about
energy dissipation is quite correct: remember that what damping is
doing is removing energy from a resonant system, and that the
measure of damping is Q, the ratio of energy stored to energy
dissipated. Look, for example, at the difference in Qt between a
damping factor of 50 and 20: the actual difference in the energy
dissipated is less than 3%. According to the theory expounded in
[2], the difference in energy dissipation should be around a factor
of 6!
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.
It is well known that 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.
6 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.
7 REFERENCES
[1] James Kraft, reply to "Amplifier Damping Factor,
Another Useless Spec," rec.audio.high-end article
2rcccn$u...@introl.introl.com, 24 May 1994.
[2] Steve (aq...@lafn.org), reply to "How can 2 amps
sound so different?," rec.audio.tech article
7go6da$b8q$1...@nnrp1.dejanews.com, 04 May 1999.
[3] A. Neville Thiele, "Loudspeakers in Vented Boxes,"
Proc. IRE Australia, 1961 Aug., reprinted J. Audio
Eng. Soc., 1971 May and June.
[4] Richard H. Small, "Closed-Box Loudspeaker Systems,"
J. Audio Eng. Soc., Part I: "Analysis," 1972 Dec,
Part II, "Synthesis," 1973 Jan/Feb.
Copyright 1994, 1995, 1998-2001 by Dick Pierce.
Permission given for one-time no-charge electronic
distribution with subsequent followups.
All other rights reserved.
--
| Dick Pierce |
| Professional Audio Development |
| 1-781/826-4953 Voice and FAX |
| DPi...@world.std.com |
Hendrik Skarpeid
Richard D Pierce <DPi...@world.std.com> skrev i
news:GE1tJ...@world.std.com
> DAMPING FACTOR: EFFECTS ON SYSTEM RESPONSE
> A TECHNICAL ANALYSIS
Ahhh.
I have been away from rat a while, and just as I came back, seing people
posting about damping, series resistance etc, and Dick is here, as always,
to guide us all onto the straight and narrow.
Feels good to see that some things never change....
BTW, I treasure your posts, DP. I usually save a copy when you post
something like this.
Hendrik
Paul van der Hulst
Ok, so amplifier output impedance doesn't matter at speaker resonance.
What about considering the full audio frequency spectrum?
Just take any frequency response graph from a stereophile amplifier
review; the frequency response is never flat into a dummy loudspeaker
load.
Partially due to the speaker being non-resistive (crossover filter,
driver mass and compliance), partially because of reactive components in
the output impedance.
Or even worse: the frequency response of switching amplifiers tike the
Tact millennium and the bel canto Evo 200.2. These amps have a LC low
pass filter at the output. In the audio frequency band, the output
impedance is inductive and will therefore increase with frequency
(Observe that these manufacturers are 'hesitant' to give you any numbers
for output impedance for frequencies over 1 kHz). The filter of the bel
canto for example is tuned for 6 ohm or so, as a result, the response at
20kHz is +0.5dB into 8ohm, -4dB! into 2 ohm.
In reality, we are working with a non resistive amplifier output
impedance, crossover filters also influence the impedance seen by the
driver.
Minimizing the magnitude of the output impedance is an effective way to
minimize reactive effects of the output impedance.
Paul van der Hulst
Arny Krueger
"Paul van der Hulst" <pvdh...@hetnet.nl> wrote in message
news:3B135BBE...@hetnet.nl...
> Ok, so amplifier output impedance doesn't matter at speaker
resonance.
> What about considering the full audio frequency spectrum?
The output impedance of the amplifier, and the impedance curve of the
loudspeaker form a filter that is effectively in series with the
speaker.
> Just take any frequency response graph from a stereophile amplifier
> review; the frequency response is never flat into a dummy
loudspeaker load.
True for any amp, audiophile, pro audio, automotive, boom box, you
name it!
> Partially due to the speaker being non-resistive (crossover filter,
> driver mass and compliance), partially because of reactive
components in
> the output impedance.
Very true. Partially due to the near-universal presence of a ca. 2
microhenry inductor outside the feedback loop, most power amps have a
rising output impedance above 5 KHz.
> Or even worse: the frequency response of switching amplifiers tike
the
> Tact millennium and the bel canto Evo 200.2. These amps have a LC
low
> pass filter at the output. In the audio frequency band, the output
> impedance is inductive and will therefore increase with frequency
> (Observe that these manufacturers are 'hesitant' to give you any
numbers
> for output impedance for frequencies over 1 kHz). The filter of the
bel
> canto for example is tuned for 6 ohm or so, as a result, the
response at
> 20kHz is +0.5dB into 8ohm, -4dB! into 2 ohm.
I can't confirm or deny your exact numbers, but they seem entirely
probable. This of these amplifiers as being a non-adjustable
equalizer that can have VERY audible effects despite the fact that
they measure reasonably flat into resistive loads.
> In reality, we are working with a non resistive amplifier output
> impedance, crossover filters also influence the impedance seen by
the
> driver.
That's one way of looking at it.
> Minimizing the magnitude of the output impedance is an effective
way to
> minimize reactive effects of the output impedance.
Absolutely!
It is also true that some power amplifiers have no output inductors.
