Impossible Task? Re-Porting Speakers?

[BlueWizard]

I realize that what I am asking is difficult, but if anyone would like to take a shot at it, or direct me to some references, it would be appreciated.

And, I apologies in advance for being so long-winded.

First, my speakers -

Woofer -
CTS 12W38C 12" 60 watt (137-7828)
fs: assumed 23 hz
I think the '38C' means 38 ounce Ceramic Magnets


Mid-
3"x9" Horn (assumed 40 to 100 watt)
HEP-40-TM
Similar to-
http://www.partsexpress.com/pe/showd...number=280-050

High-
Piezo 3.5"x3.5" (assumed 40 to 60 watt)
connected to high freq output of crossover with added 10 ohm resistor across terminals to stabilize the apparent impedance load to the crossover.
Similar to-
http://www.partsexpress.com/pe/showd...number=270-011

Crossover-
SPECO HN3-100
100 watts
3-way
Similar to -(visually identical to)
http://www.partsexpress.com/pe/showd...number=260-210

Cabinets-
Ext. 17.5"w x 13"d x 26"h
Int. 16"w x 11.5"d x 24.5"h
4508 Cu.In or 2.61 Cu.Ft.

Bass Ports -
(2X) - 3" x 3" Ports 3/4" deep
18 sq.in. port area

Reference book used in the design process-
"How to Build Speaker Enclosures" by Alexis Badmaieff and Don Davis.

I'm hoping to increase the bass response by re-porting the cabinets; that's what I need help with.

See attached photo.

Unfortunately, I built these speakers a long time ago. So long ago that I can't find any specs by searching the internet. In fact, I can barely find any reference to any of these components at all.

I don't remember what the crossover points are, but logically, I wanted the low in the 700 to 800 range, and that would make the high in the 3,000 to 5,000 range. Though since I'm using a Horn Mid, I would want to use it and would expect the high cross over to be high, in the 4000 to 5600 range. [700/5000 seems very reasonable)

Performance-
Nice, exceptionally clear, naturally with the Horn Mid I have tons of clear midrange which I dial back with an L-Pad. The Piezo tweeter is a direct connect to the XO, with a 10 ohm resistor across the Piezo terminals. The logic was that attaching it to the XO would protect it from any low freq. surges, and the 10 ohm resistor would present a stable and predictable load to the crossover. The Piezo's are fine, though I'm considering replacing them with a regular horn tweeter.

Now we are getting close to the heart of the matter. The CTS woofer is clear, but not especially loud. That is, I don't get a full powerful bass. Again, what I do hear is crystal clear, and I've been satisfied with it for years, but now I'm starting to doubt my Port calculations.

Though I remember spending countless hours determining the port size, now I see no logic in arriving at 18 Sq.In. Though I do vaguely remember I chose a port size that would have a port depth between 3/4" and 1" for my cabinet volume.

Now, as I review the book, it seems that a single 2" port 4.5" deep would have made more sense.

Impossible to find specs on the woofer, but based on extremely vague recollection and the margin notes in the design book, it looks like it is 23 hz.

So, -

2.61 Cu.Ft. internal cabinet size
23 hz Fs

How do I determine a more reasonable port size with an eye toward improved bass response?

If you can help in any way, with specs, with advice, pointing me toward a reference, whatever... it would be appreciated.

It's a long shot, but I had to ask.

Steve/BlueWizard

[Conrad Hoffman]

IMO, you need to start with the basic TS parameters for the woofer. Since it's old, even having the published specs might not be too useful. It isn't hard to measure a woofer, if you have a sig gen and meter, or a sound card and suitable software (there's freeware to do this), plus some simple cables and a resistor. This will be way better than any second hand numbers. Might be best to pick up a copy of Vance Dickason's book, measure your woofer, and recalculate from there. Another recent thread discusses the aging of woofers, and it's possible your original tuning was right, but the woofer has degraded. Symptom would be high Fs. Unfortunately, they just don't last forever.

edit- you might want to use a sound card to do an SA of the speaker response to see where it's at. Maybe adjust the porting based on that and see what the result is. It would also be wise to check the crossover components.

