Isobaric subwoofer box design – Advantages and disadvantages
How do isobaric subs work?
An isobaric subwoofer box design sounds like something that only an experienced engineer can grasp. In reality, it’s really rather simple, after you understand how it works. The term isobaric is made by two parts : iso = equal and baric = pressure. Therefore, isobaric stands for “equal pressure” or “constant pressure“. The main idea of the design is that you have 2 identical speakers, and 1 small chamber between them. As the speakers move, they do it at the same time and in the same direction. As a result, the pressure in the small chamber remains constant. We shall see how this affects the parameters, and what are the pros and cons of an isobaric subwoofer box design.
Back to the roots
Before we get to explain how the isobaric design works, we need some basic understanding on Thiele / Small parameters. Even if you don’t have this know-how, you can still understand the conclusion. However, if you want to dig deeper into the subject, you need to be familiar with the T/S parameters and how their values are affected by the isobaric subwoofer box design.
If you want to refresh your memory, check out this article :
I will try to clarify things along the way, if it get’s too confusing. Anyway, the isobaric setup implies using 2 speakers. First of all, let’s see which parameters change when using 2 speakers in a standard configuration. Then, we can move to the isobaric configuration.
Standard dual speaker configuration
When you plan to use 2 identical speakers in the same enclosure, some parameters change, and most notably, some retain their original value. Depending on how you wire the speakers, in series or in parallel, some parameters change in different ways.
Parameters that change when adding another speaker in series :
- Sd doubles (cone surface area).
- Re doubles (the DC resistance and the impedance as a result).
- Vas doubles (the equivalent compliance in liters. This translates in a bigger box).
- Pe doubles (the power limit).
- Le doubles (the inductance of the voice coil).
Parameters that change when adding another speaker in parallel :
- Sd doubles (cone surface area).
- Re halves (the DC resistance and the impedance as a result).
- Vas doubles (the equivalent compliance in liters).
- Pe doubles (the power limit).
- Le halves(the inductance of the voice coil).
- +6 dB more efficiency.
Judging by the information above, we can draw several conclusions. If your amplifier is up to the task (lower impedance loads), wiring in parallel is the obvious choice, as we get an extra boost in efficiency. The rest of the parameters are pretty much common sense : doubling the cone area, more power handling (2 speakers … duh), and an enclosure twice as large (2x Vas).
Parameters that retain their original value
When judging a speaker by its parameters, the first thing you look at is at the Fs (resonant frequency), Qts (total damping) and Vas. We already know that Vas doubles its value when adding a secondary speaker, but what about the resonant frequency and Qts?
How to design loudspeakers - video courses
Fs and Qts do not change their value regardless how many (identical) speakers you add. It’s easy to clarify. The resonant frequency depends on the driver’s moving mass and compliance. As a result, halving or doubling the impedance will not a affect Fs. On the other hand, the Q value is dependent on the shape of the impedance curve near resonance. While adding another speaker will increase or decrease the magnitude of the impedance curve, the shape will remain the same. In conclusion, Qts will remain unchanged.
Isobaric subwoofer box design
In the isobaric configuration, only one speaker is radiating sound. The other one is coupled to the first one by a small sealed chamber. This is the chamber where the pressure remains constant, as the speakers move in the same direction, at the same time. The main advantage for doing this setup is that you need only half the volume, compared to only 1 speaker.
When you wire the 2 speakers together, you have the same 2 choices : series or parallel. The most popular choice is parallel, so we are going to focus only on that. Parameters that change :
- Vas is halved.
- No is reduced by -3 dB (efficiency).
- Re is halved.
- Le is halved.
- +3 db efficiency for wiring in parallel.
While the efficiency is down -3 dB, we gain an additional +3 dB from wiring in parallel. Just 3, not 6, because only 1 speaker is radiating sound. When wiring the speaker in parallel the isobaric subwoofer box design has no efficiency loss or gain.
Why is Vas halved?
