Speaker transient analysis

Archived from groups: rec.audio.tech (More info?)

Georg Grosz wrote:

> I have found some nice software (e.g. Perfect Box) for frequency
> domain analysis of speaker designs. Does anybody know of a program
> that does time domain analysis? For that matter, if anybody has
> created an electromechanical model in SPICE, that might be the most
> useful thing.
>
> Here is my reason for asking. I am a string bassist and also a
> physicist. Among bassists, there is a fair amount of folklore about
> speakers, probably containing equal admixtures of reality and myth.
> One commonly held belief is that smaller drivers, such as 10 or 12
> inch, are "faster" than 15's and 18's. People have even thrown the
> term "transient response" around. I would like to investigate whether
> this is for real, and/or predictable from a model.
> < ...snip.. >

Hi
Sounds like a fun question to re-post over in alt.sci.physics.acoustics.
Anyway, I've been playing with system analysis using sequences of
bandwidth limited impulses. There are a lot of interesting artifacts
to be seen using these impulse probes. Response near resonance
or crossover points can be quite interesting. I've been rolling my own
software for the project. However, this has just been a side project
so the going has been slow.

Later...

Ron Capik
--

Archived from groups: rec.audio.tech (More info?)

elephantcelebes@yahoo.com (Georg Grosz) wrote in message news:<1f0556b7.0407142006.676afffb@posting.google.com>...
> I have found some nice software (e.g. Perfect Box) for frequency
> domain analysis of speaker designs. Does anybody know of a program
> that does time domain analysis? For that matter, if anybody has
> created an electromechanical model in SPICE, that might be the most
> useful thing.
>
> Here is my reason for asking. I am a string bassist and also a
> physicist. Among bassists, there is a fair amount of folklore about
> speakers, probably containing equal admixtures of reality and myth.
> One commonly held belief is that smaller drivers, such as 10 or 12
> inch, are "faster" than 15's and 18's. People have even thrown the
> term "transient response" around. I would like to investigate whether
> this is for real, and/or predictable from a model.
>
> I know the equations of motion for a speaker driven by a voltage
> input, but it would be re-inventing the wheel to try writing (and
> debugging) my own software if someone has already done it.
>
> Another question: Does anybody know the equation for acoustical power
> output of an ideal piston driver versus amplitude of motion? That is
> the one part of the speaker design equations (relating to efficiency)
> which I cannot figure out on my own. The one thing I have guessed is
> that acoustical output is proportional to velocity rather than
> displacement. Is this true?

For low frequencies and free space the absolute sound pressure is as
for the point source.

p=U*rho0*w/(4*pi*r)

where U is the volume flow in m3/s (=surface*velocity), rho0=1.2kg/m3,
w is the angular frequency, and r is the distance.
After some thinking about this equation, one can realise that sound
pressure is roportional to the piston *acceleration* (comes from w*U,
ie derivative of the flow).
For higher frequencies, when the wavelength becomes about the size of
the piston, the relation is more complex, involving bessel functions.

And, IMO the term "faster" has nothing to do with the actual speed of
anything, it is just another word for some aspect of the spectral
content of the signal.

Archived from groups: rec.audio.tech (More info?)

It depends upon the bandwidth you are asking the driver to reproduce. As a
general rule, smaller drivers will have a more extended response on the
highs side, and wider dispersion. If you are talking about what to use
below a couple hundred Hertz in a multi-way loudspeaker, there is no general
rule. The rise time of the signals at signals this low in frequency are
very long (in other words, the signals are "slow" ). Driver speed is just
not an issue. If woofer 'A' "sounds faster" or "has more punch" than woofer
'B', it is almost certainly because of one of the following:

'A' is producing more distortion than is 'B'. The distortion products are
more audible than the fundamental frequency. (Most PA or musical imstrument
low fewquency drivers are junk - 40Hz in at a decent level gives as much
80Hz and 160Hz out as 40Hz out. Many Hi-Fi drivers aren't a lot better.)

'A' has better phase/time alignment to the rest of the system than does 'B'.
(Owing to the various box designs, most low frequency systems - especially
folded horns - will require that the higher frequency drivers be time
delayed in order for them to align properly).

'B' has a badly tuned port (or a badly designed horn) and is resonating
excessively (it is 'ringing' or has a lot of 'overhang').


