tune the rear chamber for reactance annulling
I would like to find a help for the reactance annulling of my horn loaded bass speaker.
A short and condensed introduction to my system:
I started from a JBL 4550 + 2xAltec 515B, the upper 515B works till 500Hz, the below 515B works till 200Hz and then it is cut at 12dB/Oct.
After modelling the reflex by WinISD I settled up a tuning to 25Hz of the rear chamber, and cause the "regular" loose of emission below 100Hz, taking the inspiration from the Linkwitz job, I apply a kind of its transform: by a +8dB/Q=5,5 centred to 45Hz.
The frequency response of the bass way, now, is OK ... and the woofers don't move like crazy where equalized a lot.
For the Sigfried Linkwitz job read this ESP - The Linkwitz Transform Circuit from the Rod Elliot web site. It is very useful document.
After a fight with myself for years finally the response is not bad: fast and controlled till the very low frequency, without any rubber or cardboard effect of sound.
The bass sounds and traces are clear and detailed. It is a pleasure now.
But, you know, never be satisfied ... so I moved to the next step.
I have another pair of 4550 and I started with a totally new approach.
Even if what I described above is good for the ears and the feeling is not bad, I would like to improve again.
For sure using the mouth of the horn in the first octave from the cut off and below its cut off, the acoustic impedance plays a big role and, where it is reactive, for sure the response is not flat. I want to minimize this "problem" this "behaviour" this "characteristic" of the horn with its acoustic impedance not compensated.
I want to implement the reactance annulling to the 4550 + 2x515B crossed as said before around 200/500 Hz.
Of course the reflex volume is not considered because a rear chamber is now made, and it isolates the reflex volume from the woofers.
So by the reactance annulling, down to 70Hz (from the mouth size and horn position) the frequency response should be as flat as possible.
Below 70Hz I already made an open baffle sub with 4xIB15 woofers made by AE Speaker, using the whole loft over my head. Works, and how it works!
Now the problem: how to tune the right rear chamber volume to try the reactance annulling?
I started following this idea GoodSoundClub - Romy the Cat's Audio Site - Practical Guide for Back Chambers Tuning. by "Romy the Cat".
But, with the rear chamber totally filled by polyurethane foam, founded the best back chamber volume - opening a little the rear cover to have the best bass response - is quite difficult to measure the resonance frequency of this chamber.
I have a CLIO system, but the impedance measured is for sure wrong.
Probably only the CLIO, without an outside amplifier, cannot drive properly the woofers ... the loud is not enough to make the measure possible.
I will try shortly with an external amplifier.
Anyway, here I am looking for a help:
How is possible:
1) by the measurement of the impedance (amplitude + phase and not real + imaginary) and
2) by the measurement of frequency response (module and phase)
to tune the rear chamber so the reactive acoustic impedance is minimized above the cut-off of the horn?
Thanks for who wants help me and share his experience with us if any.
Read the attached paper  by Leach. Pay particular attention to the Letter to the Editor and Author's Reply that follows.
To the Forum Police: This paper is published on the author's website as well as elsewhere on the web.
That is the seminal paper on this subject. But the thing is that paper describe fullsize horns, real life horns are shorter and have smaller mouths so the equations change a lot.
If you are a scientist/engieer by all means rework the model or turn to those who have reworked/ extended the theoretical framework.
But if you simply want to make your work at it best, go emperical and try different volumes and measure and listen to what sounds best in your particular setting. Reducing the chamber volume of a driver increase the resonance frequency and also the Q of the resonance. Depending on the intrinsic Q of the driver the outcome with two diffrent drivers will be different even if you have the same horn with the cavity set to get the same Fr.
This is the response of a horn similar to LaScala but with two different 12" driver. The upper curve is a Beyma G320 midbass driver, a typical good horn driver very low Qes and low Vas. The lower curve is of far "inferior" driver with twise as high Qes and one octave lower resonence frequency so the mass roll off should be two octaves below the Beyma
The apparent Q value and frequency of tuning is different for the drivers.
So I suggest go empirical
As for chamber reduction I would fill the chamber with many small water bottles to reduce the volume and then take out what ever number is needed. Way less mess than foam
Really the Maeshall theory you can use to desing the rear chamber, but at the end of the day there is the need to check if it is satisfied or not.
This is what I am looking for ... to a way to check, by instruments, when the reactance annulling is reach ... or, better, when the reactance in minimized.
I try this way immediaetly.
Has anybody read Honeycutt's paper  ?
Reducing physical size limits for low-frequency horn loudspeaker systems
It's a dissertation. It really annoys me when university papers get locked up by a third party publisher.
From the abstract and sample, it appears to be based on work that's been done by other people. (I'm not criticising.) The infomation is out there, just not organised in one place. For example, he discusses using multiple horns and interleaving their impedance peaks. Horst Muller has done work in this area (and built examples). He posts on diyaudio and has a web page:
Scroll down to his "Double Horns".
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