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In Reply to: RE: Is there anything in production similar to a JBL 2220 for horn loading? posted by Oldbean2 on December 28, 2023 at 17:16:37
A cool thing about horns is you can put any driver on any horn and it will make sound. The flip side is there is one combination of horn parameters that gives the highest efficiency / output for a given set of driver parameters and bandwidth.
For a 2220 with a 40Hz to 270Hz efficient bandwidth, the ideal horn paramete5rs looks like this.
throat area 192in sq (.69:1)
Rear volume 2850 in^3
Front volume 654 in^3
Hyperbolic expansion =.24
N=54%
Notice the ideal throat is larger than the driver area (negative compression ratio) and the driver xmax is only 3mm. The compression ratio is a multiplier so far as how much sound vs how much excursion and one of the advantages of horn is that for a given spl, there is less driver motion and so less distortion. Most of a drivers distortion is related to how far it is moving.
The 2220 is more suited to a wider bandwidth, this spec here (all other things being equal) is what increases the ideal compression ratio.
For instance if one asked for a 40Hz to 400Hz bandwidth, the ideal horn looks like;
throat area 80in sq (1.6:1)
Rear volume 2050 in^3
Front volume 169 in^3
Hyperbolic expansion =.4
N=48%
The compression ratio means much less excursion for a given spl compared to the first and so lower distortion at normal levels. Fwiw, compression drivers often have a compression ration greater than 8 to 1.
There is a 12 inch driver in a similar category if interested, look at an 18sound 12nmb1000.
Lastly, all the math i used above is for simple full size horns, normally what can be built is smaller than that so modeling the response of what you can build is the next step.
Thankfully now days one can model horns with programs like hornresp and what i use called Akabak, this ability to model / predict is something only possible in the last 20 years or so of horn design, something the ancients couldn't do.
Big?? No problem modeling works at any scale, here is an example of 1 channel of a large subwoofer modeled this way and used for outdoor movie projections.
Tom
Follow Ups:
First, I'm not as experienced in horn modeling/building as direct radiators
So my puzzlement is not the model examples but the assumptions/requirements you took in generating the examples.
So the narrower range (40 to 250) had you model a very large variances in throat and compression ratio plus back chamber volume over a broader range model example (40 to 400). Are you just using the horn geometry to act as the band pass without as much need for xover
I guess another way to ask is , of your two model examples why wouldn't one recommend the broader range geometry but utilize a passive xover to limit that output to the origina posters 250 hz upper limit?
Hi
There are several considerations one can follow if one seeks the greatest acoustic power vs power input and lowest distortion. These are not always important unless those things are important.
A "perfect" horn/driver that is N= 50% efficient exhibits a property visible in it's impedance curve that is an indicator. In the frequency range where it is 50% efficient, it has an impedance that is resistive and about 2 times the Rdc of the driver. This means that the heating (I^Rdc) or "work" being done is 50% in the VC DC resistance and the other half is acoustic radiation.
Sound simple but what you measure is a function of efficiency AND unlike a small speaker also the system directivity AND the issue that with a large speaker (like a bass horn) the inverse square law is altered by the size of the source (the law requires a small point) and a thumb rule is measure outdoors at at least 5 times the largest cabinet dimension then calculate back to one meter..
So, so far as electrical power capacity, 50% efficiency also infers the electrical capacity has also doubled in that bandwidth.
There is also the excursion, tied to which is most of a horn and direct radiator's linearity or lack of. The horn connects the acoustic impedance of "the big end" to the driver at the small end with an acoustic shape that ideally "acts like" a transformer...with a high pass frequency set by the length and expansion rate. Like putting your bicycle in a much higher gear, each pedal rotation covers more ground and so thanks to Huygens hydraulic principal, the higher the compression ratio, the greater the air motion into the throat compared to the radiator and motor but the greater the force placed on the radiator etc (part of the idea of impedance matching the driver to the horn load).
A less often considered fact, Excess hf bandwidth is actually undesirable.
Consider a simple direct radiating woofer driver that has a frequency response that had a large rise of say +12dB at 3KHz.
Ok, it's good woofer and who cares about 3K, i will low pass this guy at 300Hz or lower. So on listening there was still something there at 3k so add a brick wall filter at 300Hz and then a passive notch filter and it never went away.
The reason was the distortion harmonics the driver always adds are all multiples of the input, the bad ones you hear most easily are 3,5,7,9,11 th and so on.
You hear these most easily because your hearing becomes much more sensitive as you climb out of the frequency basement. For example to be just detectable at 20Hz, a sound has to be around 75-80dB SPL actual and just a 7% 3rd harmonic at 60Hz sounds equally loud as the 20Hz fundamental.
