We analyze cloaking of transverse electric (TE) fields through homogenization of radially symmetric metallic structures. The two-dimensional circular cloak consists of concentric layers cut into a large number of small infinitely conducting sectors which is equivalent to a highly anisotropic permittivity. We find that a wave radiated by a magnetic line current source located a couple of wavelengths away from the cloak is almost unperturbed in magnitude but not in phase. Our structured cloak is shown to work for different wavelengths provided they are ten times larger than the outermost sectors.