Impedance matching with lossy components

Impedance matching networks couple a generator to a load. When lossless matching elements are used, the load power and the power extracted from the generator terminals are the same. Then the familiar conjugate impedance match condition maximizes , and hence . But if the matching elements are lossy ; the power difference is wasted in the matching network. Maximizing does not maximize . Suppose the load is purely resistive and that the quality factors of all elements used in the matching network must not exceed a prescribed value . If the load resistance value is not prescribed, but can be adjusted to facilitate matching, then the maximum obtainable load power is , given by Theorem 1. When is prescribed, the maximum power may be less than . However, there is a range of load resistance values, wide in many cases, for which Theorem 2 applies to deliver the same maximum power . depends on and on another quality factor of the generator. is small if , as may be the case if the generator is a short receiving antenna.