A discussion on electrically small antennas surrounded by lossy dispersive materials

For any electrically small antenna there is a fundamental lower bound on the achievable quality factor, which is defined in terms of the antenna¿s occupied volume and the operating frequency. As either the size of the antenna or the operating frequency decreases, this lower bound increases as approximately 1/(ka)3, where k is the free space wave number 2¿/¿, and a is the radius of an imaginary sphere circumscribing the maximum dimension of the antenna. The significance of both quality factor (Q) and the lower bound (Qlb) in characterizing the performance of an electrically small antenna is the fact that for most electrically small antennas, the matched Voltage Standing Wave Ratio (VSWR) bandwidth is inversely proportional to Q. So long as the inverse relation between Q and matched VSWR bandwidth holds, the lower bound on Q can be used to define an upper bound on matched VSWR bandwidth.