# Drivers spacing rules

#### Savi

##### Member
Hi,

As a hobby, I am currently spending some time to understand the physic behind speakers design (most of my readings are on this forum, diyaudio + F Toole book). There is one subject which is often discussed and is still not clear for me: drivers spacing on front baffle in particular between mid and tweeter).
Until now, I was on line with the simple theory: the closest the better (ideally within 0.5 wavelength of the XO) in order to avoid vertical off axis nulls around crossover frequency. It is easy to simulate with xdir software.

But then I read the following post of kimmosto (creator of vituixcad simulator) which clearly has a huge expertise in the subject i quote:

"As close as possible' could be 'the worst possible' for directivity index i.e. either on axis (~listening window) or power response or both should be compromised to get balanced sound.
Of course if minimal vertical lobing is priority #1 then you should locate as close as possible. Coaxial driver wins that game always, but otherwise not necessarily...probably.

With simplified theory c-c = 1/2 wave length is the worst case for power response with equal DIs, and c-c = wave length at XO is the best case. Simply because sum with difference of 1/2 wave length is null and vertical +/-90 deg have the biggest weight in power calculation (due to dual orbit data to spherical intensity conversion). Early vertical reflections have significance too and DI of different radiators are not always equal => the smoothest DI and ERDI is found when c-c = 1.0-1.4 x wave length. This means that possibility of the worst DI is when c-c = 0.5-0.7 x wave length."

If my understanding is correct, the power response of a speaker is more important than vertical off axis. Hence, in order to obtain the best drivers position on front baffle, one should measure each driver on and off axis and use a software (vituixcad for instance) to calculate the power response with respect to frequence to find the best driver spacing. The off axis dispersion is then something we deal with, not that important as long as the listener is within speaker axis.

Is my understanding correct ? If yes, do you agree with the statement ? Sorry if I missed a similar thread.

Edit : I post on the wrong place... I dont find how to move my post to "Room Acoustics and General Speaker Discussion", if a someone could help or move it ?. Thx !

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#### puppet

##### Active Member
To my knowledge there aren't any "rules" on spacing. Often you'll find a situation where 1/4 or 1/2 WL isn't possible. Don't worry too much about it. Try to keep 'em within a wavelength.

OP
S

#### Savi

##### Member
To my knowledge there aren't any "rules" on spacing. Often you'll find a situation where 1/4 or 1/2 WL isn't possible. Don't worry too much about it. Try to keep 'em within a wavelength.

Thanks for your return. Actually, for the moment I am just doing an intellectual exercice so I am not worried

In short, my question is: "let say that your drivers and approximated XO frequency choices allow you to have 0.5 WL:
1) you go for it
2) you run simulations to check power response of your baffle choice
3) something else
?

In the next weeks, I am going to download vituixcad and see what I can learn but I have to find relevant measurement files to play with it.

##### Active Member
Thanks for your return. Actually, for the moment I am just doing an intellectual exercice so I am not worried

In short, my question is: "let say that your drivers and approximated XO frequency choices allow you to have 0.5 WL:
1) you go for it
2) you run simulations to check power response of your baffle choice
3) something else
?

In the next weeks, I am going to download vituixcad and see what I can learn but I have to find relevant measurement files to play with it.
Don't forget you can trace spl's w/ vcad.

I found some nice threads and quotes:

https://www.diyaudio.com/forums/multi-way/342494-causes-axis-nulls-4.html

Kimmo quote:

Directivity is one effective parameter, but before that we could recognize few other effects due two separate sources (assuming phase match):
- dip(s) in power response (P)
- dip(s) in early reflections (ER) due to dips in vertical plane, causing
- hump(s) in early reflection directivity index (ERDI).

Vertical nulls are usually unavoidable with multi-way (without coaxial). XDir is able to show that self-evident in addition to direction of null(s), but that's it. No value.

Simple method is to initiate c-c and XO frequency so that combination of c-c or XO frequency tries to neutralize dips in P and ER, assuming that radiators are close to omni (in half space), or lower band is beaming more. c-c is 1.2-1.4 * wave length at XO frequency.

Next level would be using some estimation for directivity e.g. rigid piston, and repeat previous sim.

Close to final level is to make prototype with almost any c-c or ~1.2 * wave length at estimated XO frequency, measure radiators separately and simulate crossing with proper tool. I'm too lazy or confident to do this phase.

Final speaker is measured with final drivers and optimized by on-axis, off-axis, LW, in-room, ER and P adjusting XO frequency, orders, phase matching with acceptable compromises. This phase is able to compensate some mistakes in c-c and XO. Null exists but sound is balanced if concept and application is otherwise okay.

