# [Fwd: LF: antenna calculations]

André Kesteloot akestelo@bellatlantic.net
Mon, 15 Jun 1998 10:15:35 -0400

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Rik Strobbe wrote:

> Responding on a msg of Peter, G3LDO, I did send him a drawing of my antenna
> and asked him to put the data in the EZNEC2 software.
>
> My antenna is of the Marconi type with top load, the vertical section is
> slightly sloping and goes from 0.5 to 11.5 m above ground (total length
> 13.1m) the horizontal (top load) consists of 7 wires more or less horizontal
> (ends are 10 - 12 m above ground) and divided of about 220 degrees of the
> circle. Longest horizontal wire is 19.7 m, the shortest 2 m and the total
> length of the horizontal section is 63.4 m. The total amount of wire in the
> antenna is 76.5m. The numberous trees surrounding the antenna are used to
> hang up the wires.
>
> The results I received from Peter are :
> - radiation resistance = 0.0355 Ohms
> - ERP                  = 4.8mW
> - antenna gain         = -36dBi
> - antenna capasitance  = 335pF
>
> The data I got from antenna measurements are :
> - antenna current (for 37W HF power) = 0.37A
> - antenna capasitance                = 370pF
> The capasitance difference (35pF = 10%) could be explained by the effect of
> the surrounding trees on the antenna.
>
> The 'quick and dirty' calculations I did on the antenna are :
>
> --------------------
> - 1 :
> A 'pure vertical' antenna (no top load) of the same height (11m) would have a
> radiation resistance of 40*pi^2*(11/2200)^2 = 0.01 Ohms (2200 = wave length).
> If I would put the 0.37A into this pure vertical the average current would be
> half = 0.185A.
> - 2 :
> My antenna has 76.5m of wire and a vertical height of 11m, so in first
> aproximation I can 'model' it as an inverted L with a vertical leg of 11m and
> a top load of 65.5m. Assuming that the current at the feeding point is 0.37A,
> the current at the and of the top load is 0A and the current decrease is
> linear, the current at the top end of the vertical leg = 0.37*65.5/76.5 =
> 0.317A. So the average current in the vertical leg is 0.344A.
> - 3 :
> The radiation resistance of an antenna increases with the square of the
> average current, this means that for my antenna the radiation resistance =
> (0.344/0.185)^2*0.01 = 0.0346 Ohms
> This matches the value that G3LDO got out of EZNEC2 (0.0355 Ohms) very well,
> difference is 0.0009 Ohms or 3%.
>
> ERP
> ---
> If I have a current of 0.37A into a resistor of 0.0346Ohms then the power is
> 0.37^2*0.0346 = 0.0047W = 4.7mW.
> Again a good match to the 4.8mW from EZNEC2 (difference 0.1mW or 2%).
>
> Antenna gain
> ------------
> In first aproximation the antenna gain is the ratio of the radiation
> resistance and the loss resistance, so calculated in dB's it is :
> 10*Log(0.0346/280) = -39.1dB. Since Peter gives the gain in dBi (dB versus
> isotropic antenna) I have to take the gain of a (perfect) short vertical into
> account, this is 4.7dBi.
> So the 'gain' of my antenna is calculated as 34.4dBi.
> This is a difference of 1.6dB to the 36dB from EZNEC2
>
> Antenna capasitance
> -------------------
> My antenna has 76.5m wire, 11m vertical and 65.5m horizontal. On several
> occasions I found values of 5pF/m for the horizontal part and 6pF/m for the
> vertical part of an antenna. If I calculate the antenna capasitance based on
> this the result is 65.5*5+11*6 = 394pF.
> But the above values (of pF/m) are only valid for well separated wires (all
> wires at least 2m apart), so close to the point where all top wires come
> together the pF/m will be less. On the other hand are the ends of the
> horizontal wires close to trees what could cause an additional capasitance.
> The difference of the calculated 394pF is 59pF (=15%) the EZNEC2 result and
> 24pF (6%) with the measured value.
>
> Conclusion
> ----------
> The 'quick and dirty' calculations of radiation resistance and ERP match
> remarkable well the results from EZNEC2 (only few % difference), even the
> 1.6dB difference for the antenna gain is acceptable.
> Due to the rather 'unconventional' antenna (topload wires in all direction,
> proximity of trees) the calculation of the antenna capasitance is little less
> accurate but still within a 20% range.
> I cannot draw definive conclusions from the calculations on only one antenna,
> but it seems that with simple 'straight-forward' calculations the parameters
> of a Marconi antenna for LF can be predicted well.
>
> 73, Rik  ON7YD

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