The answer to this question lies in the formula for Vas :
Vas = 1.4 * 105 *Sd2 * Cms
In conclusion, altering the cone area of the driver (Sd) or the compliance (Cms), will result in a different Vas. Even though there are 2 speakers, only one is contributing to sound radiation, so the piston size is the same. This means we need to look at the compliance (Cms). Because the 2 speakers are interconnected by the sealed tunnel between them, their suspension systems are coupled. As a result, combining the 2 suspensions, makes for a twice as rigid speaker. In other words, half the compliance. Halving the compliance will directly result in halving the Vas.
Does the resonant frequency (Fs) remain the same?
In short, yes it does. But the compliance is half the original value, surely this means that the resonant frequency has changed. While your observation is correct, you must see the whole picture to understand why the Fs remains unchanged. Fs is dependent on the moving mass and the compliance :
Fs = 0.5π * √(1/(Cms * Mms))
We already know that compliance is half the original value. The small sealed tunnel between the speakers is joining the drivers into one standalone system. As a result, we need to add their moving masses together. So you can see that the product : (Cms * Mms) becomes (1/2 * Cms * 2 * Mms). Which is exactly the same thing. In conclusion, the resonant frequency doesn’t change.
The compound isobaric design is not very popular these days. It was widely spread several decades ago, when speakers used to have a huge Vas value. In the present, speakers are more optimized and many don’t require big enclosures. However, some companies (like Bose) use the isobaric subwoofer box design technique, for a small footprint but big on sound. The advantages and disadvantages are few and straightforward :
- Advantages :
- Reduces the box volume requirements to half.
- No efficiency loss when the speakers are wired in parallel.
- Disadvantages :
- The price paid for an extra woofer.
- Increased difficulty in building the box (not so much for the push-pull with mounting on the same baffle).
- Amplifier needs to handle low impedance loads for wiring in parallel.
- Speaker Building 201: A Comprehensive Course in Speaker Design by Ray Alden (Audio Amateur Pubns, 2004).
- Image source : link.
There are several error in this write up. First of all, it is a misconception that the pressure in the chamber between the drivers in an isobaric alignment is constant. It is not. If it were the front driver would move as if in free air, not a box with twice the volume of the rear chamber. In fact, the pressure in chamber between the drivers varies as the pressure in a box twice the rear volume would vary which is why the front driver moves as if it were in the larger box. Additionally, there seems to be confusion between voltage sensitivity, i.e. the SPL radiated for a given applied voltage, and efficiency. For a dual woofer configuration in series there is no change in voltage sensitivity. For a parallel configuration voltage sensitivity increases by 6dB. However, in both cases the efficiency (acoustic power out)/(electrical power in) increases by 3 dB. That is, for a given power input the acoustic output is 3dB greater than for a single woofer, series or parallel. For the isobaric system the same follows. In a parallel configuration there is no change in voltage sensitivity: same applied voltage, same radiated SPL. For a series configuration, same applied voltage, 6dB lower radiated SPL. In both cases for a given power input the SPL output is 3dB less, or efficiency decreases 3dB.
I don’t know from you are getting this information, but from what I studied, the pressure between the 2 cones is essentially constant. That’s the whole point. It couples the 2 cones together. By doing so, their suspension systems are coupled and you can consider the whole system like a single driver with a suspension twice as stiff. In conclusion, Cms is halved, therefore Vas is halved. Since Vas is half the value, the enclosure volume requirements are halved.
Si haces isobarico el arreglo pero ajustas fs de la bocina trasera con un port para hacerlo resonar y aumentar cierta frecuencia de la bocina con el cajón, la eficiencia en esa frecuencia aumenta 3db que combinándola con la frecuencia de la bocina frontal te da un aumento en las frecuencias bajas, esto probablemente convierta el arreglo en una doble cavidad acoplada, la cuál sería útil como subwoofer siempre y cuando no supere los 80 Hz el LPF, lo demás están en lo correcto a excepción de los errores de typo en las formulas
This has confused me..
The article says “When wiring the speaker in parallel the isobaric subwoofer box design has no efficiency loss or gain.”
