DOWNLOAD PASSIVE.XLS NOW!!  (16Kb)

Now you can download PASSIVE.XLS  An easy to use spreadsheet created with Microsoft Excel that lets you enter the known parameters of your subwoofer system and calculates the required mass for any number of passive radiators.   It's about time I put this together isn't it?   NOTE:  If you are using Internet Explorer 5.0, by clicking on the link above, you will open passive.xls in this browser window and may use the program in IE.  If you want to download the file to your computer, right click the link and "Save Target As".  

The most crucial element in making a PR system function properly is calculating the mass of the passive radiator.  Just as in a vented enclosure, the length of the vent is crucial to the tuning frequency of the box, the mass of the PR is also crucial to the tuning frequency of the box.   On this page you will find two ways to calculate the mass needed to tune your enclosure.  Both methods are identical, except that the first one, which I call The Quick Method, is a simplified version of the second one.  The second one by Brian is what you could call the proof of how Quick Method works.  This formula was derived using Dickason's LSDC V and Brian Steele's formulas.  You may also visit Bob White's Home Page where he has various downloadable DOS programs including one that does complete PR modeling with all the necessary response graphs.  You may use his program in conjunction with Passive.xls for complete designing of PR systems.

     This is my attempt to simplify the process of calculating mass required for PR systems.  This "massive" equation (no pun intended) assumes you have already determined the desired alignment, volume and tuning frequency of your box.  This equation is much simpler if you plug it into a calculator such as an HP-48G.  You can also put them into a spreadsheet, so you don't have to mess with all the numbers every time.  Here is the detail:
 
        Mass = Grams, total mass required
        fb = Hz
        Vb = Volume of box in cubic feet
        Dp = Effective diameter of passive radiator in inches = 2 x (Sd/pi)^0.5    *note:  Sd must be in square inches.  Since most Sd specs are in square meters or centimeters, you must do the proper conversion.

     All you need to do is plug in the known parameters, chug away on your calculator for a while, and out pops your total required mass.  Then you should subtract the original mass of the PR from the total mass, and that gives you how much mass to add.  Could it be any simpler?  There are a few stipulations of course.  This formula is not perfectly accurate.   It does not take into account PR compliance or box loss figures, which will alter the actual fb.  It's a good idea to start with about 10% less mass than what you calculated, and add mass from there.  As your adding the mass, you should test your box each time to be sure that it is nearing the correct frequency.  Here are three ways to measure the fb of your system:

1.  The easiest and most accurate way to measure fB is with a signal generator and an SPL meter.  Set your sub box away from any corners of your room.  Place the meter close to the driver/woofer within 1/2" and sweep the 10 - 80 Hz frequency region.  Adjust the signal generator and look for for minimum output from your driver, or for a slight dip in the output near fB.  This can be hard to find if fB is very close to the f(-3) point.  Yet there still should be a distinct drop (at fB) then rise (just below fB) then drop in output (way below fB), even if it is subtle.  It should be close to your desired fB as well.  So if you get a dip at 43 Hz and you were expecting it to be at 18 Hz, that's most likely the wrong dip.

2.  A somewhat  harder yet still accurate way to measure fB is by using an impedance analyzer, such the one described in this web site.   Using a signal generator sweep once again between 10 and 80 Hz and locate the two large impedance peaks which should be above and below fb.  Label them fh and fl respectively.  The dip in the exact middle is sometimes referred to as fB, but most times is not very accurate.  To be more precise, remove the PR and seal the opening.  This can be accomplished my using another board with weather stripping and pressing it firmly over the opening.   Now measure the impedance peak once again.  Call this fc.  Then fb is calculated by:    fb = (fl^2 + fh^2 - fc^2)^0.5 

3.  Here is another simple yet still pretty accurate way to measure fB, when all else fails.  Crank up the sub super loud, so you can see it bouncing back and forth, adjust the generator and watch closely until the driver's bouncing is reduced to a minimum.  This will be fb.  Above and below fb the driver is capable of undergoing maximum excursion,  yet due to the damping characteristics of ported speaker systems, right at fB the driver's excursion is at a minimum.  If the driver appears to bounce at all frequencies, you could have a leak in the enclosure or your port diameter or port area is too small.  First find the leaks and seal them up and do your tests again until you get consistent results. 

            These methods work just the same for ordinary ported enclosures.