Jeff Bagby (RIP):
Power response is the mathematical integration (as in calculus) of the frequency response amplitude on all axes. Technically, the number of axes is infinite, so measure away.
However, it is possible to approximate the power response from known research and math. I studied the data out there on the topic and reviewed the math involved and developed my own unique algorithm to calculate the line you see. I believe my method to be among the most accurate ones developed, and it appears some others may think so too, because I was contacted by a well-known developer of a fairly expensive acoustical simulation software package about using it in their software.

One thing to note regarding power response is that it is dominated by the 90 degree off-axis response, so driver directivity plays a key roll, which is one of the things I built into my program. The other thing that is key is that it is the non-correlated (with respect to phase) summation of all drivers. By the way, you do not want flat power response. This will not sound natural to your ear. If the high frequencies are flat in the power response this will lead to too much high frequency information coming to your ears. This is because lower frequencies are radiating 4pi and the higher frequencies are radiating 2pi, so for the power to be flat the axial response will be lifted in the high end. A natural tonal balance will be heard with a flat on-axis response and a gradual drop as frequencies increase.

As others have stated the power response is a calculated line that is irrespective of your chosen axis, so it does not change as you change your listening axis. However, what you hear from a speaker will certainly change. Our perception of a speaker's tonal balance is dominated by the first arrival on-axis sound. The power response will affect the tonal balance in a secondary, and significant lesser manner.

http://techtalk.parts-express.com/forum/tech-talk-forum/25470-power-response/page2

#### voodooless

##### Major Contributor
Forum Donor
To my knowledge there aren't any "rules" on spacing. Often you'll find a situation where 1/4 or 1/2 WL isn't possible. Don't worry too much about it. Try to keep 'em within a wavelength.

Not worrying about it won't make a good speaker. Have a look at the impact of spacing on the off-axis response with this little demo: https://www.falstad.com/interference/

#### puppet

##### Active Member
Worrying about something that you often can't change/improve won't make it better either.

#### BenB

##### Active Member
Forum Donor
It sounds to me like some programs exaggerate the importance of the response at +/- 90 degrees vertically. It's very easy for this to happen if someone applies the same number of azimuthal (horizontal) axes for every vertical angle. This comes about because it's very simple to uniformly sample a circle, but difficult to uniformly sample a sphere.
Perceptually, our expectation is that reverb has been decorrelated from the direct sound, and it will often have a spectral response that resembles comb filtering. That's fine. Early reflections on the other hand ought to have a spectral balance similar to the direct sound. With these concepts in mind, it makes more sense to place the drivers about as close together as possible, in order to have nice floor and ceiling reflections. I try to achieve 1/3 wavelength (or less) c-c if possible. (Unless I'm designing something for consistently high directivity.)

#### voodooless

##### Major Contributor
Forum Donor
Worrying about something that you often can't change/improve won't make it better either.

Of course, it will! It will lead you to make different decisions, discard some options, look for others, get creative!

#### puppet

##### Active Member
Are we still talking about C/C driver spacing?

##### Active Member
I forgot to mention, my first speaker for my desk is a 1/2 WL speaker. I am a newb and probably paid too much attention to the vertical beamwidth when simulating/comparing. I tried to find good results from all of the vcad graphs but I for sure checked the vertical directivity. Having 100% phase alignment was another focus of mine. All of these things come at a cost of the max SPL since I had to go smaller for my mid.

I have a 90.5mm C-to-C and an XO of 1700hz.

I attached some of my vert sims. I would flip between a bunch to compare them when I was deciding what drivers to use.

First, a test of how accurate a sim is. The scanspeak 10f horizontal image made from a trace of real measurements from hificompass. The vertical is made from only a single on-axis measurement and the other angles all come from the DOD model VCAD uses. I think the response looks close.

The next set of images a bunch of simulated verticals for different 3"-5" drivers and different XO's. The tweeter is the same for all. The "r5" version of the XO was the simulated winner for me. You can see how the vertical beamwidth changes with different sized drivers.

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OP
S

#### Savi

##### Member
Thxs headshake for these insights. The work you have done on vituixcad is exactly the kind of analysis I want to do. I am sure it will help me in my understanding quest. For a given mid/tweet/XO/baffle choice, I am curious to see power response and directivity with respect to ctc distance. BTW I read you thread project (bliesma/eton/seas active speaker). Really interesting. I guess this will me my next step when I feel confident with the basics and software.

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