Crossover optimization

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Have you ever asked yourself, what is the best crossover for my box ? Are you sure the filter you have chosen is the best one ? Or if you are tired computing lots of different crossovers, getting nearly the same result, if you have some difficulties to interpret these results, or if you don't know anything about filtering, this tool is made for you... In fact, you will be able to compute automatically not the best filter because it doesn't exist, some people may prefer this one or this one, but the best for you, taking into acount your preference between frequency response and phase difference between speakers.

Lets try to play with this tool and see what we'll get as a result... We will work with ideal speakers, that is to say speakers with a flat frequency response, impedance and linear phase. Go to the simulation interface in the 'Optimize Menu'. In order to use these speakers select "Constant boomer frequency response" instead of "Measured boomer frequency response". Do the same for all fields. Enter these values for parameters. Don't forget to check the box "Print command for optimization" and to enter the frequency response toggle, in our case 85 dB.

Start optimization by clicking on the "Optimize" button. You will get a first order filter for the low and high pass with the high pass filter cutoff frequency equal to 1.38 multiplied by the low pass cutoff frequency. Given that the drivers are considered as ideal and because of the crossover which modifies the driver phase, the phase gap between speakers is almost constant.

Ideal crossover result

Please note that on the bottom of the page the cost for the frequency response is 56 and the phase is 511. The frequency response is nearly perfect and that's why. If you want to get rid of the phase set 0 for the importance parameter of the phase versus frequency response. Then you will get the theoretical result 2000 Hz as cutoff frequency for the low pass and 2000 Hz for the cutoff frequency of the high pass, which is in line with the theory.

Is this filter better than the one before ? No... You may believe it because the phase is also flat, but the two speakers cross at -3dB instead of -6dB which means there will be a strong directivty pattern. If the two speakers were at the same height, it would be ok, but let say there is 20 cm between them, if you stand at 1 meter, when your ear will be just between boomer and tweeter, it will be good, but just a few centimeters below, you will have a boost of +3dB at 2000 Hz as shown on picture 1, an a few centimeters above, you will get a crash at 2000 Hz as shown on picture 2.

Picture 1

Picture 2

Now we'll try the same but we will invert tweeter connexion which invert the phase of the speaker. Check the box "Invert tweeter connexion". Look at the result obtained with phase inverted. Not surprisingly, we get the Bessel second order filter...

Now that we know everything on the theory. Let's see how distance between boomer and tweeter acoustical center may affect the result. Enter 3 cm in the corresponding field. As you can see, it does have a significant influence on the result which is now a first order filter for low and high pass. It really shows that ideal filters can't be used directly without taking extra parameters such as distance between acoustical center into account. This is also completly true with our practical case with meausred speakers. In this case, the best solution is a second order filter, not so different from a Butterworth one (Q factor 0.68). Thus, there is no general rule for filters, no one is better than the others because it depends on a lot of different parameters !

Last but not least, feel free to play with minimal and maximal values for each parameter on the right of the screen. Maybe your tweeter cannot be used with a cutoff frequency lower than 2500 Hz for example, then enter this value as the "Min value for w0 high pass".

To put it in a nutshell, this tool offer you the possibility to build and adapt the filter of your box to your speaker, taking into account your preferences between phase alignment and frequency response. The optimization with constant parameters will help you understand what your are doing and how a parameters can affect the global result.
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