Anyone know the formula for finding the F3 of a box with given Fb and Vb ? I've found several formulas for finding F3 of a xx order vented enclosure but I need it for one with a variable tuning frequency and volume.
A) Try downloading one of the several freeware programs, such as WinISD.
www.linearteam.dk
B) Formula for F3 in a vented box with optimum tuning:
[Square root of (Vas/Vb)] times Fs.
www.linearteam.dk
B) Formula for F3 in a vented box with optimum tuning:
[Square root of (Vas/Vb)] times Fs.
The reason I need the formula is because I'm writing my own software to do it ... I have several pieces Enclosure Design Software but I'm making my own.
the formulas I keep comming across are:
F3 = Qts^-1.4 x 0.26 x Fs
F3 = ((Vas/Vb)^1/2)Fs
F3 = Fs(Vas/Vb)^0.44
None of these even mention Fb which plays a major role in F3.
the formulas I keep comming across are:
F3 = Qts^-1.4 x 0.26 x Fs
F3 = ((Vas/Vb)^1/2)Fs
F3 = Fs(Vas/Vb)^0.44
None of these even mention Fb which plays a major role in F3.
Brian Steele has a wonderful page with formulas developed by Bill McFadden for the HP48 series of calculators. I extended Bill's work to 4th order bandpass enclosures, using his notation:
Go to www.diysubwoofers.org
for ported speakers go to www.diysubwoofers.org/prt
Look for frequency response equations and power response equations. Many software packages such as Boxplot, Winspeakers and WinISD beta use simple equations such as these to model enclosures.
Hint: sealed speakers can be modeled with the vented box equations by setting Fb=0
Unibox, Bassbox and other software, like Subsim (written by Isaac who frequents this board) use a slightly more complex model, but its results are really not much different from the simple model.
The simplest equations for Vb, Fb and F3 are:
Vb=20*Vas*Qts^3.3
Fb=0.42Qts^-0.96
F3=0.28*Qts^-1.4
These three equations are approximate for speakers with average losses. They are a curve fit through the data and are accurate to about 5-10% or so - which is more accurate than T/S parameters are usually measured to.
If you want a more accurate F3, you need to solve an equation by iteration. At the bottom of page:
http://www.diysubwoofers.org/prt/ported2.htm
There is the equation:
dBmag = 10*LOG(Fn4^2/((Fn4-C*Fn2+A)^2+Fn2*(D*Fn2-B)^2))
You need to plug in trial values of F (defined on the page referenced) until this equation makes dBmag = -3
Have fun!
😉
Go to www.diysubwoofers.org
for ported speakers go to www.diysubwoofers.org/prt
Look for frequency response equations and power response equations. Many software packages such as Boxplot, Winspeakers and WinISD beta use simple equations such as these to model enclosures.
Hint: sealed speakers can be modeled with the vented box equations by setting Fb=0
Unibox, Bassbox and other software, like Subsim (written by Isaac who frequents this board) use a slightly more complex model, but its results are really not much different from the simple model.
The simplest equations for Vb, Fb and F3 are:
Vb=20*Vas*Qts^3.3
Fb=0.42Qts^-0.96
F3=0.28*Qts^-1.4
These three equations are approximate for speakers with average losses. They are a curve fit through the data and are accurate to about 5-10% or so - which is more accurate than T/S parameters are usually measured to.
If you want a more accurate F3, you need to solve an equation by iteration. At the bottom of page:
http://www.diysubwoofers.org/prt/ported2.htm
There is the equation:
dBmag = 10*LOG(Fn4^2/((Fn4-C*Fn2+A)^2+Fn2*(D*Fn2-B)^2))
You need to plug in trial values of F (defined on the page referenced) until this equation makes dBmag = -3
Have fun!
😉
Using the "simplest" formulas you posted for a RFP-1415(Vas:405.8liters , Qts:0.36 , Fs:21Hz) the Vb=278.70liters(9.8cu.ft) , Fb=1.11Hz and F3=1.17Hz. That just doesn't seem right to me, beside the fact the I dont want an equation to tell me where I should tune my box and/or what the volume should be. What I am needing is the formula for finding F3 where Vb and Fb are variables in the equation. The equation you posted for bdmag will be helpful in plotting the frequency responce but will be too much work for finding F3. Surely someone on here knows the formula I need.
Fluke:
Do you have Thiele's paper and Small's paper, (separate papers) on vented boxes?
I can scan and send them to you if you don't have them.
Think that will help? I don't know if the formula is there or not, but most things related to vented boxes seem to come down to those papers.
Do you have Thiele's paper and Small's paper, (separate papers) on vented boxes?