[BlueWizard]

The TS, which I assume means 'Technical Specs' are non-existent.

I did email CTS and request a Tech Sheet, but I'm not holding out much hope.

I also emailed SPECO in hopes of getting the XO specs on the crossover, but again, hope is extremely dim.

This is all ancient history to them.

I am confident of the Fs (free air resonance) numbers as they appear in several places in the margin notes in the book, and the number 23hz is consistent with my memory. So, for now, I'm going with that.

Other specs like Le, or the various Q numbers simply aren't available unless you happen to have a spec sheet laying around (or some one else).

In another old thread here, I discovered this formula -

fp = (c/2pi) * sqrt(S/VL)

Post #6 in this thread- by Svante in Stockholm- Feb 2004
Why big port diameter?

where-
fp = resonance frequency of the cabinet
c = speed of sound = 345 M/s = 1132 ft/s = 13,583 in/s
pi = 3.1416
S = opening Size of Port (inch^2 or ft^2)
L = Length of Port
V - Volume of the Cabinet

Assuming a fixed size port opening for 2", 3", and 4" PVC pipe, and knowing the Speaker Resonance, the Cabinet Volume, choosing a desired Cabinet Resonance, and choosing a pipe diameter, I can solve for pipe/port Length.

L= ((c/2pi)/fp)^2 * S/V

...assuming my Algebra is correct.

However, when I run these calculations for various values, the result doesn't come up consistent with my book.

The book says I should have a 2" dia. port that is 4.5 inches long.

As a side note; when I was designing the cabinet, I think I was operating under the idea that if I double the port area and can halve the length of the tube and keep the same resonant frequency. Starting with 2" x 4.5" port tube, I shrunk the length to .75" and that expanded the port area to 18 sq.in. Whether that was a correct assumption or not, I don't know.

Anyway, using the formula, I calculate my cabinet is resonating at 157.7hz. If the formula can be trusted, that is a little high.

So, I used a desired resonance of 40hz and 35hz and ran the formula, and came up with a 3" pipe of 5.98" in length or two 2" pipes in a length of 5.3" (@35hz).

For a 23hz cabinet resonance, it worked out to a single 2" pipe with 7.9" length.

But again, do I trust this formula; can anyone verify or deny it.

I think at this stage, a formula like or similar to this is what I need. Someway to make the cabinet/port conbination resonate at a desired frequency, then choosing a desired frequency that will give the effect I want. I've been lead to believe that choosing a cabinet resonances that is slightly higher than the speaker resonance is desirable, and that is why I chose 35hz.

So, can anyone verify this formula, or direct me to a similar formula, or to a website with information regarding cabinet/port tuning?

For the record, I am familiar with how to determine the free-air-resonance of a speaker. Keep in mind though, that I have no money, and very limited home-make test equipment.

"pick up a copy of Vance Dickason's book" do you happen to have the title of this book?

Steve/BlueWizard

[Conrad Hoffman]

TS=Thiele-Small parameters. Google will bring up a plethora of stuff, including a large database, but start with Elliot . Dickason's book is The Loudspeaker Design Cookbook (I may not have it exact, but close) and it covers various tuning methods. There are various philosophies to tuning a ported enclosure, and it's a continuum, not necessarily a single "correct" point. What have you got for test equipment, self made or otherwise?

[Svante]

Originally posted by BlueWizard
In another old thread here, I discovered this formula -

fp = (c/2pi) * sqrt(S/VL)

Post #6 in this thread- by Svante in Stockholm- Feb 2004
Why big port diameter?

where-
fp = resonance frequency of the cabinet
c = speed of sound = 345 M/s = 1132 ft/s = 13,583 in/s
pi = 3.1416
S = opening Size of Port (inch^2 or ft^2)
L = Length of Port
V - Volume of the Cabinet

Assuming a fixed size port opening for 2", 3", and 4" PVC pipe, and knowing the Speaker Resonance, the Cabinet Volume, choosing a desired Cabinet Resonance, and choosing a pipe diameter, I can solve for pipe/port Length.

L= ((c/2pi)/fp)^2 * S/V

...assuming my Algebra is correct.