"Ron Capik" <r.capik@worldnet.att.net> wrote in message
news:40F80BAB.26A6915D@worldnet.att.net...
> Georg Grosz wrote:
>
> > < ..snip... >
> >
> > Here is my reason for asking. I am a string bassist and also a
> > physicist. Among bassists, there is a fair amount of folklore about
> > speakers, probably containing equal admixtures of reality and myth.
> > One commonly held belief is that smaller drivers, such as 10 or 12
> > inch, are "faster" than 15's and 18's. People have even thrown the
> > term "transient response" around. I would like to investigate whether
> > this is for real, and/or predictable from a model.
> > < ..snip... >
>
> Hmmm, this brings to mind another question: are the string bassists
> looking for "a sound" or are they looking to be heard on stage or what?
> ...and these 10, 12, 15, 18 inch speakers, are they for the bass amp,
> the monitor wedges, the PA, or what? [ I'm guessing you're not talking
> about home stereo speakers. ]
>
>
> Later...
>
> Ron Capik
> NJ Pinelands Cultural Society
> < www.AlbertHall.org >
> --
>
>

Archived from groups: rec.audio.tech (More info?)

"Georg Grosz" <elephantcelebes@yahoo.com> wrote in message
news:1f0556b7.0407142006.676afffb@posting.google.com...
> I have found some nice software (e.g. Perfect Box) for frequency
> domain analysis of speaker designs. Does anybody know of a program
> that does time domain analysis? For that matter, if anybody has
> created an electromechanical model in SPICE, that might be the most
> useful thing.
>
> Here is my reason for asking. I am a string bassist and also a
> physicist. Among bassists, there is a fair amount of folklore about
> speakers, probably containing equal admixtures of reality and myth.
> One commonly held belief is that smaller drivers, such as 10 or 12
> inch, are "faster" than 15's and 18's. People have even thrown the
> term "transient response" around. I would like to investigate whether
> this is for real, and/or predictable from a model.

Speed and transient response are often used inappropiately. A loudspeaker
cone will always move (accelerate) as fast as stimulated to acheive the
desired frequency. So the "speed" will always be controlled by the frequency
of the input stimulus. This is of course until the motor of the system
cannot provide enough force to accelerate the mass of total load (including
radiation impedance) and then the frequency response decays with increasing
frequency. The ideal transient response is derived directly from the
transfer function of the mechanical circuit, it is not an entity of it's
own. Thus theoretically a "heavy" 18" woofer with a stiff suspension which
has an identical resonance frequency and Qts as a "light" 8" woofer with a
compliant suspension, when tuned to an identical Qtc will have identical
ideal transient response curves. Any 2 closed systems, regardless of type of
woofer, will have identical transient behavior when tuned to the same Qtc
regardless of resonance frequency, only with a different frequency response.
Small "floppy" woofers are used these days because they are small, not
faster. A stronger motor (increased force factor) limits bass response so
there is no theoretical advantage to putting a strong motor on a small and
light woofer. A Qts of 0.10 will get you no bass at all even with a low
resonance frequency. Smaller woofers do tend to move more like a rigid
piston which is sometimes audible. This seems to be where the "speed
advantage" myth comes from. This is of course often but not always true.

An "old fashioned" big and stiff woofer used in a big bass reflex cabinet
with a small (low mass) port gives a very controlled response. And sound
very "fast". They just don't look good by modern standards.

> I know the equations of motion for a speaker driven by a voltage
> input, but it would be re-inventing the wheel to try writing (and
> debugging) my own software if someone has already done it.
>
> Another question: Does anybody know the equation for acoustical power
> output of an ideal piston driver versus amplitude of motion?

The shape is dependant on the type of system loading. But the relative
pistonic displacement to frequency curve is always inversely proportional to
the relative cone acceleration to frequency curve. Relative cone
acceleration is also the same curve as the relative sound pressure in the
acoustic domain assuming ideal conditions. In essence, if the sound pressure
(piston acceleration) curve looks like a high pass filter, the relative
displacement curve always takes the form of the symmetric corresponding low
pass filter. With a loudspeaker on its own, or in a closed box, it remains
2nd order and looks like a simple 2nd order filter response. The cone
response of the speaker itself in a 4th order system (bass reflex) has a
"dip" in it where the other reactive mechanical parts are in resonance and
take over. Ex. port mass and cabinet volume in a bass reflex system.

This is all relative of course. The absolute acoustic power is dependant in
how much you turn up the volume.

> the one part of the speaker design equations (relating to efficiency)
> which I cannot figure out on my own. The one thing I have guessed is
> that acoustical output is proportional to velocity rather than
> displacement. Is this true?

