The Mind is a Terrible Thing to Waste

I started imagining this design a few months ago while trying to stay awake through the one of my professor's boring lectures.  Though I didn't get much out of class that day, the boredom had caused by brain to wander into the deepest parts of its inventive little caverns.  I was reflecting upon the many recent discussions regarding passive radiator operation.  Especially thinking about Deon Beardon's The Beast 18" subwoofer which uses a single 18" active driver and 3 18"passive radiators.  Many people have many different opinions regarding how to make PR-based subwoofers yet I bet more than half of those people have never really sat down and put one together.  I didn't want to be another one of those people.  And since I had some knowledge both from experience and research behind me, I made up this little masterpiece I call The 10Triple10.

When Four is Better Than One

This subwoofer is a 10" woofer in a small enclosure with (3) 10" passive radiators.  That's a total of 4 radiating drivers all bouncing and booming to the rhythm of the beat.  All I can say about this subwoofer is its performance is completely remarkable.  You'll think that either your eyes or your ears are deceiving you to believe that a subwoofer this small can produce such enormous amounts of truly deep bass.   This sub loves low notes.  It's like it physically thrives off them.  It's just playing along having a good time up above 40 Hz, but when those notes start to get into the 20's, it's like the sub drops into overdrive.  So anyway, enough salesman talk, here's the real deal on the design, production, and test results of my all-mighty 10Triple10 Subwoofer.  

The Driver

The speaker starts with Ultimate Attitude's 10" AU1040 subwoofer.  A sub designed for car audio, but since I haven't seen many inexpensive home theater subs in the 10" range on the market for DIY, I went ahead with this sub.  The specs are listed here: Attitude AU1050 10" Stamp Frame Woofer.  250 watts RMS/350 watts max *Impedance: 6 ohms per coil *Frequency response: 25-200 Hz *Magnet weight: 50 oz. *Fs: 29 Hz *SPL: 89 dB 1W/1m *Vas: 3.50 cu.ft, *Qms: 8.20 *Qes: .45 *Qts: .43 *Xmax: 9.9mm. *Net weight: 9 lbs. *Dimensions: A: 10-1/16", B: 9-1/8", C: 5-1/16", D: 5-1/4", E: 1-1/4".   It's got a lame cupped spider too, so rail on the speaker if you must, but I believe it sounds great for the money.

The Passive Radiators

The passive radiators were custom built.  I didn't actually build them from scratch, but they didn't cost me $60 a piece either.  These PR's are just flat pieces of machined MDF with a large thick foam surround giving each PR an Xmax of more than 10 mm.  Imagine a real PR and take away everything but the radiating diaphragm.  These diaphragms originally would have gone into making a full-blown PR, but I got to them before they made it that far down the assembly line (in a sense).  So we're talking really cheap flat PR's but with nice thick surrounds and a solid machined MDF diaphragm.  Each PR had an initial mass of 90 grams.

Some PR Basics

The first step was to design a box for this speaker that would be optimum for a PR design.   A good rule to go by with PR's is keeping in mind that their main advantage is to allow very small enclosures to be tuned very low while keeping compression factors to a minimum.  Small box + PR = very low tuning.  The fact that PR's have such large surface areas (even more with 3 PR's) it has been theorized that this decreases nasty compression factors till they're literally non existent.  The result?  Uninhibited bass response in the lowest octaves which can mean up to and beyond 3 dB increased output.  This is all very good.  In addition PR's do not experience port noise or air turbulence noise common with ports and large drivers.  Especially small ports which are sometimes required in order to achieve the desired tuning frequency.  Large ports need to be long and there isn't room inside a small box for a bunch of big, long ports.  PR's solve all those problems.  So I wanted to stick with the idea of making the box small and tuning the box low and allowing the PR's to do all the work giving the lowest bass possible without port noise or compression factors.  Otherwise I might as well throw a puny three inch round port in the box and call it good.  But where's the creativity in that?  Where's the spunk?  Where's the innovation?  That's what I'm all about...innovation in design.   This sub definitely has satisfied my need for something different.

Modeling the Enclosure

To the right are a few thumbnails of shots taken from Brian's ported.xls.  I chose to make the box the size I did because of both aesthetics and design.  I wanted the box to look proportional with the 4 10" speakers on each side.  A cube seemed the logical choice.  I didn't want too much extra space on either side of the woofers either.  So I decided on 15" all the way around and plugged in the T/S parameters into a few programs to see if this driver would work in a 1.35 ft^3 box.  A lot of times you can get away with making the box smaller than normal if you can tolerate a hump in the frequency response.  But don't forget we're going passive!  I can get rid of any hump by tuning the box much lower than would normally be possible with an ordinary port.  Small Box + Low Tuning + PR = No Hump.  So here's the final Frequency Response Plot, SPL Plot and Excursion Plots of the 10Triple10.  I compared the box to a sealed enclosure just because the program would allow me too.  From looking at the graphs your probably thinking, "So what's so impressive about that?"  Well first off these plots are modeled after a ported enclosure.  Since I'm using passive radiators with an equivalent surface area of a 13" round port, these graphs suddenly go out the window.  I can expect similar response curves but with much more actual output.  F3 will go down and SPL will up.  The problem is excursion goes up too.  But I can get a good idea of where to tune the box and a general idea of how it will sound.

