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Date: Wed, 7 Jan 2015 09:03:24 -0800
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Subject: LF: RE: Path measurement by group delay
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Paul and Markus,

That's inspiring especially in a watt-for-watt or pound-for-pound context,
with respect to some legacy systems. At roughly 1E6 pounds for an OMEGA
transmitter/antenna-system with precision (very roughly) inversely
proportional to square of power and weight (up to the point at which
atmospheric uncertainties dominate), the result below is quite interesting;
nice work as always!

73,

Jim AA5BW

-----Original Message-----
From: owner-rsgb_lf_group@blacksheep.org
[mailto:owner-rsgb_lf_group@blacksheep.org] On Behalf Of Paul Nicholson
Sent: Wednesday, January 7, 2015 7:01 AM
To: rsgb_lf_group@blacksheep.org
Subject: VLF: Path measurement by group delay

I wrote:

 > A challenging experiment would be to measure the actual path  > length.
This requires transmitting two fairly close frequencies  > either
simultaneously or alternating with FSK.

No sooner said than done!

Markus DF6NM just happens to have a servo controlled variometer which
samples the radiated field and adjusts the tuning to maintain the phase of
the transmission - even when toggling
between two frequencies.   This, in conjunction with Spectrum
Lab's ability to generate a carrier with absolute phase, enabled the
experiment to proceed.

We used two frequencies 60Hz apart, alternating between them at 5 minute
intervals.

Some arithmetic shows that for the 60Hz separation, the group delay
corresponds to 13.88 km of path per degree of phase difference between the
two carriers.

Markus made a long transmission (after some mechanical troubles) with 10uW
ERP, beginning just before 2015-01-06 11:30 UT and the received signal was
analysed at Todmorden in a 4 hour window (sufficient to get good S/N for
accurate phase), sliding the window in 1 hour steps.

Table below lists the S/N of the two carriers, their phase (lead) and phase
difference, and the resulting path length:

  Period          S/N dB     Phases       Diff    Path
  11:30 to 15:30  19.0/17.9  -7.4/-84.3   76.9    1068 km
  12:30 to 16:30  18.5/17.2  -11.1/-85.2  74.1    1029 km
  13:30 to 17:30  17.8/16.9  -13.5/-85.6  72.0    1000 km
  14:30 to 18:30  16.3/16.5  -20.6/-94.7  74.1    1029 km
  15:30 to 19:30  15.9/17.3  -21.2/-102.9 81.7    1135 km
  16:30 to 20:30  16.8/17.3  -15.4/-111.2 95.8    1330 km
  17:30 to 21:30  16.5/17.0  -17.2/-113.3 96.1    1335 km
  18:30 to 22:30  16.9/15.4  -23.7/-111.0 87.3    1212 km
  19:30 to 23:30  15.9/13.8  -28.7/-101.9 73.3    1017 km
  20:30 to 00:30  15.8/13.2  -30.6/-95.5  65.0     902 km
  21:30 to 01:30  16.2/13.7  -27.9/-82.2  54.3     754 km
  22:30 to 02:30  16.3/15.0  -18.5/-84.8  66.2     920 km
  23:30 to 03:30  18.8/15.8  -15.2/-88.6  73.4    1019 km

The great circle distance to Todmorden is 1028 km.

Phase measurement error with the stronger signals, around +/- 60km.
For the weaker signals, about +/- 180km.

Looks like the results are upset at night due to multi-path
interference.   At VLF the ground wave is still significant at 1 Mm
and there will be several sky wave components in the mix.

Not a bad result for 10uW ERP.  A stronger signal would probably not have
improved the result, given the multi-path propagation.

A longer range test would be less affected by multiple paths.
Would require smaller frequency shift: eg about 12Hz for
6000 km.  12Hz shift is difficult though, without a strong signal.
17 dB S/N would give an error of about 500km on a 6 Mm path.

--
Paul Nicholson
http://abelian.org/
--