Many of them also have far flatter output impedance curves. I've been
measuring the output impedance of power amps for a few months, and
have measured the output impedances of maybe a dozen amplifiers. This
was stimulated by the results of DBTs posted at
http://www.pcabx.com/product/amplifiers/index.htmm which are based on
performance into a :typical:" loudspeaker load. These DBTs generally
have positive outcomes for well-trained listeners. The question was
"why". The answer is that the output impedance of power amplifiers
varies with frequency, rises at high frequencies, and causes minor
but audible frequency response variations.
Richard D Pierce
Paul van der Hulst <pvdh...@hetnet.nl> wrote:
>Hello,
>
>Ok, so amplifier output impedance doesn't matter at speaker resonance.
I didn't say it didn't matter: I said that the emphasis placed
on "damping factor" is simply ill-considered.
>What about considering the full audio frequency spectrum?
If a resonance doesn't manifest itself in the impedance curve,
i.e., if the amplifier can't know about it, there's nothing the
amplifier will do about it.
>Just take any frequency response graph from a stereophile amplifier
>review; the frequency response is never flat into a dummy loudspeaker
>load.
>Partially due to the speaker being non-resistive (crossover filter,
>driver mass and compliance), partially because of reactive components in
>the output impedance.
That's a different issue, apart from damping.
>....
>In reality, we are working with a non resistive amplifier output
>impedance, crossover filters also influence the impedance seen by the
>driver.
No doubt, and I don't claim otherwise in this article.
>Minimizing the magnitude of the output impedance is an effective way to
>minimize reactive effects of the output impedance.
Absolutely correct. But, again, I was focussing on one very
well-defined claim. The frequency-deoendent attentuative effect
of output impedance are STILL there and STILL need to be
addressed.
Randy Yates
>
> "Paul van der Hulst" <pvdh...@hetnet.nl> wrote in message
> news:3B135BBE...@hetnet.nl...
>
> > Ok, so amplifier output impedance doesn't matter at speaker
> resonance.
> > What about considering the full audio frequency spectrum?
>
> The output impedance of the amplifier, and the impedance curve of the
> loudspeaker form a filter that is effectively in series with the
> speaker.
Hmmmm. "The impedance curve of the loudspeaker" IS the ideal linear
model of the loudspeaker and thus replaces the loudspeaker and is
not placed in series with it. Did you mean to say "in series with
the amplifier" (i.e., with the amplifier output impedance)? This
would be true since the amplifier is modeled as a voltage source
and thus has a single series output impedance in its model.
--
% Randy Yates % "...the answer lies within your soul
%% DIGITAL SOUND LABS % 'cause no one knows which side
%%% Digital Audio Sig. Proc. % the coin will fall."
%%%% <ya...@ieee.org> % 'Big Wheels', *Out of the Blue*, ELO
http://personal.lig.bellsouth.net/~yatesc
Arny Krueger
"Randy Yates" <ya...@ieee.org> wrote in message
news:3B139A76...@ieee.org...
> Arny Krueger wrote:
> > "Paul van der Hulst" <pvdh...@hetnet.nl> wrote in message
> > news:3B135BBE...@hetnet.nl...
> > > Ok, so amplifier output impedance doesn't matter at speaker
resonance. What about considering the full audio frequency spectrum?
> > The output impedance of the amplifier, and the impedance curve of
the loudspeaker form a filter that is effectively in series with the
speaker.
> Hmmmm. "The impedance curve of the loudspeaker" IS the ideal linear
> model of the loudspeaker and thus replaces the loudspeaker and is
> not placed in series with it.
True enough, I wrote something diffferent. Please read what I wrote.
> Did you mean to say "in series with
> the amplifier" (i.e., with the amplifier output impedance)? This
> would be true since the amplifier is modeled as a voltage source
> and thus has a single series output impedance in its model.
No, I mean exactly what I wrote:
"The output impedance of the amplifier, and the impedance curve of
the loudspeaker form a filter..."
"...a filter that is effectively in series with the speaker."
So, what is the filter? I hoped it would be obvious that the filter
is composed of two things, namely the output impedance of the
amplifier and the input impedance of the loudspeaker.
Please also note that I did not say that this filter is in series
with the positive input terminal of the speaker... I said it is
"...effectively in series with the speaker." That was intended to
suggest a model of an idealized speaker (with resistive input
impedance) that has a spectral-shaping filter in front of it.
André Huisman
> Ok, so amplifier output impedance doesn't matter at speaker resonance.
> What about considering the full audio frequency spectrum?
IMO, generally speaking, the drivers that cover the higher range rely more
on mechanical damping than the drivers that cover the low frequencies. Qms
vs. Qes is probably a thing to look at in this case.
> Or even worse: the frequency response of switching amplifiers tike the
> Tact millennium and the bel canto Evo 200.2. These amps have a LC low
> pass filter at the output. In the audio frequency band, the output
> impedance is inductive and will therefore increase with frequency
> (Observe that these manufacturers are 'hesitant' to give you any numbers
> for output impedance for frequencies over 1 kHz).
Example to the contrary: Look on the Powersoft website (nasty flash shit, I
know). There you'll find the DigAm amplifiers (Class-D as they get). These
PA amplifiers (biggest one being 2 x 3500W) have a DF of 400 at 100Hz. At
10kHz, this DF is: 400.
> Minimizing the magnitude of the output impedance is an effective way to
> minimize reactive effects of the output impedance.
