HELP: xmax and open baffles

[cuibono]

The math for OB is different from box speakers, but has been worked out. You need software if you really want to know what is happening, particularly with cone displacement. The software mentioned above is good, and I use it, but the most comprehensive set of software is MJK's mathcad worksheets (google should find his webpage).

Here is the basic run down for OB - because the back of the driver is open to the air, and is out of phase with the front of the driver, when the two wavefronts meet, they cancel. They meet more at lower frequencies, and less at higher - and once the frequency is high enough, they no longer interact. This leads to two thing - less bass SPL, and irregular off axis response in the highs above the 'baffle peak', the point where the front and back waves are no longer interacting directly.

The frequency of the baffle peak is determined by the baffle size and geometry. This is most effectively predicted by MJK's worksheets. If you want to predict low end response or Xmax limitations, you need to factor the baffle, the drivers area (Sd), and its linear displacement (Xmax). BTW, the free software I've used (excepting Linkwitz's) was fairly inaccurate.

The bottom line is that OB's have greater excursion demands at lower frequencies because the front and back waves are canceling.

Gainphile recommended 40cm is too wide because the baffle peak frequency will be relatively low in frequency, and so the off axis response will suffer above that. Without knowing more about the driver/baffle, 5" is generally too small - it does not have enough excursion and volume displacement to create 'decent' SPL (which depends on how loud you listen). I would guess a 5" driver could only be used down to 400-600Hz, but that is a rough guess.

But people do use 5" drivers or less - but they are listening at relatively low levels, to simpler music, on (much) larger baffles, with much poorer off-axis frequency response (which to me matters a lot). Generally, an 8" mid or larger is necessary if you want decent reproduction between 100-250Hz.

here is a link to MJKs worksheets: http://www.quarter-wave.com/

[gainphile]

I can't recommend JohnK's ABCDipole program enough. At $14 it's damn accurate until the 1st peak.

or just use the rule of thumb, baffle width <= 2x driver diameter.

Large baffles will have poor off-axis response, although measured/simulated as flat on-axis. Unless you want a passive system, this is better avoided.

Bass rolloff problem is easily fixed with active xo. Not so with passive.

Example of pretty good off -axis response is something like below, an uneq'd measurement. You can see it's nice until 2.5khz or so, and then become really crappy. With large baffle, this will happen very low in the frequency region.

[Rudolf]

Pierre,

cuibono has summed the basics of the dipole behaviour pretty well. So I would just like to add some aspects:

1. Regardless of the box (or nobox) type of a loudspeaker project - to keep a given SPL level a driver needs to quadruple its excursion with every halving of its lower frequency limit. In a well designed box-type speaker there will be a frequency, where the spring force of the compressed air on the back side of the cone will limit its excursion. On OB there is no such limitation.

2. Below the lowest dipole peak the SPL will fall off with 6 dB/oct. You need to double the excursion with every halving of the lower frequency limit to keep the same SPL level.

1. and 2. will add. If you know the excursion of your driver in a closed box at e.g. 1 kHz (a frequency where a midrange driver will behave pretty much the same regardless of box or OB) and a specific SPL level, you can easily calculate the excursion for lower frequencies on OB. You will have noticed that the overwhelmingly dominant factor for the maximal SPL level is your demand for the lower frequency limit.

How do you find that lowest dipole peak?
EDGE is a very user friendly simulation program to calculate the behaviour of an open baffle. AFAIK it uses the same Backman algorithm that basicly all other OB simulation programs do. But it does NOT include specific driver TSP! Those have to be superimposed by the user himself.

Originally Posted by WDYSUN

this seems to contradict what have been said in previous posts.

You can gain some SPL with room effects, that will help you. But those are very much determinded by your individual room and speaker positioning.

I am still confused about the relation: OB vs excursion.

See explanation at the top.

How did you get this simulations?

With EDGE.

So what would be the optimal baffle width according to your simulation?

There is no "optimal baffle" width per se. It completely depends on your individual preferencies. If you strive for best controlled response off axis, as I do, the baffle width has to be small enough to keep the lowest dipole peak at the upper end of the planned passband. This will raise the EQ demand somewhat.
If you want to minimize your EQ demand, you make the baffle as wide as your wife allows. And forget about constant directivity.

The behaviour of OB at high frequency still remains a mystery to me. Troels Gravesen did an "OB study" ...
In the second part he tries several combinations with the famous Vifa P13WH, well it doesn't have a 40cm baffle, but none of the response I see here are predicted from models. I honestly wonder a bit about the accuracy of the mathematical models for OB.

I don't know any models that do account for wings. They are either for flat baffles or for "frames". Keeping this in mind those models seem to be precise enough to me. You should not forget that Troels measurements are not free from room influence.

Rudolf

[AndrewT]

if the baffle is "wide" relative to frequency, it seems that the response drops and becomes ragged.
What causes this?