I can scan and send them to you if you don't have them.
Think that will help? I don't know if the formula is there or not, but most things related to vented boxes seem to come down to those papers.
kelticwizard no I dont have em ... prolly make for some good reading. You can send em to Fluke87@pcpostal.com as long as they're not over 500kb. Thanx in advance.
FWIW, Bill's formulas are those of the Margolis-Small HP 69,97, and 41C calculator program with the exception that he uses Fs in lieu of Fsb (driver Fs with the added air mass in the box tacked on) that I used for so long before switching to BoxPlot (which uses them), and with some considerations is accurate enough if a ~golden ratio cab is used. Once it becomes long enough in one dimension to have obvious 1/4WL pipe action then their accuracy goes away with increasing aspect ratio. MK's MLTQWT spreadsheet does a good job with these.
Anyway, for Vb specified:
alpha (a) = Vas/Vb
F3 = Fs*a^0.44
Fb = Fs*a^0.31
So for your example, F3 = ~24.78hz/Fb = ~23.60Hz.
For Vb and Fb specified:
F3 = Fb*a^0.13
HTH,
GM
Using the "simplest" formulas you posted for a RFP-1415(Vas:405.8liters , Qts:0.36 , Fs:21Hz) the Vb=278.70liters(9.8cu.ft) , Fb=1.11Hz and F3=1.17Hz. That just doesn't seem right to me, beside the fact the I dont want an equation to tell me where I should tune my box and/or what the volume should be. What I am needing is the formula for finding F3 where Vb and Fb are variables in the equation. The equation you posted for bdmag will be helpful in plotting the frequency responce but will be too much work for finding F3. Surely someone on here knows the formula I need.
------------------------------------
Correction:
The simplest formulas are:
Vb=20*Vas*Qts^3.3
Fb=Fs*0.42*Qts^-0.96
F3=Fs*0.28*Qts^-1.4
These are from Small-Margolis 1981 JAES, as GM says. These equations approximate a maximally flat alignment. Typically this offers the best you can get WRT F3 for a given Box size.
The equation for F3 given Vb and Fb is transcendental. You cannot get a simple closed form solution. Any programmer worth his salt would know how to find a root. You can use Newton's method or the bisection method.
The equations for plotting frequency response will allow you to enter any Vb, Fb and plot the result. You can manually find F3 on this curve, or solve the root as I stated earlier.
Sorry for trying to help. Since you seem to know what you need more than I do, help yourself. Do a web search. 🙂
------------------------------------
Correction:
The simplest formulas are:
Vb=20*Vas*Qts^3.3
Fb=Fs*0.42*Qts^-0.96
F3=Fs*0.28*Qts^-1.4
These are from Small-Margolis 1981 JAES, as GM says. These equations approximate a maximally flat alignment. Typically this offers the best you can get WRT F3 for a given Box size.
The equation for F3 given Vb and Fb is transcendental. You cannot get a simple closed form solution. Any programmer worth his salt would know how to find a root. You can use Newton's method or the bisection method.
The equations for plotting frequency response will allow you to enter any Vb, Fb and plot the result. You can manually find F3 on this curve, or solve the root as I stated earlier.
Sorry for trying to help. Since you seem to know what you need more than I do, help yourself. Do a web search. 🙂
Not being a programmer, you lost me. The formula I listed from the M-S paper yields the plotted F3 in BoxPlot so it seems reasonable to me that it's 'close enough' for getting a starting point, though for sure plotting a FR makes more sense to me. Or did I miss your point?
GM
This discussion is beyond my technical understanding. About the only thing I can offer that might be of help is that I remember that David Weems gave a formula in his book, Designing, Building and Testing Loudspeakers that gave the output for any given frequency of a ported box. It has been years, but I think I remember Fb as being one of the variables.
I wonder if that is the HP formula that Ron was talking about.
I no longer have Weems' book. I'll check to see if I have the Journal Of The Audio Engineering Society article that Ron mentioned.
My understanding is that Qts does not matter when determining F3. Therefore, I would just eliminate Qts from that equation. I would hazard a guess that instead of solving for the output at a given frequency, just put in -3 as the answer and work backward to the frequency. Rearrange the equation, so to speak.
Well, it might be worth a shot. I work in a nontechnical field, so I can't guarantee that it will work.
As for the Thiele and Small papers, they are quite long, I am new to scanning and my experience with the Optical Character Resoultion software that came with this scanner has been dreadful. So much editing, you might just as well retype the whole article. Consequently, I scan in GIF and send it that way, and my experience with this shows that each page averages 125 KB. With only 500 KB available at your end, I would only be able to send 4 pages a day or so. That might take as long as 10 days.
