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Radiation efficiency of horizontal VLF antennas connected to ground

Radial field dependence:

Transmitting dipole moment current . length = 1 Am 

Background noise level above ground: 5 dBuV/m

red: vertical E-field in air,
black: horizontal E-field in the ground,
blue: H-field ( . 377 ohm)

Vertical electrical antenna:

Horizontal wire connected to average ground:

Horizontal wire connected to very dry ground:

Geometry of an earth-antenna:

View from top

View from side


Complex wavenumber k in lossy medium:

Fields generated by a small electrical dipole:  

Fields generated by a small magnetic dipole:  

Skin depth:  

Coupling c between vertical polarized surface wave and longitudinal electrical field:  

(applicable if antenna length l > d and l > d)

Mirror effects of the earth-air interface:

In the air above the surface, the vertical (E-field) polarisation is doubled by the image antenna, whereas the horizontal polarization is short-circuited. 

Beneath the surface, the air acts as a magnetic wall, suppressing vertical E-fields and currents.

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