So for arguments sake, if I have a 3 way speaker with 1 x 8ohm woofer at 90db/1m sensitivity- and I decide on an isobaric w/2 woofers, (obviously drawing more power and altered cab and crossover).. will the output be the same ?
Yes, the output will be the same. Considering that the amplifier is stable at 4 ohm loads, everything will be as before, except the enclosure is half the size.
John K. It is called “iso” “baric” … equal pressure. Of all things, why the hell would try to argue that they don’t have an equal pressure in the chamber? Absurd!
I have performed a mathematical analysis of the system which you can obtain here: http://musicanddesign.com/files/Isobaric_System_Development.zip or by viewing my web page, http://musicanddesign.com/Isobaric.html. The analysis was originally done to show how isobaric systems effect distortion, but it addresses the isobaric coupling. (There are a couple of typos in the paper where I refer to Eqs 2 & 4 in stead of 3 & 4, and Eqs 2 & 3 in stead of 1 & 3.)
Here is a simple way to look at the coupling of the drivers. For a single driver in a box with volume V what does the pressure in the box do? Obviously it increases as the driver moves back and decreases as the driver moves forward. The variation in pressure generates a force on the back side of the driver’s cone. That force is the only force on the driver which is different from free air operation. It is the force responsible for the change from the free air parameters, Fs, Qts, to the in box parameters, Fb and Qtb.
Now consider the front driver of the isobaric system with rear box volume V/2. As before the motion of that driver is determined by the forces acting on it. If the front driver is to behave as if it were in a box with volume V, then the forces acting on it must be the same . Again, the only force acting on the driver that is different than when in free air is that generated by the pressure in the (isobaric) chamber. It follows that the pressure in the isobaric chamber must vary in approximately the same way, and with the same approximate magnitude as the pressure in the box when a single driver is mounted in the box with volume V.
A similar argument can be applied tot he rear driver. Since the box volume is V/2 the pressure variation in the box, hence the force on the rear driver , will be twice that which it would be in a box of volume V. But the pressure in the isobaric chamber will again be equal to that which would occur for a driver in a box of volume V. Since the pressure forces on front and rear act in opposite directions, the net pressure force on the rear driver is thus that which it would experience if mounted in a box of volume V.
The misconception that the pressure is constant comes from making the simplifying assumption in the analysis that both drivers move identically with the same amplitude and phase. See the discussion after Eq 7, page 2, of the analysis. In reality, the front and rear drivers do not (can not) move exactly in unison or with the same amplitude, and the pressure in the isobaric chamber is not constant. The strength of the coupling is a function of the isobaric volume and there are always amplitude differences in driver motion. In fact, the front driver must always have somewhat greater excursion than the rear.
Hope this clears things up.
Very impressive article, John. Nice of you to share it. But remember that not all of us are experienced engineers, and simplifying things is not always a bad approach. In fact, in engineering there is a well known statement of “good enough”, because you can’t get everything perfect. If I move my speakers to another room, I’m not going to panic that Vas has changed because the air has different humidity/temperature, and my system is now misaligned. We accept that there are some variables we cannot control, and we simplify for convenience. People will have an easier time digesting information when it’s presented in a simple fashion. It’s like looking on a spec sheet of a speaker, and seeing that the impedance is 4 ohms (not an impedance vs frequency graph). And for most of us, that’s “good enough” ;).
John, please update the Soundeasy design guide to 4th edition; not 4rd edition.
Doesn’t the fact that both speakers create pressure in a dual enclosed 1/2 type design?
I mean, a single speaker in that enclosure has a maximum force and attack to either create pressure when the cone is retracting into the box or decreasing pressure when extending out of that box, however, when a 2nd speaker is added to it, even facing the air, that force and attack is doubled in strength so, you now have the mechanical power of two driven coils creating that pressure in the sealed box of the first driver and in the opposite motion, pushing on the free air outside the box that is also creating the decreasing pressure inside the chamber at the same force of both speakers??