But let's never go overboard on this. I know of a certain DUTCH PA manuf
that quotes huge DF numbers (well in the thousands if not higher). Not only
is this somewhat irellevant (for it'll only have an effect when we leave out
all wiring INCLUDING that thin piece of wire called the voice coil) but it
can also only be achieved through enormous amounts of feedback (which might
just bring along it's own pet peeves (can of worms probably is a better
word)).
For feet on earth stuff: Average piece of 2 x 2.5mm speaker wire, some 10
meters long (PA talk here) has a resistance of some 0.3 Ohms. An average
DF300 amp has an output impedance some 10% of that. A DF3000 amp has an
output impedance some 1% of that. Changing room temperature by some 1 degree
will quite probably have a MUCH larger effect than changing the DF from 300
to 3000. And then there is the voice coil...
--
André Huisman
New Line licht & geluid
hui...@new-line.nl
http://www.new-line.nl
--- pardon my French, I'm Dutch ---
Paul van der Hulst
>
>
> Example to the contrary: Look on the Powersoft website (nasty flash shit, I
> know). There you'll find the DigAm amplifiers (Class-D as they get). These
> PA amplifiers (biggest one being 2 x 3500W) have a DF of 400 at 100Hz. At
> 10kHz, this DF is: 400.
Nice
> > Minimizing the magnitude of the output impedance is an effective way to
> > minimize reactive effects of the output impedance.
>
> But let's never go overboard on this. I know of a certain DUTCH PA manuf
> that quotes huge DF numbers (well in the thousands if not higher).
I know another one who claims this and THD<0.005 at 200W/4ohm (=full
power), IMD<<-90dB (15kHz&500Hz full power). (It even sounds great)
>Not only
> is this somewhat irellevant (for it'll only have an effect when we leave out
> all wiring INCLUDING that thin piece of wire called the voice coil) but it
True if you ignore the crossover filter in between. Otherwise you simply
cannot say these are 2 faces of the same coin. Also, you are assuming
the output impedance is purely resistive. If it's not purely resistive,
you're opening another can of worms.
> can also only be achieved through enormous amounts of feedback (which might
> just bring along it's own pet peeves (can of worms probably is a better
> word)).
I am aware of this.
Paul van der Hulst
Randy Yates
> [...]
> Please also note that I did not say that this filter is in series
> with the positive input terminal of the speaker... I said it is
> "...effectively in series with the speaker." That was intended to
> suggest a model of an idealized speaker (with resistive input
> impedance) that has a spectral-shaping filter in front of it.
Making up your own meanings for common terms like "speaker" without
defining precisely what you mean is confusing.
Richard D Pierce
>Arny Krueger wrote:
>> [...]
>> Please also note that I did not say that this filter is in series
>> with the positive input terminal of the speaker... I said it is
>> "...effectively in series with the speaker." That was intended to
>> suggest a model of an idealized speaker (with resistive input
>> impedance) that has a spectral-shaping filter in front of it.
>
>Making up your own meanings for common terms like "speaker" without
>defining precisely what you mean is confusing.
Well, to be honest, Thevenin lets you do just that.
If, by "idealized speaker," Arny means a purely resistive load,
which is in series with a frequency-dependent impedance, all of
which is in series with the output impedance of the amplifier,
it's a valid model for the scope of the analysis at hand.
Thevenin would say it makes no real difference where you put the
pieces: you are concerned ultimately with the combined effects
of the pieces on the total volume velocity of the speaker vs
frequency given, now, the ideal voltage source sitting behind
the Thevenin quivalent of the output impedance of the amplifier,
etc..
Randy Yates
I agree that the model Arny proposed is perfectly valid. My
comment was rather about how that model was communicated. We would
all be wise to follow the advice of Tertulus, who said "Do not
aim to be possible to understand, but impossible to misunderstand."
Arny Krueger
> Richard D Pierce wrote:
> I agree that the model Arny proposed is perfectly valid.
Tnnka you.
> My comment was rather about how that model was communicated. We
would
> all be wise to follow the advice of Tertulus, who said "Do not
> aim to be possible to understand, but impossible to misunderstand."
IME anybody who wishes to write only that which can't possibly be
misunderstood will never write anything.
Richard D Pierce
Arny Krueger <ar...@hotpop.com> wrote:
>
>"Randy Yates" <ya...@ieee.org> wrote in message
>news:3B273C5B...@ieee.org...
>would
>> all be wise to follow the advice of Tertulus, who said "Do not
>> aim to be possible to understand, but impossible to misunderstand."
>
>IME anybody who wishes to write only that which can't possibly be
>misunderstood will never write anything.
I don't understand.
Arny Krueger
"Richard D Pierce" <DPi...@world.std.com> wrote in message
news:GEvBG...@world.std.com...
> In article <6AHV6.1949$St3.72...@newssvr17.news.prodigy.com>,
> Arny Krueger <ar...@hotpop.com> wrote:
> >
> >"Randy Yates" <ya...@ieee.org> wrote in message
> >news:3B273C5B...@ieee.org...
> >> My comment was rather about how that model was communicated. We
> >would
> >> all be wise to follow the advice of Tertulus, who said "Do not
> >> aim to be possible to understand, but impossible to
misunderstand."
> >
> >IME anybody who wishes to write only that which can't possibly be
> >misunderstood will never write anything.
>
> I don't understand.
ROTF!
