Theory of the corner-driven square loop antenna

The general problem of determining the distribution of current and the driving point impedances of a square loop or frame antenna is formulated when arbitrary driving voltages are applied at each corner or when up to three of these voltages are replaced by impedances. The loop is unrestricted in size and account is taken of the finite cross-section of the conductors. Four simultaneous integral equations are obtained and then replaced by. four independent integral equations using the method of symmetrical components. These equations are solved individually by iteration and first-order formulas are obtained for the distributions of current and the driving-point admittances. By superposition the general solution for the abritrarily driven and loaded loop is obtained. Interesting special cases include a corner-reflector antenna and the square rhombic (terminated) antenna. An application of the principle of complementarity permits the generalization of the solution to the square slot antenna in a conducting plane when driven from a double-slot transmission line at one corner.