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Roscoe East
 
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Default convert Thiel-Small parameters to optimum enclosure volume, & vice-versa?

Is there a straightahead method for determining the optimum volume for
a loudspeaker enclosure based on a particular driver's Thiel-Small
parameters?

And conversely, is there a way to determine the optimum Thiel-Small
parameters (or, really, to select an appropriate driver) based on an
existing enclosure's volume & port size?

And is there a way to determine how a given driver will perform in a
given enclosure if you have all that information?

Thanks.

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Though this same set of questions was posted in rec.audio.tech
several days ago, I'm responding to the questions here as well.

Roscoe East wrote:
Is there a straightahead method for determining the optimum
volume for a loudspeaker enclosure based on a particular
driver's Thiel-Small parameters?


Yes, if you are willing to define what you mean by "optimum."
The problem being is that optimum is a multi-dimensional system.
For example, does optimum mean maximum bandwidth, flattest
response, greatest low frequency excursion limited output,
best transient response, smallest size and so forth? Or some
combination thereof? Which performance parameter(s) are you
willing to compromise to optimize some other parameter(s)?

You may answer "I want maximally flat (Butterworth) response"
as "optimum," and then learn that the driver you have simply
can't get you there in ANY enclosure. Another driver might get
you there, but at significant cost, for example, a driver with
a Qts of 0.2 COULD be used in a maximally flat, sealed box
system, to be sure, but you'd end up with a very efficient
system with a very high cutoff frequency, most likely. After
you spent all that money on this driver with it's big magnet,
you might be justified in concluding that a sealed box system
is not an "optimal" design.

And conversely, is there a way to determine the optimum
Thiel-Small parameters (or, really, to select an appropriate
driver) based on an existing enclosure's volume & port size?


Again, if you can answer the question I posed above, the answer
is yes.

And is there a way to determine how a given driver will
perform in a given enclosure if you have all that information?


Yes, to a very great extent, especially in the so-called "piston
band" region of operation.

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Roscoe East
 
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wrote:
Though this same set of questions was posted in rec.audio.tech
several days ago, I'm responding to the questions here as well.

Roscoe East wrote:
Is there a straightahead method for determining the optimum
volume for a loudspeaker enclosure based on a particular
driver's Thiel-Small parameters?


Yes, if you are willing to define what you mean by "optimum."
The problem being is that optimum is a multi-dimensional system.
For example, does optimum mean maximum bandwidth, flattest
response, greatest low frequency excursion limited output,
best transient response, smallest size and so forth? Or some
combination thereof? Which performance parameter(s) are you
willing to compromise to optimize some other parameter(s)?


I would have defined "optimum" as "the best balance between all those
parameters" but I do see your point, that trade-offs among those
parameters are preferential and so leave a lot of leeway. Is there a
direct formula or simple rule of thumb for translating T-S parameters
to "optimum" dimensions for each of the qualities you describe?



And conversely, is there a way to determine the optimum
Thiel-Small parameters (or, really, to select an appropriate
driver) based on an existing enclosure's volume & port size?


Again, if you can answer the question I posed above, the answer
is yes.


Okay, see my answer (above). Now how do I go about determining what
those sonic variables will be based on the information I have at hand
(in this case, existing enclosure's volume & port size)?

And is there a way to determine how a given driver will
perform in a given enclosure if you have all that information?


Yes, to a very great extent, especially in the so-called "piston
band" region of operation.


I didn't realize I had posed a Yes or No question! Allow me to
rephrase: How does one go about determining how a given driver will
perform in a given enclosure, assuming one knows the different driver's
T-S parameters & the candidate enclosure's dimensions? Thanks.

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Wessel Dirksen
 
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Roscoe,

Get yourself a copy of Vance Dickenson's Loudspeaker Cookbook.

It's a very good book that explains alot in practical terms in a way
almost anyone can understand. You will have to invest some time and
devotion in to its content, but after some days with this book you
could probably explain to us here the very answers to your questions.

Enjoy the search,

Wessel

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Roscoe East wrote:
Is there a straightahead method for determining the optimum
volume for a loudspeaker enclosure based on a particular
driver's Thiel-Small parameters?


Yes, if you are willing to define what you mean by "optimum."


I would have defined "optimum" as "the best balance between all those
parameters" but I do see your point, that trade-offs among those
parameters are preferential and so leave a lot of leeway.


Fine, define what the "best balance" is between low-frequency
cutoff, power handling and response smoothness. What might be
"best" for you might not be for someone else. For example, if
you were a client of mine looking to design a system, I would
try to convince you that trading increased power handling for
bass extension is "best" because it will reduce after-sales
support costs.

Is there a direct formula or simple rule of thumb for
translating T-S parameters to "optimum" dimensions for
each of the qualities you describe?


No, there is not. There are approximate equations, but the
especially in the case of vented systems, there are no closed-
form equations that get you there. One finds procedures such
as "find the largest positive real roots of this 4th order
equation and then ..."

And is there a way to determine how a given driver will
perform in a given enclosure if you have all that information?


Yes, to a very great extent, especially in the so-called "piston
band" region of operation.


I didn't realize I had posed a Yes or No question!


Well, here's your question:

"is there a way to determine how a given driver will
perform in a given enclosure if you have all that
information?"

Sure looks like something requiring a yes or no question to me! :-)

Allow me to
rephrase: How does one go about determining how a given driver will
perform in a given enclosure, assuming one knows the different driver's
T-S parameters & the candidate enclosure's dimensions? Thanks.


One finds the appropriate formulae, takes the appropriately scaled
parameters and solves the formulae.

That was done in detail in Small's work in the early 70's and has
been amplified upon by any number of people. Several, including
myself, have gone so far as to encode various forms of those
formulae and their derivatives into programs that one can use.
I might suggest that you explore them internet for any number of
inexpensive or (even) free modeling packages for this purpose.
Someone else suggested Dickason's work, which while not the best
in terms of an exposition of the underlying theory, does, like
a cookbook, getr you to the point of eating fairly quickly, even
if youm don't understand WHY you cooked the meal that way.

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convert Thiel-Small parameters to optimum enclosure volume, & vice-versa? Roscoe East Pro Audio 7 September 25th 05 06:25 PM
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