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lowerFE

Ultimate bass from a small speaker - some questions on woofers

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lowerFE    35

Hello fellow bassheads - After going on AVSForum and Data-Bass, I feel like my man card is forever revoked for only having 2 15'' subs. So after hearing scores of voices yelling things like "That's a bathroom setup!" and "My SEOS tweeter's bigger than your sub!", and the last straw was "with subs like that, you might as well stain it pink!". So I stained my sub with red stain, and the plywood actually didn't take the stain well, and the red looked like pink instead (that's actually true...)

 

So realizing I'm clearly not gonna be the manliest guy on the block, I said, F it, I'll pimp another way. I'll be the most wife accepted guy on the block instead. So I'm going to build the highest WAF speaker basshead wives have ever seen - a sound dock. :blink:  

 

But (saying this in the manliest voice possible), it has to be the bassiest sound dock I could possibly build. 

 

Now for the boring technical requirements. So far, the speaker is envisioned as a 14'' x 6'' x 6'' speaker. The plan is to use four approximately 5'' woofers (nope, it isn't missing a 1 in the beginning) in a sealed dual dual opposed configuration. Yes, that 2 duals you see there, a pair of dual opposed woofers.  :D The woofers will have their frames cut off to reduce the size so they can actually fit in the cabinet. I'm aiming for extension flat to 30Hz, and as much <60Hz output as possible. The goal is at least 95dB at 40Hz. Not one, but 2 miniDSPs will be used to EQ the speaker. One for the speaker itself, and one to be used as a 4 band compressor. I'll be using the SMSL SA-98E 2x160W amp to power the 4 woofers. Each woofer will get around 50 watts of power since I don't think the amp can actually put out 160W a channel. 

 

(I can already hear the "stop calling a 5'' driver a woofer!" screams)

 

Now I have a series of questions.

 

how do I pick drivers? My knowledge for speaker design is for small signals, not large signals. What parameters should I be looking for when selecting woofers optimal for small sealed enclosures? What are parameters and designs that would indicate the driver could be low distortion at higher volumes?

 

I will also ask a more specific question that I've been curious about. Generally, a low Fs is desirable for a woofer. You can achieve a low Fs by either increasing mass or increasing compliance. However, when you increase mass, you lose efficiency, which is undesirable, but most subwoofer drivers do this for some reason. What's the advantage of a tight suspension? Is it because a tight suspension would stay more linear at very high excursion levels? However I see increasing compliance to lower Fs done in pretty much all high end drivers of 5-7'', and yet some of those drivers have high excursions and stay clean at those excursion levels. 

 

Why is a very low Qts desirable for vented enclosures and not for a sealed enclosure? A low Qts can signify high motor strength, wouldn't that be desirable for both vented and sealed? It is possibly because the excursion utilization for a given power input would be lower on a very low Qts woofer in a sealed enclosure?

 

Here are some drivers I'm looking at using. Could anyone comment on the driver that is most likely to be optimal for this build?

 

1. SEAS ER15RLY - perfect size, good all around parameters, used in the highly acclaimed Salk SongTowers, but not sure how well suited for bass at high levels

 

https://www.madisoundspeakerstore.com/approx-5-woofers/seas-prestige-er15rly-h1455-5.5-reed-paper-cone-woofer/

 

2. SEAS L16RN-SL - a bit bigger than I'd like, but it is said to be specifically designed for high output sealed use. However it models very poorly (and weird) in a small enclosure. It takes 3-4x more power to reach xmax compared to most 5'' drivers. 

 

https://www.madisoundspeakerstore.com/approx-5-woofers/seas-prestige-l16rn-sl-h1480-5-aluminum-cone-woofer/

 

3. SB Satori MW13P - High quality neo motor, maybe it'll be better for distortion? Expensive though, and the Sd is a bit small. 

 

https://www.madisoundspeakerstore.com/approx-5-woofers/satori-mw13p-8-5-egyptian-papyrus-cone-woofer-8-ohm/

 

Final question: Is it me, or does it seem like modelling programs grossly overestimate the amount of power needed to reach xmax? I did a build of 4 Dayton ND105's in a similar box size, powered by a stereo amp with each channel driving 2 woofers. Simulations showed me I needed 30 watts to reach the 4mm xmax. However, I used a SMSL SA50 amp, which is a tiny class D amp rated at 2x50W. Not only I was able to reach xmax, I came close to reaching the 10mm xmech with only 25 watts per woofer. Since I was running a continuous sine wave, I highly doubt the tiny amp is capable of 2x50W continuous. The power supply ratings say otherwise. So the amp is outputting more like 2x25W continuous, which means I reached ~8mm of excursion with ~10W of power when the simulation says I need 30 watts just to reach 4mm. I see this on another speaker as well, where I bottomed the driver out when modelling shows I shouldn't even reach xmax with the amplifier power I have. 

 

We made it to the end. I hope my attempt at humor was enough to keep you interested in a thread asking about 5'' woofers. :D  Any help with this ladies speaker would be appreciated!

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SME    211

I know this isn't the answer you are looking for, but I can't resist.  My 12" mid-range drivers have more Sd than those 4 x 5" woofers.  Maybe they should be used as tweeters?  :P

 

More seriously, can you be more specific about your goals?  What kind of response shape and extension are you hoping to achieve?  How much total output?  How much amp can you put on it?  You did say in another thread that you will be using DSP, and this increases your flexibility quite a lot.  Ultimately, though, there are trade-offs to be decided before picking a woofer.

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lowerFE    35

I know this isn't the answer you are looking for, but I can't resist.  My 12" mid-range drivers have more Sd than those 4 x 5" woofers.  Maybe they should be used as tweeters?  :P

 

More seriously, can you be more specific about your goals?  What kind of response shape and extension are you hoping to achieve?  How much total output?  How much amp can you put on it?  You did say in another thread that you will be using DSP, and this increases your flexibility quite a lot.  Ultimately, though, there are trade-offs to be decided before picking a woofer.

 

 

I'm improving! The previous speaker only had a single 4'' woofer!

 

I'm aiming for extension flat to 30Hz, and as much <60Hz output as possible. The goal is at least 95dB at 40Hz, 1 meter outdoors. Not one, but 2 miniDSPs will be used to EQ the speaker. One for the speaker itself, and one to be used as a 4 band compressor. I've edited the post with this information. I'll be using the SMSL SA-98E 2x160W amp to power the 4 woofers. Each woofer will get around 50 watts of power since I don't think the amp can actually put out 160W a channel. 

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Contrasseur    17

 

I will also ask a more specific question that I've been curious about. Generally, a low Fs is desirable for a woofer. You can achieve a low Fs by either increasing mass or increasing compliance. However, when you increase mass, you lose efficiency, which is undesirable, but most subwoofer drivers do this for some reason. What's the advantage of a tight suspension? Is it because a tight suspension would stay more linear at very high excursion levels? However I see increasing compliance to lower Fs done in pretty much all high end drivers of 5-7'', and yet some of those drivers have high excursions and stay clean at those excursion levels. 

 

Fs only really has significant meaning in infinite baffle scenarios. Fs is driver free air resonance. When you put it in a sealed box, tapped horn, or ported box, it's not in free air anymore, is it?

 

SYSTEM resonance is what matters when you're predicting the performance of a system. Now lets look at your particular usage case. You're looking at a tiny, tiny box. Assuming it's made of 1/2" plywood, your interior volume (before adding drivers) is 5.3L. This tiny air space isn't very compliant. Compressing a 5L space by 1L takes tremendously more force than compressing a 50L volume by 1L.

 

Your free air resonance (Fs) is determined by compliance and moving mass. So is Fb, but we have to include the box's compliance. The pushing on the cone of the Seas Prestige ER15RLY is equivalent to pushing on a volume of 15L (this is what Vas means- compliance equivalent volume). If you cram 4 of these into 5.3L, each driver has 1.3L of air space behind it. Now if you try to push on the cone of your Seas woofer, you're also compressing this 1.3L volume. See what happens here? Compressing a 1.3L volume by a certain amount takes more than 10 times the force to compress 15L by the same amount. The compliance of the woofer is negligible in this scenario.