The only other variable is the second suspension creating a low/high between the two cones that would result in slight delay as the pressure compresses and decompresses for a second time.
Or am I out of my mind.
Call me wind because I am aboesutlly blown away.
you are both totally forgetting that the humidity of the axiom ratio is doubled as you expel the gumshion response of the twin co-engrasion dynamics thereby rotating the residual gravity perpendicular to its directional mandates which greatly increases its reciprocal osmodic pressure relief!!!so on the basis of that you must continue expel the frequency shollops to a constant degree otherwise you’ll increase the gronyiwoops profoundly for gods sake!!
Can’t believe I missed this little detail. Now this is embarrassing … 🙂
Gronyiwoops are impedance stable, however. So the flabergasm gained by the doubling of the humididty of the axiom ratio is offset by the gumshion response, as long as said response is linear. Doesn’t everyone know that?!?
Pulled the front speaker out of an Orange OBC212 cabinet and noted three 1/4″ holes on the backside of the cone beneath the dust cap. Assuming it was to cool the voice coil?
Anybody know the origin of this design? I built several from the dimensions, the 2″ front baffle had a slot, the sides were cut at 45 degree angles. The resonant frequency was 110Hz (A2) the air movement out of the slot would blow out a lighter @ 12ft.
Don’t know exactly what you are asking, but the small holes you are talking about, are indeed for cooling the voice coil.
Does wiring 2 speakers in series reverse one’s polarity?
No, it doesn’t.
I am about to use the push pull arrangement to smooth out the peak above resonance , which I believe is caused by too small a box on some car audio woofers .. I also plan to wire them in series as I am using them with a solid state home amplifier and they are 4 ohm speakers .. I am not worried about the loss in efficiency as both pairs are in a small bedroom where i do my listening.. am i right to assume that car woofer boxes are to small in most cases
Yes, car woofer boxes are small because of space issues. Also, a small box yields that bump in the response you talk about. This is good for commercial reasons, because most people interpret that as more bass, not as loss of linearity.
Thanks for your fast response.. I have another issue .. I am without resources and want to speed up the process by facing them without as spacer between the surrounds which will cause the surrounds to touch .. they are rubber at least .. foam would probably destruct .. i cant put one behind the baffles as they are already built boxes.. has anyone had success this way? I probably need a spacer but …
You definitely need a spacer. That fact that the surrounds touch each other, will affect the impedance chart of the driver, and it will sound different. Furthermore, over time, damage can occur to the speakers as they are rubbing against one-another. Another reason why this is a bad idea, it’s because you cannot guarantee a perfect seal without something in between the 2 speakers.
Thought you would say that …. I was going to say “why dont they sell this on ebay”. as a joke . so I looked it up … THEY DO whow what a world huh? isobaric spacers on ebay in multiple sizes
Leedh subwoofer is a “simulated infinite load” with two 38 cm (outside) and two 23 cm drivers (inside).
The internal drivers needs x15 more power than the outside ones to make the pressure work. In this case the pressure between the coupled drivers is actually constant.
I put two woofers in a clamshell setup in an h frame, and the output increased by 3db. Does this make sense? Or my measurement was wrong?
I don’t know what you mean by H frame. Aren’t the woofers enclosed in a box?
No, the box is open on both ends (front and back), the woofers are mounted in the middle.
Well, there’s your answer. Lots of unpredictable stuff happen in an open design.
The setup is like this: http://www.musicanddesign.com/u_frame.html
I have 2 8″ DVC 4 ohm subs. MB Quart discuss to be exact. If I parallel the voice coils on each sub to drop the ohm load and then run each to the amp, one normal, one reverse polarity, will it change my ohm load from 2 ohms to 4 ohms?
If you parallel the coils on each sub, you will have two 2 Ohm subs.
If you wire them individually to the same amp channel, you are basically wiring them in parallel and dropping the impedance to 1 Ohm.
If you have a 2 channel amp and wire each sub to its own separate channel then you have each sub at 2 Ohms.