I don't mind sending a few pages a day, but do you have a mailbox with a little more room?
I wonder if that is the HP formula that Ron was talking about.
I no longer have Weems' book. I'll check to see if I have the Journal Of The Audio Engineering Society article that Ron mentioned.
My understanding is that Qts does not matter when determining F3. Therefore, I would just eliminate Qts from that equation. I would hazard a guess that instead of solving for the output at a given frequency, just put in -3 as the answer and work backward to the frequency. Rearrange the equation, so to speak.
Well, it might be worth a shot. I work in a nontechnical field, so I can't guarantee that it will work.
As for the Thiele and Small papers, they are quite long, I am new to scanning and my experience with the Optical Character Resoultion software that came with this scanner has been dreadful. So much editing, you might just as well retype the whole article. Consequently, I scan in GIF and send it that way, and my experience with this shows that each page averages 125 KB. With only 500 KB available at your end, I would only be able to send 4 pages a day or so. That might take as long as 10 days.
I don't mind sending a few pages a day, but do you have a mailbox with a little more room?
I didn't find the equation that I was looking for, but here is a reference to the Journal Of The audio Engineering Society that has the Margokis-Small calculator program. Those repritns cost about 5 bucks each, as I recall.
"Personal Calculator Programs For Approximate Vented-Box and Closed-Box Loudspeaker System Design", G. Margolis and R.H. Small, J. Audio Eng. Society, Vol. 29, No. 6, June 1981, pp. 421-441.
"Personal Calculator Programs For Approximate Vented-Box and Closed-Box Loudspeaker System Design", G. Margolis and R.H. Small, J. Audio Eng. Society, Vol. 29, No. 6, June 1981, pp. 421-441.
kelticwizard, I didn't know you had to scan em ... dont worry about it man I'll find what I'm looking for eventually.
GM, I tried the formula for F3 you posted ... seems acurate at first ... until you tune the box high. but thanx anyway man ... you seemed to get what I'm needing.
Ron E ... I'm sorry you "tried" to help too. I wasn't saying that I need a formula using JUST Vb and Fb ... but one that included them ... seems how when you change either of them your F3 will also change.
I'm ALMOST positive that all of the software ava. doesn't start a loop slighly increasing a var until it finds F3. There has got to be a formula for finding F3 for an enclosure that's not "optimal" or a 4th,6th... order butterworth align.....
GM, I tried the formula for F3 you posted ... seems acurate at first ... until you tune the box high. but thanx anyway man ... you seemed to get what I'm needing.
Ron E ... I'm sorry you "tried" to help too. I wasn't saying that I need a formula using JUST Vb and Fb ... but one that included them ... seems how when you change either of them your F3 will also change.
I'm ALMOST positive that all of the software ava. doesn't start a loop slighly increasing a var until it finds F3. There has got to be a formula for finding F3 for an enclosure that's not "optimal" or a 4th,6th... order butterworth align.....
>GM, I tried the formula for F3 you posted ... seems acurate at first ... until you tune the box high. but thanx anyway man ... you seemed to get what I'm needing.
====
Oh?! Compared to what? It matches BoxPlot up as high as I select, but then it's derived from the simplified math used to create it so it's to be expected. 😉 While it's not accurate enough for the anally retentive, it's fine for a first approximation for comparison purposes or simple designs IMO.
GM
====
Oh?! Compared to what? It matches BoxPlot up as high as I select, but then it's derived from the simplified math used to create it so it's to be expected. 😉 While it's not accurate enough for the anally retentive, it's fine for a first approximation for comparison purposes or simple designs IMO.
GM
Fluke87 said:
Scanning isn't even the issue. It takes me about 20 seconds to scan a page. The scanned page file is 200+ KB.
It's just that I am not going to mess with the Optical Character Recognition software to reduce the file size. The page will print out beautifully in GIF, and that is how I am going to send it. If you want me to send you a few pages a day, I'll be more than happy to. Fact is, I am going to scan both these papers anyway, because other DIYers will no doubt want them. If the recipient wants to mess around with Optical Character Recognition software to reduce file size on his end, that's dandy. On my end, my Optical Character Recognition software and myself don't "mesh". Aside from that, the rest of the scanning experience is entirely satisfactory.
Do you have a bigger mailbox that you would want me to send it to? If you don't want to put the address on the thread, use diyAudio Email service and let me know. I've already scanned some of it, not just for you but for anyone who wants the papers.
kelticwizard, if that's the case you could send em 2 a day if you dont mind.