 

Let's take a look at moving mass. Lower masses are easier to move, and provide a better impedance match with air, i.e. they have greater efficiency. 

<see attached file #1>

This is a simulation of a T3-19 in a 100L box. You can see the efficiency of the regular woofer (grey line), and if the woofer had a more reasonable moving mass of 400g (black line). The lower moving mass results in greatly improved efficiency overall. Look at the low end though. There's no gain to be had between 40 and 50Hz, and actual improvement to be had below 45Hz. Remember the response curve of these tiny sealed boxes? You have to use EQ to boost the bajeezus out of the low end to get a flat response, more so if you want a desirable, downward-sloping curve. So by the time you're done, you're dumping way more power into the low corner of your system. If your heavier system is 3 times less efficient at 100Hz, a 50% increase in 40Hz efficiency means you're using less power if you're pumping 10x the power into 40Hz as 100Hz.

 

How can we gain efficiency anywhere by adding mass? Because it reduces Fb, pushing the impedance peak lower.

<see attached file #2>

As we just discussed, compliance cannot be changed because it's determined by the tiny box size, so we can only influence Fb by altering mass. Furthermore, have you checked out the Xmax Investigation thread? Ricci's data proves that Xmax is increased at and around Fb. You already know that the lower you go in frequency, the more excursion you need. If you're using a system down to 40Hz, wouldn't it be nice to have an excursion boost at 40Hz where you need it, rather than 60Hz where you won't reach the limits anyways?

 

Distortion also increases below Fb. Look at the distortion charts for every one of Ricci's sealed systems. They all show marginal variation above Fb and all the way down to Fb, but below that, the motor starts fighting the compliance, and distortion increases. Ideally, your Fb will be at the very bottom of the bandwidth.

 

Is this always a good thing? No. Like you saw, you're sacrificing massive efficiency on the top end for marginal gains on the low end. You'll have to do the math to see which alignment has lower power draw over the intended bandwidth (~40-300Hz), with the intended signal spectrum (music, which typically has a downward sloping power spectrum), EQ'ed to the desired frequency response (typically flat, 3db/octave downward slope, or somewhere in between).

 

On the Xmax consideration, your airspace is tiny and your cones are light. If your Fb ends up at 100Hz, you might have to add an impractical amount of mass to get your Fb all the way down to 40Hz. If you can only get your Fb down to 60Hz, you're not gaining any extra excursion where you need it. You'll have to model the different options to see how well it works in your application.

post-4069-0-61784000-1469971131_thumb.png

post-4069-0-85639400-1469971131_thumb.png

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Contrasseur    17

Why is a very low Qts desirable for vented enclosures and not for a sealed enclosure? A low Qts can signify high motor strength, wouldn't that be desirable for both vented and sealed? It is possibly because the excursion utilization for a given power input would be lower on a very low Qts woofer in a sealed enclosure?

Let's look at Qts. Formulas drawn from Wikipedia. It's determined by Qms and Qes. With the exception of some dipole woofers and tweeters, Qes is much lower than Qms, so Qms is negligible for our calculation of Qts. Therefore we only care about Qes.

 

Let's look at Qes. You can see it's (2pi*Fs*Mms)/(Bl^2/Re). Bl^2/Re is motor strength. We already discussed Fs and Mms for your enclosure, so we only care about motor strength right now.

 

Let's look at motor strength. Increasing BL or decreasing Re does the same thing. If you look at 16ohm and 4ohm versions of the same driver, you'll notice they have the same performance because they have the same motor strength. Changing Re means we also have to change voltage to get 1 watt comparisons, so let's only change BL to see the effect of changing motor strength.

 

Let's look at BL. Taking the same T3-19 in a 100L enclosure, if we drop BL from 19.1 to 12.1, motor strength is cut by 60%. You can see from the impedance chart that Fb hasn't changed, so none of our previous discussions on Fb apply.

 

Above Fb, sensitivity is decreased. No surprise there. At Fb, sensitivity is increased. Isn't this a good thing? Did our speaker become louder with a weaker motor? But when you look at the impedance chart you'll see the impedance has been reduced. The higher BL is creating more back-emf, and reducing the power draw. We need to know if the boost in sensitivity is bigger than the increase in power draw. We have to look at efficiency to see the real picture. As you can see, efficiency for the higher BL system is better at every frequency.

 

Why would anyone recommend a high Q system for sealed systems then? Well look at the frequency responses. With a high Q, you can get a much flatter response. The low Q system requires a huge EQ boost in low frequency and will sound like garbage without it. Since you're using equalization, the stronger the motor, the better.

 

This is the theory behind Powersoft's IPAL system efficiency. A low Q woofer will have better efficiency but sound terrible. A high Q woofer will have low efficiency but a nice frequency response. By EQing a low Q woofer, you get the best of both worlds.

post-4069-0-13865000-1469973425_thumb.png

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lowerFE    35

Contrasseur, WOW! Can I ship you a six pack? That was incredibly informative and made several aspects of subwoofer performance clear to me. 

 

Josh, could you comment on simulated power requirement vs actual power consumption? Do you see an overestimation of the power required vs actual power needed?

 

What factors are there in determining the efficiency of a woofer in the bass region? I know you talked about some in your previous post such as motor strength and system Fb, which is related to the Mms. However, I'm trying to figure out why the SEAS L16RN-SL needs 3x more power to hit 5mm of excursion vs most other 5'' woofers, which is a huge difference and I'd like to know what could cause that.

 

Based on my understanding from your post, the higher Mms should help efficiency down low. The BL^2/Re is normal compared to the other woofers. The only difference is Qtc is much higher on the L16 (1.57) vs other 5'' woofers like the SEAS ER15RLY (~1). I remember a post by Mark Seaton mentioning how he tested various 15'' woofers and most of them needed 1.5-2x power to hit the same SPL as the Submersive driver. While there is no T/S parameters for his woofers, it is fairly obvious given the efficiency up top the Mms has to be fairly low for a 15''. The driver doesn't look like it has crazy high motor strength either. So there has to be something else.

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lowerFE    35

I figured out why the L16RN-SL needed so much more power compared to the ER15RLY. At xmax, the L16RN-SL is actually producing about 4.5dB more output than the ER15RLY. It has 30% higher Sd as well as 20% more xmax for a total of 56% more displacement, which is roughly ~3dB. The higher Qts causes about a 1dB loss in efficiency. Add them up, it explains everything. 

 

On the other hand, it looks like I will need my iNuke to power this darn thing for testing! If I use 4 L16's, I'm going to need ~1000 watt just to hit xmax on all 4 woofers!

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Ricci    652

Josh, could you comment on simulated power requirement vs actual power consumption? Do you see an overestimation of the power required vs actual power needed?

 

I find that the opposite is true. Nearly all systems require more power / voltage to reach a specific excursion versus simulation. This is due to the speakers performance degrading at higher output levels. Simulations usually consider the transducer to be perfectly linear to its limits. If the simulation does not match the real result then the simulation is not accurate.

 

 

What factors are there in determining the efficiency of a woofer in the bass region? I know you talked about some in your previous post such as motor strength and system Fb, which is related to the Mms. However, I'm trying to figure out why the SEAS L16RN-SL needs 3x more power to hit 5mm of excursion vs most other 5'' woofers, which is a huge difference and I'd like to know what could cause that.

 

Identifying higher overall low power efficiency very simply= Drivers with lower qts / higher BL^2/Re (normalized for SD)

Identifying higher overall high power efficiency very simply= In addition to above look for: High xmax/xmech, larger voice coil mass, better gap cooling, spread power across multiple drivers, try to operate under xmax, use large areas for vents and horns to keep airspeeds as low as possible.

 

Also try to optimize placement of impedance peaks to cover the range of interest. In very small airspaces where H.I.L. is having a large effect, this will mostly be set by the enclosure.