If you wire one in reverse polarity make sure they are set in push pull configuration.
No it will still be 2 ohms as the coils are still in parallel. The only thing that does is reverses the direction the one woofer will travel compared to the other. And just a note you only want to do that in an isobaric setup or, when you have two opposing subwoofers in a room.
Wow! So much misinformation here I won’t even go into that. Just know that I’ve been designing, building, and testing speaker cabinets for over 40 years. I have built almost every configuration you can dream of, multiple times, Home, Auto, Night Club, etc… Just believe me when I tell you isobaric is great. Anytime you have the opportunity to build an isobaric enclosure, go ahead. You wont regret it. And yes, going isobaric will allow you to use a smaller enclosure, but it does not demand it. Feel free to add another driver on the front of your existing enclosure and try it for yourself. Enjoy
One comment. . even though everybody is saying that sensitivity will increase but does it mean that it will increase pressure cause the cone diameter stays as is. So the sensitivity stays the same but in parallel the efficiency rises but does it double the power handling. I dont believe it. Thanks for great article.
In a perfect world where the amplifier can handle half the impedance load, and deliver twice the power at that load, you basically have the same pressure as one speaker but with half the box size. There is no increase in sound pressure, only reduction of box size.
I am looking at using two 16 Ohm Kef low frequency drive units in a project and have found the above to be very helpful. would I be correct in assuming that in Isobarik configuration the impedance of the combined Isobarik drive units will change to 8 Ohm, and that therefore the theoretical crossover design only needs to account for one 8 Ohm base drive unit ?
Yes, you are correct
go electronic crossovers and one amp channel per woofer.
Been running isobraric – clamshell configuration in car audio for 20+ years and the only thing that’s different from making a regular box is cutting a spacer ring for the face to face mounting, plus there are some complications when your material that your mounting to is 1/4” aluminum. I ended up using long bolts that run through the top speaker, 3/4” spacer, the bottom speaker and then through the metal. Using double locking nuts has proven to be best.
A special note: there has to be some type of access to the back side of the speakers when mounting to tighten them properly. I have tried numerous screw configurations that have the bottom speaker mounted using 4 of the 8 holes with sheet metal screws and then running 4 long screws through the entire stack and 4 short screws that just run into the spacer. The screws always seem to come loose on the metal and it’s difficult to get everything lined up perfect so there could be some movement after time that causes the tension to relax.
On my system, if I disconnect even 1 speaker from the amp it reduces the sound output by a huge amount. So there is a definite increase in output and the depth of the bass is improved. All technical aspects aside, and no real world testing results being done other than a simple RTA, there is a gain in output that enables the lower frequencies to be magnified by a significant amount and the RTA shows it. I also want to add that the effect works even when the drivers are not exactly matched. Infact I’ve used 4 different drivers and heard no real change in overall sound. I use all 4 ohm 12” drivers and I used some of the cheapest drivers at the time. In 2001 Fry’s sold 12 Fusion subwoofers for $20 each and I ran a 1600 watt RMS amp with a 1 ohm load for 12 years and never an issue with my amp or drivers, I sold all 4 drivers for the same $80 I bought them for. Replaced them with 4 different drivers and have been revolving new drivers as I repair them. They all take their turn as they are tested before selling. I have a few ultra cheap coustic 12” paper cone subs with a 3” torn hole repaired on 1 driver that always stay in the system unless I have 4 repaired speakers that need testing. The other 2 right now are an old MTX and a common kicker, total cost for sub and box is $30 since I use my spare wheel well for the box. Lined with sound deadener, 2 ports 3” x 4” x 14” long made of sheet metal and deadened. There’s enough bass to get pulled over in California, and that’s playing regular rock music like van Halen, rap makes the entire car vibrate and sets off car alarms.