I see the LF requirement, I cannot see the HF conflict.

[Inductor]

Originally Posted by Rudolf

The falling response below 300 Hz is purely due to the dipole baffle loss. The driver itself does not work less below - it has to work more!


It is absolutely necessary IMHO. And you will need at least 12 dB/oct.

Regarding the baffle width: The diagram below shows the response of a 40 cm wide rectangular OB on axis (green) and at 30 deg (red). A baffle of that width is not optimal above 1 kHz, if constant directivity is a design goal.

Rudolf

Isn't that true?! The green line is typical of the Jamo R 907 Open Baffle with the dip at ~1KHz.

[Rudolf]

Originally Posted by AndrewT

if the baffle is "wide" relative to frequency, it seems that the response drops and becomes ragged.
What causes this?

The lowest dipole peak is followed by a dipole dip at twice that frequency. Both are followed by more peaks and dips. Peaks whenever front and back wave are in phase, dips whenever they are 180 deg out of phase. Off axis those peaks and dips occur at different frequencies than on axis:

See Linkwitz:

Originally Posted by Inductor

Isn't that true?! The green line is typical of the Jamo R 907 Open Baffle with the dip at ~1KHz.

That's right. We have tried to explain that for the R 909 at Open Baffle Speakers. Look for reply #4 and 5.

[AndrewT]

Hi Rudolf,
are you interpreting Linkwitz correctly?

If the baffle gets wider, then the rear radiated path length gets longer. That is not addressed by the graphs you linked to.
When the path length gets longer the first null will be pushed higher in frequency and less deep. That is opposite to your interpretation of Linkwitz.

Please explain further in case my cursory scan of Linkwitz has picked this up incorrectly.

[gainphile]

You need to take into account driver's directivity compared to the width in acoustic term.

Quoting the guru himself:

"By making the baffle narrower the transition to the oscillatory region moves higher in frequency, e.g. to above 2000 Hz in the above example. As the driver itself, due to its piston diameter, becomes more directional with increasing frequency, it also illuminates the panel edge with less strength, which then reduces response irregularities caused by diffraction. "

http://linkwitzlab.com/faq.htm#Q8

This is not only a theory but can be done empirically. I've had multiple iteration with my speakers:

P13WH on 45cm baffle:



Look at Johnk's simulator with for the same setup:




P13WH on 30cm baffle, +tweeters. Note 1kHz region. Basically the baffle is still too large. The tweeters is always the achiless heel of typical dipole setup.




P13WH on 20cm baffle. Smooth up to 2kHz

[Rudolf]

Originally Posted by AndrewT

Hi Rudolf,
are you interpreting Linkwitz correctly?
If the baffle gets wider, then the rear radiated path length gets longer.

Yepp.

That is not addressed by the graphs you linked to.

That's right. The graph is only about the dips and peaks and their change with angle.

When the path length gets longer the first null will be pushed higher in frequency and less deep.

In this case it's the other way round.

Please explain further in case my cursory scan of Linkwitz has picked this up incorrectly.

I am not sure I understand where you want my explanation. So I just did a sim with two different baffle width. Would you mind to guide me to the effects you were writing about - if they show up in the graphs?

[otto88]

. . and gainphile your rule of thumb: baffle width <= 2x driver diameter is accurate,
which it seems is broadly supported by Rudolf your sims with two different baffle widths for the Vistaon . .

And someone (me) is considering *different midrange drivers,
then am I right that ~ other things being equal ~ smaller mid drivers and smaller baffles push dipole peaks higher, therefore offer better controlled response off axis - over a wider frequency range?

For a dipole system, my situation:
I have a pair of very good “midbass” drivers (97 dB Lambda 15”) which might run up to between 500 – 800 Hz, the crossover frequency to determined by experimenting.
For above them, I had been looking at either:
- 6.5” mids (95 db B&C or PHL that I have, with tweeters above) or
- 6.5” full ranges (eg the 95 db Fostex 166/ 167)

Recently I learnt of the benefits of multiple small drivers, especially lowering driver distortion and less compressed dynamics, and am now considering 8* Fountek 3” drivers, to also give c 96 dB. (As the amp is a 35 watt tube amp, high sensitivity for good overall dynamics is a key design goal).

With 3” drivers instead of 6.5”, if I understand this thread correctly, with the baffle width above the midbass roughly halved: you should get better controlled response off axis, to a higher frequency with (multiple) 3” drivers?

Maybe just horizontally? (to me, that is more important).

I know that a small line of drivers has a different dispersion pattern to a single driver: wider, but less vertical dispersion; and lower drop in SPL in relative to distance,
but (if one can accomodate that, subject to enough Vd) – have I got it right that multiple smaller drivers on a narrower baffle will give better response off axis over a wider frequency range?

Thanks