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Path: utzoo!linus!decvax!genrad!panda!teddy!rdp
From: rdp@teddy.UUCP
Newsgroups: net.audio
Subject: Re: RAW SPEAKERS
Message-ID: <1098@teddy.UUCP>
Date: Mon, 5-Aug-85 17:53:32 EDT
Article-I.D.: teddy.1098
Posted: Mon Aug  5 17:53:32 1985
Date-Received: Wed, 7-Aug-85 02:27:02 EDT
References: <3177@decwrl.UUCP> <28400013@smu> <1036@teddy.UUCP> <9570@ucbvax.ARPA>
Reply-To: rdp@teddy.UUCP (Richard D. Pierce)
Organization: GenRad, Inc., Concord, Mass.
Lines: 131
Summary: 

[]

In reply to my discussion about small woofers (see referenced article:

In article <9570@ucbvax.ARPA> klein@ucbvax.UUCP (Mike Klein) writes:
>It is generally recognized that smaller woofers have more distortion
>than larger ones, all other things being equal.  And this is indeed why:
>
"Generally recognized" does not constitute "proven in fact", as we shall see..

>
>Fundamental resonance is determined mainly by the cone and voice coil mass
>and the suspension compliance.  Note that small woofers usually have very soft
>suspensions and larger ones usually have stiffer suspensions.  On the whole,
>smaller woofers have a higher fundamental resonance, but the difference may
>not be nearly as much as you'd expect.
>
Yes, fundamental resonance is a function of total mechanical stiffness
and the inverse of total moving mass, but, I'm afraid, the assumption that
small woofers usually have soft suspensions is not so. If you have specific
product data to back your claim, fine. I do, on the order of about 800 samples
of drivers.

One way of measuring true effective compliance is to specify what is refered
to as the "equivalent volume of compliance". This is the restorative force
presented by an enclosed vloume of air that is the same as the mechanical
stiffness of the woofer.

Let's take two relatively well known drivers from KEF in England. The 5
inch B110 (the same driver used in the BBC LS3-5A) has an equivalent
compliance volume of about 7.5 liters, whereas the B200, an 8 inch driver
having the same spider assembly, the same magnet and voice coil, and the same
suspension cross section, as a figure more like 25 liters. There are, in my
archives, nearly 150 other examples that I refuse to bore the network with.

Most driver manufacturers do not make their suspensions, but buy them from
a variety of sources such as Mueller, Seas, and so forth. Their own product
data do not support the above claims. Note also, that within a given
manufacturers line, the same spider assembly is used, and that is often the
overriding source of stiffness.

Let's also look at this from another viewpoint. If you look at a range of
suspensions from someone like Mueller, you find that the cross-sections are
the same, regardless of diameter. This would imply that the stiffness per
linear run of suspension is uniform. This further implies that the stiffness
of a suspension is proportional to its diameter. However, the mosing mass
is proportional to the square of the diameter. This would then mean that for
a given range of drivers (say from KEF or Dalesford or what have you) that
the fundamental resonance is a function of the square root of the diameter,
because of the compliance, and the inverse of the diameter, because of the
mass. Low and behold, it turns out the the mass becomes the more important
term. Interestingly enough, the manufacturers product data supports this
fully. I have this data for about 45 manufacturers, and have confirmed it for
most, have you?

>
>Small woofers are massively overdamped because they are designed to go
>in a small box which raises the system's overall Q more than a larger box would.
Wrong, small woofers, in the vast majority of cases, are overdamped because
it is more economical for a driver assembler to stock fewer diverse magnet
assemblies. This I know because I once was intimately involved with several
of them.

To go one step further, most small high-quality drivers are to far overdampled
for any practical sized enclosures.

Case in point. The Dalesford d110 has an equivalent compliance volume of
about 8.3 liters, and a system Q of about .22 with a 40 cycle resonance.
Now, the final system aparameters can be determined by square root of the
ratio of the driver compliance to box compliance. Let's seek a target system
Q of .7, which is the best compromise of maximally flat, minimal phase error,
etc, etc (i.e. Butterworth characteristics) In order to achieve this, we
need a driver Q to system Q ratio of .7/.22 or roughly 3. Refering to the
experts (Small, JAS about 78 or so), we find that that requires a ratio
between driver compliance and box compliance on the order of 8 or 9, meaning
that the box must be about 1 liter in size. This is smaller than the driver
itself. On the other hand, one variant of the KEF b110 has a system Q of .5,
which when combined with a box of about 7 or 8 liters, results in a system
whose Q is around .7, cutoff is about 70 Hz, etc. In practice, I have found
through manufaterers data sheets and my own extensive testing, that small, 
high quality woofers are far to overdamped to be usable as bass drivers.
Ain't nuthin like REAL data, is there? :-)

>This is not a design defect!  It is also not the real reason why efficiency
>suffers.  Efficiency, system cutoff frequency,  and box volume are the three
>fundamental factors that must be traded off, and it's not very fair to
>the frequency:
>
>	best efficiency = (constant) * (box volume) * (cutoff frequency ^ 3)
>
>A woofer in a small box trying to have a low cutoff frequency is
>*fundamentally* constrained to have a low efficiency.  It actually
>does not depend on the woofer size.  (this equation holds for free-field
>radiation.)
>
Why is it independent of diameter? Because your asking this little tiny
woofer to do far more excursing to produce a given sound level, thus
driving it farther into it's non-linear operating regions!
>
>>re: use of non-paper materials in loudspeakers to prevent breakup, etc.
>
>This is really true!  Recent research has shown that newfangled materials
>can actually behave very well through the breakup region.  Paper is not
>one of them.  Bextrene and polypropylene are very good.
>
Recent? KEF was using Bextrene (polystyrene with a rubber over-coat) in the
60's. My experimentation with polypropylene was done in 1972. Ho-hum,
more breakthroughs....
>
>Also -- The "tightness" of the bass has nothing to do with size of the
>woofer, but with the overall damping of the woofer system.  However,
>some people may assign the word "tightness" to a frequency response that
>emphasizes the 60-100 Hz range, because that's the frequency range that
>hits your gut hardest.  The typical smaller woofer in a smaller box
>may very well have this kind of frequency response, and may appear
>to have a "tight" bass.

Gee, I hope your not accusing ME of saying that!!! :-)

The upshot of all of this is that is seems that a lot of so-called
information seems to be rumor, guessing and so forth. I am not necessarily
accusing the above respondant of such, but my original remarks are base
od quite a bit of real research. I have probably 10 feet of experimental
data to extract my conclusions from. I do not expect results, I measure
them. Only after there is a considerable body of experimental data to
prove or disprove something do I (and should anyone) make a conclusion.

In the above case, some of the respondants conclusions might well be
intuitively correct, but real product data proves otherwise. Sorry.

Dick Pierce