The driver wasn't overly "bad" in linearity but magnifying all the distortion harmonics by that +12dB or 16X made them detectable and made the speaker "locate-able" when eyes were closed..
Free sound and localization you don't want, not part of the input signal.
With a horn, there is the front volume to consider, if sized correctly, it can actually extend the hf corner some (just like the vented box is a low pass filter driven differently that does the same at the bottom end) ...in exchange for a sharper hf and lf acoustic low pass roll off.
This acoustic "low pass" between the driver and horn rolls off the distortion components that enter the horn and radiate unlike a passive or active electrical filter and is part of all the Synergy Horns.
This front volume appears to have been considered in your model and as Bill suggested, these models usually don't consider HF directivty which increases the on axis level vs total sound power.
I have not used hornresp, does it produce an impedance curve?
Happy New Year!
Tom
I'm not doing good job of communicating my question
Original poster wanted horn loading from 40 to 250 for a specific driver
You responded with a model to fit that 40 to 250, but you also gave a model of 40 to 400 as more suited to the driver. BUT the models are vastly different just to cover extra 251 to 400.
I would think that models based on same driver and design principles would result in the two models being closer in parameters, especially since the difference is up in frequency not lower in frequency.
So that as backdrop, my question is are these models vastly different based solely on that additional 251 to 400, OR where the models vast difference a result of you using different design principles between the two models to illustrate a more suited model for the original poster's specific driver?
HornResp does give an impedance curve, and just about anything else you could want. I never warmed up to AkAbak, so I can't say how they compare, but HornResp is very,very good. On the subject of the high frequency accuracy it's just as good as box programs like WinISD, which is to say not very. It's not about directivity so much as the general inability to predict response more than two octaves or so above Fs from T/S specs alone.
Hi Bill
I am in a similar boat, i started with the old Akabak when PSpice was the only way to model crossovers and never got around to trying Hornresp. Akabak can be as detailed as you care to make the model AND it's usefulness is only as great as it's ability to predict what you have built and not how cool it looks on screen.
In that area, there are some fudge factors one needs to add in Akabak to get a high degree of accuracy and those values you can deduce from the measured results (if it's that important).
This is exactly the same when simulating electronic circuits and that often means a "C" is 2 or 3 or more components in the model depending on what your looking for and how closely.
I would assume Hornresp in the model here and figures i derived are for the region where the driver / radiator has available mobility, this would be the region seen as the big impedance peak when in a sealed box.
THAT (the region under that peak) is the region where horn loading can greatly increase the efficiency by loading that area with an acoustic radiation load. IF one has a horn that is around 50% efficiency, one see's instead of a big wide impedance peak like a sealed box, most of the time the impedance under that peak is now around 2X Rdc. Thank heaven for high directivity as a typical hf compression drivers here actual broad band efficiency is rather low even with a high compression ratio..
Another way to describe that active area is the upper part of the impedance slope is controlled by the moving mass and the lower slope by the system compliance (box and suspension stiffness). At the high end, one can add some extension in exchange for 1 order steeper roll off with the right size front volume when applicable.
In between those slopes one can load the driver significantly AND importantly, adding a horn, the air mass in the throat is part of the new impedance curve AND that added mass (looks like a capacitor) increases as the frequency falls as one approaches the knee in the response.
Reactance annulling is when the change in air mass as the frequency falls (a property with some adjustment in the hyperbolic expansion rate) is offset by by the system compliance, in effect making it "at resonance" not at one frequency but over some added range extending the availability of the driver to be loaded to a lower frequency. As if in a parallel R,L, C circuit, the C was automatically variable over some small range to maintain the peak in the impedance.
I don't know about Hornresp but in Akabak, the assumption is a simple piston and i am not sure how it deals with horn loaded piston radiators that are larger than K=1. It does show directivity for any size radiator and horn. For sure, with a good compression ratio, one does not get as good measured results vs predicted above that.
Happy New Year
Tom
All horns are bandpass. One doesn't necessarily try to incorporate the high frequency knee into the design rather than use a crossover, but you can if you wish. HornResp makes it easy, as you can use its Design Wizard tool to set both the low frequency and high frequency knees. The main changes are to the front and rear chambers. If lowering the HF knee made the cabinet smaller you'd say do it, but by and large it doesn't. It can even make it larger.
Also note that like all programs that use T/S specs it's only accurate within the region of pure pistonic response. The actual high frequency limit can go higher than the program predicts, sometimes a lot higher.
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