Just remember that the L in that formula is the effective length of the vent. The actual physical length is a bit shorter due to that the air just outside the tube also has a mass. You should subtract two end corrections from it, one for each end of the vent. This end correction is roughly 0.85 times the radius of the vent. So if the diameter of the vent is 5 cm, you should make the vent 2*0.85*2.5 cm shorter than what the formula says.

Also, the volume V of the box will seem slightly larger than the physical size if you have any damping material inside it. This is due to heat exchange between the air and the stuffing (also called isothermalization). For a box completely filled, the volume increase may become 20-30% with a theoretical maximum of 40%. If less volume is occupied with stuffing, the number decreases accordingly.

And last; it is not nessecarily so that fs and fp should be the same. In order to sort that out you would need the T/S (Thiele/Small) parameters of the driver and a simulation program.

[BlueWizard]

Conrad Hoffman, thanks, I'll search for "Thiele-Small" and see what I leads me too; should be helpful.

For test equipment I have 2 digital multimeters of the very cheap variety, 1 cheap analog volt/ohm/amp meter, and a two channel oscilloscope.

Plus, a function generator which produces a nice sinewave, but the output voltage shifts as I adjust the frequency. The frequency ranges are (1-100hz), (10-1k hz), (100-10k hz), and (1k-100k hz). No frequency counter and the dial simply sweeps the range with no calibrated marks. It's been a while since I used it, but I don't think the dial is all that linear either. It is based on the EXAR XR-2206CP.

Chip details for those interested -
http://www.chipdocs.com/pndecoder/da...XR-2206CP.html

Svante,

So glad you responded, you seem to have the minimalist approach I need.

First, did I understand your original formula correctly?

Second, is my algebra correct in resolving the equation to find 'L'?

As to the new information -

This end correction is roughly 0.85 times the radius of the vent. So if the diameter of the vent is 5 cm, you should make the vent 2*0.85*2.5 cm shorter than what the formula says.

Small point of confusion on this part, though it is not critical, the formula seems to be 2Kr, where K is the constant (0.85) and 'r' is the radius. Since you are taking 2r, why not use the diameter instead of the radius, or does that '2' come from some place unrelated to the Radius, like one correction factor for each end of the tube?

the volume V of the box will seem slightly larger than the physical size if you have any damping material inside it.

Based on the book I have, the typical internal displacement of a 12" speaker is about 0.4 cu.ft., so I've been debating whether to use 2.2 cu.ft. as my box volume, or to use 2.6 cu.ft. as the volume. The difference is about 18%. The cabinet has five sides covered with roughly an 1 inch to 1.5 inches of standard house fiberglass insulation.

Based on what you are saying, I can reasonably use 2.6 cu.ft. for my calculations? By ignoring the internal displacement of the speaker itself, I should be able to roughly compensate for the dampening material?

And last; it is not necessarily so that fs and fp should be the same.

I've been lead to believe from a variety of sources, that a box resonance slightly higher than the speaker resonance is desirable. Especially when my speaker resonance is so low (assumed 23hz). While, the T-S parameters may turn up something different, I have been trying for a box resonance of 35hz. Does this make sense, or am I completely lost?

Next, how confident are you of this formula -

fp = (c/2pi) * sqrt(S/VL)

Have you used it with good results? Is if from a specific reference book or based on general knowledge? If a reference book, what book?

I found another on-line Port Length calculator that uses similar parameters, but the results aren't the same. Though I haven't checked them against the new information you've given me here.

http://www.linearteam.dk/default.asp...ventcalculator

If I could find two sources that agree or somewhat agree, I could feel confident working from there. But every formula or resource I find produces different numbers. Though I am starting to see a trend. It looks like two 2 inch tubes or one 3 inch tubes with a length of 4 inches to 6 inches for a box resonance of 35hz.

At this stage, I simply want to pick a reasonable box resonance relative to my speaker resonance, and calculate the length and cross-sectional area of the tubes based of on available parameters. True I could get it perfect with a ton of work and a lot of expensive equipment, but for what I am trying to do, that seems like overkill.

So, in short, is this a theoretical formula, or is it one you have applied successfully in the past?

