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Multi-Way Conventional loudspeakers with crossovers

So you want to design your own speaker from scratch!
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Old 18th January 2019, 01:31 AM   #11
wintermute is offline wintermute  Australia
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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 01:44 AM.
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Old 18th January 2019, 01:32 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.

Placeholder. Unfortunately that's it for now but 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 01:45 AM.
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Old 18th January 2019, 01:33 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 01:45 AM.
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Old 18th January 2019, 01:34 AM   #14
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Default placeholder

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 01:46 AM.
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Old 18th January 2019, 01:35 AM   #15
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So you want to design your own speaker from scratch!
Default placehoder

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 01:46 AM.
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Old 18th January 2019, 01:35 AM   #16
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Default placeholder

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 01:47 AM.
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Old 18th January 2019, 01:36 AM   #17
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Lets keep this thread uncluttered, A separate Designing your own speaker from scratch discussion thread has been created.

Last edited by wintermute; 18th January 2019 at 01:48 AM.
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Old 18th January 2019, 02:00 AM   #18
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Old 18th January 2019, 09:11 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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