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SME    211

I should probably update my post on this subject.  Via further study, I found that BL^2/Re should *not* be normalized for SD when looking at low end efficiency.  There are two reasons I reached the incorrect conclusion:

 

(1) I noticed that multiple smaller drivers often modelled better than a single larger driver with the same total Sd in particular small enclosure.

(2) I assumed "small" enclosures of interest are so small that their air spring stiffness overwhelms the suspension stiffness.

 

The assumption in (2) led me to conclude that better performance was due to the (BL^2/Re) of the multiple smaller drivers summing to a greater amount than the (BL^2/Re) of the single driver.  However, assumption (2) proved to be wrong when I looked more closely at the data.  In principle, the stiffness of the driver suspension sums with the stiffness of the air spring, so the smaller the box gets, the less the driver stiffness matters (as a %).  However, in my study, I found that even "small" boxes are still large enough for driver stiffness to matter most of the time.

 


 

More generally, the physics of subwoofers are greatly simplified when considering the very lowest of frequencies, way below resonance.  If we let V(t) equal our input signal (volts from the amp) as a function of time, then I(t), the current through the coil as a function of time is simply:

 

  I(t) = 1/Re * V(t)

 

with Re being the DC resistance.  The current in the coil induces a net force on the moving assembly, proportional to BL and I(t):

 

  F_motor(t) = BL * I(t) = BL/Re * V(t)

 

The motor force is opposed by the restoring force of driver suspension and box air spring, which is proportional to its stiffness and the driver displacement, X(t):

 

  F_spring(t) = -K * X(t)

 

Note that K is the sum of driver stiffness and air box stiffness and can be calculated from Vas and the box volume, Vb:

 

  K = rho*c^2*Sd^2 * (1/Vas + 1/Vb)

 

At such low frequency, the driver moves so slowly that changes to its momentum can be treated as zero (very small relative to the forces involved).  As such, the two forces are approximately in balance:

 

  BL/Re * V(t) = rho*c^2*Sd^2 * (1/Vas + 1/Vb) * X(t)

 

Solving for displacement as a function of time, X(t), we get:

 

  X(t) = BL / [ Re * rho * c^2 *Sd^2 * (1/Vas + 1/Vb) ] * V(t)

 

Actual pressure @ 1 meter, P(t), depends on the acceleration of the driver and its surface area.  The acceleration depends on the displacement and frequency.  Note that we could safely assume acceleration a(t) is zero for the purpose of estimating displacement, X(t), but acceleration is in fact non-zero, albeit very small (we are way below resonance).  For sine waves with frequency f, the acceleration is given (mathematically via the second derivative, for those who know any calculus) by:

 

  a(t) = -4*pi^2*f^2*X(t)

 

The pressure at one meter, p(t), is given by:

 

  p(t) = rho*Sd / pi * a(t) = -4*pi*rho*Sd*f^2*X(t)

        = - 4*pi/c^2 * BL/[Re * Sd * (1/Vas + 1/Vb)] * f^2 * V(t)

 

I re-arranged this equation for convenience.  The first factor (4*pi/c^2) is always the same because it depends only on physical and mathematical constants.  The other terms are:

 

  * Sealed box parameters: "BL/[Re*Sd*(1/Vas + 1/Vb)]"

  * Frequency squared "f^2"

  * Voltage signal "V(t)"

 

The minus sign indicates that the response of pressure vs. voltage is inverted.  In other words, a positive voltage produces a negative pressure, and visa-versa. This relationship is only true for frequencies well below resonance.

 

The f^2 part is where the "2" in "2nd-order roll-off" comes from.  This factor characterizes the 12 dB/octave roll-off.

 

The factor with the sealed box parameters is where things get interesting because they point the way toward getting the most output at the extreme low end.

 

To discuss this further,  I want to clarify the difference between two terms: sensitivity and efficiency.  Sensitivity refers to the pressure @ 1 meter of a system for a given amount of input *voltage*.  Efficiency refers to the pressure @ 1 meter of a system for a given amount of input *power*.  In general, both sensitivity and efficiency vary with frequency.  However, you will often see figures published named either "sensitivity" or "efficiency" that are derived using any number of methods.  Let's ignore that here and stick to these straight-forward definitions.

 

Both sensitivity and efficiency are important in system design.  The shape of the sensitivity vs. frequency curve is the same as the frequency response.  Amps generally have a maximum voltage that they can output regardless of power.  If this figure isn't published, then you can usually get a rough estimate by taking the square root of power rating multiplied by the impedance at the highest impedance value it's rated at.  For example, an amp rated @ 1000W @ 8 ohm and 1500W @ 4 ohm likely has a max voltage not much higher than: sqrt(1000*8) = 89.4V.  The max voltage represents a best case scenario limit of the amp's performance.  In reality, the amp may struggle to maintain that output voltage if the overall power demanded from it is too high.  This is where power ratings at lower impedances come into play.  Ideally, the power output will double for every halving of impedance, but real amps rarely achieve this in practice.  The actual power demanded from the amp for a particular input voltage depends on the system impedance, which varies by frequency.  If the woofer is higher efficiency for the content being reproduced, then the amp won't have to deliver as much power and will be able to maintain max voltage more easily.  Efficiency is also important because it indicates how much power actually gets dissipated in the coil, and this impacts power compression and some modes of distortion, not to mention longevity and resistance to catastrophic failure.

 

Are we clear on sensitivity vs. efficiency?  It's important to always understand the distinction because both are important for somewhat different reasons.

 

OK.  So getting back to our analysis of the extreme low-end.  For these frequencies, the impedance is constant, equal to the DC resistance, so efficiency and sensitivity are trivially related.  This is not true in general, especially around the system resonance where efficiency may increase substantially.  Our last formula above represents sensitivity.  It has P(t) on the left side and a bunch of stuff multiplying V(t) on the right side.  The f^2 indicates the 12 dB/octave roll-off in sensitivity.  The factor whose variables that can be changed in the design is:

 

  BL/[Re * Sd *(1/Vas + 1/Vb)]

 

The BL on top means extreme low end sensitivity is proportional to force factor BL.  All else the same, each doubling of BL is +6 dB extreme low end output per volt.  The Re on bottom means sensitivity is inversely proportional to resistance, Re.  All else the same, each doubling of Re is -6 dB extreme low end output per volt.  The last part is Sd * (1/Vas + 1/Vb), which expresses that linear stiffness of the suspension and air spring.  Extreme low end sensitivity is inversely proportional to system stiffness.  So a doubling of stiffness leads to -6 dB extreme low end output per volt.  If the box is so small that Vas can be neglected, then halving the box causes -6 dB output.  In reality, Vas still contributes some, so halving the box results in the loss being somewhat less.

 

Note that Sd does not appear anywhere here.  Extreme low end sensitivity/efficiency is not influenced by cone area at all.  All that really matters is the BL/Re of the motors (these numbers don't sum for multiple drivers) and the overall system stiffness, which depends on the Vas for each driver and the overall box volume V.  Whoops, got this wrong.

 

The counter-intuitive result is that all else the same, greater cone area actually harms extreme low end sensitivity.  How is that possible?  For a given volumetric displacement (proportional to output level), the restoring force from the air spring, which limits the cone travel, depends on both the box volume *and* the cone area.  The volume displacement causes a pressure difference between the inside and outside of the box.  The force on the driver is this difference times the cone area.  Therefore larger cones require more force to move against the pressures inside the box.

 

Here we've ignored Vas, assuming it's the same between the two drivers.  This is very unlikely in reality.  In fact, even if a large driver and small driver share the same spider (and assuming the surrounds don't matter), the compliance, Cms will be the same between the drivers, not the Vas.  Vas depends on Sd^2 times Cms times some constants.  So if you half the surface area, you actually end up with 1/4 the Vas.  Suppose you are comparing two drivers that use the same motor and suspension (same Cms), but one has less cone area.  Which driver has greater low end sensitivity will depend on the box size!  The smaller the box, the more likely the small drivers will win the race.  In I.B., the larger driver will always win.  As one more note, I understand that many larger drivers necessarily use a suspension with a higher Cms to ensure mechanical stability, so when comparing drivers for low-end sensitivity and efficiency, it's always good to look at *all* the relevant parameters.

