Analytical Development of the Far-Zone Radiation Integral for an Arbitrary Planar Spiral Antenna

The planar spiral antenna´s radiation integral is both conceptually and computationally complex. In the past, the far-field pattern has been found by either approximating the spiral´s shape to make the computation tractable, or by using a numerical approximation. In this paper, the radiation integral for an arbitrary planar spiral antenna is now derived without approximating its shape, using a readily understandable differential-geometry analysis. This allows for physical insight into the radiation mechanisms and contributions from the various current components that are otherwise intractable using modern computational codes, and provides a significantly more efficient algorithm in cases when mutual coupling can be neglected. In addition, this analysis and physical insight leads to an effective spiral antenna design tool. Current numerical integration techniques are applied to find the far-zone electric field for an Archimedean spiral antenna using this development. The results are compared with a numerical solution of the electric-field integral-equation formulation to validate the analysis.