Numerical evaluation of the two-dimensional generalized exponential integral

An exact technique for the evaluation of the two-dimensional generalized exponential integral-as required in structures involving rectangular planar radiators and transmission lines-is presented. It is shown that the singularity is integrable if integration is performed in polar coordinates. The integral can be calculated exactly and with minimal computational effort, even if integration over the origin of the coordinate system is required-regardless of whether the origin is an internal or boundary point of the integration region. Comparison with a standard technique proves the presented approach superior. Stability of the algorithm and convergence is discussed. Performance is demonstrated for the example of an asymmetrically edge-fed patch antenna