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Multi-Way Conventional loudspeakers with crossovers

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Old 18th January 2019, 02:31 AM   #11
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So you want to design your own speaker from scratch!
Default Step 5. Designing the Crossover

This is the easy bit right? Just go to an online calculator put in the frequency you want to crossover at and it will spit out the values right? Or just go to partsexpress and purchase a ready made crossover that crosses over at a suitable frequency.

If only it were this easy. If speakers had a completely flat frequency response, and a completely flat impedance, and the distance from each driver to your ears was the same then yes that would work*, however that is not the case in reality and we need to take these things into account.

A crossover filter does not just cut off the frequency at a particular frequency, it gradually rolls off the speakers responses over a fairly large range. In this range BOTH drivers are adding together to form the sound. For this to work ideally, both drivers need to be adding together equally and need to be in phase with each other through this range.

Lets see what happens with our theoretically flat speaker with a completely flat impedance using our text book crossover. For this we have two speakers which are both 90db efficient, completely flat and have a completely flat 8 ohms resistance. Now if you had such drivers you wouldn't be making a crossover in the first place, but it serves to demonstrate what is happening.

The schematic is for a textbook 2nd order linkwitz riley crossover at 3Khz. Calculated using this online calculator Speaker Crossover Calculators by V-Cap
designing a speaker from scratch images thread-2nd_order_lr_textbook-png
The graph is showing the summed response of the two drivers and the rolloff of each driver. See how wide the range is where it is both drivers that are summing together to make the flat response (It's almost from 200Hz through to 20Khz)!
designing a speaker from scratch images thread-2nd_order_lr_textbook_response_flat_drivers-png
Note how there is a step in the frequency response. This is due to the resistance inherent in the inductor which is in series with the woofer. For this sim I used 0.29 ohms for the DCR of the coil. It is not too significant but it does show that even with our perfect drivers we have not got a perfectly flat result with out text book crossover.

Next we will show what happens if we use actual impedance curves for real drivers (but still with our perfectly flat frequency response). I've chosen a Dayton RS150P-8 for the woofer and a Morel DMS37 for the tweeter, as I happen to have frd and zma's for both. Everything is the same except for the real-impedance curves being used in the sim.
designing a speaker from scratch images thread-2nd_order_lr_textbook_response_flat_drivers_real_impedances-png
Whoah!! What happened to our nice flat response!! Textbook crossovers only give a text book response with a flat impedance, which the above demonstrates very well . Now it is possible to greatly improve this by using impedance compensation on the drivers, but that is not necessarily something you need to do as you will see later when we do a more optimal crossover.

So now we add in the real responses of the Dayton and Morel drivers and see what we get.
designing a speaker from scratch images thread-2nd_order_lr_textbook_response_real_drivers_real_impedances-png
Probably not really what we want! So you can see that if we just used our text book crossover with our two new drivers, that we would likely have a bit of a tweaking job on our hands!

Note that even the above is a very crude estimate of what would really happen, as we have not taken into account how the baffle effects the frequency response of our drivers, or how differences in driver offset on the baffle affects their phase relationship to each other, in reality the above probably looks even better than it would in real life!

One of the things that people starting out with crossover design fail to grasp is that it is the acoustic rolloff of the speaker that is the real goal not the electrical order of the filter. When we say we want a 2nd order linkwitz riley crossover, that doesn't necessarily mean that it will be an electrical linkwitz riley filter (for newbies I would actually suggest that a fourth order LR or bessel filter is much more likely to give them results that they will be happy with, 2nd order acoustic filters are not easy!) After having said that, what I come up with later, does appear to be a 2nd order electrical filter on both the woofer and the tweeter, but it doesn't always have to be. When doing 4th order targets I have achieved it with 2nd order on the woofer and 3rd order on the tweeter, it all depends on the drivers and the frequency you cross them at.

We can demonstrate this concept by adding some target slopes to the third graph. The red lines in the fourth graph are our target 2nd order L/R at 3Khz. These show how our speaker should roll off to get the best blending (assuming we also get the phase right, but more on that a bit later).
designing a speaker from scratch images thread-2nd_order_lr_textbook_response_real_drivers_real_impedances_with_taregts-png
As can be seen the drivers are not following the target curves very well at all and the resulting frequency response is pretty awful. I'm sure if you got a result like this you would not be happy and wondering where you had gone wrong! We would be looking at quite a lot of tweaking by ear to sort out this mess, and without actually knowing whether it was the woofer, the tweeter or both that is causing the issue we would be stabbing in the dark.

