A classical and traditional method for building passive crossovers of the speakers is to use a RTA microphone, connected to a computer, using frequency sweep, read the graphs shown on computer, and alter passive components in crossover networks until obtained decent curves. Am I correct?
By the way, I have found an alternative method for designing the crossovers where I may say it might be better than the traditional method mentioned above, that is to using something involving Laplace transform, pole & zero, Bode and Nyquist plots.
Nevertheless, to my understanding, the Laplace method may simply be an additionally mathematical modeling which is an optional part in the procedure of the tradition way. Am I correct?
Finally, I’d like to ask that is there anyone using the Laplace method in your crossover designs? Could you please share your experiences to us? I wonder whether it requires the same tools, i.e., a RTA mic, a software like REW, and frequency sweeps, etc. like what requires in the traditional way. In all, could you briefly explain the procedure of this process, please?
By the way, I have found an alternative method for designing the crossovers where I may say it might be better than the traditional method mentioned above, that is to using something involving Laplace transform, pole & zero, Bode and Nyquist plots.
Nevertheless, to my understanding, the Laplace method may simply be an additionally mathematical modeling which is an optional part in the procedure of the tradition way. Am I correct?
Finally, I’d like to ask that is there anyone using the Laplace method in your crossover designs? Could you please share your experiences to us? I wonder whether it requires the same tools, i.e., a RTA mic, a software like REW, and frequency sweeps, etc. like what requires in the traditional way. In all, could you briefly explain the procedure of this process, please?
The basis is: how can sound be represented/Explained? One answer is that a (sample of) sound contains many synusoids so those can be calculated in a LTI system. Transformation and antitransformation are the means to overcome a long series of integrals and derivatives
No you're not correct. The traditional way is to determine the crossover frequencies and filter types and orders; transform the frequencies into time constants; and then turn the time constants into RC or LC circuit elements, so as to determine the response analytically rather than experimentally: a process which makes implicit use of the Laplace transform. You can do it by trial and error as well as you describe, but it’s a good way to just waste time.
Your best reference might be the Linkwitz site where he discusses dipole equalization. He talks about using poles or zeros in the equalizer frequency response to compensate zeros or poles in the speaker system response. But that is an outlier; using his method to design equalizer or crossover is the hard way and only worked to the extent that it did because he had a mathematical model for the system he wanted to design active analog crossover+equalizer filters for. The interesting thing is his model excluded room effects. From one point of view, this allowed him to design it absent precision in room measurements; OTOH, he may have needed to do some room equalization at a later stage. Today, doing dipole equalization with DSP and measurements is so much easier.
At the moment, the most curiosity of the method of using advanced mathematics i.e. Laplace and Fourier transforms, Nyquist and Bode plots in loudspeaker’s crossover design is whether it needs the same tools, i.e., RTA mic and REW software, as the traditional method does.
I’m still hoping for the kind people to tell his/her experiences as well.
I’m still hoping for the kind people to tell his/her experiences as well.
Designing a good crossover is a multi-step process. As time becomes available, I am slowly working on a system myself.
The first thing you will need to do is gather all of the drivers' specs. For example, if you are working with compression drivers in a horn-based system, many drivers will list the lower recommended crossover frequency and the order of the filter. Then, you should use your test equipment to get the actual frequency response of each driver in your enclosure separately and also measure the complex impedance as a function of frequency.
With this data, you can use Laplace techniques to design your crossover. You can work with the necessary filter order and characteristics to optimize the theoretical response for the driver. With Laplace you can get the system poles and zeros and use that as a starting place for your design. Laplace is not especially difficult - I used to tell my students that it turns calculus into algebra - what's not to like?
There is also an excellent tool that you might wish to consider, and it is free—pcfilt from the ALK Engineering website. The UI is a bit clunky, but once you get used to it, it works quite well.
In the end, no matter your approach, you will have to tweak the values to your tastes. The transforms and theoretical design will get you close, and provide reasonable starting values, which is much better than starting from scratch and guessing.
Something else to consider - if you join AES you will get access to all of their papers as part of your membership. There are many papers on crossover design, and many are written with the practitioner in mind.
Good luck, and keep us posted on your progress.
The first thing you will need to do is gather all of the drivers' specs. For example, if you are working with compression drivers in a horn-based system, many drivers will list the lower recommended crossover frequency and the order of the filter. Then, you should use your test equipment to get the actual frequency response of each driver in your enclosure separately and also measure the complex impedance as a function of frequency.
With this data, you can use Laplace techniques to design your crossover. You can work with the necessary filter order and characteristics to optimize the theoretical response for the driver. With Laplace you can get the system poles and zeros and use that as a starting place for your design. Laplace is not especially difficult - I used to tell my students that it turns calculus into algebra - what's not to like?
There is also an excellent tool that you might wish to consider, and it is free—pcfilt from the ALK Engineering website. The UI is a bit clunky, but once you get used to it, it works quite well.
In the end, no matter your approach, you will have to tweak the values to your tastes. The transforms and theoretical design will get you close, and provide reasonable starting values, which is much better than starting from scratch and guessing.
Something else to consider - if you join AES you will get access to all of their papers as part of your membership. There are many papers on crossover design, and many are written with the practitioner in mind.
Good luck, and keep us posted on your progress.
That is the pre 1978 method for Kef & Co, and for amateurs pre 1988, when CALSOD 1.0 became available for the diy crowd.
It got even better in 1994 when our own fabulous Bill Waslo presented the IMP PC build it yourself measurement suite in Speaker Builder Magazine, whereas the CALSOD 3.1, issued at almost the same time, enabled the user to directly import .frd (spl measurement files) and .zma ( impedance) files.
You start with textbook filtercomponent values, indicate/choose a desired target response, and the optimizer does the rest. That was the classic method as described in KEFTopics 3 in 1978.
Nowadays for true state of the art design off axis is also measured, whereas VituixCad is your simulator of choice, ARTA and REW being the most popular measurement software. Read the guides our own Dcibel, Kimmosto and Ente have written. All this software has dedicated threads here on DIYA.
The problem with techniques like Laplace or designing with "named", classical filter shapes is that loudspeaker drivers are very ill-behaved beasts. Their impedances aren't like an 8 ohm (or other) resistor, their output spectrum varies depending on what angle you look at them from, their frequency responses aren't remotely flat and usually have significant resonances, and they have different travel times (time-of-flight delays) from where they mount to where the sound goes. You might be able to get away with pretending you are working with a SomethingWorth filter shape if you use DSP filters and a lot of response and delay corrections, but if you're working with passive components the only practical way is an educated trial-and-error method. That's why crossover simulator programs exist, so the trial-and-error part doesn't have to involve having lots of different components around and a soldering iron involved.