Andy, all,
Last year, I did a MathCad analysis of the fields from a small vertical
and a small magnetic loop at 137 kHz. The program calculated the vector
E and H fields, and the magnitude of E/H for distances from 1 to 10 km.
For the vertical, there are three terms to consider for the E field, and
two for the H field. The situation is reversed with the loop, with three
terms for the H field, and two for the E field.
Comparing the calculated |E/H| values with the "far field" value of 377
ohms, the error was about 12% at 1 km and 1% at 3 km for both types of
antenna. The errors at 1 km were in opposite directions, as one would
expect, favoring the E field for the vertical, and the H field for the
loop.
If you grant a measurement error of 1%, then it would be best to take
readings no closer than 3 km from a small 137 kHz antenna, which would
be lambda/(0.73). If higher errors are permissible, then you can move
in, but I'd have trouble recommending the 1 km figure at that frequency.
As Andy points out, there is at least one other far-field concept that
doesn't apply to us LF hobbyists. That only refers to large antennas,
where the height of a vertical, for example, is significant compared to
the distance. A corollary occurs with multi-element arrays, where the
directional pattern is distorted if the spacing between the towers is
significant compared to the distance.
John Andrews, W1TAG
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