# What's the equivalent of multiple drivers?

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#### tcpip

I was trying to model the vented box for a line array that a friend is keen to try --- the inspiration for my friend is the Bottlehead Straight 8. This line array which I'm toying with will have six 5" drivers in each box, plus a dome tweeter perched above them. Since this is six drivers, Unibox doesn't know how to do the calculations out of the box (pun not intended), so I need to synthesize the parameters of a hypothetical single driver which will be equal to the combination of all six put together. Then I can tell Unibox that I have just one driver, and ask it to do its thing.

I was thinking of making two series-strings of 3 drivers each, and then paralleling these two strings. Since each driver's Re is about 6 Ohms, I'll get a final configuration with an Re of about 9 Ohms, which should be easy on the amp.

My knowledge of the equivalent T/S parameters is a bit flaky, so I thought I'd ask for your guidance. Please can you tell me whether each of the points below are correct?

• Vas and Sd of the equivalent single driver will be six times the corresponding values of each small driver.
• Qts of the equivalent driver will be the same as that of each driver. (Will it? Will the Qts depend on the electrical connection topology of the drivers? Will I have to wire up six drivers on an open baffle and take impedance measurements to get the Q of the final setup?)
• Re will be 9 Ohms as described above.
• Le will be calculated using formula for series and parallel impedances just like I did with Re.
• Fs for the equivalent single driver will be the same as that of each small driver.
• Xmax for the equivalent big driver will be the same as that for each small driver.

Incidentally, I've read the section on compound woofers in Dickason's Cookbook, and I'm quite confident I've understood how to calculate equivalent parameters for two drivers. I'm just not certain how to do it for six, specially since some posts on this forum have mentioned that damping changes sharply if drivers are connected in series, etc.

Did I miss out anything? Am I on the right track?

#### bobhayes

I think you've covered it pretty well.
Dickason states that with two woofers, the Q remains the same, so three should also remain unchanged for the purposes of your calculations.
Paralleling them to another chain of three woofers would bring the parameters closer to that of a single unit, if there was any doubt.
I would go ahead using the theory you stated.

#### chipco3434

Take the basic sensitivity on the speakers and you can get the params for multiples this way.

If the single speaker is 88 a 1m 1 watt then

Array efficiency= 88 + 10*(log of the n number of drivers)

Array efficiency= 88 + 10*(log 6)

Array efficiency= 88 + 10*(.78)

Array efficiency= 88 + 7.8

Array efficiency= 95.8

I'm not so sure I wouldn't put the tweeter in the middle of the drivers... i.e., MMMTMMM.

If you are on a budget, try the dayton neo tweeter... 5 bucks sounds pretty good.

Series/parallel is SOP for arrays.

Start building now. You will never go back. Try it first in an open baffle. You might save yourself alot of wood.

The other reading is Jim Griffin's paper on line arrays.

Griffin on line arrays

definitely put the tweeter in the middle! the line array effect is very pronounced...

#### RJ

Nice experiment, but the enclosure is going to be tall. Taller then 34".
If the box is going to be ported the tall box will act as a tube creating standing waves which will screw up the port resonances. In essence it'll be a hybrid transmission line - bass reflex.
My experience with line arrays has taught me to build them in seperate boxes. My first array started out to be ported. I could never get the port tuned right. I then added baffles to load the drivers and break up the standing waves and I still couldn't tune the port. I went sealed and loved it. It still had bass and more then I expected.
The line arrays I'm building now 'are' in seperate boxes. 3 of them to be exact. The 3 will be glued together and an outer cover of finished plywood and 1/2" MDF will cover the seams and add a constrained layer to the box to help stop box resonances. Making them sound dead.
You could also add a shelf half way in your box thus making two seperate enclosures. 2 ported boxes will be easier to tune then one tall one.

Have you checked out Dual Chambered Reflex Boxes???
http://www.diysubwoofers.org/prt/dual_chamber.htm
http://paginas.terra.com.br/educacao/claudionegro/english/

If the 5" drivers model well with 2 ports then this would be a good direction to go. It's sound and characteristics is that of a cross between sealed and ported. Better group delay and no below resonance flutter from the driver.

Just adding fuel to the brain, Good Luck! ,Rudy

Oh yeah, the formula for transmission lines are;

(1128/Fs of the speakers) /4 = 1/4 wave in feet
Feet x 12 = length in inchs

If the driver Fs is 55 hz. then 1128/55 = 20.5 ft.
20.5/4 = 5.13 quarter-wave feet.
5.13 x 12 in. = 61.5 "

A 32" tall box would create 1/8 wave resonances or harmonics.

