  This paper analyses the surface wave mode propagating along a simplified
planar Goubau line consisting of a perfectly conducting circular wire on top of
a dielectric substrate of finite thickness but infinite width. An approximate
equation for the propagation constant is derived and solved through numerical
integration. The dependence of the propagation constant on various system
parameters is calculated and the results agree well with full numerical
simulations. In addition, the spatial distribution of the longitudinal electric
field is reported and excellent agreement with the numerical simulation and
previous studies is found. Moreover, validation against experimental phase
velocity measurements is also reported. Finally, insights gained from the model
are considered for a Goubau line with a rectangular conductor. These results
present the first step towards an analytic model of the planar Goubau line.
