Compensation networks, RC dampers (Zobels) and resonating (notch filter) dampers are discussed in this document. The pseudo-first-order filter is discussed, and there's enough information that you can clearly see its purpose and how it works. It's an often overlooked matter, worth mentioning that a coil in series with a (voice) coil is a voltage divider, not a filter. The part that makes it a filter is the complex reactance of the loudspeaker, but this also makes the voltage division more complex than a simple first-order filter, hence the name "pseudo-first-order".

Higher order networks like those used in Pi Speakers with compression drivers will be discussed later, and the models for them are already included in the Spice models distribution on the Pi Speakers website. Be sure to grab a copy, so you can see the circuit analysis for yourselves. With this copy of Spice, you can also run the analysis shown in the document, and try some of your own designs.

I have printed this paper and after I go over it in depth, I will get back to you.

Thanks for the excellent analysis!

The crossover used within Pi Speakers uses a third order filter for the tweeter and a matching filter for the woofer, with crossover point and slope dependant on the woofer chosen. In addition to the basic crossover frequency-splitting high-pass and low-pass filters, top-octave compensation is employed for compression drivers for response shaping, to make power response flat.

I highly encourage you to download a copy of the accompanying executable Spice models, which are currently available and online. That way you can manipulate the models shown in this document yourself - changing crossover components to modify crossover frequency and filter slope. There are models of the sample filters shown in this crossover document, and there are models of the specific crossover designs I recommend for use in Pi Speakers shown as well.

Be sure to check periodically for additions to this document. When it's done, it will have second-order and a third-order designs and a discussion of the strengths and weaknesses of each. It will also show the power across each part used in Pi crossovers, so a person can know how to select appropriate components.

Thanks for the detailed answer. I do plan to play with the Spice model. I'm always lurking around here in the background. I just don't post unless I have something to say.

Dave