The investigation was concerned with the techniques used with the Smith Chart when developing matching networks for broadband antennas. The basic problems involved in the application of these techniques are covered in detail, with illustrations showing each step on the Smith Chart. These various problems concern the matching of broadband antennas although this does not indicate that the chart techniques apply to such cases only. They are adapted to single frequency antennas as well. The only difference is that the problems then become considerably simpler and, instead of striving for a 3:1 standing wave ratio, one settles for nothing less than a 1:1. A problem of this type is included, because it is felt that, after the techniques are mastered with broadband antennas, the procedure for obtaining a match for a single frequency antenna will suggest itself.