Matching Limits for Single-Band and Dual-Band Mobile Phone Antennas

There have been many studies about the limit of the broadband impedance matching problems, since the early work from Bode [1], Fano [2] and Youla [3], more recently extended by Carlin et al. [4]. Previous work has presented applications of the theory of Youla and Carlin to circuit models of two different antennas (a single-band and a dual- band antenna-chassis combinations) and provided the matching limits for both circuit models. The accuracy of the obtained limit depends on how close the quality factors (Q) of circuit model and antenna impedances are. This paper presents the relationship between Q and the minimum achievable amplitude of reflection coefficient (|S₁₁|_min)of a particular circuit model which describes generally well a single-band antenna-chassis combination impedance. The case of a dual-band system with two non-contiguous bands is also studied, showing that the simultaneously achievable S|₁₁|_min of each band can be approximately obtained by evaluating the S|₁₁|_min for two independent single-band circuit models. Applications for the derived results are presented for three different kinds of mobile phone antennas.