What third family of circles is often added to a Smith chart during the process of designing impedance matching networks?
Why The printed Smith chart itself contains two orthogonal families: constant-resistance circles and constant-reactance arcs. When you use the chart to design a matching network, you typically draw circles centered on the chart's prime center (1.0 normalized); every point on such a circle has the same standing wave ratio. Those constant-SWR circles let you see at a glance whether a trial matching element brings the load inside your target SWR, and moving along a lossless line simply rotates you around one of them.
Watch out Line length is shown on the chart, but as the wavelength scales around the rim and rotation angle, not as a family of circles, so the transmission line or coaxial length choices describe markings that are not circles. Radiation patterns have nothing to do with the Smith chart at all.
Smith chart families: resistance circles, reactance arcs, and SWR circles centered on the middle. Rotate around center = constant SWR.