The RF field excitation homogeneity problem of MRI at high resonance frequencies is investigated on the basis of the simplest two-dimensional setup including a cylinder phantom with spatially constant but frequency-dependent material parameters and an impressed surface current distribution between the phantom’s surface and a surrounding perfect electric conductor (PEC) shield. This simple arrangement has been chosen intentionally in order to reduce the set of parameters to a minimum and therefore maximize the physical insight, which allows quite general and helpful statements about the B1+ pattern quality for the widely used first-order circularly polarized (CP) excitation mode. The coefficient of variation (CoV) of the B1+ distribution is most suited as a figure of merit for the homogeneity, since it normalizes the standard deviation to the mean value of the field pattern. Only two parameters of the arrangement in Fig. 1 have been varied – the excitation frequency ranging from 30 MHz up to 450 MHz and the diameter of the phantom ranging from a few centimeters up to 40 cm, which covers more or less every MR imaging scenario. A characteristic B1+ pattern will be introduced, which indicates the transition between a regime with the well-known central brightening and another one without.