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> The Smith chart from electrical engineering is the image of a Cartesian grid under the function f(z) = (z − 1)/(z + 1). More specifically, it’s the image of a grid in the right half-plane.

Well, I'm already confused. The domain is complex numbers where the real part is >= 0? I think it would be helpful to make that clear from the get-go. When I see "Cartesian grid", I think R^2, not C.

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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.

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