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Date: Wed, 08 Mar 2000 11:01:38
To: rsgb_lf_group@blacksheep.org
From: "Rik Strobbe" <rik.strobbe@fys.kuleuven.ac.be>
Subject: Re: LF: antennas for 136kHz
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At 11:02 7/03/00 -0800, you wrote:
>If I may I would like to pose a simple question, to which all the experts
>are invited to reply:
>If to the top of a vertical an equal vertical descender is added, insulated
>from Earth at the bottom, but otherwise the same length as the original
>vertical and coming straight down (like an old-fashioned hair-pin), and
>assuming that this is resonated and matched to 50 ohms, will the new antenna
>radiate more power, less power or the same power for the same input and why?
>This might for example be the other wire of a sufficiently well spaced
>feeder (no voltage breakdown), effectively short-circuited at the top and of
>low RF resistance.

This 'hairpin antenna' can be approached in 2 ways :

1. Consider it the minimal version of a meander antenna (2 elements)
In this case you would have a SRF (Size Reduction Factor) of about 0.8,
what means that a 10m high 'hairpin' would be equal to a 12.5m 'straight
vertical'. This would mean a gain of 1.9dB

2. Look at the currentdistribution over the antenna
Assuming a linear decrease from feedingpoint to end (and a current of 1A at
the feedingpoint) this would mean that the current at the top is 0.5A and
at the end of the hairpin it wil be 0A. So the average 'upgoing current' is
is +0.75A but we have also an average 'downcoming current' of -0.25A. As
long as the spacing of the hairpin is small (compared to the wavelength) we
can just add both currents. The result is an average current of 0.5A,
exactly the same as what you would have with a 'straight vertical'. So the
radiation resistance will not change.
But the antenna capacitance will increase (as you put more wire in the
air). Based om my experience with multiple topload wires, with a spacing of
1m the capacitance can increase from 6pF/m to 9pF/m. This means an increase
of the antennacapacitance by 50% and thus a decrease of the loadingcoil by
the same ammount (= less loss in the loadingcoil). For a 10m high antenna
(assuming 50 ohm groundloss and a loadingcoil with Q = 300) a gain of 1dB
can be expected.

Personnaly I think that the second approach is more correct as in the
article on meander antennas they assume that the antenna is brought to
resonance just by 'meandering' (with a loadingcoil).
So a small gain can be expected from a 'hairpin antenna'. but keep in mind
that you can get more gain (using the same length of wire and the same
antennaheight) with a simple inverted-L or T antenna.