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From: Paul Nicholson <vlf0403@abelian.org>
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Date: Thu, 26 Oct 2017 19:48:46 +0000
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Subject: Re: VLF: 300 mA on 5170 Hz
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Stefan wrote:

 > My ERP on 5170 Hz is 2 dB lower than on 6470 Hz.  But the SNR we
 > observe seems not to differ much from that on 6470 Hz.
 > The opposite of what all the curves predict!!!!!!

Not really.  Attenuation is higher per unit distance, so the
background from long distance sferics will be much lower.

Attenuation of relatively close signals is not so much, so
at this sort of range, you may find better S/N, not worse.

Markus wrote:

 > shouldn't the conductivity from the free electrons rather
 > resemble a metal-like electric boundary,

It depends on the angle of incidence.  It's complicated!

The reflection coefficient at the ionosphere is a matrix of
four complex numbers - and there are two complex refractive
indexes.

For the TM mode, the relevant reflection coefficient is
maybe magnitude 0.5 to 0.9 and the phase is close to
zero for high angles of incidence (small zenith angle).
For large zenith angles (grazing incidence) the phase
shift can be closer to 90 deg.

Eg, from my ray model for the 1-hop, some examples of the
sky wave reflection matrix at 5170 Hz:

Day, 100km range, zenith angle 30 deg:

  s->mat  9.0e-01/-6.9   1.2e-01/-141.6
          1.2e-01/-141.4   9.2e-01/174.6

where the four components are

          TM to TM     TE to TM
          TM to TE     TE to TE

and each is given as magnitude/phase_degrees.  The important
one for us is the top-left component, TM to TM.

Day, 2000km range, zenith angle 80 deg;

  s->mat  4.5e-01/-72.6   1.7e-01/-159.6
          1.7e-01/-157.2   9.5e-01/176.4

Now we have quite a lot of phase shift.

The TE to TE component involves a phase inversion and it is
interesting to note that its magnitude is generally higher
than the TM/TM coefficient.  Eg see

  http://www.dtic.mil/get-tr-doc/pdf?AD=AD0740578

I don't really understand this propagation stuff, but I make
some notes to try to learn.  For example

  http://abelian.org/vlf/tmp/pn1214.pdf

which is unfinished (I'm stuck on the groundwave stuff) and
some of the graphs need replotting.  But sections 12 and 15
might be useful.  The s->mat matrix above is [S] in equ 15.1

--
Paul Nicholson
--