An inexpensive planar antenna fabricated as a plurality of parallel layers of multi turn spiral loops co-located with conductive material at the center of the loops, there being an exclusion zone free of conductive material between the innermost loop and the conductive material at the center. The conductive material may comprise circuit elements, for example batteries, amplifiers, antenna drivers or other functional elements as well as passive elements. In one embodiment, the loop traces may be staggered. In another embodiment, the loop traces are varied in width as a function of position within the loop cross section. In further embodiments, the planar form is integrated with additional orthogonal planar antennas substantially coplanar with the first planar antenna and having axes orthogonal to the first planar antenna and to one another. In further embodiments the exclusion zone is extended by design rules and confining routes in a circuit section. The antenna system may be configured as a three dimensional omnidirectional antenna and is well adapted for small form factor hand held and portable wireless applications.