A loudspeaker can be considered to be a resonant 2nd order mechanical system
with mass, compliance, and resistance subject to a common velocity. So yes,
the acoustical output is directly proportional to the velocity (not the
force applied) with the square of Sd (pistonic surface area) as the link
between the mechanical and acoustic domains.

Archived from groups: rec.audio.tech (More info?)

"Georg Grosz" <elephantcelebes@yahoo.com> wrote in message
news:1f0556b7.0407142006.676afffb@posting.google.com...
> I have found some nice software (e.g. Perfect Box) for frequency
> domain analysis of speaker designs. Does anybody know of a program
> that does time domain analysis? For that matter, if anybody has
> created an electromechanical model in SPICE, that might be the most
> useful thing.
>
> Here is my reason for asking. I am a string bassist and also a
> physicist. Among bassists, there is a fair amount of folklore about
> speakers, probably containing equal admixtures of reality and myth.
> One commonly held belief is that smaller drivers, such as 10 or 12
> inch, are "faster" than 15's and 18's. People have even thrown the
> term "transient response" around. I would like to investigate whether
> this is for real, and/or predictable from a model.
>
> I know the equations of motion for a speaker driven by a voltage
> input, but it would be re-inventing the wheel to try writing (and
> debugging) my own software if someone has already done it.
>
> Another question: Does anybody know the equation for acoustical power
> output of an ideal piston driver versus amplitude of motion? That is
> the one part of the speaker design equations (relating to efficiency)
> which I cannot figure out on my own. The one thing I have guessed is
> that acoustical output is proportional to velocity rather than
> displacement. Is this true?

After re-reading my own reply, I forgot to supply the formulae you asked
for. I'll supply them below. As a physicist you should be able to get a lot
out of the following references:

Theory and Design of Loudspeaker Enclosures" J.E. Bensen. Synergetic Audio
Concepts
IMO the best loudspeaker basic theory book on the planet. Bensen was Small's
PhD thesis promotor and the true brain behind Thiel and Small's work.

Vol 1 and 2 of the AES loudspeaker anthologies from AES press


Svante already supplied the basic relative efficiency equation

1. Closed box cone relative acceleration (same as rel SPL): s^2/(s^2
+s*2*pi*Fc/Qtc+1)
As you can see this is a standard 2nd order high pass filter transfer
function

2. Closed box cone relative displacement: 1/(s^2 +s*2*pi*Fc/Qtc+1)
This is a standard 2nd order low pass filter transfer function and symmetric
from above around Fc

Transient response can be expressed in the impulse response or step function
both of which are derived from the acceleration transfer function. D(s)=
polynomial denominator of either equation above

Impulse response: Inverse Laplace (s^2/D(s))
Step Response: Inverse Laplace (s/D(s))

The transient reponse formulae hold for all types of speaker alignments,
obviously the denominator differs

Just for fun there is a very cool general universal equation for calculating
the input impedance for any loudspeaker alignment as well (not including
Lvc):
D(Qt)=denominator using Qt (regular denominator)
D(Qm)= denominator using Qm instead of Qt

Z(s)=Rdc*(D(Qt)/D(Qm))

Archived from groups: rec.audio.tech (More info?)

"Ron Capik" <r.capik@worldnet.att.net> wrote in message
news:40FEFB2B.A70A31F1@worldnet.att.net...
> Wessel Dirksen wrote:
>
> >
> > < ...snip... >
> > After re-reading my own reply, I forgot to supply the formulae you asked
> > for. I'll supply them below. As a physicist you should be able to get a
lot
> > out of the following references:
> >
> > Theory and Design of Loudspeaker Enclosures" J.E. Bensen. Synergetic
Audio
> > Concepts
> > IMO the best loudspeaker basic theory book on the planet. Bensen was
Small's
> > PhD thesis promotor and the true brain behind Thiel and Small's work.
> >
> > Vol 1 and 2 of the AES loudspeaker anthologies from AES press
> >
> > Svante already supplied the basic relative efficiency equation
> > < ..snip.. >
>
> Somehow I don't know if speaker theory will help find a solution to
> George's quandary. I get the feeling some of the distortion that takes
> place in real world, on stage situations gives a false impression of
> clarity. IMHO, I believe experimental measurements of transient response
> need to be taken on various systems and those results need to be
> correlated with folklore and bassist perceptions. I have a feeling the
> cleanest, flattest response system won't win. I also believe what works
> best on stage may not be best for the FOH system.