There was minimal technical studying required to achieve this, most time was spent figuring how to cover the opening and attach it to the car. Had a center divider mounted across the center originally but cut holes in it to allow air to cross over but still have the strength to keep the metal from moving when all 4 speakers are moving the plate will flex an inch, 4 screws across the center and it’s rock solid. I might not be setting records but $ per decibel ratio is off the charts. I’m an old fart and when I tell young installers what I’ve done with zero time spent working with box design software and using a ”clamshell” configuration, they think I’m just another looney old guy who knows nothing and has some crap tossed together using $30 worth of repaired missmatched drivers. Untill I turn it on and open the trunk and my trunk looks empty with just 2 subs mounted with magnets up, then the bass hits and their giggles and uninterested eye rolls change to jaw dropping and suddenly their necks start stretching as they look around for something that isn’t there. Then when it’s turned down there’s a million questions and no more treating me like I’m the local old crazy guy telling stories of days gone by.
Entire cost for system under $200 with indash DVD and NAVI, cost for competition system that won a 2nd place trophy (biased judges couldn’t allow me to beat their own installs but had to give me something knowing i deserved to win) = $6000 ($200 just in connectors and wires to make custom RCA amp connections) hundreds of hours tweaking, studying, making changes, and shopping for stuff. I think my current system has a better sound and goes as loud, no HO alt, no $2000 head unit and changer, no dual mono ⅓ octive EQs, line driver, 2 way 4 channel crossover, cap or 2nd battery. Now just 2 amps instead of 6, with the same quality installation just no room lost to components + using 2 more subs than before. I was running 2 of Rockford’s best subs in a custom professionally made box that lacked everything soundwise but took up my entire hatchback to do it!
Hey! Quick question. I have a pioneer GM-D8601 class D mono 1600 watts amp. Can I run 2 pioneer TSW126M 12″ on it?
Yes you can. Make sure you wire them in parallel.
Perfect explanation about the Isobaric subwoofer box design. I really appreciate your efforts. Thanks
I had to return to see if anything has changed here. After reading through it once again, I see that there are several points made by others that I have always considered to be true. The back speaker is definitely doing more work at the initial start of movement simply because air compresses. The pulling of the front speaker between the cones is not like they are physically linked as one unit no matter how many times you say it. The air will need to be slightly changed in density to create enough force to actually move the cone due to its suspension. Albeit they are both moving at the same time the air pressure on the front drivers cone is acting as if it’s a free air type of enclosure where the front and rear are seeing less resistance to movement than a sealed or ported box. But things get complicated once the rear driver moves. It’s cone has to work harder to start moving to overcome the dampening effect that happens as it travel outward. That effect will increase as it travels and air pressure changes (sealed rear box) that’s when the front driver will start doing more work trying to pull the rear speakers further and creating an even higher change in pressure that a single driver could not do.
In a vented rear box, the front driver and rear driver difference of work is much more even, the initial start if the rear cone sees much less resistance and can react faster, the front cone will not be pulling as travel increases but both are restricted only by their own design, spider(s) and surround material will play the biggest roll on the excursion along with coil length and magnetic flux area ultimately ending the push or pull of each driver. Conceivably the rear driver should be stronger in both ported and sealed but sealed requires a stronger rear driver, the front driver should have more travel ability since the space between them compresses, the cone should be able to travel passed the point where the rear driver stops until it reaches a point where the air pressure stops it’s movement and the rear speaker starts to pull it back.
I believe optimal sound can be achieved when using these basic ideas. Both drivers being exactly the same us not the only way to do this, but it would take some research to narrow down possible matches that could yield better results, of course only real world controlled testing will reveal the optimum matches.
I have found little difference when using mismatched subs, the one thing that remains true is if 1 driver out of 4 is disconnected there is a huge loss in overall output. It makes no difference which driver, front or back still reduces output dramatically. All 4x 4 ohm drivers are connected in parallel to 1 mono amplifier rated at 1 ohm.
Perfect explanation about the Isobaric subwoofer box design. I really appreciate your efforts. Thanks
I really enjoy reading your articles so thanks for that. Having completed 3 of your courses and 3 speaker designs (bookshelf, larger 8′, smaller bookshelf, 12″ sub), I have decided to step up my game: dual woofer/single tweeter in floor standing speaker cabinet – high end focus. Questions/thoughts:
– anything different about the design approach: using your course basics, WinISD? I note here that you list the differences when wired in parallel including a 2x Vas. Is this Vas what is plugged into the parameters for box tuning?
