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On Convergence of the Upper Bound on the Ratio of Gain to Quality Factor



Alex Yuffa, Marc Valdez, Benoit Derat


An antenna's practical far-field distance can be estimated from the upper bound on the ratio of its gain to quality factor. This upper bound is an infinite series that can be truncated based on the desired far-field accuracy. We investigate the convergence properties of this bounding series. We find that the number of terms required for convergence depends on the antenna's electrical radius in a way similar to the Wiscombe criterion used in Mie scattering theory. For typical experimental accuracy requirements, such convergence can significantly reduce the effective far-field distance.
Proceedings Title
Proc. Antenna Meas. Techn. Assoc.
Conference Dates
October 24-29, 2021
Conference Location
Daytona Beach, FL, US
Conference Title
43rd Annual Meeting and Symposium of the Antenna Measurement Techniques Association (AMTA)


antenna, far field distance, Wiscombe, gain, quality factor, convergence


Yuffa, A. , Valdez, M. and Derat, B. (2021), On Convergence of the Upper Bound on the Ratio of Gain to Quality Factor, Proc. Antenna Meas. Techn. Assoc., Daytona Beach, FL, US, [online],, (Accessed April 22, 2024)
Created December 6, 2021, Updated November 29, 2022