Thanks for the update, I will run your formula again using the correction factor you mentioned, and see what I come up with.

I assume the correct way to apply it is -

L= {((c/2pi)/fp)^2 * S/V} - 2Kr

or more simply

Lf = Lc - (2Kr)

Lf = Final Length
Lc = Calculated Length

Thanks again for everyone's help, it is greatly appreciated.

Steve/BlueWizard

[les winter]

You may have already tried this:

Madisound and Zalytron are two suppliers who offer replacement drivers for old speaker systems. They likely have a library of old drivers and your CTS TS specs.

Failing that, they probably have a low cost replacement that will work in your cabinet; have TS specs and will optimize your situation.

By the way, the Speco x-over probably is equipped with electrolytic crossover capacitors. I would replace these.

best of luck
Les

[Svante]

Originally posted by BlueWizard
Svante,

So glad you responded, you seem to have the minimalist approach I need.

First, did I understand your original formula correctly?

Second, is my algebra correct in resolving the equation to find 'L'?

I think so and yes.

Originally posted by BlueWizard

As to the new information -

This end correction is roughly 0.85 times the radius of the vent. So if the diameter of the vent is 5 cm, you should make the vent 2*0.85*2.5 cm shorter than what the formula says.

Small point of confusion on this part, though it is not critical, the formula seems to be 2Kr, where K is the constant (0.85) and 'r' is the radius. Since you are taking 2r, why not use the diameter instead of the radius, or does that '2' come from some place unrelated to the Radius, like one correction factor for each end of the tube?

Well, it is just a way to get a physical interpretation of the formula. The 0.85*r is really 8/3pi and is derived from the rediation impedance of a baffled piston. Ugly things like bessel functions show up doing this. Anyway, these added masses occur on both sides of the vent, so this mass should be doubled.

But you are right, if you just want a formula and don't care about the physics, you could say that the correction should be 0.85 times the diameter.

Originally posted by BlueWizard

the volume V of the box will seem slightly larger than the physical size if you have any damping material inside it.

Based on the book I have, the typical internal displacement of a 12" speaker is about 0.4 cu.ft., so I've been debating whether to use 2.2 cu.ft. as my box volume, or to use 2.6 cu.ft. as the volume. The difference is about 18%. The cabinet has five sides covered with roughly an 1 inch to 1.5 inches of standard house fiberglass insulation.

Based on what you are saying, I can reasonably use 2.6 cu.ft. for my calculations? By ignoring the internal displacement of the speaker itself, I should be able to roughly compensate for the dampening material?

If you are talking about the space the driver itself occupies (and not the displacement by the cone motion (which hardly could be 0.4 cu ft (I am terribly poor with non-metric numbers))) the two might cancel one another.

Originally posted by BlueWizard

And last; it is not necessarily so that fs and fp should be the same.

I've been lead to believe from a variety of sources, that a box resonance slightly higher than the speaker resonance is desirable. Especially when my speaker resonance is so low (assumed 23hz). While, the T-S parameters may turn up something different, I have been trying for a box resonance of 35hz. Does this make sense, or am I completely lost?

This is a question of design philosophy. It is becoming more and more common today to lower the fp below the resonance of the speaker (fs). Otoh if the speaker's fs is 23 Hz there is little poit in reducing fp down to, say 15 Hz, since we don't hear these frequencies. And, really, there is a lot more to this that has to be sorted out and the tool to do this is to get the T/S parameters one way or another and simulate a bit.

Originally posted by BlueWizard

Next, how confident are you of this formula -

fp = (c/2pi) * sqrt(S/VL)

Have you used it with good results? Is if from a specific reference book or based on general knowledge? If a reference book, what book?

I am confident that it is the formula to calculate the resonance of a helmholtz resonator, considering the corrections for volume and port length above. I just checked in the book I use when I teach, and I have seen it in several other books. I could derive it for you too if I needed to convince you more (it comes from the equations for acoustic capacitance and acoustic mass).

