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access icon free 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.


    1. 1)
    2. 2)
    3. 3)
      • 4. Brannan, D.A., Esplen, M., Gray, J.J.: ‘Geometry’ (Cambridge University Press, 2009).
    4. 4)
      • 3. Sanchez, P.C., Mingo, J., Ducar, P.G., Carro, G., Valdovinos, A.: ‘Figures of merit and performance measurements for RF and microwave tunable matching networks’. European Microwave Integrated Circuits Conf., Manchester, UK, 2011, pp. 402405.
    5. 5)
      • 1. Gilmore, R., Besser, L.: ‘Practical RF circuit design for modern wireless systems – active circuits and systems’ (Artech House, 2003), Vol. 2.
    6. 6)
    7. 7)
    8. 8)
    9. 9)
      • 9. Robertson, D.I., Lucyszyn, S.: ‘RFIC and MMIC design and technology’ (IEE, London, UK, 2001).
    10. 10)
      • 7. Muller, A.A., Soto, P., Dascalu, D., Boria, V.E.: ‘The 3D Smith chart and its practical applications’, Microw. J., 2012, 5, (7), pp. 6474.

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