Closed-form approximations for link loss in a UWB radio system using small antennas

A critical need in the evaluation of an ultrawideband (UWB) radio system is the calculation of the energy link loss between the source at the transmit antenna and the receiver load. While the rigorous calculation of link loss in a wideband pulsed system requires a full transient electromagnetic solution for the transmit and receive antennas, we show in this paper that accurate approximations for link loss can be obtained for the special cases of electrically small dipole or loop antennas, with Gaussian or Gaussian doublet (monocycle) generator waveforms. We also consider the error involved with applying the much simpler narrowband Friis transmission formula. It is found that the use of the basic Friis formula can result in link loss errors of more than 60 dB for a UWB system having severely (impedance) mismatched antennas, but may give results correct to within a few dB for well-matched narrowband antennas, or if the formula is augmented with an impedance mismatch correction factor. It appears that the dominant limitation of the Friis formula, when applied to UWB systems, is the broadband effect of mismatch between the transmit/receive antennas and their source or load impedances. Numerical examples are presented for electrically short dipoles, resonant dipoles, and broadband lossy dipoles for both Gaussian and monocycle input pulse waveforms.