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| Subject: | LF: Re ELF…12.67Hz, ELF Resistance Model |
| From: | James Hollander <[email protected]> |
| Date: | Fri, 15 Mar 2019 21:04:34 +0000 (UTC) |
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Hi ELF, Do KV’s of ELF on a TX antenna offset or
divert a tiny amount of atmospheric current entering the RX antenna? Suppose
the atmosphere has equipotential surface(s) high in a an electrically resistive
air mass in which the ELF TX and RX antennas are embedded at ground
level. If so, what happens
quantitatively?
I’m trying out different math models to
describe the atmosphere around the DK7FC 12.67Hz site to see if any model might
be supported by actual numbers and performance Stefan may develop.
Call one an “ELF Resistance Model” as if the
atmosphere has some fixed resistance R1 coming down from an equipotential plane
at altitude. In the model, R1 connects
to a disk of air represented by a large number N of parallel resistances Rsky going down to earth. Each
such parallel resistance represents the
resistance of a vertical column of air having cross-sectional area proportional to antenna height-squared A = Co hAnt2. Currents in the parallel resistances Rsky compete with each other
to divide up the current coming down from the equipotential plane high above.
The TX antenna and RX antenna have equal height hAnt. If the antennas instead have a top hat area A that is bigger than hAnt2 , then area
A is whichever top hat mesh area or
square of top hat wire length applies. (The
horizontal length of an inverted-L is considered its top hat wire length.)
Picture the disk of air several kilometers
radius with DK7FC 12.67Hz TX antenna at its center and RX antenna at a distance
r meters
away, say at 3500m or you name it. The
TX antenna delivers many KV of 12.67Hz ELF voltage to just one of the
resistances Rsky.
After the math is done,
the results say that the voltage on the RX antenna declines slowly at shorter
distances and then declines as an inverse-square (1/r^2) farther away. That’s
a lot less favorable than a radio antenna.
In a radio antenna the voltage merely declines inversely (1/r).
Signal strength dB in this ELF model would fall as -40 log10 r at the farther
distances, which is -12dB for every doubling of distance. Ouch!
If Stefan were able to set
up a second identical RX antenna and RX-integrator setup at a second distance r2 and compare its
performance with his setup at current distance r1, the model allows one to calculate the value of a constant
K that the model needs to predict
signal strength at any distance r. Basically, this constant K lumps together sky resistances with the antenna-based area A.
Specifically, the model
formula for antenna voltage at any distance r says:
VRX(r) = VRX(r1) (K+r12) / (K+r2).
In dB, a model formula recognizes power ratio V-squared and the
inverse-squared distance:
VRX(r)
/ VRX(r1) in dB = -40 log10[ (r / r1)
sqrt[(1+K/r2)/(1+K/r12)] ].
Constant K is defined to be (1/π) (Rsky/R1) A.
Constant K is calculated from reception
voltages (volts, not dB) at two RX stations using equal integration times,
according to this calculation:
K = [VRX2 r22 - VRX1 r12] / [VRX1
- VRX2].
I hope the equation
formats haven’t been too badly mangled by the email and the LF reflector! I’m also considering a disk-shaped lossy
RLC transmission-line model of the ELF atmosphere, which probably would predict
different behavior. Maybe someday,
amateur work can tell us which model(s) are garbage or useful material for advancing ham
ELF aspirations.
GL & 73, Jim H W5EST
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