The excitation of a helicon plasma source by an azimuthally symmetric antenna is considered in comparison with anti-symmetric excitation. The resonances and anti-resonances at the wave excitation, as well as the peculiarities of the power absorption, are shown to be very similar for symmetric and anti-symmetric excitation. The plasma resistance turns out to be higher in the case of symmetric excitation for very short devices. The non-monotonic variation of plasma resistance with density is found to be intrinsic for both methods of excitation as a result of decreasing the power absorption at anti-resonances. This is shown to give rise to abrupt density jumps at varying input power.