Understanding the Element-Gain Paradox for Receiving Arrays Using Poynting Streamlines

Energy flow directions around receiving array antennas can be modeled by generating streamlines of Poynting vector fields near the antenna. The geometrical shape of array effective area can be calculated from the locus of Poynting streamlines that terminate on the array element loads. The decrease of array directivity due to mutual coupling effects, or the element-gain paradox, can be explained by the overlap of element effective area shapes leading to the decrease of array effective area shape. The critical element distance for the element gain paradox effect is equal to the width of the effective area shape for a single isolated array element. These results provide a new, intuitive, and visually oriented tool for understanding a variety of effects in the theory and design of receiving antennas and arrays.