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Date: Sat, 26 Feb 2000 14:00:10 +0000
To: rsgb_lf_group@blacksheep.org
From: "Andy Talbot" <drassew2@interalpha.co.uk>
Subject: LF: Re: Low loss inductors
Precedence: bulk
Reply-To: rsgb_lf_group@blacksheep.org
Sender: <majordom@post.thorcom.com>

I find that rather impossible to believe - 300m of thick cable being a dummy
load at 137kHz !

Go back to the fundamental equations and calculate properly rather than rely
on tables and software used for the wrong purpose .

This may be a better way to estimate the performance....

Inductive reactance of a shorted length of line  Xl =  Zo.TAN(2 . PI . L  /
vf  / Wavelength) 
With Wavelength = 2188m,  velocity factor = 0.67,  Zo = 50
this gives 171 ohms  (= 200uH at 137k)   you must have slipped a digit
somewhere to get 2mH.
This is the reactance looking into the coax, shorted at the far end and
neglecting any losses.  

To get 2mH  Xl = 1722 ohms,  L = 0.245 wavelength (in air)  =  373m of coax.
Not very much of an increase on 300m and shows how critical the length is
and how fast   Xl will change with frequency.
(In fact,since a lot of the numbers above have been rounded  and we are very
close to a shorted quarter wave, a back calculation using the rounded values
to check gave Xl = 1600 rather than the 1720 ohms used in the forward
calculation - that's how twitchy this technique will be)

For an estimate of losses :

Skin depth of copper at 137kHz is approximately 0.18mm      From    D = 503
SQRT(Resistivity / Freq / uo)
For Cu    Resistivity = 1.7E-8 Ohms / m,   and uo (magnetic permeability) = 1
Diameter of centre conductor = 2.5mm  (near enough anyway)
so cross sectional area of conducting path is 
0.18mm * 2.5mm =  0.45E-6  m^2

RF Resist   =   Resisivity * Length / Area       =   1.7E-8  *  370m  /
0.45E-6m^2    =    14 ohms. 

For a quick estimate assume the braid losses are a lot less than the centre
conductor as they have a much larger surface area, so can be ignored
(although that may not necessaily be the case) and we can also ignore
dielectric losses (a reasonable assumption at these freqs)  so Q =  Xl / R
=     1722 / 14 =  123  
Which is about what I got on my 5mH conventional coil of 1.5mm wire,   300mm
diameter and 400mm long.

In other words, a very expensive, very large and heavy 'coil' - making it
from coax

However, if you have a lot of large coax available think about this ....

Make a transmitting loop out of the coax, using the outer braid as the loop
element.  Use the inner / outer capacitance to resonate the loop by
connecting the inner to the OPPOSITE end of the outer at ONE end only.
Feed by personal preference as for any mag loop antenna.   

For topband a loop made this way from LDF350 (roughly similar dimensions to
UR67/RG213 but solid copper sheath and foam dielectric) is self-resonant
when at 1.9m diameter.  This tested out in practice.
A quick calculation for 137kHz suggests a loop of 29m diameter of the same
material will be self resonant,  or at least  possibly 90m of cable forming
a loop of some shape other than a circle might be.  A very rough and ready
calculation but it does suggest that a 100m reel of UR67 would contain all
the conductor and capacitance needed for a decent loop at 137kHz.

I wrote a spreadsheet prog for designing these self resonating mag loop
antennas, and one of 28m diameter using LDF-350 for 137kHz suggests a gain
of -28dB is feasible (neglecting ground proximity losses).   A bit pointless
when that is in the same region as the gain from a 12m high tee antenna.  If
anyone wants a copy (Excel 97), contact my other EMail account
actalbot@dera.gov.uk

Andy  G4JNT


>Resistive part of impedance at load: 0.0001
>(I typed 0 Ohms, but the program apparently changes that into 0.0001 -
>PA0SE)
>Reactive part of impedance: 0
>SWR at load: 4793489.50
>SWR at line input: 16.67
>Additional line loss due to SWR: 60.281 dB
>Total line loss: 60.803 dB (100.0%)
>
>At line input, Zin = 49.42 + j 172.52
>At 1500 W, max. rms voltage on line: 988.6 V
>Distance from load for peak voltage = 984 ft
>