Tuning Frequency

I deciding on a tuning frequency of 30 Hz, since that dropped the hump from +3 dB to only +1.3 dB.  I could have gone as low as 25 Hz for the tuning and probably had acceptable results as well.  But I wanted to keep from having to add too much mass to each PR.  I was afraid that if they were too heavy, they'd cantilever out of control long before I'd want them too.  Since adding mass to a flat PR can be tricky to ensure that each you don't end up massing down one side just a few grams more than the other and in effect making it "lopsided".  I used 9 washers that weighed 18 grams a piece to mass down each passive. 

How to Calculate Tuning Frequency of a PR System

Now your asking how in the world did I know to add 9, 18 gram washers?  I used passive.xls.   Which is available here at my site.  I entered in the parameters of my passives and the fB and size of the enclosure.  I found Sd by measuring across the diameter of the PR plus 1/3 of the surround on either side.  This came out to be really close to 7.50"   See the picture to to the right.  Although you can't see what the ruler says, this shows how it is possible to find the Sd of a driver or PR.  Sd = pi*(D/2)^2.  Then do the proper conversion to cm^2 or m^2.  This is where your HP-48 comes in handy.  I measured from where the 1" starts to 8.5" so don't let the edge of the ruler throw you off.  So from the spreadsheet it looked like I would need to add 160 grams (for a total of 250 g) to each PR for a tuning of 30 Hz in a box totaling 1.35 ft^3.  And that was that.  All the designing was done, now it was time to build the box and put the PR's together.  I won't go into any detail on box construction.  I figure this page is about PR's and such so construction tips I won't be giving.  But you can see quite easily from the pictures how the box was made.  3/4" MDF with 1/8" mahogany plywood and a rad slab of green marble on the top framed by a black border.  Yeah, this sub basically looks awesome.  It's stained in Light American Oak from Minwax.

The Pictures

To the right you'll find pictures of the last stages of building this subwoofer.  That's all I have to say for now.  I do have response plots coming in the near future.   From an initial comparison, this sub was keeping up with a single Shiva in a 3 ft^3 ported enclosure.  Now that was an amazing thing to hear!  But more about that later.

The Results

After I put the box together and screwed in all the speakers, I did an fB test to see if I hit my targeted 30 Hz.  Would you believe that I hit the 30 Hz perfectly?  I couldn't believe it either, but sure enough, I was right on the money.  Cha-ching!  Now that's good design.   Just a little bit of info regarding  how the frequency response was measured.  The sub was measured in my front yard so as to avoid all reflections from walls and ceilings.  This is about the best anechoic response you can get.  Only the ground is capable of interfering with the results.   I used a precision frequency generator, frequency counter, amplifier, and my trusty Radio Shack analog SPL meter.  The sub was placed in the grass as far way from the house and any walls as possible, while the SPL meter was placed at exactly 1 meter from the front baffle at the same height as the dust cap.  I ran 9.75 volts into the driver which has a nominal impedance of 3 ohms which roughly equates to 31 watts.  Since impedance varies with frequency, we can't say exactly how many watts the driver was dissipating, but we can get an idea of how hard the sub is being pushed.  31 watts is very conservative but even still I was able to get the PR's to cantilever at 30 Hz and below.  I then plotted the SPL at 5 Hz increments starting at 15 Hz working my way up to 100 Hz.  I accounted for meter correction and plotted the results in Excel.  That is the graph you see to the right.  In-room response of the sub would improve the low end by about 10 dB starting at 20 Hz.   The extra hump you see below 30 Hz I believe was due to a loud knocking sound that the PR's began producing as they began to cantilever. 

Now this was just using a pure sinewave, not your typical bass material you'd get from a movie or even most music.  When watching movies the passives do not move enough in a consistent motion to begin this rhythmic cantilevering action, they actually behave fine and cause no problems.  The biggest drawback to this design in the 10" driver bottoms out easily at low power.  Explosions and car crashes cause the drive to pop badly.  My theory behind this goes back to the reduces compression factors within the box.  So reduced that the drive almost behaves as if its in no box at all, or operating in free-air.  Without any restoring energy behind the cone from the box, the cone just bounces out of control causing the voice coil to slap into the magnet.  That and the driver is pretty crappy and a 30 Hz tuning doesn't help.  Any content below 30 Hz will drastically cause the driver to exceed its Xmax.  For future designs, tuning needs to be closer 20Hz and the driver needs more Xmax.