GM, I wasn't trying to make you mad ... I compared it to BassBox 6 Pro v6.0.15 and Speaker Simulator v1.0.
check it ...
A=Vas/Vb ... A=14.33/5 ... A=2.866
5ft^3 tuned at 30Hz
BassBox says F3 = 32.81
Speaker Simulator says F3 = ~33
F3=30*2.866^0.13 says F3 = 34.40069 .... pretty close
5ft^3 tuned at 85Hz
BassBox says F3 = 60.67
Speaker Simulator says F3 = ~62
F3=85*2.866^0.13 says F3 = 97.468623 ... not near close enuf to call anyone "anally retentive"
I could post screenshots of the programs I used showing these results if needed.
GM, I wasn't trying to make you mad ... I compared it to BassBox 6 Pro v6.0.15 and Speaker Simulator v1.0.
check it ...
A=Vas/Vb ... A=14.33/5 ... A=2.866
5ft^3 tuned at 30Hz
BassBox says F3 = 32.81
Speaker Simulator says F3 = ~33
F3=30*2.866^0.13 says F3 = 34.40069 .... pretty close
5ft^3 tuned at 85Hz
BassBox says F3 = 60.67
Speaker Simulator says F3 = ~62
F3=85*2.866^0.13 says F3 = 97.468623 ... not near close enuf to call anyone "anally retentive"
I could post screenshots of the programs I used showing these results if needed.
I'm not mad, we just had a 'failure to communicate'. 😉 My remarks were based on pushing Fb up as high as I would ever do in a BR. For extreme alignments such as horn compression drivers, I rely on other, more accurate programs that takes the changing air mass/compliance into account, as the original version of this formula does, Fsb instead of Fs. Use it, and the formula is 'accurate enough'. 😉
Have fun,
GM
Have fun,
GM
I took a glimpse at a book* we once used to design a two-way PA speaker about 14 years ago.
The first formula given by Fluke87 (F3 = Qts^-1.4 x 0.26 x Fs) is the one given by Hoge** as an approximation to Small's tuning chart for a QL of 7.
I.e. this one will approximate a 4th order Butterworth response and the remaining values have to be calculated as already stated above by others:
Vb=15 * Vas * Qts^2.87
fb=0.42 * Fs / Qts^0.9
Back then we found the cutoff frequency to be a bit too high and followed the alternate path of determining the desired volume first. This gave an approximate (formula mentioned above as well) F3 of
F3 = Fs * SQRT(Vas/Vb)
The tuning frequency was determined by:
Fb = Fs * (Vas/Vb)^0.32
Volumes larger than the optimal one will give a premature rolloff but better transient response and those smaller than optimum will have a bump in their response and a worse transient behaviour.
The bump can be calculated (dB, approximately) by the following formula:
R=20 * log (2.6 * Qts (Vas/Vb)^0.35)
I can't remember the exact details of the tuning we chose back then, but the sound of the complete boxes was very nice and they are still in use by a bigband who regularly use them for vocals and soloists.
Regards
Charles
*Michael Gaedtke: Parametermessungen an Lautsprecher-Chassis
ISBN 3-7723-7821-8
**W.J.J. Hoge: Switched on Bass, Audio, Vol.60, No8, Aug 1976, p.34
The first formula given by Fluke87 (F3 = Qts^-1.4 x 0.26 x Fs) is the one given by Hoge** as an approximation to Small's tuning chart for a QL of 7.
I.e. this one will approximate a 4th order Butterworth response and the remaining values have to be calculated as already stated above by others:
Vb=15 * Vas * Qts^2.87
fb=0.42 * Fs / Qts^0.9
Back then we found the cutoff frequency to be a bit too high and followed the alternate path of determining the desired volume first. This gave an approximate (formula mentioned above as well) F3 of
F3 = Fs * SQRT(Vas/Vb)
The tuning frequency was determined by:
Fb = Fs * (Vas/Vb)^0.32
Volumes larger than the optimal one will give a premature rolloff but better transient response and those smaller than optimum will have a bump in their response and a worse transient behaviour.
The bump can be calculated (dB, approximately) by the following formula:
R=20 * log (2.6 * Qts (Vas/Vb)^0.35)
I can't remember the exact details of the tuning we chose back then, but the sound of the complete boxes was very nice and they are still in use by a bigband who regularly use them for vocals and soloists.
Regards
Charles
*Michael Gaedtke: Parametermessungen an Lautsprecher-Chassis
ISBN 3-7723-7821-8
**W.J.J. Hoge: Switched on Bass, Audio, Vol.60, No8, Aug 1976, p.34
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