Calculating LF-antenna with top load

[Andre' Kesteloot]

Rik Strobbe wrote:

> For those who do not have acces to antenna-software there is still the
> possibility to calculate the radiation resistance and the capasitance of
> the antenna yourself.
> If a simplified model is taken and you have no 'slooping' tophat,the
> results are remarkable accurate (compared to MININEC and K6STI-software).
> The calculations are done in a few simple steps :
>
> 1. Calculate the radiation resistance of your antenna if it had no tophat :
> Rv = 0.0000816 x Lv^2 (Lv = length of the vertical section in metres, Rv =
> radiation resistance in Ohms)
> This formula is based on a frequency of 136.75kHz
>
> 2. Calculate the capasitance of the vertical and tophat section of your
> antenna :
> - vertical section : Cv = 6pF for every meter of wire
> - tophat section : Ct = 5pF for every meter wire (regardless of shape of
> tophat).
> The total antenna capasitance Ca = Cv + Ct.
>
> 3. Calculate the average current in the vertical section (with a
> base-current of '1').
> Herefore we assume that in every pF of the antenna capacitance the same
> ammount of current 'dissapears'. In that case the current at the top of the
> vertical section equals Ct / Ca and the average current Iav = (Ca + Ct) /
> (2 x Ca).
>
> 4. The radiation resistance of the antenna is proportional to the square of
> the average current (in the vertical section). For a vertical without
> tophat the average current is 0.5, so the square of the average current is
> 0.25 (or 1/4).
> Therefore the radiation resistance of your antenna (Rs) is :
> Rs = 4 x Iav^2 x Rv (Rv is calculated in step 1)
>
> Below you find a comparisation of the results of the K6STI-software (by
> PA0SE), MININEC (by DF3LP) and the 'do-it-yourself' calculations.
>
> 1. No top load
> K6STI software (PA0SE)   : Rs = 0.0078 Ohm , Ca = 65 pF
> MININEC (DF3LP)          : Rs = 0.0079 Ohm , Ca = 66 pF
> Own calculations (ON7YD) : Rs = 0.0082 Ohm , Ca = 60 pF
>
> 2. One horizontal top load wire of 5 m
> K6STI software (PA0SE)   : Rs = 0.0139 Ohm , Ca = 93 pF
> MININEC (DF3LP)          : Rs = 0.0138 Ohm , Ca = 93 pF
> Own calculations (ON7YD) : Rs = 0.0137 Ohm , Ca = 85 pF
>
> 4. One horizontal top loading wire of 10 m
> K6STI software (PA0SE)   : Rs = 0.0176 Ohm , Ca = 120 pF
> MININEC (DF3LP)          : Rs = 0.0176 Ohm , Ca = 121 pF
> Own calculations (ON7YD) : Rs = 0.0173 Ohm , Ca = 110 pF
>
> 6. One horizontal top loading wire of 20 m
> K6STI software (PA0SE)   : Rs = 0.0221 Ohm , Ca = 175 pF
> MININEC (DF3LP)          : Rs = 0.0220 Ohm , Ca = 176 pF
> Own calculations (ON7YD) : Rs = 0.0215 Ohm , Ca = 160 pF
>
> 7. Two horizontal top loading wires of 5 m  (T-antenna)
> K6STI software (PA0SE)   : Rs = 0.0174 Ohm , Ca = 117 pF
> MININEC (DF3LP)          : Rs = 0.0174 Ohm , Ca = 118 pF
> Own calculations (ON7YD) : Rs = 0.0173 Ohm , Ca = 110 pF
>
> 9. Two horizontal top loading wires of 10 m (T-antenna)
> K6STI software (PA0SE)   : Rs = 0.0220 Ohm , Ca = 171 pF
> MININEC (DF3LP)          : Rs = 0.0219 Ohm , Ca = 172 pF
> Own calculations (ON7YD) : Rs = 0.0215 Ohm , Ca = 160 pF
>
> 11. Two horizontal top loading wires of 20 m (T-antenna)
> K6STI software (PA0SE)   : Rs = 0.0260 Ohm , Ca = 280 pF
> MININEC (DF3LP)          : Rs = 0.0261 Ohm , Ca = 281 pF
> Own calculations (ON7YD) : Rs = 0.0255 Ohm , Ca = 260 pF
>
> 12. Four horizontal top loading wires of 5 m (90 degrees between wires in
> horizontal plane)
> K6STI software (PA0SE)   : Rs = 0.0214 Ohm , Ca = 157 pF
> MININEC (DF3LP)          : Rs = 0.0212 Ohm , Ca = 158 pF
> Own calculations (ON7YD) : Rs = 0.0215 Ohm , Ca = 160 pF
>
> 14. Four horizontal top loading wires of 10 m
> K6STI software (PA0SE)   : Rs = 0.0259 Ohm , Ca = 256 pF
> MININEC (DF3LP)          : Rs = 0.0257 Ohm , Ca = 257 pF
> Own calculations (ON7YD) : Rs = 0.0255 Ohm , Ca = 260 pF
>
> 16. Four horizontal toploading wires of 20 m (T-antenna)
> K6STI software (PA0SE)   : Rs = 0.0290 Ohm , Ca = 466 pF
> MININEC (DF3LP)          : Rs = 0.0289 Ohm , Ca = 467 pF
> Own calculations (ON7YD) : Rs = 0.0285 Ohm , Ca = 460 pF