 

But wait!  Where does BL^2/Re come into play?  It comes into play with regard to efficiency.  For the extreme low end, we have a formula for p(t) vs. V(t).  Now we need one for p(t) vs. P(t), where capital P(t) is instantaneous power:

 

  P(t) = V(t) * I(t) = V(t)^2 / Re

 

  ==> V(t) = sqrt{ P(t) * Re }

 

We make this substitution for V(t) in the equation for sensitivity:

 

  p(t) = - 4*pi/c^2 * BL/[sqrt(Re) * Sd * (1/Vas + 1/Vb)] * f^2 * sqrt{ P(t) }

  ==> p(t)^2 = 16*pi^2/c^4 * {BL / [sd * (1/Vas + 1/Vb)]}^2/Re * f^4 * P(t)

 

We squared both sides of the equation so that it's in terms of P(t) and not sqrt{ P(t) } because the power requirement scales with pressure squared.  (I.e., doubling pressure requires 4X power.)  Here we see the emergence of (BL)^2/Re.  In terms of power efficiency, a doubling of (BL)^2/Re leads to a doubling of efficiency.  At the same time, a doubling of (1/Vas + 1/Vb) leads to 1/4 the efficiency.  For the smallest boxes, half the box size means 1/4 efficiency.  Ouch.  And finally, doubling Sd also leads to efficiency that is 1/4 as much, in the worst case (tiny boxes).  But see notes above regarding Vas vs. Cms and the dependence on Sd.

 

When designing a sub system, one typically chooses a driver voice coil resistance and driver network configuration (i.e., series vs. parallel) to optimize the load impedance presented to the amp so as to obtain the most power output possible.  As a consequence, the efficiency is usually more interesting than sensitivity when comparing performance of multiple drivers without regard to what amp will be used.  The sensitivity comes into play when it's time to actually match the amp with the drivers and assess the limits of the system around the resonance frequency where impedance is almost always so high that amp voltage is what matters.

 

Anyway, sorry if all the math is overwhelming.  And please note one more time that most of the formulas above are only valid for extreme low frequencies, well below resonance, for any system.  These results may or may not be relevant to the design, depending on the resonance of the completed system.  If you can find woofers with a lot of mass, you can get the resonance frequency down quite low, but not without considerable compromise to sensitivity and efficiency in the upper frequencies.  In this case, the performance at the low end will be governed by the behavior of the system at/near resonance rather than the "extreme low end".  The behavior at resonance depends on the Qtc of the system.  Higher Qtc offers greater sensitivity and efficiency very near the resonance.  Lower Qtc offers better sensitivity and efficiency in the frequency region somewhat below and somewhat above the resonance.  This frequency region could be called the "transition region" where sensitivity transitions between being flat at the upper end to rolling-off at 12 dB/octave at the lower end.  The lower the Qtc, the wider this transition region is and the greater the range of frequencies that benefit from the sensitivity and efficiency improvement provided by the mechanical resonance.  A high Qtc allows for very high sensitivity and efficiency, but only for a very narrow region of frequencies centered at the resonance.

 

Some other general notes.  All else the same:

  * Increasing Mms: shifts resonance down in frequency; increases Qtc; decreases upper end sensitivity and efficiency; increases sensitivity and efficiency at the resonance; increases efficiency (more so than sensitivity) below (but not too far below) resonance; and has no effect on extreme low-end sensitivity or efficiency.

  * Increasing system compliance (via bigger box or less suspension stiffness): shift resonance down in frequency; decreases Qtc; increases lower end sensitivity and efficiency; decreases senstivity and efficiency at the resonance; decreases efficiency (more so than sensitivity) above (but not too far above) resonance; and has no effect on extreme high-end sensitivity or efficiency.

  * Increasing motor strength (BL^2/Re): decreases Qtc without shifting the resonance; increases sensitivity on the upper and lower ends; decreases sensitivity near resonance, and increases efficiency everywhere (less near the resonance).

 

Hopefully this discussion provides insight into your design.  Let me know if you have questions.

 

Correction: Higher BL^2/Re does not harm efficiency at the resonance, but the efficiency increase is usually much less here.

Correction: I lost a factor of 1/Sd in the result for sensitivity and 1/Sd^2 for efficiency.  If the box is small enough, smaller drivers with otherwise similar parameters to larger ones can have more sensitivity/efficiency in the extreme low end, but as the box gets larger and Cms doesn't change, the smaller drivers could also be less efficient.

Edited by SME
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Ricci    652

Note that Sd does not appear anywhere here.  Extreme low end sensitivity/efficiency is not influenced by cone area at all.  All that really matters is the BL/Re of the motors (these numbers don't sum for multiple drivers) and the overall system stiffness, which depends on the Vas for each driver and the overall box volume V.

 

 

???...

You take the same motor and voice coil driving an 8" cone and then use it to drive a 21" cone and place both in 80L sealed. There will be very large sensitivity and efficiency differences directly related to the SD of the diaphragm even down to 10Hz and below.  

 

 

   * Increasing motor strength (BL^2/Re): decreases Qtc without shifting the resonance; increases upper end sensitivity and efficiency; decreases sensitivity and efficiency at resonance; and increases efficiency and sensitivity at the low end;

 

While increasing BL^2/Re harms sensitivity and efficiency at the resonance somewhat, it increases sensitivity and efficiency everywhere else.

 

Why do you say that it harms efficiency at resonance? Increasing BL^2/Re decreases mid band sensitivity at and around the resonance yes. Efficiency actually increases at resonance if only by very little. Efficiency (and impedance) increases everywhere not just above and below resonance.

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SME    211

???...

You take the same motor and voice coil driving an 8" cone and then use it to drive a 21" cone and place both in 80L sealed. There will be very large sensitivity and efficiency differences directly related to the SD of the diaphragm even down to 10Hz and below.

 

That depends on the suspension of each driver.  If they have the same Vas or if the Vas of both drivers is very big compared to Vbox, then they will have about the same efficiency at the bottom end.  Why?  Because at the lowest frequencies, the only thingss that affect the cone motion are the motor force and the restoring force of the suspension and air spring.  If the motors are the same, then the motor force will be the same for a given amount of input power.  If the sum (1/Vas + 1/Vbox) is the same for both systems, then the restoring force will be the same for a given amount of volume displacement.  The size of the air mover(s) is unimportant.

 

Of course, the 8" will run out of excursion long before the 21" will, so in a practical implementation, you'll want to use N drivers so that total volume displacement is the same.  What happens to efficiency then?  The motors are the same, so each driver exerts the same force for the same power input.  For a given amount of output, the restoring force on each driver due to the air spring does not change because it only depends on the proportion of air in the box that's displaced, which is unchanged if the total box volume is the same.  What's left to consider is the restoring force of the suspension on the driver.  Because each driver doesn't need to move as far for the same total output, the restoring force of the suspension on each driver is reduced.  An I.B. system is a best case example where you'll get an extra 3 dB (doubling) of efficiency with a doubling of drivers, but there will be diminishing returns with smaller boxes.  Once 1/(N*Vas) is much larger than Vbox, then adding drivers provides no efficiency gain at all.

 

So when looking for a driver to maximize extreme low end efficiency in small boxes, you want to max BL^2/Re in whatever driver or drivers you choose, and as the box gets larger, Vas/Vd also becomes important.

 

Mid and high frequencies are a different story because the cone motion is controlled less by the suspension + air spring stiffness and more by the driver momentum.  Momentum is velocity times mass, and a high Sd driver with the same Mms as a low Sd driver will move more air and have more output for the same momentum.  So the 21" with the same motor, Mms, and Vas will have an efficiency advantage over the single 8" that increases with frequency.  Of course, this performance gap can be closed by using multiple 8" drivers as well.  In the highest frequencies, where only motor strength and momentum matter, doubling the drivers will always give you a +3 dB efficiency gain.  The motor strength and mass are the same, but each driver only moves with half the velocity for the same output.