Randy Yates
Arny,
Let me interpret this for you since you apparently cannot understand
its meaning unaided. When someone says "Aim for the stars," does that
mean they expect to hit their target? No, of course not. In the same
way, Tertulus is not expecting that anything can actually be written
that is impossible to misunderstand, but rather he is suggesting
that this be a (albeit impossible) goal.
And if that is too deep for you to grasp, let's take another
tack. Your original statement was:
The output impedance of the amplifier, and the impedance curve of the
loudspeaker form a filter that is effectively in series with the
speaker.
Since my beef with you is your use of the word "speaker" implicitly
to mean "an ideal voltage-to-pressure transducer, having infinite
input impedance," perhaps you can quote me other places which use
the word "speaker" in a similar manner. Anywhere would be fine - textbooks,
AES articles, USENET articles, etc.
--
Randy Yates
DSP Engineer
Ericsson Inc.
Research Triangle Park, NC, USA
randy...@ericsson.com, 919-472-1124
Arny Krueger
"Randy Yates" <eus...@rtp.ericsson.com> wrote in message
news:3B279463...@rtp.ericsson.com...
> Arny Krueger wrote:
> >
> > "Randy Yates" <ya...@ieee.org> wrote in message
> > news:3B273C5B...@ieee.org...
> > > Richard D Pierce wrote:
> >
> > > I agree that the model Arny proposed is perfectly valid.
> > Thank you.
> > > My comment was rather about how that model was communicated.
We would
> > > all be wise to follow the advice of Tertulus, who said "Do not
> > > aim to be possible to understand, but impossible to
misunderstand."
> > IME anybody who wishes to write only that which can't possibly
be
> > misunderstood will never write anything.
> Let me interpret this for you since you apparently cannot
understand
> its meaning unaided.
Mr. Yates, you seem to want to cloud what you say with insults.
Could you state things in a way that would be even MORE humiliating
and insulting?
> When someone says "Aim for the stars," does that
> mean they expect to hit their target? No, of course not. In the
same
> way, Tertulus is not expecting that anything can actually be
written
> that is impossible to misunderstand, but rather he is suggesting
> that this be a (albeit impossible) goal.
Mr. Yates, given the insulting and humiliating introduction to this
statement of the obvious, it's clear that there is nothing that I can
write that you can't twist and misinterpret for your own personal
satisfaction.
And that was exactly my point. There are people who spend their time
twisting and misinterpreting what others write. Satisfying them just
isn't a priority with me.
> And if that is too deep for you to grasp, let's take another tack.
Ah, so you want to twist the knife again, Mr. Yates?
>Your original statement was:
> The output impedance of the amplifier, and the impedance curve of
the
> loudspeaker form a filter that is effectively in series with the
> speaker.
> Since my beef with you is your use of the word "speaker" implicitly
> to mean "an ideal voltage-to-pressure transducer, having infinite
> input impedance," perhaps you can quote me other places which use
> the word "speaker" in a similar manner.
There is no need for the "speaker", as I used the word, to be an
ideal voltage-to-pressure transducer with infinite input impedance.
For example, the filter I proposed could have a very low output
impedance.
Jason Walsh
is there any manufacturer making amps with low or without damping? The manual
for my monitors says that I should be using something like that, (urie 813c) they
of coarse were trying to sell their amps which are hard to find now.
Arny Krueger
"Jason Walsh" <j...@chicagonet.net> wrote in message
news:3B395AE9...@chicagonet.net...
You can decrease the damping factor of a high damping factor
amplifier by just sticking a resistor in series with one of the
speaker leads, or using very small speaker wire. Depending on the
length of the speaker wire, you might want to try some 24 gauge. It's
cheap enough and readily available.
Jason Walsh
to death. I guess you cant get 200 watts through 22 gauge wire. thanks
anyway. maybe I will find the amp that goes with these speakers on e-bay
or something. does anyone know when they started building this into amps,
I got the impression from the manual that it was a new thing when these
were new.
Tomi Holger Engdahl
> I tried that and lost about half the volume and it distorted the signal
> to death.
The speaker cable does not cause same kind of distortion which
overdriving the camplifiaer causes (the most commonly what
is called distortion). Too this wire can cause poor damping
and if it is very thin dynamics compressions (if wire gets very
hot which causes resistance to increase considerably).
> I guess you cant get 200 watts through 22 gauge wire.
One 22 gauge wire is rated maximum of 2.1 A continuois current.
That's the maximim you should try to push through it.
If you try more you can overhat it. 2A to 8 ohm load
would give 32W of power safely...
> thanks
> anyway. maybe I will find the amp that goes with these speakers on e-bay
> or something. does anyone know when they started building this into amps,
> I got the impression from the manual that it was a new thing when these
> were new.
>
> Arny Krueger wrote:
>
> > "Jason Walsh" <j...@chicagonet.net> wrote in message
> > news:3B395AE9...@chicagonet.net...
> > >
> > >
> > > is there any manufacturer making amps with low or without damping?
> > The manual
> > > for my monitors says that I should be using something like that,
> > (urie 813c) they
> > > of coarse were trying to sell their amps which are hard to find
> > now.
> >
> > You can decrease the damping factor of a high damping factor
> > amplifier by just sticking a resistor in series with one of the
> > speaker leads, or using very small speaker wire. Depending on the
> > length of the speaker wire, you might want to try some 24 gauge. It's
> > cheap enough and readily available.
