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Message-ID: <3.0.1.16.20000228121916.0907718e@mail.cc.kuleuven.ac.be>
Date: Mon, 28 Feb 2000 12:19:16
To: rsgb_lf_group@blacksheep.org
From: "Rik Strobbe" <rik.strobbe@fys.kuleuven.ac.be>
Subject: Re: LF: Re: "Low loss inductors" ..EW&WW
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There have been some mails about using a (rather big) piece as inductor.

Dick (PA0SE) gave us the results of a computer calculation (TRA from N6BV)
and that seems quite OK to me, except for the fact how to interprete the
'Additional line loss due to SWR' :
When you use a coax as a transmission line you want to get as much power as
possible into the load (= antenna) at the end of the line. Therefore this
load must be matched to the impedance at the end of the line, otherwise a
part of the power is reflected back into the line (we all know the as
famous 'SWR').
But if you use a piece of coax as inductor you deliberately make a
short-circuit at the end of the coax, creating a 100% reflection there. In
case of a lossless coax the SWR at the other end of the coax would be
endless (all power is returning).
For a 'non perfect' coax a part of the power is absorbed in the cable,
making the SWR less than endless.
TLA takes an attenuation of 0.053dB/100ft (= 0.177dB/100m) for RG213. So
for 300m this is 0.53dB, but the signal has to travel twice the length of
the cable (once to the end and then back to the begin as 'reflected
signal') so total attenuation is 1.06dB. This means that, whatever power
you send into the cable, you wil get 78.3% back as reflected power. Based
on the formula:

         SWR = (1+sqrt(R))/(1-sqrt(R))    
         where R = reflection coificient (% / 100) and sqrt = square root

78.3% reflected power equals an SWR of 16.4 (matches pretty good with the
16.67 SWR from the TLA software).

But (and here comes the BIG BUT) if we use the coax as an inductor this
reflected power is not a loss, in contadiction as we try to make a high-Q
coil we just want to get all the power back (with as less powerloss as
possible in the coax). So the 'perfect coaxial inductor' must have a
endless SWR, in practice it means the higher the SWR (and so called
'Additional line loss due to SWR') the better.

Apart from the above I think that making a 3mH coil from coax is rather
expensive and heavy (300m of RG213 weight 46kg) and, as you will loose
21.7% of the TX power, the Q will be not so good :
Assume you run 1kW into an antenna with a enviroment loss of 50 Ohm and use
the coax as coil. Then you will loose 217W in the 'coil' and the remaining
783W (minus a few 100mW radiated) in the 50 Ohm enviroment loss. This means
that you antennacurrent will be 4A (calculated from P and R) and thus the
217W coil-loss equals a resistance of 13.6 Ohm. With 3mH = 2560 Ohm (at
136kHz) the 'coax coil'
will have an equivalent Q of about 190.
I am sure that it is easier (and cheaper and lighter) to make a more
traditional loadingcoil with a better Q.

73, Rik  ON7YD


>
>With the ARRL "Antenna Book"  comes a floppy disk with a Transmission Line
>computer program called TLA, written by N6BV. I used version 1.0 .
>
>The program does not know the British type UR65 but from another source I
>understand it can be compared to RG-213.
>
>For 300 m (984 ft) of RG-213, short circuited at one end, the program
>produces the foillowing results::
>
>Frequency: 0.137 MHz
>Transmission line characteristic impedance: 50.0 - j 2.30 Ohms
>Matched -line loss, dB per 100 ft: 0.053 dB
>Velocity factor of transmission line: 0.660
>Maximum voltage rating of transmission line: 3700.0 V
>Matched-line attenuation = 0.522 dB
>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
>
>So as a dummy load it would not be too bad ....
>
>73, Dick, PA0SE
>JO22GD
>D.W. Rollema
>V.d. Marckstraat 5
>2352 RA Leiderdorp
>The Netherlands
>Tel. +31 589 27 34
>E-mail: d.w.rollema@freeler.nl
>or
>pa0se@amsat.org
>
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