So instead we can do some virtual tweaking and see what the results are with our sim. As previously stated I have not properly prepared these FRD's or put in proper offsets for drivers so this result is invalid, but is useful for demonstration purposes.

I spent maybe an hour playing around with some tweaks to get a result that is roughly +- 1.5db from approx 70 hz to 16Khz. It also has a good deep reverse null (meaning the drivers are in phase at the crossover frequency). Now of course I already have experience so that makes it faster, but I'm sure that trying to tweak this by ear would take an awful lot longer!

The new circuit is below:
designing a speaker from scratch images thread-custom_crossover-png
You can see that there has been a few additions, and also changes to values from our original textbook crossover. I used the optimizer on C2 and R4 which is why they have strange looking values, I would normally change them to the nearest standard value but was being lazy.

Below is the resulting frequency response using this new crossover.
designing a speaker from scratch images thread-custom_2nd_order_lr_rev_simple-png
Looks quite a bit better doesn't it?

Next is the reverse null response which shows how well (or not) the drivers are in phase at the crossover frequency.
designing a speaker from scratch images thread-custom_2nd_order_lr_rev_null-png

Now we show the individual driver responses and how well they track to the target LR2 curves. Also this graph shows each drivers phase. They do overlap at the crossover frequency but in general the overlap is fairly small, ideally you would have a much wider range where the drivers are in phase...
designing a speaker from scratch images thread-custom_2nd_order_lr_phase-png
The coil and resistor on the tweeter circuit are there for phase adjustment only. Without them the tweeter follows the target curve better at lower frequencies but the phase alignment is bad at the crossover point.

One last image shows the difference between our custom crossovers response (black) compared to our textbook crossover (blue).
designing a speaker from scratch images thread-custom_vs_textbook-png

Hopefully this has helped show why a text-book crossover almost certainly will not give you the result that you want.

*if such drivers existed, there would not be any need for a crossover in the first place

Lets keep this thread uncluttered, A separate Designing your own speaker from scratch discussion thread has been created.

Last edited by wintermute; 18th January 2019 at 02:44 AM.
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Old 18th January 2019, 02:32 AM   #12
wintermute is offline wintermute  Australia
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So you want to design your own speaker from scratch!
Default Step 5a Using Manufacturers curves.

So this part is just about what we need to do with those traced manufacturers curves if we are to have a chance of approximating the response on our real baffle and in our real box. Note that this is just an approximation, Ideally you want real measurements of the final implementation for designing your crossover, but as you will hopefully see this can be useful for fine tuning your design before you even cut any wood. Obviously this is optional

There are a few things about using manufacturers measurements that make them not ideal fro modeling our crossover.

1. They are likely taken on an IEC baffle or an infinite baffle (though sometimes they may even be baffleless). Unless we are planning on mounting our speakers baffles into our wall or have the speakers hard up against a wall then we are most likely going to have to take the baffle step into account.
2. The box (or lack of) used when testing woofers will affect the low end response in the manufacturers curves. Some manufacturers do state all measurement conditions, a lot don't. Most common would be a sealed box (which may vary in size depending on the woofer under test, but 20L is a good guess) or alternatively the driver is just mounted on a large baffle with no box behind. Seas is one company that provides excellent information on their measurement setup DATASHEETS

So what we are going to talk about here is manipulating those manufacturers curves so that we can make them more applicable to our intended use. This guide by Dave Dal farra http://audio.claub.net/software/Dave...ign%20ver2.pdf is where I first learned about doing these things and is recommended reading

I'm going to use vituixcad and Jeff Bagby's Baffle diffraction Simuator spreadsheet for doing these steps. We will use the SB17-MFC35-8 that we traced earlier and an SB26STCN-C000-4 tweeter which I have chosen simply because I like the look of it for a not too expensive tweeter.

Now depending on how far you want to take things, we can in fact subtract the IEC baffle response (both SB drivers were measured on an IEC baffle) before we apply our own baffle effects to the measurements. It's an additional step but if you want the highest accuracy it is probably worth doing. If you just want to get a ball park idea how the drivers will go in your design then you can probably skip it (Note that that comment should not make you think that this method is super accurate, but it is better than using the raw manufacturers curves).

Now something I wasn't aware of is that the IEC baffle is not a fixed size but in fact varies depending on driver size. From what I have been able to find it seems that for drivers smaller than 8" it is the same size, but for drivers bigger than 8" it scales up in proportion to the baffle dimensions for the 8" driver. I've done a spreadsheet (attached) which calculates the baffle dimensions and offset for the speaker based on this info I found from the IEC paper on the subject.
Click the image to open in full size.