I think the 1st or 2nd harmonic is the killer, not sure. I'm gonna check on that.
http://www.quarter-wave.com/

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#### simon5

You could just use WinISD Pro that simulate up to 100 drivers.

#### wintermute

Paid Member
simon5 said:
You could just use WinISD Pro that simulate up to 100 drivers.

Doesn't winisd pro only allow modelling with drivers in parallel??? or did I miss something

Actually I just had a look, and there was a newer version (one point rev higher than I had) and there are a lot of nice new features.... but on playing with multiple drivers it doesn't seem to calculate the impedance at all.... no matter whether I put in 1, 2,3 or more drivers the only change to the impedance plot is a slight change in the resonant freq, the overall magnitude stays the same.... not how it should be me thinks

Tony.

#### tcpip

Thanks guys. You all are amazing. You've not only answered my questions, you've touched upon some of my unspoken fears and doubts.

First of all, I'm glad that the equivalent driver parameters thing has been sorted out. Thanks for confirming that I'm on the right track.

Now for my thoughts and plans. I'm playing with this driver from Peerless India.

(This driver is quite interesting even to non-Indians, incidentally, because a modded version of this has apparently been supplied under OEM order to GR Research and is sold in the North America as their famous M130. The key diffference between what I'm getting here and what the M130 gives, as far as I can see, is the Fs.) I'm getting an Fs of 80Hz, much higher than I'd like.

The published parameters are tallying well with my SW-measured values. The Vas that I got after my quick-and-dirty added-mass measurement is about 4.8L. (I'll do a sealed-box measurement later.)

So, for a vented box of 5L per driver, I'm getting a manageable 30L total internal volume, but that's too little bass (F3 of box at 58Hz or so). Using Unibox and moving to something like 15L per driver, I can drive down the F3 to about 44Hz, which, together with a down-firing port and ground coupling, will probably give me adequate bass. (Remember, I'm new to all this, I could be wrong... so please shout loudly if you think I am.)

Therefore, at a total volume of 90L, plus lots of bracing, I'm looking at a box which is tall and slim from the front but will probably extend more than two feet at the back. So it won't be a slim and sexy column any more, except from on-axis. And then comes the problem of vent diameter. With an equivalent driver diameter of something like 15", I don't think I should use just a 2" vent. So I wanted to build a 4" or 6" vent, and that makes the duct quite long.

I had toyed with the idea of doing one chamber per driver, maybe with each having its own slim little ducted port. What should I do? Regarding the TL behaviour of my big box, I don't think that danger is very serious. This is because at 90L, I'm not going to get a tall slim box... I'll probably go for a large box with narrow front baffle but with a sloping back, extending to a base which might be two feet long. In other words, the shape of my enclosure may be more like a triangle than a column. See the Aksonic speaker's design to get an idea:
An externally hosted image should be here but it was not working when we last tested it.

except that my box will probably extend at the back much more.

Therefore, I'm now wondering whether I should go in for one large down-firing port in one big triangular box, or whether I should make multiple chambers, each with its own vent. (With the multiple-vent approach, I lose the ability to have a down-firing port to enhance bass via ground effect.)

What do you think?

Another thing that I was wondering about was the tweeter. I had originally thought I'd put it on top, like the Bottlehead Straight 8. But do you feel a tweeter in the centre is much better? If I do that, I can increase my box height too, and then maybe my box will begin to look like your tall slim columns. Which is better?

#### simon5

wintermute said:
but on playing with multiple drivers it doesn't seem to calculate the impedance at all.... no matter whether I put in 1, 2,3 or more drivers the only change to the impedance plot is a slight change in the resonant freq, the overall magnitude stays the same.... not how it should be me thinks

Yeah, but it will give you an idea about the SPL curve. If you have 4 drivers in series-parallel the impedance will stay the same and WinISD will show you the new SPL you can achieve with the same power imput.

Also, if you know some maths, you can easily guess what will be the impedance curve if you put only two drivers in series (multiply impedance curve by two) )or two drivers in parallel (divide impedance curve by two).

Because you know the new nominal impedance, you can easily calculate the SPL sensivity at 2.83 volts too.

#### simon5

tcpip said:
Therefore, at a total volume of 90L, plus lots of bracing, I'm looking at a box which is tall and slim from the front but will probably extend more than two feet at the back. So it won't be a slim and sexy column any more, except from on-axis. And then comes the problem of vent diameter. With an equivalent driver diameter of something like 15", I don't think I should use just a 2" vent. So I wanted to build a 4" or 6" vent, and that makes the duct quite long.

Another thing that I was wondering about was the tweeter. I had originally thought I'd put it on top, like the Bottlehead Straight 8. But do you feel a tweeter in the centre is much better? If I do that, I can increase my box height too, and then maybe my box will begin to look like your tall slim columns. Which is better?