Originally posted by BlueWizard

I found another on-line Port Length calculator that uses similar parameters, but the results aren't the same. Though I haven't checked them against the new information you've given me here.

http://www.linearteam.dk/default.asp...ventcalculator

If I could find two sources that agree or somewhat agree, I could feel confident working from there. But every formula or resource I find produces different numbers. Though I am starting to see a trend. It looks like two 2 inch tubes or one 3 inch tubes with a length of 4 inches to 6 inches for a box resonance of 35hz.

At this stage, I simply want to pick a reasonable box resonance relative to my speaker resonance, and calculate the length and cross-sectional area of the tubes based of on available parameters. True I could get it perfect with a ton of work and a lot of expensive equipment, but for what I am trying to do, that seems like overkill.

Well, you need a resistor that costs $0.10 and some free software for your computer, assuming that you have a sound card.

Originally posted by BlueWizard

So, in short, is this a theoretical formula, or is it one you have applied successfully in the past?

It is a theoretical formula, and I apply it eg in my simulator (in my sig) and also in the speakers I have built and in the labs I designed for my students.

Originally posted by BlueWizard

Thanks for the update, I will run your formula again using the correction factor you mentioned, and see what I come up with.

I assume the correct way to apply it is -

L= {((c/2pi)/fp)^2 * S/V} - 2Kr

or more simply

Lf = Lc - (2Kr)

Lf = Final Length
Lc = Calculated Length

Yes.

But given the difficulties in estimating the isothermalizing effects of the stuffing, it might be wise to measure the fp after the design is made and possibly adjust the length of the tube accordingly.

[Conrad Hoffman]

You've got a scope, so you can tell what frequency and amplitude your sig gen is doing, even if the dial isn't great. That, and a resistor, is all you need to get the important parameters of your woofer. Armed with that, there are any number of box tuning programs that will predict the response curve for various tunings. I've got one I wrote from the old Speaker Builder articles on TS parameters that runs in a DOS window (never bothered to update it) if you like, or a search should find you various others that are substantially more modern. I did put in the step by step procedure for measuring driver parameters. IMO, with only the Fs, little can be accomplished.

[BlueWizard]

Thanks again to Svante for taking so much time to assist me. I realize things are much more complicated than I would like them to be, but I've lived with this speaker for years, and I'm just trying to improve the bass a bit, not design the perfect speaker. I think what you have given me is sufficient.

I already have TWO 3 inch by 3 inch square holes, that should make it easy to insert TWO 2" diameter PVC pipes.

I've just run your calculations again in a spreadsheet. Without the corrections, TWO Ports of 2 inches in diameter, would have a length of 5.336 inches. After the correction, it comes out to 3.636 inches. I can't flair the edges, but I might be able to find someone to round them off a bit with a router.

I can buy 2 feet of 2 inch PVC for $2.18 or 10 feet for $4.44. That is a lot of pipe to play around with and test. For $8.13, I can get a 2 foot by 4 foot 3/4 inch MDF. That is a lot of 3" x 3" squares to fit with test pipes.

And...I understand how you feel about trying to think of things in Metric vs American measurements (we are the last hold-out aren't we). Because I'm the same way in reverse. Thinking of cabinet volume in Liters makes me think of cabinets filled with bottles of milk; it's just illogical. But, I found a nice converter on-line so I can covert between them.

I read through the T-S spec testing procedure at the website referenced, and while it is technically slightly over my head, there is a spreadsheet that makes all the calculations, and really in the end, there are only a few measurement to make.

So, while I'm not sure I will apply that to this speaker cabinet, I use it everyday, it looks like I could learn a lot from it by trying it on a random test speaker. All I really need is a standard box. I've already got several 8 ohm power resistors (25 watt; heatsinked), and a signal generator, sad as it is. I also have a spare stereo amp I'm not using. Unfortunately, I don't have a lot of uncluttered space to work in. I'll either have to do it in my living room or out on the deck. And how do I mount a speaker for free air resonance testing? Do I hang it from the ceiling? Do I set in on a tall sand filled column? On the horizontal plane, I'll be lucky if I can get it 6 feet (1.8 meters) from nearby object in every direction.

I do have some other questions, but they are off this topic, so I will make them separate posts.

Thanks again to everyone who replied. I'm still open to comments though.

Steve/BlueWizard