            Please also visit my PR Mass Addition Kit to learn an easy way to add and remove mass from you PR.

     Since a passive radiator needs to be capable of displacing between 2 and 4 times the amount of the driver, sometimes it is necessary to use more than one PR.   For example, let's say I wanted to use one 12" Shiva with 3 12" PRs.  Using the above formula,  I would first need to find the PR equivalent diameter of all three PRs.  This is done using the formula:  Eq 1.2

Where Dptotal = Total Effective Diameter of all Passives
           Dp = Effective Diameter of Single PR
           Np = Number of Passive Radiators Used

     With this newly derived PR diameter, I plug that back into Eq 1.1 to get a total moving mass for all PR's in the system.  I then divide that total mass by the number of PRs I am using, and this gives me the mass for each PR.  It's that simple!  (On paper anyways. =)  In my example I have 3 12" PRs with an effective diameter of 10" each.  So Dptotal = (10^2 x 3)^0.5 which comes out to be 17.32".  I plug that into the Eq 1.1 and  I'll choose for this example Vb = 5 ft^3 and fB = 19 Hz.  That gives me a mass of 1584 total grams.  I divide that by 3 to get a mass of 528 grams for each PR.  Then  I do an fb test using one of the above methods, and I'm done.  Note: With multiple PRs, it is crucial that each PR have exactly the same mass and that each PR be identical in make.  For more info on Passive Radiators, please visit Lambda Acoustics.  They also carry there own line of PR's from 10" to 15" of varying masses that are reasonably priced.  Adire Audio also carries the PR-15 which displaces a whopping 310 cubic inches or 5.1 L!  More than any commercial PR on the market today, (I believe).

     One of my favorite DIY sites on the web is done by audio enthusiast Brian Steele.  He has loads of information for anyone interested in building their own subwoofer whether it be big or small.   To try out another (somewhat more challenging) method for tuning PR's, please visit Brian Steele's Site.  He explains in detail how to design for a passive radiator speaker system.  Below I have shown how to use his method for Shiva. 

Example of Brian's Method Using Shiva

     This is what I got when I plugged in Shiva's parameters into the formulas for calculating box volume, fb, port length, etc.  This is using Ported.xls from Brain Steele as well.   Many thanks to Brian and all his wonderful efforts.  His site is great and he's updated ported.xls to include a few more graphs.   This Excel Spreadsheet works great for designing boxes and gives you all the details you need to build the perfect size box.  Go to his site again and download it!   Don't forget to accurately measure effective diameter.  If you're unsure of this value it can be measured with a ruler.   Just measure the diameter of the face of the passive and add 1/3 of the surround.   Or if you have the specified Sd, that works best to calculate effective diameter and radius of your passive.
 
        Use the formula:
                                      Radius  =  Square root of (Sd / Pi)
                                      Diameter = 2 x Radius

 
Now we do as he did in his example.  Find the mass we need to add to our passive radiator so that the box resonates at the correct frequency.

        Diameter of port = diameter of passive radiator
        So 12.74" is port diameter and Port radius is 6.37
        Calculate port length
        Port length = 159.6 inches (for QB3 design)
        Find volume occupied by port and convert to meters cubed
        Port volume = (PI * r^2) * length
        Port volume = 3.1415*6.37^2) * 159.6
        Port volume = 20344.6 inches cubed
                           = 11.77 ft cubed
                           = 0.333 meters cubed
        Mass of passive = Port volume * Air Density
                           = 0.333 * 1.21   =  403 grams

So my passive needs to be 403 grams in weight and the box needs to be 3.75 cubic feet.  The box will be tuned at 23.3 Hz.    The passive originally designed by Avatar weighed 438 grams.  This would have presented problems for a lot of alignments, because the PR was already too heavy.  They have since fixed that little problem and redesigned the PR to only have a mass of 285 grams.  The PR's they are shipping out right now have this mass.  So don't be confused.  The machined MDF is only 1/8" instead of 1/4".  Don't worry, it's still incredibly rigid.  Now in the example to get the correct tuning, I just need to add 118 grams of either clay, or nickels, or putty, or whatever you feel works best.  Or even better, use my new PR Mass Kit method for adding mass.  It works great!  I have found that the formulas tend to overshoot the correct tuning by about 10%  So, it's a good idea to start with about 90% of the calculated mass, and add small amounts of mass till the correct fb is reached.   Use the above aforementioned methods for finding fb.