Your equivalent diameter is big yes, but the Xmax is low, so the vent speed will be OK. You could double check it in WinISD Pro. I would use a single 3 inches vent or 4 inches if you want to go overkill.

The tweeter should be at ear level. So unless your column is very high, it should be at the top of it.

Good luck!

#### tcpip

simon5 said:
Your equivalent diameter is big yes, but the Xmax is low, so the vent speed will be OK. You could double check it in WinISD Pro. I would use a single 3 inches vent or 4 inches if you want to go overkill.
Okay. I guess I'll do a reasonable sized vent.

BTW, a lot of you are referring to WinISD Pro. Is it very good? Incidentally I tried using the non-Pro WinISD, and I found it very simple, with very little information being either accepted or generated. I liked Unibox much more. What do you think of Unibox? I know this is a bit OT, but I'd really like to know what you guys think of it for just low-freq modelling and box design. I found it better than both SW and WinISD, in terms of the amount of information it displays, the way it lets me play with the values, and so on.

The tweeter should be at ear level. So unless your column is very high, it should be at the top of it.
Yes, that was pretty clear. I was just wondering between
• putting the tweeter in the middle of the column, and extending the column, making it taller, to keep the tweeter at ear level, or
• making a more "normal" 3-feet or 4-feet enclosure and keeping the tweeter at the top.
Which is better?

#### RJ

I can drive down the F3 to about 44Hz, which, together with a down-firing port and ground coupling, will probably give me adequate bass.

The bass notes will travel faster through the floor.
I tried modelling that driver in UniBox but I need an Xmax number to get a better idea what that driver can do.
Also a tall triangular box is a Voight Pipe....but at an 80 hz Fs your 1/4 wave is 42" the 2nd wave is at 84" with smaller ripples at multiples of 42...
If you go with a downfiring port, leave yourself some wiggle room. You'll need to tune it manually by shortening the length of the port.
You could also have a hole ready in the rear in case floor coupling produces a boomy bass.

#### tcpip

RJ said:
I tried modelling that driver in UniBox but I need an Xmax number to get a better idea what that driver can do.
In Unibox terminology, Xmax is half of Xp2p. So, for those purposes, assume Xmax to be 1mm. I am certain this driver will go more than 2mm peak-to-peak, but let's keep to this 1mm to be safe.

Also a tall triangular box is a Voight Pipe....but at an 80 hz Fs your 1/4 wave is 42" the 2nd wave is at 84" with smaller ripples at multiples of 42...
I didn't understand a word of what you said, starting with Voight pipe.

If you go with a downfiring port, leave yourself some wiggle room. You'll need to tune it manually by shortening the length of the port.
You could also have a hole ready in the rear in case floor coupling produces a boomy bass.
I think this is a brilliant idea! I don't know why I didn't think of it before, considering I always think of all the brillliant ones I can certainly keep ready-made cutouts at both bottom and rear. After experimentation, I'll cover one up with a neat little hatch which will be gasket-sealed, and the other will have the port. Kewwwl!

#### RJ

Also a tall triangular box is a Voight Pipe....but at an 80 hz Fs your 1/4 wave is 42" the 2nd wave is at 84" with smaller ripples at multiples of 42...

Any box that starts exceeding the 'Golden Ratio' and starts getting taller and narrower becomes a pipe. A pipe doesn't have to be round. It could be square, rectangular or triangular. curved, bent, folded or straight.
A Voight pipe is straight. It looks like a bass reflex/ported box but it's tuned to a 1/4 wave and then becomes a transmission line.
I've seen and read a lot of coool arguments about 'When does a Bass Reflex/ported box become a transmission line.
Even Martin King doesn't know and he programmed the worksheets for TL's. He also has worksheets on sealed, ported, bass reflex and horns.
It's using the formula for a TL can be useful in determining the box resonance for standing waves, 1/8 and 1/4 waves....
That's why I failed in my first line-arrays to tune it to be a ported box.

#### tcpip

Here are the parameters and the output from Unibox, when I tried modelling it as an "equivalent driver". The parameters of each driver were: Fs=80Hz, Vas=5.3L, Qes=0.63, Qms=2.53, Le=0.292mH, Re=5.8Ohm, and Sd=95 cm2.

By calculating the equivalent parameters for my line-array of six, I got the following and put them in Unibox, telling it that this is a single-driver design:
An externally hosted image should be here but it was not working when we last tested it.

Then, by playing around with the box model, I'm getting this set of values:
An externally hosted image should be here but it was not working when we last tested it.

What do you think? The box size is huge, but I may be able to build it as a tall box with a slim front baffle and a lot of extension towards the back. Will it work as a vented box?