I agree that George's quandary is larger than the above if you assume a real
world situation including non-ideal artifacts. You could think about what
happens when cone movement is non-linear due to suspension hysteresis, cone
break-up which is non-pistonic, and maybe even artifacts from the
inefficient overhung voicecoils on the smaller long excursion woofers. But,
this is mainly about transient response which is, except for artifacts,
defined within the frequency response equation itself.

I think this whole issue comes about when smart people intuitively assume
that a large heavy cone will have more "uncontrolled" irnertial problems.
It's easy to think that if the mass is small and the motor powerful that
things will be "faster" and more precise. It doesn't work like that. Inertia
is internalized in the transfer function because a cone must move back and
forth to produce the frequency required by the signal. Regardless of cone
diameter, by definition two woofers will have identical mass to force factor
ratios if their Fs and Qts are the same. So the inertia "behavior" is the
same for both them, and the transient response will be the same for them.
You could say a "faster" woofer has a more extended high frequency response,
but it doesn't move any faster or more transiently at lower frequencies
compared to a "slower" counterpart.

Archived from groups: rec.audio.tech (More info?)

"Wessel Dirksen" <wdirksen@p-we.com> wrote in message news:<40ff5c2e$0$32184$ba620e4c@news.skynet.be>...

> I think this whole issue comes about when smart people intuitively assume
> that a large heavy cone will have more "uncontrolled" irnertial problems.

I am beginning to think that this is the essence of the problem -- a
misconception that a bigger mass cannot be accelerated as quickly.
Also, the bigger speakers may actually have too much low end, giving
rise to an undesirable tone quality that is interpreted as "slow"
response. A lot of successful commercial bass speakers have cutoff
frequencies in the ballpark of 100 Hz, which is counterintuitive given
that the lowest note on the bass is 40 Hz.

Now I have another quandary. Speaker efficiency is rated in dB SPL at
a given power and distance. But this does not tell you which speaker
will be louder when plugged into a given amplifier because two
speakers could have different impedance, hence different power for a
given voltage input.

How is this efficiency really rated? Does 1 Watt really mean 1 Watt,
or (for an 8 Ohm speaker), does it really mean 2.8 V RMS?

Archived from groups: rec.audio.tech (More info?)

"normanstrong" <normanstrong@comcast.net> wrote in message news:<CAwMc.23113$8_6.2972@attbi_s04>...
> "Georg Grosz" <elephantcelebes@yahoo.com> wrote in message
> news:1f0556b7.0407231900.37649730@posting.google.com..
>
> > Now I have another quandary. Speaker efficiency is rated in dB SPL
> at
> > a given power and distance. But this does not tell you which speaker
> > will be louder when plugged into a given amplifier because two
> > speakers could have different impedance, hence different power for a
> > given voltage input.
> >
> > How is this efficiency really rated? Does 1 Watt really mean 1 Watt,
> > or (for an 8 Ohm speaker), does it really mean 2.8 V RMS?
>
> Speaker "efficiency" is almost always a misnomer. (To begin with,
> efficiency is a dimensionless quantity less than 1.) What they really
> mean in sensitivity, and it's virtually always expressed as SPL output
> with 1 watt input. Unfortunately, it's very difficult to measure the
> actual wattage at the input, since the impedance of a speaker varies
> all over the map as a function of frequency. But, if you feed the
> speaker a constant voltage, the SPL will not vary too much with
> frequency. Because such a test is much easier to perform, all speaker
> manufacturers rate their speakers' sensitivity as so-and-so db SPL
> with 2.83 volts rms at the input. It should be noted that this gives
> a 3db advantage to speakers with 4 ohm impedance instead of 8 ohms, in
> the same 2.83 volts is twice the power into 4 ohms.
>
> Norm Strong

Thanks. That's as I expected. And I did mean "sensitivity."

Archived from groups: rec.audio.tech (More info?)