– I have seen some of you rother floor standing designs and you seem to have the woofers in a separate sealed cabinet from the other driver? Are there any guidelines?
– lastly, crossover design. Your thoughts would be great.
I know I am asking a lot here but you have offered sound, practical advice in the past.
1) If you use WinISD you simply select 2 speakers. The excel spreadsheet doesn’t have this option so the workaround is to double the Vas value.
2) If your design is a 2-way with 2 woofers and a tweeter you don’t need to separate anything. If it’s a 3-way with a woofer midrange and tweeter, than yes, you need to separate the midrange from the woofer.
3) There is no advice to be given for the crossover. Each crossover is unique, so, just follow the steps in the crossover design course and you will get there.
As a tip, make sure you use some form of damping material on the inside. Since they are tall speakers, there is a high chance that nasty standing waves will form inside and you need to attenuate them. If it’s a bass reflex enclosure, line the walls with some high density stuff. It it’s a sealed enclosure just fill the whole box with poly fill or similar.
Hi, that’s an impressive discussion. I wonder if it is possible to take advantages from 4 woofers in isobaric parallel couples connected in series.
Hi Marius, I just have one (fairly detailed) question! Let’s say I have a midwoofer with a sensitivity of 85dB, and a nominal impedance of 8 ohms. Further in this scenario, placing two of these drivers wired in parallel into a 10L sealed cabinet yields an F3 of 70hz and, I believe, a sensitivity of 91dB due to a doubling of cone area and halving of impedance. If I were to build a 5L isobaric box using four of these drivers, with the inside and outside pair wired in parallel and then wired together in series, am I correct in assuming that the new and improved 5L isobaric box would yield the same F3 as the 10L box? More importantly to me, would I be correct in saying that the 5L isobaric box would then have an efficiency of 88dB? In my mind this makes sense, because the cone area is doubled and the impedance is constant as compared to the original driver with its 85dB efficiency and 8 ohm nominal impedance. The reason I am asking is because I’m looking to build a three-way semi-compact desktop speaker that uses Peerless 4” midwoofers for the low end, which have an efficiency of around 85dB in the region in which they will be playing in my system. My issue is that my actual midrange has an efficiency of around 89dB, and while padding it down with an L-pad would be acceptable, I would much rather increase the woofers’ efficiency to be closer to that of the midrange. The main issue I’ve come up with is size, which increases drastically when adding another woofer. I see isobaric loading as the best option to remedy my enclosure size issue while increasing efficiency just enough, but I’m not solid enough in my understanding of efficiency yet to be certain that it would really work the way I want it to. Anyways, that’s my issue. I want to thank you for your contribution to this community, and also for your incredibly helpful Udemy courses which were a wonderful asset to me on the issue of measurement, box design and crossover design. I really appreciate the work you do. Thanks!
Hello! Your first assumption is correct. Doubling cone area will yield +6 dB, if the speakers receive the same amount of power. And they do, since impedance is halved. However, in the 2nd scenario (isobaric speakers in parallel and wired in series between them) it yields a total impedance of 8 ohms and each speaker will receive 1/4 of power. So, for example if the speaker is rated at 85 dB at 1 W, it will radiate 82 dB at 1/2W and 79 dB at 1/4W. Since only 2 of these speakers radiate sound to the exterior, we add +6 db to account for the additional speaker. So, 79 + 6 = 85 dB. As a result, you don’t get an efficiency boost, unless you wire everything in parallel which will net 2 Ohms. This might be too low, however, the crossover should raise the impedance anyway (since you need an inductor there for sure). Maybe it will work out.
Ah! Okay. That makes a little more sense. Thank you very much for your swift reply! I think I should probably stick to a single woofer then. The details about splitting power are very helpful to visualize this scenario.