Putting the baffle dimensions for 8" speaker into Jeff's spreadsheet and changing driver diameter to 6" and measurement distance to 12 inches (to match our 6" SB driver and measurement conditions) We have the below:
Click the image to open in full size.
Click the image to open in full size.
We can save the above diffraction curve and subtract it from our manufacturers measurement to get a true infinite baffle response. However we need to scale the measurement first as we need it to have a zero db reference, and the frd file produced by the baffle diffraction modeler changes the loss if the distance is under 1M. This is necessary because we are going to use divide and multiply functions to subtract our IEC baffle and add in our own baffle, and they need to be at the same baseline or it will mess up our results.

Vituix cad has a calculator menu under tools. We can load our IEC baffle diffraction into slot A in the calculator (you will need to adjust the y axis to show the curve as it is under 0db) when we do this we can see that our measurement is centered on -5db (see below)
Click the image to open in full size.
We can now delete this from slot A as we know we need 5db of offset, which can be applied in the scale db box above the measurement. We actually want to load our baffle diffraction file into slot B, and our manufacturers curve into slot A. We will have to readjust the Y scale again when we load our manufacturers curve.
Click the image to open in full size.

The image above shows our manufacturer curve loaded and the IEC baffle subtracted from the response. The difference is quite subtle, but will be more pronounced if the manufacturers curve you are using was measured at a distance of 1M (and you used that distance when doing the baffle sim). It's not intuitive, but to subtract a response you do not use the subtract function, you use the divide function.

We can now save this modified response curve using the calculate and save button. Pay attention to the dialog box that pops up, it tells you where the frd was saved! You will probably want to copy it somewhere more convenient (and rename it to something that you know what it is) as next time you do a calculation it may overwrite what you have just saved. We will use this just saved response curve for applying our proposed baffle response to.

We now need to calculate the baffle diffraction effect of our own baffle. For this I would recommend setting the distance at at least 3ft (1M) as it will give us a more realistic diffraction (unless you are designing nearfield monitors). Back in the first baffle step post (post #6) we came up with a box with dimensions 513mm X 229mm X 287mm I've done sims with both 513H X 287mm wide, and 513H X 229mm wide, I'm leaning towards the narrower baffle, as the response peak is lower with the narrower baffle (which was a bit of a surprise).
Click the image to open in full size.
Click the image to open in full size.
This is the baffle effect for our 287mm wide baffle. As you can see when this is applied to our manufacturers measurement it is going to look quite a bit different.
Click the image to open in full size.
Click the image to open in full size.
This is with the 229mm wide baffle. My gut feeling is that this will give the better result, but we will apply both and compare to see.

With both of the above sims I decided to leave the woofer centered (horizontally) on the baffle and moved it up and down in the sim until I found something I was happy with. This is where you potentially can try and use the dips and bumps in frequency response to counteract dips and bumps in the speakers response. It won't always work out though, sometimes they can coincide making things much worse, but that is why we want to do this step! Better to be forewarned rather than get a nasty surprise!


Note that you should be able to model the IEC baffle in vituix cad as well. We will use vituixcad for subtracting and adding our baffle effects.

So assuming we have saved the above two baffle responses, we can now load these (along with our IEC baffle corrected response into vituix cad, and apply the baffle step. Load the IEC baffle corrected response into slot A and the baffle simulation we want to apply into slot B. Then use the multiply A X B option.
Click the image to open in full size.
You can swap between no baffle step and baffle step by toggling between "real A" and Multiply A * B Click on the calculate and save button, and go grab the resulting file and copy it somewhere useful, changing the name to indicate which baffle width it was. I did the same with the 229mm width baffle.

I then loaded each of the original manufacturers curve, the 287mm baffle and the 229mm baffle resposnes into speaker workshop (an old favourite) to put each on the same graph to compare.
Click the image to open in full size.
Green is the original manufacturer curve. Blue is the 287mm baffle, and black is the 229mm baffle. One thing is apparent, the bass drops off quite significantly under about 320Hz with either of our chosen baffles!

We can follow the same approach for the tweeter, you may be surprised by how much of an effect the baffle can have on it too.

