Radiated cross-power from two antennas

The concept of cross-power is examined for the case of electrically small antennas. The motivation for this study is the existing belief that a substantial increase in the radiated power can be achieved with the cross-coupling of the field of two (or more) antennas. The concept is also known as Poynting vector synthesis. We present a new theorem, which proves that radiated cross-power exists in the far zone only if the sources are mutually coupled in the near zone. We show that certain increase of the radiated power can be achieved by suitable coupling of the radiating elements. This increase, however, cannot break the known fundamental limitations of electrically small antennas.