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Message-ID: <000901c6b337$7bf89660$b1458351@w4o8m9>
From: "James Moritz" <james.moritz@btopenworld.com>
To: <rsgb_lf_group@blacksheep.org>
References: <000001c6b17e$4823a8d0$e6a4c593@RD40002> <44C94628.9030404@ukonline.co.uk>
Date: Sat, 29 Jul 2006 18:50:30 +0100
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Subject: Re: LF: Tapped loading coil design spreadsheet
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Dear Peter, LF Group,

> Experimental work in 1996 to 1998 on the 73kHz band was concerned mainly
> with how to transfer RF power from the amplifier to the antenna. Most of
> the amplifiers used at the time were high power audio amplifiers with an
> output impedance of 4ohms so the 50ohms system was a bit irrelevant.
> The tapping point (loading) was affected by the resonance adjustment
> (tuning). In fact I used a 8 turn multi-tapped coupling link on a 7mH
> coil, normally tapped at 4 turns (73kHz).

Reflecting on this, there are some quite good reasons to use a 50ohm
impedance level for coupling bits of the system, even at LF. This is down to
the fact that the resistive part of the antenna impedance is usually of the
order of 50 ohms also. Given that any type of LC matching network will have
limits on the ratios of impedances which can be matched, having the two
resistances reasonably close to one another does help.

On the spreadsheet, you can change the TX output impedance to 4 ohms or any
other resistance. Doing this reveals that you can achieve a match to 4 ohms
with fairly reasonable antenna resistances, by tapping at a smaller number
of turns. But for any given coil, the maximum antenna impedance that can be
matched is lower than for 50 ohm TX impedance. Also, the change in matched
resistance between adjacent taps is large, often by a factor of 2 or more
when the tap is changed by 1 turn for feasible sizes of coil, which would
lead to poor accuracy of matching. A seperate link winding as G3LDO
describes would be better, because there is more flexibility in the
relationship between the self inductance of the link winding and its mutual
inductance with the main winding than there is with the tapped coil. But it
also means more variables in the design to cope with. Another related factor
which the spreadsheet does not consider is that, with greatly differing TX
output resistance and antenna resistance, there will be a big difference
between the TX output current flowing into the coil tap, and the antenna
current flowing out of the hot end of the coil. For 4 ohms output
resistance, this would mean a much larger current flowing in the turns
"below" the tap, and so probably increased loss for a given coil.

Then there is the question of the transmission line to connect the TX to the
antenna tuner, if these are not side by side. You could make a 4 ohm
transmission line, but that would be much less convenient than a standard
impedance. You might say "well, its only a tiny fraction of a wavelength at
2200m, so using 50 ohm coax won't make a big mismatch". But this isn't quite
true - if you do the sums, a run of 50ohm coax with electrical length of 1%
of lambda (about 15m of normal coax), with a 4 ohm load, results in an SWR
of over 2:1 at the 4ohm TX end (with Z = about 4 + j3.1 ohms, mainly due to
the distributed inductance of the coax). This would require the antenna
tuner to provide an impedance with a hefty capacitive component in order to
get a match, placing more restrictions on the design. Since most of the
losses are due to resistance of conductors, using the same size wires in the
4ohm system would result in about 12 times as much loss as in the 50ohm
system.

So there is some serendipity in standardising on 50ohms; it does work out
better in many cases, even at LF.

Cheers, Jim Moritz
73 de M0BMU