I chose a small face tweeter from SB accoustics an SB26STCN-C000-4 for the hypothetical speaker I am building. The below screenshot shows how the diffraction looks when I place the tweeter very close to the midbass (reducing the distance between the tweeter and the midbass helps to control lobing).
Click the image to open in full size.
Sorry for the change in image size, I got a new laptop with a higher resolution screen..... Anyway what this shows us is that our tweeter is also going to diverge from what we thought was a quite a flat response if we place it on the baffle in this position, and we just have a standard sharp 90deg edge on our baffle.
Click the image to open in full size.
It does get somewhat better if we move it up the baffle around an inch. This is where those tradeoffs come in again! We can move it up a bit to smooth it somewhat but it may have an effect on how we design the crossover as the distance between M and T will be greater.
We could of course revisit our M's placement and see whether moving it up a bit seems acceptable. You may be starting to see the value in doing these sims. It is pretty quick to get a rough estimate of how your baffle design and layout is going to potentially affect your speakers performance. You can save a lot of time and resources! Imagine how much more time and resources is required to keep making new baffles to test another configuration!

But there is another trick we have up our sleeve. We can round or chamfer the baffle edges (felt may also be an option). Lets see what happens if we put a 1" radius on our baffle. Note I'm not sure if this is a chamfer or a roundover, more complex sims such as the FRD consortium one can do both.
Click the image to open in full size.
This is the original positioning close to the midbass but with a 1" radius on the edge. As you can see it is significantly smoother. Note that my own experience using a 1" chamfer was that I probably should not have done the chamfer on the bottom of the baffle. In my Case the speaker sits on top of another speaker (sub) and the chamfer forms a cavity that actually introduces some anomalies which are not there without it. This was a good lesson for me about why it is smart to do a prototype!! It's not major so I decided to live with it.

Having found the above we may want to go back and revise the midbass sim (and check that there is enough space now on our baffle to accommodate it!!). Once we have settled on a baffle configuration we can apply our midbass and tweeter Baffle diffraction curves and we are ready for the next step.

I was originally going to cover how to deal with the difference that our box alignment may make in this post as well, but since it is getting so long we might put that into a separate post! A hint of what I'm talking about is in this post First project (revised)

Oh and I probably should re-iterate. There is no substitute for doing real measurements of the speakers in their actual enclosure. All of the above is to give us an idea, and hopefully help us with design decisions before we cut any wood. It probably can get you a better result (or perhaps I should say starting point) than you would get if you didn't do any measurements at all, but ideally we want to be doing proper measurements in order to get the best idea of what is really going on with our speaker.

One other important point! The effects of the bass drop showing in the baffle step sims above will vary depending on the speaker placement and room, and that needs to be considered when designing the crossover. If you design to completely compensate for this theoretical drop, in a real life setting you will quite likely end up with something out of balance.

Lets keep this thread uncluttered, A separate Designing your own speaker from scratch discussion thread has been created.

Last edited by wintermute; 16th November 2019 at 12:20 PM.
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Old 18th January 2019, 02:33 AM   #13
wintermute is offline wintermute  Australia
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So you want to design your own speaker from scratch!
Default step 5b doing a real crossover sim

Stay tuned.

Lets keep this thread uncluttered, A separate Designing your own speaker from scratch discussion thread has been created.

Last edited by wintermute; 18th January 2019 at 02:45 AM.
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Old 18th January 2019, 02:34 AM   #14
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future posts.

Lets keep this thread uncluttered, A separate Designing your own speaker from scratch discussion thread has been created.

Last edited by wintermute; 18th January 2019 at 02:46 AM.
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Old 18th January 2019, 02:35 AM   #15
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future posts.

Lets keep this thread uncluttered, A separate Designing your own speaker from scratch discussion thread has been created.

Last edited by wintermute; 18th January 2019 at 02:46 AM.
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Old 18th January 2019, 02:35 AM   #16
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Lets keep this thread uncluttered, A separate Designing your own speaker from scratch discussion thread has been created.

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Old 18th January 2019, 02:36 AM   #17
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Lets keep this thread uncluttered, A separate Designing your own speaker from scratch discussion thread has been created.

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Old 18th January 2019, 03:00 AM   #18
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Old 18th January 2019, 10:11 AM   #19
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So you want to design your own speaker from scratch!
Oh and just in case all of my footers scare anyone off. If you do have any supplementary material to post (as I am only scratching the surface), suggestions or corrections, then please do so in this thread

I've put a number of placeholder posts. I may not use them all, the idea is just to give me enough room to finish what is somewhere (still not fully gelled) in my brain. I was originally going to wait till I had finished all of the material before posting, but it had sat idle for over three years, and was awakened by a post by fatmarley, so after some prompting by Planet10 I decided to bite the bullet and put it out there.

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