Linkwitz Transform on 4th order bandpass

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HOW TO MODEL A 4th order Bandpass plus a Linkwitz Transform circuit

The LT is designed to work with sealed boxes. This is because the response of a driver in a sealed box can be modeled by a second order transfer function. Here I'm talking about the low frequency regime, where T/S parameter models are a good representation of the response. The LT circuit implements TWO second order transfer functions - one in the numerator and one in the denominator. A transfer function is simply the function that described the output when given the input, both for frequency response and phase. By supplying the LT transfer function as a signal to your power amp, and connecting that to the speaker, you essentially can cancel the transfer function of the woofer (located in the denominator of the LT transfer function) and replace it with another one of your choosing (located in the numerator of the LT transfer function). This is possible because the output of the LT circuit, fed to the speaker via the amp, has become the input of the speaker's transfer function, so they are just multiplied together.

So, with that said, back to your original question. Your system is not a sealed box (2nd order system) but a bandpass (4th order system). The BP transfer function is the product of the driver in the sealed box portion of the BP (a 2nd order transfer function) and the other section of the box with a vent/port (another 2nd order transfer function). The extra second order transfer function floating around that is determined by the vented portion of the bandpass enclosure is the fly in the ointment so to speak, however you can gain some control over the part of the BP response determined by the driver in the sealed box part of the BP enclosure if you use the LT.

You need to model the system response of the LT+BP in order to determine how the LT can be used to change the response. I know a two-step way to accomplish this. You will need the following (Free) modeling programs:
Get Jeff Bagby's Woofer Box and Circuit Designer at this link
Get UniBox speaker modeling software at this link
Open both spreadsheets in two Excel applications. The modeling is done by creating the LT function in WB&CD, exporting that electrical function in to an FRD file, then importing that in to Unibox where you are modeling the 4th order bandpass system that you want to build. You have to go back and forth, changing the LT parameter in WB&CD, exporting, importing the FRD file in to Unibox, and then seeing the result of the change. I have done this before, and it is not too bad once you get the hang of it. If you get stuck, you can send me a message or post in this thread and ask for help.

Remember, the LT only allows you to change the sealed box portion of the BP. Given that, I am sure that the LT will make it easier to design a BP box and to tailor the response as you see fit. This will probably come at the expense of increased demands for amplifier power, and driver excursion.

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