Apollonius unilateral transducer constant power gain circles on 3D Smith charts

Unilateral transducer constant power gain circles play an essential role in the design of radio‐frequency amplifiers and active modulators, as they help to determine optimal impedance matching conditions to meet gain and stability specifications. It is shown that these gain circles are a subfamily of Apollonius circles. For better visualisation, unilateral transducer constant gain power circles have been plotted for the first time on the three‐dimensional (3D) Smith chart. To this end, a natural relationship from an inversive geometry was required, in order to relate the gain circles with cutting planes for the 3D Smith chart.