>
--
Tomi Engdahl (http://www.iki.fi/then/)
Take a look at my electronics web links and documents at
http://www.epanorama.net/
Arny Krueger
> I tried that and lost about half the volume and it distorted the
signal
> to death.
You probably inadvertently shorted something.
>I guess you cant get 200 watts through 22 gauge wire.
At worst, it should get warm.
Richard D Pierce
Jason Walsh <j...@chicagonet.net> wrote:
>> "Jason Walsh" <j...@chicagonet.net> wrote in message
>> news:3B395AE9...@chicagonet.net...
>> > is there any manufacturer making amps with low or without damping?
Why would you want such?
First of all, amplifiers do NOT have damping: that's one of the
slaient points of my analysis: the damping issue ONLY applies to
the entire amp-speaker/lead combination and must be analyzed in
that context. Secondly The only amp/speaker combination that
would have NO electrical damping is one where the output
impedance of the amplifier is infinite, i.e., a perfect current
source. Such, practically, can never exist.
Again, why do you want no electrical damping? That puts you at
the mercy of the mechnical damping of the speaker, which is
nototiously variable, unreliable, environment dependent, and so
forth.
>> > The manual for my monitors says that I should be using
>> > something like that, (urie 813c) they of coarse were trying
>> > to sell their amps which are hard to find now.
>> You can decrease the damping factor of a high damping factor
>> amplifier by just sticking a resistor in series with one of the
>> speaker leads, or using very small speaker wire. Depending on the
>> length of the speaker wire, you might want to try some 24 gauge. It's
>> cheap enough and readily available.
>
>I tried that and lost about half the volume
Well, of course. ANY series resistance will reduce the volume,
along with reducing the so-called "damping factor." That's the
way it works, that's the way it's SUPPOSED to work.
>and it distorted the signal to death. I guess you cant get 200
>watts through 22 gauge wire.
Wrong. If it's "distorting to death," it has nothing to do with
not being able to "get 200 watts through 22 gauge wire." You'll
find the voice coils of woofers capable of dissipating 200 watts
wound with smaller wire than 22 gaugeme, yet they don't
"distort to death." You either shorted out the amplifier, are
overdriving things, or some other fault unassociated with the
wire.
Jason Walsh
my monitors (urie 813c studio monitors) they warn about the use of amplfiers
with high damping. Obviosly they were trying to get you to buy the amps that
they manufacture. The problem is that these monitors havent been the studio
standard in about 15 years and the company was bought out by JBL so
information and support is very hard to come by. The only thing harder to
come by is these amplifiers themselves, so I am trying to find something
compatable. Somehow they managed to make the speaker, x-over, cabinet
combination with low damping in mind. The manual says that use of the wrong
amp will result in a loss of low end. I beleve I am having that problem now
seeing as how I have 4 15 inch speakers with 200 watts per side staring me
in the face and I'm just not feeling it. And yes the speakers are in good
working order.
Don Pearce
have good bass. Obviously, with good damping and bass under control,
they are a bit lightweight. But with the cone flapping in the breeze
and generally doing its own thing, you get an impression of some
actual bass going on.
Use an amplifier with good damping, see if the tone suits you, and if
not, apply some bass boost.
d
On Mon, 02 Jul 2001 15:08:04 -0500, Jason Walsh <j...@chicagonet.net>
wrote:
_____________________________
Telecommunications consultant
http://www.pearce.uk.com
Eugene A. Pallat
> In article <3B400A03...@chicagonet.net>,
> Jason Walsh <j...@chicagonet.net> wrote:
> >> "Jason Walsh" <j...@chicagonet.net> wrote in message
> >> news:3B395AE9...@chicagonet.net...
> >> > is there any manufacturer making amps with low or without damping?
>
> Why would you want such?
>
> First of all, amplifiers do NOT have damping: that's one of the
> slaient points of my analysis: the damping issue ONLY applies to
> the entire amp-speaker/lead combination and must be analyzed in
> that context. Secondly The only amp/speaker combination that
> would have NO electrical damping is one where the output
> impedance of the amplifier is infinite, i.e., a perfect current
> source. Such, practically, can never exist.
>
> Again, why do you want no electrical damping? That puts you at
> the mercy of the mechnical damping of the speaker, which is
> nototiously variable, unreliable, environment dependent, and so
> forth.
Years ago (40+ ?), several amplifier companies got on the "variable damping
factor" wagon with an adjustable pot. One magazine had a review, and the
gist of it was setting the control beyond "critically damped" bought you no
additional benefits, but under damping wasn't good at all. The net result
is that no manufacturer bothered to offer that "feature" any more.
Gene Pallat
Richard D Pierce
Jason Walsh <j...@chicagonet.net> wrote:
>Admitedly I don't know what I'm talking about, but in the owners manual for
>my monitors (urie 813c studio monitors) they warn about the use of amplfiers
>with high damping. Obviosly they were trying to get you to buy the amps that
>they manufacture. The problem is that these monitors havent been the studio
>standard in about 15 years and the company was bought out by JBL so
>information and support is very hard to come by. The only thing harder to
>come by is these amplifiers themselves, so I am trying to find something
>compatable. Somehow they managed to make the speaker, x-over, cabinet
>combination with low damping in mind. The manual says that use of the wrong
>amp will result in a loss of low end.