 

Why do you say that it harms efficiency at resonance? Increasing BL^2/Re decreases mid band sensitivity at and around the resonance yes. Efficiency actually increases at resonance if only by very little. Efficiency (and impedance) increases everywhere not just above and below resonance.

 

Thanks for the clue check here.  You are absolutely right.  I will edit my post to correct.  At the actual resonance, BL^2/Re *does* increase rather than decrease efficiency but the difference is usually insignificantly small.  You'll only really see an improvement if Qes is similar to or greater than Qms.  If don't know if that's ever the case in practice.

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Ricci    652

That depends on the suspension of each driver.  If they have the same Vas or if the Vas of both drivers is very big compared to Vbox, then they will have about the same efficiency at the bottom end.  Why?  Because at the lowest frequencies, the only thingss that affect the cone motion are the motor force and the restoring force of the suspension and air spring.  If the motors are the same, then the motor force will be the same for a given amount of input power.  If the sum (1/Vas + 1/Vbox) is the same for both systems, then the restoring force will be the same for a given amount of volume displacement.  The size of the air mover(s) is unimportant.

 

Of course, the 8" will run out of excursion long before the 21" will, so in a practical implementation, you'll want to use N drivers so that total volume displacement is the same.  What happens to efficiency then?  The motors are the same, so each driver exerts the same force for the same power input.  For a given amount of output, the restoring force on each driver due to the air spring does not change because it only depends on the proportion of air in the box that's displaced, which is unchanged if the total box volume is the same.  What's left to consider is the restoring force of the suspension on the driver.  Because each driver doesn't need to move as far for the same total output, the restoring force of the suspension on each driver is reduced.  An I.B. system is a best case example where you'll get an extra 3 dB (doubling) of efficiency with a doubling of drivers, but there will be diminishing returns with smaller boxes.  Once 1/(N*Vas) is much larger than Vbox, then adding drivers provides no efficiency gain at all.

 

So when looking for a driver to maximize extreme low end efficiency in small boxes, you want to max BL^2/Re in whatever driver or drivers you choose, and as the box gets larger, Vas/Vd also becomes important.

 

Mid and high frequencies are a different story because the cone motion is controlled less by the suspension + air spring stiffness and more by the driver momentum.  Momentum is velocity times mass, and a high Sd driver with the same Mms as a low Sd driver will move more air and have more output for the same momentum.  So the 21" with the same motor, Mms, and Vas will have an efficiency advantage over the single 8" that increases with frequency.  Of course, this performance gap can be closed by using multiple 8" drivers as well.  In the highest frequencies, where only motor strength and momentum matter, doubling the drivers will always give you a +3 dB efficiency gain.  The motor strength and mass are the same, but each driver only moves with half the velocity for the same output.

 

Still don't agree with the statement that SD does not matter as regards to efficiency of converting electrical power into acoustic power in the deep bass or in any part of the frequency range... :P

 

Can you show a real world measured example of this or even a simulation showing a single 8" driver with the same deep bass efficiency as an 18 or 21" in the same enclosure volume? I believe that the math may be correct at extremes. Your math kungfu is better than mine, but I believe it is missing the forest for the trees so to speak.

 

SD has to matter. Otherwise you are saying that you can place the same motor / coil, etc...driving a single 2" cone and a 24" cone and put both in  150L sealed and assuming that the 2" driver has infinite excursion and both have the perfect set of parameters needed to match, both will produce the same SPL output at let's say 8

Hz with 1W of input power? Do you mean some infinitely deep frequency down below 1Hz? The acoustic conversion efficiency would directly tie to the SPL.  I believe the error may be in the definition of what frequencies are being considered (<1Hz?) either that or are you perhaps not looking at the acoustic power produced and considering only the electrical domain? You seem very sure but it makes absolutely no intuitive sense to me and doesn't match any data I've seen either.

 

Why would the same motor and coil, driving a spring system with nearly identical properties and assuming the same mass in the moving assembly, cause the coil to be displaced about 7 times as far from center when driving a 10" cone versus a 24" cone with the exact same electrical input power? That is what has to happen in laymans terms for the 10" driver to have the same efficiency as the 24" at any frequency.

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SME    211

Upon closer inspection, my reasoning above is indeed erroneous, and I made a math error that caused my conceptual reasoning look correct when it's not.

 

However, I think you will find my revised results to be even more counter-intuitive.  They indicate that in many cases (especially very small boxes), a smaller driver with the same motor will be *more* efficient than the larger driver.  This is because the smaller driver actually experiences less restoring force from the air spring for the same volume displacement.  The discussion gets more complicated, however, when you look at somewhat larger boxes where you take into account the suspension as well, and in reality, it is unlikely that you'll find two drivers with different Sd that share the same motor, Mms, and Vas.

 

I will make the necessary corrections and offer a more detailed discussion when I get more time to work on this.  I'd rather not have to correct myself a third time, if I can avoid it.  Being good at math only goes so far without good peer review, and I am very thankful for your input, even if you aren't able to comment on the math directly.  I'll also try to give a better answer to your question about just how low in frequency you have to look for these results to be valid.  It has to do with the other physical parameters of the system.  For most systems, I'm fairly certain it will be higher than 1 Hz.

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Kyle    62

Hello fellow bassheads - After going on AVSForum and Data-Bass, I feel like my man card is forever revoked for only having 2 15'' subs. So after hearing scores of voices yelling things like "That's a bathroom setup!" and "My SEOS tweeter's bigger than your sub!", and the last straw was "with subs like that, you might as well stain it pink!". So I stained my sub with red stain, and the plywood actually didn't take the stain well, and the red looked like pink instead (that's actually true...)

 

So realizing I'm clearly not gonna be the manliest guy on the block, I said, F it, I'll pimp another way. I'll be the most wife accepted guy on the block instead. So I'm going to build the highest WAF speaker basshead wives have ever seen - a sound dock. :blink:  

 

But (saying this in the manliest voice possible), it has to be the bassiest sound dock I could possibly build. 

 

Now for the boring technical requirements. So far, the speaker is envisioned as a 14'' x 6'' x 6'' speaker. The plan is to use four approximately 5'' woofers (nope, it isn't missing a 1 in the beginning) in a sealed dual dual opposed configuration. Yes, that 2 duals you see there, a pair of dual opposed woofers.  :D The woofers will have their frames cut off to reduce the size so they can actually fit in the cabinet. I'm aiming for extension flat to 30Hz, and as much <60Hz output as possible. The goal is at least 95dB at 40Hz. Not one, but 2 miniDSPs will be used to EQ the speaker. One for the speaker itself, and one to be used as a 4 band compressor. I'll be using the SMSL SA-98E 2x160W amp to power the 4 woofers. Each woofer will get around 50 watts of power since I don't think the amp can actually put out 160W a channel. 

 

(I can already hear the "stop calling a 5'' driver a woofer!" screams)

 

Now I have a series of questions.

 

how do I pick drivers? My knowledge for speaker design is for small signals, not large signals. What parameters should I be looking for when selecting woofers optimal for small sealed enclosures? What are parameters and designs that would indicate the driver could be low distortion at higher volumes?

 

I will also ask a more specific question that I've been curious about. Generally, a low Fs is desirable for a woofer. You can achieve a low Fs by either increasing mass or increasing compliance. However, when you increase mass, you lose efficiency, which is undesirable, but most subwoofer drivers do this for some reason. What's the advantage of a tight suspension? Is it because a tight suspension would stay more linear at very high excursion levels? However I see increasing compliance to lower Fs done in pretty much all high end drivers of 5-7'', and yet some of those drivers have high excursions and stay clean at those excursion levels. 

 

Why is a very low Qts desirable for vented enclosures and not for a sealed enclosure? A low Qts can signify high motor strength, wouldn't that be desirable for both vented and sealed? It is possibly because the excursion utilization for a given power input would be lower on a very low Qts woofer in a sealed enclosure?

 

Here are some drivers I'm looking at using. Could anyone comment on the driver that is most likely to be optimal for this build?

