Really cool! BTW since you're here, have you checked https://github.com/malloydata/malloy/ and their visualizations? it seems it could be a nice fit for ObservableHQ

that's beautiful!

Really really nice. Thanks for this!

> f(z) = (z − 1)/(z + 1)

Also known as the Bilinear Transform https://en.wikipedia.org/wiki/Bilinear_transform

Used for mapping between s-plane and z-plane when discretising using the trapezoidal rule.

Not knowing enough about Smith Charts, do the intermediary frames have any meaning in terms of actual practical problems or calculations?

It seems like the chart itself would be a member of an entire family of chart types that would go through the entire 3D rotation with several versions that were "nearly tangent circles" and eventually concentric circles at the center of the graph, along with some of the intermediary frames shown in the animation.

This software is so good it is as enjoyable as any game, it taught me to love Smith Charts

https://www.ae6ty.com/smith_charts/

I’m just amazed there isn’t a nearly impenetrable Greg Egan book based on them.

Oh, found a picture of one of these plastic ones flikr:

https://www.flickr.com/photos/jonsphotos/218609214/in/album-...

If you liked the Smith Chart, you'd love using the Spirule to solve root locus problems.

https://en.wikipedia.org/wiki/Root_locus_analysis

I felt the same way. At some point shortly after graduation, I found a heavy plastic Smith chart that was designed to be written on with a grease pencil, and erased with a cloth when you're done.

So you can continue it beyond that circle if you like, it just happens to be the case that the thing electrical engineers and others dealing with waveguides are plotting in the source space, is impedance. (Well, a ratio of impedances—a load impedance divided by a transmission line impedance.) The real part of impedance is resistance, and negative resistance is very uncommon. The area outside the unit circle so mapped, I think also corresponds to reflected amplitude ≤ transmitted amplitude, with the center of the diagram being a perfectly matched impedance, and no reflection.

Heh, this reminds me, don't worry:

One of my extremely intelligent roommates in the 80s switched from EE to CS, seemingly due to Smith charts and Electromagnetics coursework.

He went on to make a large fortune in software.

No. The RF equivalent of that would be an antenna pattern. The smith chart is a particular mapping of complex impedance that allows for fairly straightforward calculation and visualization of things like conjugate matches. It's related to the impedance plots for speakers, but audio engineers generally don't use it. RF engineers will plot impedance vs frequency on it though. If you come across curlicue plots on it, those are typically frequency sweeps i.e. they plot impedance vs frequency. You might have to look for the frequency legend or endpoints.

No. Sorry, that is not a helpful comparison.

I remember using these for impedance matching back when I was in college. Basically when you connect two transmission lines (like coax cables), you need to match their impedances so the signal does not bounce back. (Ik this is a gross oversimplification but yeah)