Dualling Master: Swap Current and Voltage for Easier Filter Design
The story so far...
We designed a passive lowpass ladder filter in Filter Wizard #13 (Filter Design using the Million Monkeys Method). Well, I say designed, but really we just let Excel's solver indulge in some cleverly targeted component value adjustment. That way, we didn't have to bother about optimization theory, we just made use of a general purpose tool that's widely available.
Using optimization to design circuits (some might call it organized guesswork for some algorithms, that's a pretty good description) isn't a new insight. In the late 1960s, Ron Rohrer, teaching optimization at Berkeley, foresaw that the falling cost of numeric computation, and the rising complexity of electronic circuits, would eventually make circuit design-by-analysis cheaper and more effective than design-by-synthesis. All he needed was a way to analyze circuits effectively on a computer. Larry Nagel, the father of SPICE, was one of his students; the rest is history.
But back to our filters. Last time, in Filter Wizard #14 (Match Point: Why Maximum power means Minimum Sensitivity), we discovered the handy insensitivity of the doubly-terminated ladder filter to component variations. This validates one of the choices made for the Million Monkeys design. But you're all gasping to know how we're actually going to use this well-behaved bunch of passive components to design a useful active filter. Some readers were a bit underwhelmed that the monkeys' end product was just a bunch of interconnected Ls, Cs and Rs, producing a lowpass filter (albeit nice and sharp), cutting off at 0.159Hz and having a very low input impedance. What use is that? After all, no-one uses passive filters down at this frequency, with inductors and capacitors that are both electrically and physically huge.
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