Bounds of uncertain interference between closely located antennas

In connection with the rapidly growing use of radio communication, antennas operating at different frequencies must often be placed in close proximity due to space limitations, such as those on towers. Perini and Hirasawa (1973) and Adams and Warren (1971) have reported that, in cases in which antennas are closely spaced, the original characteristics of each antenna may be changed because of mutual coupling between antennas. The present investigation is concerned with two closely located antennas operating at different frequencies. A numerical example is considered, taking into account a dipole and a loop antenna which are in close vicinity and operate at different frequencies. The formulation of antenna performance indexes is obtained on the basis of the ratio of quadratic functions of the load impedance, and exact formulas are derived for the rapid calculation of the bounds of the input impedance, the reflection coefficient, the radiation field, and the power gain.