This paper proposes a quasi-static conformal mapping analysis to analytically evaluate the input resistance of Archimedean spiral antenna at its radiation region. The deviation from the original constructs of band theory for two-wire spiral antennas leads to the concept of common slot-line mode radiation. The per-unit-length capacitance and the characteristic impedance of the quasi-TEM fundamental propagating mode in periodic coplanar waveguide (PCPW) structure are obtained in terms of spiral parameters including substrate properties. This formula enables little computational effort on the computation of input resistance at the radiation mode of balanced-excited two-arm Archimedean spiral antennas. The numerical simulation demonstrates the accuracy of derived formulas both in free space and when a dielectric layer is presented.

Abstract-While Archimedean spiral antennas were invented a half-century ago, only selfcomplementary impedance can be evaluated directly from the Babinet's principle. This paper examines the effects of metal width and arm spacing on printed spiral's input impedance. A model is proposed based on examination by decomposition of planar spiral. A closed-form expression for the input impedance of Archimedean spiral antenna is obtained by evaluating the proposed model with conformal mapping techniques. Full-wave numerical simulations, Babinet's principle, and a fabricated antenna demonstrate the accuracy of the proposed model. The expression in this work can be used to find the impedance of a variety of spiral complementary structures analytically. The examination and discussion on the effects of other parameters and features in addition to the spiral itself are also provided through numerical simulation.