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Date: Tue, 08 Feb 2000 11:54:41
To: rsgb_lf_group@blacksheep.org
From: "Rik Strobbe" <rik.strobbe@fys.kuleuven.ac.be>
Subject: Re: LF: rik-short vert
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At 20:22 7/02/00 +0000, G3KEV wrote:
>Is Rik saying that a 1 metre vertical suitably loaded and resonant and
>with the appropriate amount of rf supplied to it to emit 1w erp is  the
>same as a 50 metre vertical again suitably loaded and resonant and with
>the appropriate amount of rf  to emit 1 w erp THE SAME THING.
>It is NOT the same as far as propogating a signal is concerned beyond
>the near field.
>When it is so easy to generate Killowatts from power mosfets these days
>why bother about antennas just pump megawatts into a broom stick and
>according to Rik you will just do as well as the guy with the same erp
>but a 40 metre tower.
> ...
>73 G3KEV


When you generate 1 Watt ERP (effective RADIATED power) your signal will
have a certain fieldstrength at a certain distance. The only thing that
will affect the fieldstrength (besides the ERP) is the radiation pattern of
the antenna. As far as I know, from books and antenna simulation software,
the length of a vertical antenna does NOT affect the radiation pattern. So
(assuming a lossless loading coil) pumping 100W into a 40 meter vertical
will generate the same ERP as pumping 400W into a 20 meter vertical,
pumping 1.6kW into a 10 meter vertical and ... (in theory) pumping 160kW
into a 1 meter vertical.
But of course there are practical limitations, the shorter your antenna is
the more power you need and the larger the loadingcoil has to be. For very
short verticals (as the 1 meter) this will lead to inpractical values for
the loading coil and excessive voltage at the antenna.

An example to show what I mean : 
Assume at a certain location you have a 'groundloss' of 30 Ohms (a
realistic value if you have the space and wire to put an extensive
radialnetwork in the ground).

1. A 40 meter vertical (without toploading - to keep it simple) will have a
radiation resistance of 0.131 Ohms and a capacitance of 240pF. That means
that you will need an antennacurrent of 1.6A to generate 1 Watt EIRP
(taking into account that a short vertical has a gain of 4.8dBi). Further
you will need a loadingcoil of 5.64mH to bring the antenna to resonance.
Assuming a Q of 300 the loss in the coil will be 16 Ohms, so the total
loss-resistance will be 46 Ohm.
To get the antennacurrent of 1.6A you need a RF power of 120 Watts and the
antennavoltage (built up over the coil) will be 7.75kV.
All of the above are very practical values and it will be easy to the the
wanted 1 Watt EIRP (and even much more).

2. For a 20 meter vertical the radiation resistance will be 0.033 Ohms and
the antennacapacitance 120pF. You will need 3.2A to get 1 Watt EIRP and the
loadingcoil has to be 11.3mH. At the Q of 300 the coil-loss will be 32Ohms,
resulting in a total loss of 62 Ohms. One will need an RF power of 635
Watts and the antennavoltage will be 31kV.
The antennavoltage is rather high, so you will need proper isolation but
apart from that 1 Watt EIRP is still realistic.

3. For a 10 meter vertical the radiation resistance will be 0.008 Ohms and
the antennacapacitance 60pF. You will need 6.4A to get 1 Watt EIRP and the
loadingcoil has to be 22.6mH. At the Q of 300 the coil-loss will be 64
Ohms, resulting in a total loss of 94 Ohms. One will need an RF power of
3.85 kW and the antennavoltage will be 124kV.
With this antenna is will be very difficult to get 1 Watt EIRP in practice,
the antennavoltage will be the big burden.

4. Doing the same calculations all over for a 1 meter vertical will result
in a loadingcoil of 0.226 Henry, a RF power needed of 87MW and a
antennavoltage of 13MV. Not very pracical values !

5. A last example to point out the importance if good toploading : assume
that we have a 10 meter vertical with extensive toploading. In that case
the radiation resistance wil be about 0.03 Ohms and the antennacapacitance
can be up to 500pF. For this antenna the loadingcoil needs to be 2.7mH
(coil-loss = 8 Ohms). The antennacurrent needed will be 3.3A resulting in a
RF power of 420 Watts and an antennavoltage of 7.75kV.
This seems quite acceptable values to me, so in the right circumstances
(low losses) 1 Watt EIRP can be achieved with 'normal' antennas.

73, Rik  ON7YD