 

1. SEAS ER15RLY - perfect size, good all around parameters, used in the highly acclaimed Salk SongTowers, but not sure how well suited for bass at high levels

 

https://www.madisoundspeakerstore.com/approx-5-woofers/seas-prestige-er15rly-h1455-5.5-reed-paper-cone-woofer/

 

2. SEAS L16RN-SL - a bit bigger than I'd like, but it is said to be specifically designed for high output sealed use. However it models very poorly (and weird) in a small enclosure. It takes 3-4x more power to reach xmax compared to most 5'' drivers. 

 

https://www.madisoundspeakerstore.com/approx-5-woofers/seas-prestige-l16rn-sl-h1480-5-aluminum-cone-woofer/

 

3. SB Satori MW13P - High quality neo motor, maybe it'll be better for distortion? Expensive though, and the Sd is a bit small. 

 

https://www.madisoundspeakerstore.com/approx-5-woofers/satori-mw13p-8-5-egyptian-papyrus-cone-woofer-8-ohm/

 

Final question: Is it me, or does it seem like modelling programs grossly overestimate the amount of power needed to reach xmax? I did a build of 4 Dayton ND105's in a similar box size, powered by a stereo amp with each channel driving 2 woofers. Simulations showed me I needed 30 watts to reach the 4mm xmax. However, I used a SMSL SA50 amp, which is a tiny class D amp rated at 2x50W. Not only I was able to reach xmax, I came close to reaching the 10mm xmech with only 25 watts per woofer. Since I was running a continuous sine wave, I highly doubt the tiny amp is capable of 2x50W continuous. The power supply ratings say otherwise. So the amp is outputting more like 2x25W continuous, which means I reached ~8mm of excursion with ~10W of power when the simulation says I need 30 watts just to reach 4mm. I see this on another speaker as well, where I bottomed the driver out when modelling shows I shouldn't even reach xmax with the amplifier power I have. 

 

We made it to the end. I hope my attempt at humor was enough to keep you interested in a thread asking about 5'' woofers. :D  Any help with this ladies speaker would be appreciated!

 

I'm trying to cut to the meat here. Is this supposed to be a small subwoofer or a full range speaker?  If the latter, do you intend the woofers be cross'ed with the tweeter(s) or is this a 3-way system with another midrange? The latter would be better because you're asking the 5" drivers to cover quite a few octaves if you want them crossed to any given tweeter.
 
As for the drivers, its not the size thats the problem, its trying to find a low freq design that only 5". Normally 5" speakers are almost always a midrange/midbass sorta deal so they are not really suited for LF 30Hz stuff. If it were me, I would raise the speaker up on rubber feet and add a shallow style down firing true subwoofer thats 8" or even 10" in diam. These do exist and I would also power it with more power and you'll need to separate the base volume from the other speakers if this is a 2 or 3 way system for best results.
 
 
edit Oh... 14x6x6 won't fit a down firing 8, i was thinking 14x14x6.  hmmm. back to drawing board...

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lowerFE    35

 

I'm trying to cut to the meat here. Is this supposed to be a small subwoofer or a full range speaker?  If the latter, do you intend the woofers be cross'ed with the tweeter(s) or is this a 3-way system with another midrange? The latter would be better because you're asking the 5" drivers to cover quite a few octaves if you want them crossed to any given tweeter.
 
As for the drivers, its not the size thats the problem, its trying to find a low freq design that only 5". Normally 5" speakers are almost always a midrange/midbass sorta deal so they are not really suited for LF 30Hz stuff. If it were me, I would raise the speaker up on rubber feet and add a shallow style down firing true subwoofer thats 8" or even 10" in diam. These do exist and I would also power it with more power and you'll need to separate the base volume from the other speakers if this is a 2 or 3 way system for best results.
 
 
edit Oh... 14x6x6 won't fit a down firing 8, i was thinking 14x14x6.  hmmm. back to drawing board...

 

 

Hey Kyle, it is a 3 way speaker with a midrange. I just posted the full design of the speaker in this thread if you're interested in finding out more.

 

http://data-bass.ipbhost.com/index.php?/topic/566-the-ultimate-small-speaker-final-design-peer-review-thread/

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Ricci    652

However, I think you will find my revised results to be even more counter-intuitive.  They indicate that in many cases (especially very small boxes), a smaller driver with the same motor will be *more* efficient than the larger driver.  This is because the smaller driver actually experiences less restoring force from the air spring for the same volume displacement.  The discussion gets more complicated, however, when you look at somewhat larger boxes where you take into account the suspension as well, and in reality, it is unlikely that you'll find two drivers with different Sd that share the same motor, Mms, and Vas.

 

If you can supply some driver parameters, even if they are impossible, that will allow simulation of such a scenario I'd like to see them. I suspect this requires impossible, very specific or at least highly improbable scenarios such as a unbuildable small enclosure volume for the larger SD driver and/or only applies over a very narrow frequency bandwidth?

 

It's not that I cannot check the math but I've never been a math savant by any means and I've never had a love for it. My algebra and calculus is very rusty!

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SME    211

If you can supply some driver parameters, even if they are impossible, that will allow simulation of such a scenario I'd like to see them. I suspect this requires impossible, very specific or at least highly improbable scenarios such as a unbuildable small enclosure volume for the larger SD driver and/or only applies over a very narrow frequency bandwidth?

 

It's not that I cannot check the math but I've never been a math savant by any means and I've never had a love for it. My algebra and calculus is very rusty!

 

No worries.  I don't expect anyone to check my math unless it interests them or they have use for it and run into problems or have questions.

 

I want to give a detailed response here, but it's taking me a while to compose my thoughts.  If you want an interesting real world example to study, try modelling a single SI HST-18d2 vs. a single SI HS-24d2 in boxes of the same internal volume using the manufacturer's published T/S paramters.  Experiment with different sizes, and see how this impacts the relative low end efficiency of each driver.  Can you guess which one is more efficient in small boxes?  How about in large boxes and I.B.?  Note that the HS-24 has a similar but slightly higher (BL)^2/Re.

 

In time, I will publish an explanation for the results, which are likely to be somewhat surprising.

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Ricci    652

No worries.  I don't expect anyone to check my math unless it interests them or they have use for it and run into problems or have questions.

 

I want to give a detailed response here, but it's taking me a while to compose my thoughts.  If you want an interesting real world example to study, try modelling a single SI HST-18d2 vs. a single SI HS-24d2 in boxes of the same internal volume using the manufacturer's published T/S paramters.  Experiment with different sizes, and see how this impacts the relative low end efficiency of each driver.  Can you guess which one is more efficient in small boxes?  How about in large boxes and I.B.?  Note that the HS-24 has a similar but slightly higher (BL)^2/Re.

 

In time, I will publish an explanation for the results, which are likely to be somewhat surprising.

 

I see where the confusion is now. I am holding the Fb or impedance of the systems constant to compare only the effect of increased SD. In which case the extra SD wins.

 

If you move to a comparison like the HST vs 24 there are a lot more variables.

 If the airspace becomes very small for the amount of SD involved the unit with smaller SD will have a naturally lower resonance which will of course increase the efficiency since the much larger SD has a resonance a lot higher in frequency. Placeent of the impedance maximum has a huge effect on the efficiency so of course the lower resonance system will have advantage in the lower frequencies. The FS of the suspensions also impacts this. In the case of the 24 vs HST-18 about the smallest cab you can fit the 24" in is probably about 100L or so. With both drivers in that cab the Fb of the 18 is much lower as is the system Qtc so of course it has higher lower end efficiency. It has a much lower resonance. Let's not forget that the 24" is an IB style driver. It really wants about 800L for a 0.707 Qtc, while the 18 only wants 70L. The 24 is being shoved into a system with a resulting Qtc of 1.3 in 100L.  

 

What happens when we increase the airspace to 250L and sim both drivers again? Now the 24 has greater sensitivity and equal or better efficiency everywhere above 10Hz. It is still in a greatly undersized system with a Qtc of 0.95 due to the IB driver like behavior. This is what I meant about impractical applications. Yes the HST may have better efficiency at some point below 10Hz say at 5Hz but how useful is that? Is anyone going to put the 24 driver into a cab that is many times smaller than the recommendation or specs suggest? If the air space is increased further beyond 250L the 24 only gets stronger.

