A simple scheme for choosing the optimal frequency for small portable devices given the required bandwidth and restricted antenna size

We consider the link budget for electrically small antennas for use in small portable devices where the required bandwidth (BW) and maximum antenna size is given. By balancing the BW and antenna efficiency we find the optimal frequency of operation is f_opt = [c/(2πa)]^0.75 (BW/γ)^0.75, where γ ~ 10-30% is a constant characterizing antenna radiation quality, BW is the 3 dB bandwidth, c is the speed of light, a is the radius of the minimal sphere enclosing the antenna. For lower frequencies than optimal the transmission deteriorates rapidly with f⁶ for device to device and f² for device to base station. For higher frequencies than optimal the transmission decreases by f² as predicted by Friis´ transmission equation. The results may easily be taken into consideration when designing new portable devices for communication, sensor, or medical surveillance purposes.