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Message-ID: <3.0.1.16.19990917151852.08171c8a@mail.cc.kuleuven.ac.be>
Date: Fri, 17 Sep 1999 15:18:52
To: rsgb_lf_group@blacksheep.org
From: "Rik Strobbe" <rik.strobbe@fys.kuleuven.ac.be>
Subject: Re: LF: LF-antenna with top load
In-reply-to: <37E1250D.69B2AD45@nephro.uni-kiel.de>
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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