Gain and Q Bounds for Coupled TM-TE Modes

The possibility of minimizing the bound on the Q of an antenna by resonating TM modes with TE modes has been described in many papers. Other papers have dealt with maximizing the gain by combining these modes in an optimum manner. However, there are fundamental relations for the phasing of the two modes which prevents minimum Q and maximum gain from being realized simultaneously. These phase restrictions have been neglected in some papers, leading to the presentation of incorrect results. This paper explores the relationships between phase, gain, bandwidth, and the Q lower bound, particularly for electrically-small antennas.