Theoretical Brillouin (κ-β) diagrams for monopole and dipole arrays and their application to log-periodic antennas

In this paper, we derive the characteristic equation for the complex propagation constant in a transmission line periodically loaded with dipole elements. This equation is solved for real and imaginary parts of the mode propagation constants. The effect of mutual impedance between antenna elements is included in the formulation and calculation. Theoretical calculations are compared with experimental results reported by Mayes and Ingerson [9]. The usefulness and limitation of the Brillouin ( ) diagram for analyzing log-periodic (LP) structures are discussed briefly.