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Passive fiilters - musings on inductors and topologies

Posted 5th August 2013 at 12:58 AM by abraxalito
Updated 5th August 2013 at 01:02 AM by abraxalito

I've spent many hours recently poring over webpages and catalogues of inductors, looking for the best bang-for-the-buck in relation to anti-imaging filter inductors.

The gold standard, where performance is uppermost and cost and size are subsidiary, looks to be still the gapped ferrite pot cores I started out using. Their disadvantages are they need to be custom wound, not being available off-the-shelf, and their consequent higher cost. They also produce relatively bulky filters when a dozen or more are called for in a design. I've found nothing to beat them in performance, particularly accuracy and repeatability of their value and in terms of achievable Q (I've seen 500-plus in some cases on my meter).

I do hanker after a more portable and easier to replicate design though hence my investigations into cheaper alternatives.

Right down the bottom of the pile are the bobbin-wound coils, available in a wide variety of values here, at stunningly affordable prices. My last bag of 500 3mHs cost me about $25. While the accuracy of my first bag of 10mHs was extremely good (most within 1%) these have turned out to be not quite on the same level, but so far all measured have bettered 5%. A filter design which can tolerate such tolerances would be ideal, but it seems that elliptic filters require better, at least in the most critical positions. Even where I hand-wound a design with pot-cores, I failed to achieve the simulated 70dB stop-band rejection close to the band edge. Since then I've been on a hunt for a more robust kind of filter. At least in simulation, I have made some progress.

The next-best filters (on paper) for selectivity after elliptics are chebyshevs. They do give up something in terms of steepness of band edge when compared alongside elliptics but they do have a couple of advantages in terms of how they perform in practice. Firstly because their stop band responses are determined by poles (rather than zeroes) the stop-band is monotonically decreasing with frequency. Whereas elliptics have stop-band ripple. This characteristic appeals to me for audio because one of my rules of thumb is that the higher the frequency the greater the audio degradation. Thus whilst its important to keep immediate ultrasonics out, its even more important to keep out grunge as the frequency goes up. Chebyshevs do this as a matter of course but elliptics don't as they aim for stop bands which never exceed a maximum which is constant with frequency.

The second main advantage is not unrelated to the first - they appear to be much more tolerant of component value tolerances in that the stop band rejection is more robustly delivered.

To make up for the inferior steepness I have played with a design which has more inductors. But at 5c a pop, even eleven inductors won't exactly break the bank. The shortcomings of such a filter are that the inductor finite Q causes considerable droop towards the HF. My 3mHs measure about 4ohms at LF rising to 10ohms at 20kHz. In theory, with an active post-amplifier this can be corrected with the appropriate RC networks if not too severe - in effect, a 'cable equalizer'.There's also the fact that according to the filter design tables, the inductor values do not turn out to be all equal for a minimum ripple design. Equal inductor values is exceedingly desirable from the point of view of ease of manufacturing and attractiveness to DIYers (lower cost).
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