I think what you are seeing is a speaker manufacturer not
understanding that dam,ping factor simplyt does NOT behave as
claimed. Unless the damping factor is VERY low, say below 10,
the difference in the low end simply is NOT going to be very
big.
>I beleve I am having that problem now
>seeing as how I have 4 15 inch speakers with 200 watts per side staring me
>in the face and I'm just not feeling it. And yes the speakers are in good
>working order.
Yes, and even still they may well NOT have any real low bass. A
lot of pro-sound or "monitoring" speakers with 15" woofers
simply did not go very low in frequency, often having a cutoff
frequency of 50-75 Hz. Not very impressive.
So, if you're looking at your speakers, and assuming that 4
15" woofers MUst have a lot of deep bass, and they don't, about
the LAST thing I wouls blame would be the amplifier and some
contrived nonsense about damping factor. The very first place,
assuming it's an equipment issue, is the speaker.
Bill Watkins
says...
>
>On Mon, 02 Jul 2001 18:01:27 -0400, "Eugene A. Pallat"
><eapa...@apk.net> wrote:
>
>>Years ago (40+ ?), several amplifier companies got on the "variable damping
>>factor" wagon with an adjustable pot.
>
The term "damping" is somewhat of a misnomer. What happens
with a "low damping factor" is that the amplifier voltage
rises in the low end and dumps more power into the speaker.
Rather than failing to "damp" the speaker and letting the
cone "run away", the amp is feeding in more power. IOW
the amp is moving away from constant voltage, and in the
direction of constant current operation.
Bill W.
Jason Walsh
impressive against recent stuff. I probably shouldn't try to compete now with
state of the art 1979 equipment. I'll e-bay these and get genelecs like everyone
else. Thank you for your help.
Richard D Pierce wrote:
>
>
> I think what you are seeing is a speaker manufacturer not
> understanding that dam,ping factor simplyt does NOT behave as
> claimed. Unless the damping factor is VERY low, say below 10,
> the difference in the low end simply is NOT going to be very
> big.
>
Randy Yates
>
> In article <0i02kt8rb298ud1ee...@4ax.com>, fle...@free.fr
> says...
> >
> >On Mon, 02 Jul 2001 18:01:27 -0400, "Eugene A. Pallat"
> ><eapa...@apk.net> wrote:
> >
> >>Years ago (40+ ?), several amplifier companies got on the "variable damping
> >>factor" wagon with an adjustable pot.
> >
> >Well, it was basically a variable feedback scheme AFAICT.
>
> The term "damping" is somewhat of a misnomer.
Whatever string of the alphabet you use to represent it, what it
actually *is* is the ratio of the load impedance (which is usually
assumed to be 8 ohms) to the output impedance of the amplifier.
> What happens
> with a "low damping factor" is that the amplifier voltage
> rises in the low end and dumps more power into the speaker.
More than what?
If you model the amplifier as a perfect voltage source in series
with a non-ideal source impedance > 0 ohms (at the low frequencies),
then the voltage delivered to the speaker at low frequencies should
be less than that delivered by an amplifier with a higher damping
factor. Viewed another way, assuming the speaker impedance is constant over
frequency, the voltage across the speaker from a low-damping factor
amp should drop as the frequency gets lower.
I suppose this could be a "fix" to a boomy speaker design...
Bill Watkins
says...
>
>Bill Watkins wrote:
>>
>> In article <0i02kt8rb298ud1ee...@4ax.com>, fle...@free.fr
>> says...
>> >
>> >On Mon, 02 Jul 2001 18:01:27 -0400, "Eugene A. Pallat"
>> ><eapa...@apk.net> wrote:
>> >
>> >>Years ago (40+ ?), several amplifier companies got on the "variable
damping
>> >>factor" wagon with an adjustable pot.
>> >
>> >Well, it was basically a variable feedback scheme AFAICT.
>>
>> The term "damping" is somewhat of a misnomer.
>
>Whatever string of the alphabet you use to represent it, what it
>actually *is* is the ratio of the load impedance (which is usually
>assumed to be 8 ohms) to the output impedance of the amplifier.
>
>> What happens
>> with a "low damping factor" is that the amplifier voltage
>> rises in the low end and dumps more power into the speaker.
>
>More than what?
An amplifier with a lower damping factor than ~20 will
increase it's voltage output in the region of higher
impedance at fundamental resonance, usually below 100
Hz, relative to the voltage level above resonance,
assuming a flat input signal and flat amplifier
response above 100 Hz.
>If you model the amplifier as a perfect voltage source in series
>with a non-ideal source impedance > 0 ohms (at the low frequencies),
>then the voltage delivered to the speaker at low frequencies should
>be less than that delivered by an amplifier with a higher damping
>factor. Viewed another way, assuming the speaker impedance is constant over
>frequency, the voltage across the speaker from a low-damping factor
>amp should drop as the frequency gets lower.
Not sure of that theory, since I've seen no such speaker,
but I believe you may be in error. Perhaps Mr. Pierce
would care to comment.
BEAR
sensitivity - ie. playing loudly.
They do NOT have particularly good low frequency extension - I've measured
them sitting mouted *flush* in a wall (best case for bass, usually) and they
drop like a stone at 50Hz. You need EQ to get them flat to 40 Hz...
They are merely updated versions of the venerable Altec "big red" coaxial
drivers...
