Modal impedances of planar, non-complementary, N-fold symmetric antenna structures

Planar N-arm rotationally symmetric antennas are commonly used in applications that demand wideband, multiple-mode, dual-polarization, and conformal geometries. Antennas included in this category are spirals, log-periodic dipole arrays, bow-tie antennas, and sinuous structures. An analytic expression for the modal impedances of these complementary planar structures has been available for many years. This paper extends the theory to non-complementary planar /V-fold symmetric antennas, and provides equations valid for any arm-to-gap width ratio, arm width, expansion rate, and low-loss electrically thin substrate materials. The equations are based on quasi-TEM coplanar stripline theory, and provide a band-averaged approximation of the input impedance of the antenna for each characteristic mode of operation. Predicted modal impedances are compared to spiral antenna measurements. In addition, a procedure for accurately measuring the dielectric constant of the substrate material is discussed.