BTW, what's "flush end" for a port in Unibox? I thought the opposite of flared was flush. But if that's true, how come Unibox gives me the option of "no flush end"? It'll either be flush or flared, so what's this "no flush end"? Is there a third type of port end?

#### Svante

tcpip said:
Here are the parameters and the output from Unibox, when I tried modelling it as an "equivalent driver". The parameters of each driver were: Fs=80Hz, Vas=5.3L, Qes=0.63, Qms=2.53, Le=0.292mH, Re=5.8Ohm, and Sd=95 cm2.

I was about to do a Basta simulation, but I need the Bl value for that. BTW, this does not seem to be the same driver as you linked to before, am I right in that?

Peerless driver

#### simon5

BTW, what's "flush end" for a port in Unibox? I thought the opposite of flared was flush. But if that's true, how come Unibox gives me the option of "no flush end"? It'll either be flush or flared, so what's this "no flush end"? Is there a third type of port end?

Flush end means your port ends flush with a wall.
No flush end means your port ends in the middle of nowhere.

Usually the outside part ends flush with the box wall and the inner part ends in the middle of nowhere so you have one flush end. This will add a correction factor for the length of the port.

This is not the same issue as flared or not flared port. If you use flared you need to add another correction factor.

Is it very good? Incidentally I tried using the non-Pro WinISD, and I found it very simple, with very little information being either accepted or generated. I liked Unibox much more. What do you think of Unibox? I know this is a bit OT, but I'd really like to know what you guys think of it for just low-freq modelling and box design. I found it better than both SW and WinISD, in terms of the amount of information it displays, the way it lets me play with the values, and so on.

Yes WinISD Pro is very good. You have some graphs that Unibox doesn't have, like the Impedance Phase response and Group Delay. You can also model with more than one driver, up to 100 drivers, but you have to figure out what final impedance it will make because they will simulate SPL graphs, excursion graphs, group delay graphs with as many drivers you entered, but the impedance and phase graphs will stay similar.

WinISD is also good to simulate with filters, highpass, lowpass, linkwitz transform, 2nd order peaking highpass, parametric EQ, static gain, allpass...

Unibox is also very good, modifying Qa, Qp, Ql and port end correction factor is more intuitive with the drop down menus. It's also good for alot of external factors that you can enter at the start of the simulation like the resistance of wires and the like.

In the end, I would say... use both of them to check everything hehe!

I just saw that wind speed was available in Unibox so forget my answer about that. Just use Unibox and you'll see that you don't need a 5 or 6 inches diameter pipe.

Yes, that was pretty clear. I was just wondering between...

It depends, as long as the tweeter is at ear level it's ok. If you make the line of woofers longer, you'll get more SPL with the same power imput. It will also be high WOW factor. I would consider using a tweeter with sensivity higher if you go with the longer line just to make the crossover easier.

#### tcpip

Svante said:
I was about to do a Basta simulation, but I need the Bl value for that.
What's a Basta simulation?

BTW, this does not seem to be the same driver as you linked to before, am I right in that?
Actually, the differences are minor. I'd earlier pointed to the published spec sheet, now I've posted my measured parameters. The Fs matches very closely, the Vas was missing in the published spec sheet, and the only parameter which differs very widely is the Sd. I have good reason to believe the published Sd was a typo: 65 sqcm when the corrrect value should be 95 sqcm. Other than that, it's the same driver.

I couldn't even connect to diyaudio last night. It's now Sunday morning here, and I'm able to connect once again. Was the site out of action sometime about 12 hours ago?

#### tcpip

simon5 said:
Flush end means your port ends flush with a wall.
No flush end means your port ends in the middle of nowhere.

Usually the outside part ends flush with the box wall and the inner part ends in the middle of nowhere so you have one flush end. This will add a correction factor for the length of the port.
Thanks. Now at least I understand what this thing means. I guess for most designs, the correct choice will be either "one flush end", or "one or two flared ends", right? In my case, I guess it'll be "one flush end". However, what I can't figure out is how will anyone ever have "two flush ends"? How is this possible?

It depends, as long as the tweeter is at ear level it's ok. If you make the line of woofers longer, you'll get more SPL with the same power imput. It will also be high WOW factor.
Got it. I guess then in my case, I'll put the tweeter at the top of the array, given that my entire array will fit in 36" height or thereabouts. Thanks.

#### simon5

Two flush ends can happen. For example if you want to have the port strongly attached on the inside, you could have a piece of wood there.

If you do a slot port on the bottom taking the full width of the box, the port will be flush end on three sides (approximately hehe there's a better formula for that case).

About 36 inches high? Yeah better stay with top of the line. It's because some people do 84+ inches high line arrays so if you use a single tweeter you put it in the center of the line.

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