Add a suitable subwoofer if you want bass from these puppies... If you want
imaging, be sure to sit centered, with the tweeter horns aimed appropriately.
The manufacturer probably felt that a little less DF would "help" the badly
aligned ported box/driver combo eak out a bit more bass, and that the "fatter"
sound above that point that is generally produced by a low DF amp in this
circumstance would make they whole thing sound a bit nicer.
Try a standard high power tube amp for these, and biamp for best results
anyhow...
As I alluded to before, if you want anything close to a flat response, you'll
have
to do some reasonably sophisticated tests and probably EQ them.
They do play very loudly though.
_-_-bear
Jason Walsh wrote:
--
_-_-bearlabs
... please disregard the netzero sigfile... nothing is really
"free."
Richard D Pierce
Bill Watkins <bwat...@mounet.com> wrote:
>In article <3B41D3BC...@rtp.ericsson.com>, eus...@rtp.ericsson.com
>>>
>>> The term "damping" is somewhat of a misnomer.
>>
>>Whatever string of the alphabet you use to represent it, what it
>>actually *is* is the ratio of the load impedance (which is usually
>>assumed to be 8 ohms) to the output impedance of the amplifier.
And, as a means of describing the control of resonant energy, is
effectively useless, since the largest dissipating agent of the
energy stored in a speaker resonance is NOT the amplifier, but
the DC resistance of the voice coil. If nothing else, the
RECIPROCAL of the "damping factor" is a measure of how much the
amplifier is in control of damping the speaker.
>> >>> What happens
>>> with a "low damping factor" is that the amplifier voltage
>>> rises in the low end and dumps more power into the speaker.
>>
>>More than what?
More than it does at regions where the electrical impedance of
the speaker is lower Second order systems have a local maximum
in the impedance at resonance. That freqequncy dependency means
that more voltage is developed across the speaker at resonance
than elsewhere, assuming a source impedance that's reasonably
constant with frequency. With is a trivially verifiable fact.
> An amplifier with a lower damping factor than ~20 will
> increase it's voltage output in the region of higher
> impedance at fundamental resonance, usually below 100
> Hz, relative to the voltage level above resonance,
> assuming a flat input signal and flat amplifier
> response above 100 Hz.
Actuially, this will happen on ANY amplifier with ANY finite
output impedance: it's just that once you get a "damping
factor" greater than a couple of dozen or so, the effect becomes
essentially negligable.
>>If you model the amplifier as a perfect voltage source in series
>>with a non-ideal source impedance > 0 ohms (at the low frequencies),
>>then the voltage delivered to the speaker at low frequencies should
>>be less than that delivered by an amplifier with a higher damping
>>factor. Viewed another way, assuming the speaker impedance is constant over
>>frequency, the voltage across the speaker from a low-damping factor
>>amp should drop as the frequency gets lower.
Huh? With relatively few rare exceptions, the low frequency
output impedance characteristic of most amplifiers is
predominatly resistive and thus does not and can not behave as
you suggest. Thus, you end up with a voltage function across the
speaker terminals that is a somewhat complex but direct function
of impedance.
Assume the impedance function of the loudspeaker is Z(f) and, at
the relevant range of frequencies, the amplifier output is Rg:
the response deviation due to source attenuation is reasonably
approximated by:
Z(f) + Rg
Gz(f) = 20 log -----------
Z(f)
For example: assume Z(f) has a minimum of 8 ohms in the audio
band, and a local maximum at resonance of 40 ohms (hardly
atypical). And compare the deviation in the response cnsidering
four amplifiers with damping factors of 5, 50, 500 and 5000,
(corresponding to source resistances of 1.6, 0.16, 0.016, and
0.0016 ohms). The effective boost in response at resonance will
be:
D.F. Gz(f) Gz(f) Relative
@8 ohms @40 ohms Boost (dB)
5 -1.58 dB -0.34 dB 1.24 dB
50 -0.17 -0.034 0.14 dB
500 -0.017 -0.0034 0.014 dB
5000 -0.0017 -0.00034 0.0014 dB
Whether the resulting 1.24 dB peak at resonance contributes
audibly is another matter: the fact is, the answer to the
question, "more than what" is "more electrical power at resonace
or other regions of high electrical impedance than would obtain
where the impedance is lower, and the effect is more significant
with higher source impedances than with low.)
> Not sure of that theory, since I've seen no such speaker,
Nor have I.
> but I believe you may be in error. Perhaps Mr. Pierce
> would care to comment.
Can I? :-)
Bill Watkins
>
>In article <tk3up85...@news.supernews.com>,
>Bill Watkins <bwat...@mounet.com> wrote:
>
>
>> An amplifier with a lower damping factor than ~20 will
>> increase it's voltage output in the region of higher
>> impedance at fundamental resonance, usually below 100
>> Hz, relative to the voltage level above resonance,
>> assuming a flat input signal and flat amplifier
>> response above 100 Hz.
>
>Actuially, this will happen on ANY amplifier with ANY finite
>output impedance: it's just that once you get a "damping
>factor" greater than a couple of dozen or so, the effect becomes
>essentially negligable.
Agreed, it's a matter of degree, but with a damping
factor of above ~20, further damping becomes rather
insignificant.
Excellent explanation and data. Thanks.
>> but I believe you may be in error. Perhaps Mr. Pierce
>> would care to comment.