Ron Capik <r.capik@worldnet.att.net> wrote in message news:<40FEFB2B.A70A31F1@worldnet.att.net>...
> Wessel Dirksen wrote:
>
> >
> > < ...snip... >
> > After re-reading my own reply, I forgot to supply the formulae you asked
> > for. I'll supply them below. As a physicist you should be able to get a lot
> > out of the following references:
> >
> > Theory and Design of Loudspeaker Enclosures" J.E. Bensen. Synergetic Audio
> > Concepts
> > IMO the best loudspeaker basic theory book on the planet. Bensen was Small's
> > PhD thesis promotor and the true brain behind Thiel and Small's work.
> >
> > Vol 1 and 2 of the AES loudspeaker anthologies from AES press
> >
> > Svante already supplied the basic relative efficiency equation
> > < ..snip.. >
>
> Somehow I don't know if speaker theory will help find a solution to
> George's quandary. I get the feeling some of the distortion that takes
> place in real world, on stage situations gives a false impression of
> clarity. IMHO, I believe experimental measurements of transient response
> need to be taken on various systems and those results need to be
> correlated with folklore and bassist perceptions. I have a feeling the
> cleanest, flattest response system won't win. I also believe what works
> best on stage may not be best for the FOH system.
> YMMV
>

Hi Ron, I need to proof read my replies more because I failed to
emphasize that I agree with what you are generally stating here. Basic
ideal formulas don't cut it as the bottom line in audio reproduction
and there is alot going on that is not in our control. Distortion and
other factors play also play a role to where, as you correctly state,
there is way more to this than a basic analysis of the frequency
response, time domain, and IM and THD distortion alone. If one
considers that no speaker cone is completely rigid, and many
mid-woofers are specifically designed to ripple to "enhance" high
frequency response, there is certainly artifact mini transient
behavior going on with every cone ripple and thus has it's own
transfer function albeit at a small fraction of total output. This is
only the beginning, there are almost uncountable areas that can
produce a small inaudible artifact, but with all artifact behavior
added up, it gets downright mysterious and no longer negligable
despite not being dominantly. Awhile back, I posted an opinion in a
thread that even the most sophisticated 24/192 kHz measurement system
does not represent what a loudspeaker truly does when it reproduces a
cello. I didn't get the idea that that idea was widely accepted.

Archived from groups: rec.audio.tech (More info?)

"Arny Krueger" <arnyk@hotpop.com> wrote in message news:<AfidnR7ktqhrCp7cRVn-qA@comcast.com>...
> "Wessel Dirksen" <wdirksen@p-we.com> wrote in message
> news:87db8cb7.0407250247.6f2ba93a@posting.google.com
>
>
> >
> > Hi Ron, I need to proof read my replies more because I failed to
> > emphasize that I agree with what you are generally stating here. Basic
> > ideal formulas don't cut it as the bottom line in audio reproduction
> > and there is alot going on that is not in our control. Distortion and
> > other factors play also play a role to where, as you correctly state,
> > there is way more to this than a basic analysis of the frequency
> > response, time domain, and IM and THD distortion alone. If one
> > considers that no speaker cone is completely rigid, and many
> > mid-woofers are specifically designed to ripple to "enhance" high
> > frequency response, there is certainly artifact mini transient
> > behavior going on with every cone ripple and thus has it's own
> > transfer function albeit at a small fraction of total output.
>
> Hence my earlier post:
>
> "One problem is that a fairly complex model is required to predict the high
> frequency performance of a speaker."

Right.

>
> >This is
> > only the beginning, there are almost uncountable areas that can
> > produce a small inaudible artifact, but with all artifact behavior
> > added up, it gets downright mysterious and no longer negligable
> > despite not being dominantly.
>
> That is a matter of quantification.

Absolutely in theory, except I'm wondering if it is practically
quantifiable.

>
> > Awhile back, I posted an opinion in a
> > thread that even the most sophisticated 24/192 kHz measurement system
> > does not represent what a loudspeaker truly does when it reproduces a
> > cello.
>
> True for many reasons. One is that the most sophisticated high-res
> measurement systems don't as a rule provide an accurate representation of
> the speakers response in all 4 pi steradians. The data involved is nearly
> impossible to take, difficult to store and analyze, even by modern
> standards and with modern tools.
>
> >I didn't get the idea that that idea was widely accepted.
>
> The counterpoint is that 24/192 is way overkill - all we have to capture is
> the audible performance.

Right, we're not even getting everything out of 16/44.1. I would say
24/196 is theoretically enough precision to capture all audible
Fourier components out of a complex signal, so measurement precision
is not the roadblock. But then what to do if you could get more out of
a test suite. For a speaker designer, it would currently be a mute
issue as you are really only connecting the dots with an existing
system with LCR filter techniques. I think advancements in the
theoretical simulation of driver behavior and measurement techniques
to capture them could be of practical benefit in technology
development, driver design, and potentially manufacturing processes.