Constant Mismatch Loss Boundary Circles and Their Application to Optimum State Distribution in Adaptive Matching Networks

An adaptive matching network provides a number of states between which it can be reconfigured. At a certain frequency, the matching network transforms a reference impedance to different impedances for the different states. The circuit will be able to match those impedances perfectly to the reference impedance, and impedances close to those will also be fairly well matched. The matching will, however, decline for impedances further away and eventually become too low. By defining the level of acceptable matching, a boundary can be formed that identifies an area of impedances that are matched well enough. In the same manner, a boundary is possible to form for constant mismatch loss. It is shown that the boundaries are circular if plotted in a Smith chart and that the sizes of the circles depend on the location of z_L. With these results, it is then investigated how the impedances should be distributed to minimize the number of states while still achieving the matching performance and coverage.