Tunable matching networks are crucial for agile radio frequency circuits. To optimally design such networks the overall coverage needs to be determined. In this work, analytical formulas for the coverage area within the Smith chart of a three-element tunable-network are derived. It has been found that up to sixteen circles bound the coverage area. Analytical expressions for the centers and radii of these circles have been derived and verified by circuit simulation as well as measured data. The formulas in this work can be readily integrated into CAD tools, thus provide a valuable tool for the design of tunable circuits.
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