Updated: Tuesday, 21 February 2017

Selected Posts on Audio Topics
by John L. Murphy

Subject:   Equalizers for Vented Box Loudspeakers

(posted 25Apr01  to Bass List)

...back to the original topic for a moment...

Mark wrote:

> a vented alignment has a tuning frequency set by the port length (lets
> just ignore PR's for now). is it possible to artificially move this tuning
> freq. lower with electronics?

My short answer would be the same as the other responses to this post:
No, you can't change the F(B) with equalization.

That said, however, I don't think we should dismiss the idea of using EQ
with vented boxes quite so quickly. After all, of the 28 alignments in
Thiele's original alignment table for vented boxes (circa 1961!) only the
first 9 were for purely acoustic vented boxes. Alignments 10 through 28 (the
majority) called for a vented box combined with equalization to achieve the
overall system response.

Some of Thiele's "assisted" alignments called for an acoustic system that
was peaked combined with a first order highpass filter that flattened and
extended the response. Other assisted alignments called for the use of a
peaked 2nd order highpass filter in combination with a "droopy" acoustic
system. Of the assisted alignments, the 6th order alignments are probably
the best known. Several commercial offerings have been based on the 6th
order assisted alignment.

Ignoring the obvious excursion complications for the moment, it is quite
possible to transform the 4th order highpass response of a vented box into
some other (more desirable) response in much the same way we can transform
the response of a closed box using a Linkwitz Transform (pole shifter circuit).
(for more on Linkwitz Transform circuits see: https://www.trueaudio.com/st_lkxfm.htm )

Any 4th order highpass response function can be mathematically factored into
two separate 2nd order highpass response functions. In fact, higher order
filters are usually synthesized as combinations of 2nd order stages (with a
first order stage added for odd order responses). So our vented boxes can
be modeled as two 2nd order highpass stages in series. In general it is
possible to transform each of these 2nd order stages into new responses
using the same pole shifting circuit we use for closed boxes. This means
that we can transform the response of any vented box into any other response
we wish to achieve. We may not be too pleased with the large signal
limitations (excursion limited power rating) but it is possible nonetheless.
We face these same problems when we transform closed boxes but we find ways
to make it work to our advantage.

One way to offset the potential excursion related complications of a "vented
box transform" would be to severely detune the vented box so that the
excursion minima (which occurs at F(B)) would be low enough to allow a good
extension in low frequency bandwidth while maintaining reasonable power
handling capability. I'd bet there are some useful combinations that would
offer new options to speaker designers. Since much real world loudspeaker
design is based on a "given driver" it would be nice to have more options
for vented boxes than just the 5th and 6th order assisted responses first
proposed 40 years ago. Once we identify the two 2nd order responses that
make up any given 4th order acoustic response we can proceed to design an
equalizer to transform the system response into a new 4th, 5th, 6th or
higher order response. Although a transform from a 4th order response to a
3rd, 2nd or 1st order response is possible, such a transform would run afoul
of the excursion limitations of the driver much more so than a 4th order to
4th order (or higher) transform. In theory, a transform to a lower order
response would require infinite boost from the equalizer as the response
approached 0Hz (DC).



John L. Murphy
Physicist/Audio Engineer
True Audio
Check out my recent book "Introduction to Loudspeaker Design" at Amazon.com

PS: Oh yes, back to the guitar string thread...we usually formulate the
vibrating string problem by specifying the "mass per unit length" of the
string. In this traditional view of the problem the resonance frequency is
said to increase as the string is made shorter by stopping the string with
the finger...with or without a fret. The mass and spring view is also
valid. The offset between strings at the guitar bridge is as much to
compensate for the varying string diameter as anything else. I've noticed
that the "enclosure" on one of my acoustic guitars is tuned to 100 Hz by way
of the enclosure volume and the vent formed by the sound hole and the top
side material thickness. The 100 Hz tuning gives an open G chord (low G on
guitar is about 98Hz) a nice full resonance. The bodies of all similar
instruments are indeed Helmholtz resonators. Don't let the complex shape of
the F holes in the classic instruments fool you...they are still vents. The
tuning is determined by the body volume, total vent area and thickness of
the top piece...just like a speaker.

Now Playing: Steely Dan, cousin dupree           ...how 'bout a kiss for your cousin dupree...

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