Half Wave Dipole at 3 GHz

A resonant half wave dipole of length 5 cm is aligned at the origin along the x axis. The target dA =.01 m^2 is at range 10 cm (one wavelength) , zenith 0, along the z axis. The Poynting vector at the target is 12.77 mW/m^2. The peak current along the element is set to 5.229 mA to set the power level at 1 mW (0 dBm). This is in agreement with the theoretical power level at this current and wavelength.

The instantaneous electric field at the target is -3.09 V/m. The instantaneous magnetic field at the target is -8.25 mA/m. The Poynting vector 12.8 mW/m^2 is a time average, in the z direction away from the source.

The power impinging on the target dA= .01 m^2 is 95.09 mW. The fields in spherical coordinates at the target are shown in the lower right.

dA shows the polarization of radiation in the x direction at the target. Path shows the integrands of electric and magnetic field to be integrated around the perimeter of dA to express Faraday's and Ampere's laws.

dr shows the transverse electric and magnetic fields along dr, which is four wavelengths in length, in the spherical coordinate system. Cyan corresponds to the theta coordinate, yellow to phi.

Element shows the distribution of current along the resonant half wave element of length 5 cm.

dP/dA is formed at the target as a quotient of differentials. It is approximately equal to the radial Poynting vector. The directivity in the direction of the target is estimated by differentials of area and of solid angle subtended by dA.

The target range is increased to 10 wavelengths. Estimates of directivity converge.

The target dA is decreased. Estimates of directivity converge on the theoretical 1.64.