Why resistor in parallel with inductor in low pass crossover?

Yup, you ran into the problems I was having with series crossovers. The low order (near first-order there) looks promising, but falls on its backside with treating the drivers nicely. It's one of Lynn Olson's detested "Little Girl with a Guitar" speakers, that plain distorts with complex music. Trying to equalise out the tweeter Fs and woofer resonance then leads to too much complexity. :)

Let's recap what a time-aligned speaker looks like:

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Seems better to me to get well-behaved drivers and give them second order filters leading to a higher order acoustic response. Might as well get an easy impedance too. Then it sounds good with any amp.

There is a nice theorem by Sidney Darlington that you can simplify the resistances in a filter down to one or two: Equivalent impedance transforms - Wikipedia, the free encyclopedia. No don't spend time on it, it all gets quite deep. The story of filters giant Wilhelm Cauer, who has the elliptical filter named after him, is more accessible and shocking.

Also interesting is the pattern that appears in the complex maths of filters where you realise that all the various solutions are just placing the poles and zeroes on ellipses, circles or anything else you fancy. This, for instance is the lovely hexagonal symmetry that lurks in the 3rd. Order Butterworth filter:

An externally hosted image should be here but it was not working when we last tested it.


It is, in fact, a phase or all-pass network that is quite doable with opamps. What it does is produce pure group delay. No surprise you find neat ratios like 3:1 then. It becomes a geometry problem in the end. Which is neat. :cool:
 
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Also interesting is the pattern that appears in the complex maths of filters where you realise that all the various solutions are just placing the poles and zeroes on ellipses, circles or anything else you fancy. This, for instance is the lovely hexagonal symmetry that lurks in the 3rd. Order Butterworth filter:

An externally hosted image should be here but it was not working when we last tested it.


No surprise you find neat ratios like 3:1 then. It becomes a geometry problem in the end. Which is neat. :cool:

Very cool - NOW I see where all your geometry inferences were pointing! I had heard about elliptical filters and had no idea what they were. You have put this in perspective for me. Clearly a lot to learn, but it really helps to have this framework. - Thanks again
 
I'm glad you enjoyed that. Not for bricklayers, eh? You either crawl round on your belly in the ditch, or fly like an eagle over the entire landscape. :D

I'll give you the final piece of filtering from a higher mathematical point of view. Just to look at and enjoy without frying your brain too much.

This (correct) pole/zero view of filters:

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Suppose you wrap that plane around a Riemann sphere, so the origin (low frequencies) and infinity (high frequencies) just go to the South and North poles respectively, and the poles and zeroes are on the equator.

An externally hosted image should be here but it was not working when we last tested it.


It's a 1:1 mapping that starts to look extremely elegant. In fact it's also related to the Mobius Transformation and Conformal mapping. With these tools, filters and room and cabinet properties become rather simple. It's worth remembering that a mechanical filter like a speaker driver and an electrical filter share the same overall mathematical properties, we are just combining them at this forum.

Interestingly, Cauer started as a specialist in General Relativity, which means he knew ALL this stuff. :cool:
 
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I take that a bit personally! Shame the images are lost.

Nvr2manybikes went on to build some of the most innovative speakers we have ever had at this forum....

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This was years before Troels Gravesen got the Bee in his Bonnet about stepped baffles.

Series filters too:

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(No, I don't know what the 4uF/0.25mH does either. Call it artistic license.)

You can't buy those in shops! :D
 
Please do not take personally.
I marvel at many of your posts to be honest.
I’m just a simple man that likes to work with his hands. ;)
I am an admitted long time admirer of John Dunlavy and understand today there are many ways to achieve what his design goals were and what he prioritized as important.
I admire what you are able to achieve but honestly have a hard time deciphering a phase plot that’s still “wrapped up”-I believe I’ve seen that quoted like that before- I’m really just a dim parrot honestly
I enjoy reading about DIY designs similar to JD’s and have always wondered how he got critically damped alignments in smaller enclosures. Such as his Athen/Corinthians using a Scanspeak 25w8565-00 in a 2.25 ft3 enclosure using only dampening material -open cell foam.
Please keep up the great work.
 
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It was an interesting idea:

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Everything lined up nicely including phase. I separated out the bafflestep which is the 1mH/6R. Impedance was poor though. Not SET amp friendly.

Never heard it though.

These days I might refine the idea:

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This was using Jeff Bagby's filter values which make everything fall into place:

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But I found you could achieve a lot of the same thing with parallel filters.

Flat Impedance and Flat Power response design.

So I really don't know if is worth pursuing. Some of the recent 6" Jeff Bagby and Joachim Gerhard Satori designs have been a bit like this.