 

What happens when we simulate drivers at the other end of the spectrum? Things like the M-force system or the Ipal drivers?

 

All of that aside the above comparison reinforces that SD must be considered as part of the calculation. It has a huge effect in the behavior. The 24 requires a huge airspace because of the extra SD compared to the 18. The suspension compliance, MMS, SD, BL^2/RE and the air volume all matter. You cannot throw out the SD from the equation. That is why I originally commented was the comment that SD doesn't have to be considered.

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SME    211
If the airspace becomes very small for the amount of SD involved the unit with smaller SD will have a naturally lower resonance which will of course increase the efficiency since the much larger SD has a resonance a lot higher in frequency. Placeent of the impedance maximum has a huge effect on the efficiency so of course the lower resonance system will have advantage in the lower frequencies. The FS of the suspensions also impacts this. In the case of the 24 vs HST-18 about the smallest cab you can fit the 24" in is probably about 100L or so. With both drivers in that cab the Fb of the 18 is much lower as is the system Qtc so of course it has higher lower end efficiency. It has a much lower resonance. Let's not forget that the 24" is an IB style driver. It really wants about 800L for a 0.707 Qtc, while the 18 only wants 70L. The 24 is being shoved into a system with a resulting Qtc of 1.3 in 100L.

 

I have to disagree with this point in bold.  Impedance maximum has a huge effect on the efficiency only within the close vicinity of the resonance, wherever it falls.  A lowered system resonance should be seen as more of a side effect of having reduced the in-box stiffness by using the HST-18 with smaller Sd instead of the HS-24.  What actually matters is the in-box stiffness.

 

For example, suppose that instead of making the box for the HS-24 bigger you increase its mass instead in order to get to that lower resonance?  That does give you a bit more low end sensitivity, but efficiency goes down everywhere except for the extreme low end (where it has no effect at all) and the narrow region of frequencies around the new resonance point.  The added mass hurts high frequency efficiency even more.

 

Also, for what it's worth, my sims show the HST-18 winning or tying the HS-24 for efficiency (but not sensitivity) from 16 Hz on down when in I.B.  The HS-24 would do a lot better here compared to HST-18 if its suspension were less than twice as stiff as the HST-18 suspension.  To the extent that suspension stiffness must be increased for larger cones to ensure mechanical stability, there are may be diminishing returns in low end performance and using drivers with more cone area, even in larger boxes and I.B..

 

Another thing to try is a sim with 2 x HST-18s in the same box size as 1 x HST-18 and 1 x HS-24?  Arguably this is also of more practical interest because it has similar total displacement capability.  If the box is small enough, the additional woofer actually *decreases* low end efficiency compared to using a single driver.  This efficiency loss, however, is not as great as the loss from using a single driver with the same total Sd.  A such, the HST-18 pair retains an edge against the HS-24 in tiny boxes.  In larger boxes, the additional driver improves efficiency.  In I.B., the HST-18 pair beats the HS-24 at 18 Hz and below instead of just 16 Hz and below.  It also closes most of the gap with the HS-24 at higher frequencies.  In a fairly "realistic" box size of 150L, the HST-18 pair is more efficient than the single HS-24 for 35 Hz and below.  Again, the HS-24 would fair a lot better in this example if its suspension were less stiff.

 

An important consideration missing from this discussion is where the transition lies between "large" box and "small".  It would be helpful to be able to nail this down.  The answer does, in fact, depend a lot on Sd.  I've done a fair bit of work to answer this question, but I haven't looked at multiple drivers in enough detail yet.

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Ricci    652

I have to disagree with this point in bold.  Impedance maximum has a huge effect on the efficiency only within the close vicinity of the resonance, wherever it falls.  A lowered system resonance should be seen as more of a side effect of having reduced the in-box stiffness by using the HST-18 with smaller Sd instead of the HS-24.  What actually matters is the in-box stiffness.

 

For example, suppose that instead of making the box for the HS-24 bigger you increase its mass instead in order to get to that lower resonance?  That does give you a bit more low end sensitivity, but efficiency goes down everywhere except for the extreme low end (where it has no effect at all) and the narrow region of frequencies around the new resonance point.  The added mass hurts high frequency efficiency even more.

 

 

 

We'll have to disagree on the effect of the resonance on efficiency then. If you shift the resonance down 1/3rd of an octave the efficiency will be increased over a very large part of the effective lower bandwidth of the subwoofer compared with the original. I thought we were specifically talking about the deep bass and near the resonance? We already know that greater SD increases efficiency in the upper bandwidth. I'm disagreeing with the statement that SD does not factor in to deep bass efficiency. Your original point that I disagreed with was that SD didn't matter in regards to low bass efficiency. Specifically you seemed to be saying it only mattered at high frequencies but not lower frequencies but I don't recall a definition of exactly what those "high" and "low" frequencies were? Also since the deep bass specifically bumps up against HIL there has to be some definition of the airspace used as well. We probably need to define all of that to get on the same page.

 

If you are saying that the moving of the resonance has little effect then I can assume that we are considering both the large SD and small SD system as having the same resonance in the same air space for the comparison, regardless of the specs needed being improbable?

 

The in-box stiffness is set by the suspension compliance, the moving mass, the air volume and the SD. This was my whole point. Let's say that we have a 45Hz system resonance in a sealed design and we want it to be 35Hz to increase the efficiency below 40Hz down to 20Hz. We can add moving mass, we can increase the suspension compliance, we can increase the air volume or we can decrease SD. The SD must be considered and cannot be thrown out.

 

Also, for what it's worth, my sims show the HST-18 winning or tying the HS-24 for efficiency (but not sensitivity) from 16 Hz on down when in I.B.  The HS-24 would do a lot better here compared to HST-18 if its suspension were less than twice as stiff as the HST-18 suspension.  To the extent that suspension stiffness must be increased for larger cones to ensure mechanical stability, there are may be diminishing returns in low end performance and using drivers with more cone area, even in larger boxes and I.B..

 

Another thing to try is a sim with 2 x HST-18s in the same box size as 1 x HST-18 and 1 x HS-24?  Arguably this is also of more practical interest because it has similar total displacement capability.  If the box is small enough, the additional woofer actually *decreases* low end efficiency compared to using a single driver.  This efficiency loss, however, is not as great as the loss from using a single driver with the same total Sd.  A such, the HST-18 pair retains an edge against the HS-24 in tiny boxes.  In larger boxes, the additional driver improves efficiency.  In I.B., the HST-18 pair beats the HS-24 at 18 Hz and below instead of just 16 Hz and below.  It also closes most of the gap with the HS-24 at higher frequencies.  In a fairly "realistic" box size of 150L, the HST-18 pair is more efficient than the single HS-24 for 35 Hz and below.  Again, the HS-24 would fair a lot better in this example if its suspension were less stiff.

 

An important consideration missing from this discussion is where the transition lies between "large" box and "small".  It would be helpful to be able to nail this down.  The answer does, in fact, depend a lot on Sd.  I've done a fair bit of work to answer this question, but I haven't looked at multiple drivers in enough detail yet.

 

Our simulations look WAY different. :huh: I'll try to throw some together and post them. What I'm looking at in no way matches what you've posted.

 

Comparing 2 HST drivers versus the 24 is a different subject. That's effectively increasing the motor force/decreasing the Qts. We already know that improves efficiency.  Not to mention improvements in thermal stability / reliability

.

 

An important consideration missing from this discussion is where the transition lies between "large" box and "small".  It would be helpful to be able to nail this down.  The answer does, in fact, depend a lot on Sd.  I've done a fair bit of work to answer this question, but I haven't looked at multiple drivers in enough detail yet.

 

Agreed. This would help. So we agree that SD does matter? :D  I suspect it may be the glossed over details which are causing us to look at this differently.

