Matching limits for a dual-band mobile phone antenna

This paper applies the theory of Youla and Carlin et al. to a simplified circuit model of a dual-band PIFA (Planar Inverted-F Antenna) and gives the minimum simultaneously achievable amplitude of reflection coefficient vertical bar S-11 vertical bar for two given non-contiguous bands. A good agreement to the obtained limits is shown in simulations with high-order matching circuits. The limits are then applied to a dual-band mobile phone numerical model. The corresponding circuit model is found by a least-square based optimization program. The accuracy of the obtained matching limits depends on how closely the impedance of the antenna-chassis combination is modeled by the impedance of the circuit model, or more exactly, by the resemblance of the quality factors of the two systems. It is also noteworthy that the vertical bar S-11 vertical bar for two given bands are "exchangeable quantities", trying to reduce the vertical bar S-11 vertical bar for one band leads to an increase of vertical bar S-11 vertical bar in the other band.