>
>Can I? :-)
I had faith you could. :-)
Bill Watkins
Richard D Pierce
>The URIE 813's were designed for high output levels, and relatively high
>sensitivity - ie. playing loudly.
>
>They do NOT have particularly good low frequency extension - I've measured
>them sitting mouted *flush* in a wall (best case for bass, usually) and they
>drop like a stone at 50Hz. You need EQ to get them flat to 40 Hz...
Yup. that corroborates my data well, save that you didn't
mention the fairly large hump above 50 Hz.
These sorts of things produced prodigious amounts of BOOM and
blessed little bass.
>As I alluded to before, if you want anything close to a flat response, you'll
>have to do some reasonably sophisticated tests and probably EQ
>them.
I'm not sure that EQ'ing them won't make them worse, becasue of
their weird response.
>They do play very loudly though.
Yes, regrettably. It's things like the UREI's that led to the
now unfortunate practice of monitoring at ear-splitting levels.
It's too bad that when people have bad sound at normal levels,
they somehow think that more bad sound is better.
Randy Yates
> [...]
> >> >>> What happens
> >>> with a "low damping factor" is that the amplifier voltage
> >>> rises in the low end and dumps more power into the speaker.
> >>
> >>More than what?
>
> More than it does at regions where the electrical impedance of
> the speaker is lower Second order systems have a local maximum
> in the impedance at resonance. That freqequncy dependency means
> that more voltage is developed across the speaker at resonance
> than elsewhere, assuming a source impedance that's reasonably
> constant with frequency.
Good clarification. I am in total agreement.
> >>If you model the amplifier as a perfect voltage source in series
> >>with a non-ideal source impedance > 0 ohms (at the low frequencies),
> >>then the voltage delivered to the speaker at low frequencies should
> >>be less than that delivered by an amplifier with a higher damping
> >>factor. Viewed another way, assuming the speaker impedance is constant over
> >>frequency, the voltage across the speaker from a low-damping factor
> >>amp should drop as the frequency gets lower.
>
> Huh? With relatively few rare exceptions, the low frequency
> output impedance characteristic of most amplifiers is
> predominatly resistive and thus does not and can not behave as
> you suggest.
Sorry, my mistake here. What I was thinking (erroneously, for a
reason I cannot determine at this point) is that someone had said
the damping factor itself was a function of frequency and was
dropping at lower frequencies. Further, I made the mistake (apparently,
for I cannot begin to know speakers as well as you, Dick) of
mischaractarizing a speaker's impedance as constant over frequency.
For this things, mea culpa.
> Thus, you end up with a voltage function across the
> speaker terminals that is a somewhat complex but direct function
> of impedance.
>
> Assume the impedance function of the loudspeaker is Z(f) and, at
> the relevant range of frequencies, the amplifier output is Rg:
> the response deviation due to source attenuation is reasonably
> approximated by:
>
> Z(f) + Rg
> Gz(f) = 20 log -----------
> Z(f)
>
Actually, it's the reciprocal of that, but that is what you've
calculated in the table below.
> For example: assume Z(f) has a minimum of 8 ohms in the audio
> band, and a local maximum at resonance of 40 ohms (hardly
> atypical). And compare the deviation in the response cnsidering
> four amplifiers with damping factors of 5, 50, 500 and 5000,
> (corresponding to source resistances of 1.6, 0.16, 0.016, and
> 0.0016 ohms). The effective boost in response at resonance will
> be:
>
> D.F. Gz(f) Gz(f) Relative
> @8 ohms @40 ohms Boost (dB)
>
> 5 -1.58 dB -0.34 dB 1.24 dB
> 50 -0.17 -0.034 0.14 dB
> 500 -0.017 -0.0034 0.014 dB
> 5000 -0.0017 -0.00034 0.0014 dB
>
> Whether the resulting 1.24 dB peak at resonance contributes
> audibly is another matter: the fact is, the answer to the
> question, "more than what" is "more electrical power at resonace
> or other regions of high electrical impedance than would obtain
> where the impedance is lower, and the effect is more significant
> with higher source impedances than with low.)
Agreed.
My less-relevent point, however, was simply that the ABSOLUTE
LEVEL at a specific frequency actually DECREASES as damping factor
decreases, which can be seen from your table above. However, I
acknowledge now that what is much more relevent is the response,
i.e., the levels at various frequencies for a given damping factor.
--
Randy Yates
DSP Engineer
Ericsson Inc.
Research Triangle Park, NC, USA
randy...@ericsson.com, 919-472-1124
.
Richard D Pierce
Randy Yates <eus...@rtp.ericsson.com> wrote:
>> Huh? With relatively few rare exceptions, the low frequency
>> output impedance characteristic of most amplifiers is
>> predominatly resistive and thus does not and can not behave as
>> you suggest.
>
>Sorry, my mistake here. What I was thinking (erroneously, for a
>reason I cannot determine at this point) is that someone had said
>the damping factor itself was a function of frequency and was
>dropping at lower frequencies.
In fact, the ouytput impedance of most amplifiers IS frequency
dependent, but for the vast majority of solid-state units, at
the frequencies of interest (i.e., low frequencies where the
motional impedance of speakers is at its greatest), the
impedance is resistive and largely constant with frequency.
> Further, I made the mistake (apparently,
>for I cannot begin to know speakers as well as you, Dick)
Oh, indeed you can!