Approximate formulas for the far fields and gain of open-ended rectangular waveguide

Approximate formulas are derived for the far field and gain of standard, open-ended, unflanged, rectangular waveguide probes operating within their recommended usable bandwidth of frequencies. (Such probes are commonly used in making probe-corrected near-field antenna measurements.) The formulas, which yield forward far-field power patterns and on-axis gains of X-band and larger waveguide probes to within about 2 dB and 0.2 dB accuracy, respectively, assume (sin theta-cos theta) azimuthal angular dependence and an E-plane pattern given by the traditional aperture integration of the TE-10 mode Eand H-fields in the Stratton-Chu equations.