This paper examines the transmission line structure of a planar Archimedean spiral antenna. A novel analysis is performed by unwinding the spiral into an equivalent straight transmission line to understand its impedance properties and the radiating mechanism. A relation between the input impedance of the spiral antenna and the characteristic impedance of our proposed model is established. The analytical solution completes the lossy transmission line modelling for the input impedance of the spiral antenna. The value of the stable input resistance in the spirals radiation region is found not due to the radiation resistance of the loop antenna, but it is dominated by the propagation characteristics of the slot-line mode, that is the travelling wave on the spiral. The accuracy of this proposed model is verified by full-wave simulations, the Babinets principle, and measurements. Examination of the radiation mechanism and discussion on the effects of other parameters such as feeding design are also provided. \ 2014 Taylor & Francis.