Antenna Q calculation using radiated modes and reflection coefficient

Optimisation techniques are currently being used to design antennas with Q values close to theoretical limits. In order to evaluate how closely these designs approach the limits, it is necessary to calculate their Qs from measured or simulated data. Many standard techniques are accurate for large Qs, but yield values significantly below the actual Q for low Q cases. In this study, equations are derived to bracket the actual value of Q, and the issues involved in attempting to determine an exact value are discussed. Both time-averaged and time-varying energies are considered. The derivations and conclusions are different from those previously published. Data from electromagnetic simulations of design examples are used to illustrate.