 

Edit: Adding some screen shots. I'm using the factory HS-24 specs without all the inductance, BL detuning, massaging needed to match the measured response, etc...The comparison is the HST-18. I've modded some specs slightly in order to reduce the number of variables to a minimum per the discussion. In theory if the HST-18 uses the same motor and coil as the 24 as well as the same spiders, which is the scenario I brought up earlier, the BL, Re, Le and in theory the Cms, should/could be the same as only the surround would be different and could end up close to the same compliance as the larger diameter one.This reduces the variation between drivers to the Mms and Sd both of which are higher for the 24. Of course this still affects the parameters of both greatly.

 

Driver specs used.

post-5-0-89599100-1471019067_thumb.png

post-5-0-54300800-1471019073_thumb.png

 

Both drivers in 120L sealed. I chose this size because the 24 isn't going to fit in much less than this practically and it's a good match for the HST-18. I've attached the voltage sensitivity, impedance, efficiency and the 1 watt applied output. The 24 is the light gray background trace in all.

post-5-0-45437800-1471019106_thumb.png

post-5-0-19799700-1471019113_thumb.png

post-5-0-79662300-1471019121_thumb.png

post-5-0-90850700-1471019125_thumb.png

 

250L Sealed

post-5-0-95097300-1471019155_thumb.png

post-5-0-50438500-1471019160_thumb.png

post-5-0-76468100-1471019167_thumb.png

post-5-0-03854100-1471019172_thumb.png

 

2000L Sealed to represent IB thought this is actually quite a bit undersized for true IB for the 24. Close enough though.

post-5-0-88125600-1471019198_thumb.png

post-5-0-45508500-1471019204_thumb.png

post-5-0-65946300-1471019216_thumb.png

post-5-0-94924000-1471019228_thumb.png

 

The smaller SD lower Qts 18" does kick the 24's butt for deep bass efficiency in the 120L box, but in the 2000L IB the 24 wins decisively. 250L is a close match for the two in the deep bass. The only places the 18" has higher efficiency corresponds to the impedance curve and system resonance being lower it seems in this example.

 

 

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SME    211
Edit: Adding some screen shots. I'm using the factory HS-24 specs without all the inductance, BL detuning, massaging needed to match the measured response, etc...The comparison is the HST-18. I've modded some specs slightly in order to reduce the number of variables to a minimum per the discussion. In theory if the HST-18 uses the same motor and coil as the 24 as well as the same spiders, which is the scenario I brought up earlier, the BL, Re, Le and in theory the Cms, should/could be the same as only the surround would be different and could end up close to the same compliance as the larger diameter one.This reduces the variation between drivers to the Mms and Sd both of which are higher for the 24. Of course this still affects the parameters of both greatly.

 

I see.  I plugged in all the manufacturer specs verbatim.  You opted to use their specs as a starting point but carry out the experiments with everything the same between the two except the Mms and Sd.  One major difference is that the HS-24 suspension is actually about twice as stiff as the HST-18.  Do you know if it uses the same spider?  Maybe it just uses two of them.  That would probably do it.  The doubled suspension stiffness holds back the HS-24 in ULF in I.B. a lot compared to the HST-18.  This is important because, as I understand it, suspension stiffness must often be increased to maintain mechanical stability of larger cones.  I expect this was the case with the HS-24.  This also holds back the IPAL-21 quite a bit in the deep / ULF bass.

 

I've been thinking about how to reply to the rest of your post.  You raise some good questions and I need to clarify my language carefully.  "High" and "low" are definitely relative to the resonance, but a lower resonance frequency does not guarantee deep bass efficiency.  This may seem counter intuitive but is very important.  The resonance is an emergent property of the system that results from putting a driver with a certain Kms, Mms, and Sd into a box of size Vb.  Changes to any of these parameters can have tangible effects on efficiency.  This deserves a more thorough discussion.

 

I also need to clarify "small" box and "large" box.  The short answer, at least for single driver systems, is to look at Vb relative to Vas.  However, because Vas emerges from Kms and Sd together, changing the cone size alone alters the criterion for "small" vs. "large".  This should make some intuitive sense at least.  Halving the cone area makes the box effectively larger by this definition, and it also drops Fb.  However, as far as low end efficiency (below resonance) is concerned, the smaller Sd may help or hurt, depending on the other parameters.  The one thing I still haven't tried hard to work out is how to evaluate multiple drivers in a single box.

 

In any case, I want to be able to give a good description of how the sealed system behaves (still ignoring inductance) throughout its frequency range.  I'm thinking of giving detailed qualitative descriptions of driver motion, velocity, and output and how the forces / factors involved in controlling their motion change vs. frequency.  These could be supported up with a few simple formulae for quantitative support where appropriate without getting too involved in math.  I think I can link all of this back to what is observed in the response and impedance measurements and the combined effect on efficiency.  It may take me a while to get it put together, especially since I have a backlog of my own fun projects, but I want to do it.

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I see.  I plugged in all the manufacturer specs verbatim.  You opted to use their specs as a starting point but carry out the experiments with everything the same between the two except the Mms and Sd.  One major difference is that the HS-24 suspension is actually about twice as stiff as the HST-18.  Do you know if it uses the same spider?  Maybe it just uses two of them.  That would probably do it.  The doubled suspension stiffness holds back the HS-24 in ULF in I.B. a lot compared to the HST-18.  This is important because, as I understand it, suspension stiffness must often be increased to maintain mechanical stability of larger cones.  I expect this was the case with the HS-24.  This also holds back the IPAL-21 quite a bit in the deep / ULF bass.

 

I've been thinking about how to reply to the rest of your post.  You raise some good questions and I need to clarify my language carefully.  "High" and "low" are definitely relative to the resonance, but a lower resonance frequency does not guarantee deep bass efficiency.  This may seem counter intuitive but is very important.  The resonance is an emergent property of the system that results from putting a driver with a certain Kms, Mms, and Sd into a box of size Vb.  Changes to any of these parameters can have tangible effects on efficiency.  This deserves a more thorough discussion.

 

I also need to clarify "small" box and "large" box.  The short answer, at least for single driver systems, is to look at Vb relative to Vas.  However, because Vas emerges from Kms and Sd together, changing the cone size alone alters the criterion for "small" vs. "large".  This should make some intuitive sense at least.  Halving the cone area makes the box effectively larger by this definition, and it also drops Fb.  However, as far as low end efficiency (below resonance) is concerned, the smaller Sd may help or hurt, depending on the other parameters.  The one thing I still haven't tried hard to work out is how to evaluate multiple drivers in a single box.

 

In any case, I want to be able to give a good description of how the sealed system behaves (still ignoring inductance) throughout its frequency range.  I'm thinking of giving detailed qualitative descriptions of driver motion, velocity, and output and how the forces / factors involved in controlling their motion change vs. frequency.  These could be supported up with a few simple formulae for quantitative support where appropriate without getting too involved in math.  I think I can link all of this back to what is observed in the response and impedance measurements and the combined effect on efficiency.  It may take me a while to get it put together, especially since I have a backlog of my own fun projects, but I want to do it.

 

I applaud the destronstruction attempts but let me clear a few things up about my drivers since the HST-18 and the HS-24 have been the two drivers being compared. 

 

The suspension stiffness increase of the HS-24 vs the HST-18 comes from the surround, not the spider(s). Both the HS-24 and the HST-18 use the same two layer nomex natural color 10" OD spider pack. 

 

Suspension increase is not an absolute necessity with larger diaphragms (within reason). Increased stiffness does NOT equal increased linearity if the stiffness of the suspension is adequate to hold the soft parts in place without damage. You don't want a super soft suspension holding up 20 lbs of moving mass, but that is a given and would probably be used against me in this thread if I didn't say it. Proper placement of the mass negates the need for increased stiffness. Stiffness of the suspension system can be changed to achieve desired results but increased stiffness does NOT yield an increase in the linearity of the parts (assuming you have placed your mass properly). 

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lowerFE    35

I decided to reread some of the old responses to see if I can have a better understanding of everyone's responses now. I suspect there were things that went over my head when I first read this almost a year ago. I understand what everyone's saying perfectly now. I even got new understanding reading it again now. I was even able to follow SME's math! Thank you everyone who shared their knowledge. 

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