Analytical Formulas for the Coverage of Tunable Matching Networks for Reconfigurable Applications

Tunable matching networks (MNs) are essential components for agile radio frequency systems. To optimally design such networks, the total area they cover on the Smith chart needs to be determined. In this paper, the coverage areas of typical MNs have been determined analytically for the first time. It has been found that the coverage area is encompassed by up to five arcs. Analytical expressions for the centers and radii for these arcs have been derived. The theoretical analysis is provided for four typical MNs and verified by circuit simulation and measured data. Moreover, a dynamically load-modulated power amplifier has been designed using the presented theoretical techniques, which demonstrates a measured improvement in the power added efficiency of up to 5% in the frequency range of (0.8-0.9) GHz.