I made an interactive implementation here: https://observablehq.com/@mbostock/smith-chart
that's beautiful!
How to make a Smith chart
11–20 of 36 posts
Re: How to make a Smith chart
#12This animation is helpful:
https://en.wikipedia.org/wiki/Smith_chart#/media/File:Animat...
Re: How to make a Smith chart
#13Re: How to make a Smith chart
#14"Escher's art, Smith Chart and Hyperbolic Geometry"
https://www.researchgate.net/publication/3427377_Escher's_ar...
"A conceptual relation between Circle Limit IV, an artistic creation by M.C. Escher, and Smith Chart, geographical aid for microwave engineering created by P.H. Smith, was established. The basis of Escher's art and Smith chart can both be traced back to invariance of the cross ration of four complex numbers under Möbius transformation on the domain of complex numbers. The Smith chart can be used as an aid for constructing Escher-like drawings that display periodic mosaic patterns and at the same time convey the perception of infinite progression within a unit circle."
Re: How to make a Smith chart
#15I've used Smith charts many times on my NanoVNA analysing antennas, but despite being mathematically inclined I never thought of the complex plane mapping involved
f(z) = (z − 1)/(z + 1)
The Smith chart is useful to electronic engineers because a given VSWR (the thing you try to minimise to get a good antenna) becomes a circle about the center of the Smith chart
VSWR= (1 + | Γ |)/(1 - | Γ |)
So to make your antenna better, get the plot closer to the center. Whether it is above the line or below tells you whether the antenna is inductive or capacitive and hence which kind of loading to add.
Re: How to make a Smith chart
#16Why would you use one?
Re: How to make a Smith chart
#17Btw, as all Möbius transforms, a Smith chart can be understood by looking at the complex plane as a sphere:
Re: How to make a Smith chart
#18Terrifying. My nightmares will return.
Re: How to make a Smith chart
#19I've used Smith charts many times on my NanoVNA analysing antennas, but despite being mathematically inclined I never thought of the complex plane mapping involved f(z) = (z − 1)/(z + 1) The Smith chart is useful to electronic engineers because a given VSWR (the thing you try to minimise to get a good antenna) becomes a circle about the center of the Smith chart VSWR= (1 + | Γ |)/(1 - | Γ |) So to make your antenna b…
> 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.
Re: How to make a Smith chart
#20I have PTSD from learning Smith charts in school. My prof even said to me "If you'd pay attention, you'd understand this!". I was the only one who was brave enough to ask questions about it!
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.
Sounds like it was the right decision then.