Hi all,
re Jim's question about transmatches, and Scott's reply:
Scott correctly states that an L configuration gives the minimum loss, and
highest bandwidth matching network. If two resistances R1 and R2 are matched
with an L network, if all losses are in the inductor, and the inductor has a
given Q, then the fraction of power lost is (to a very good approximation)
F = sqrt(R2/R1  1)/Q
where R2 is the greater of the resistances.
Assume we match a 50 ohm transmitter to a 10 ohm load, with an inductor having
Q = 100. Then the fraction of power lost in the inductor is 2%.
Assume a frequency of 3.55 MHz. Then the components required for a lowpass L
are about
L = 1.1 uH, C = 2200 pF
The capacitor in particular is inconveniently large. Now consider the
highpass Tee. There are an infinite number of reactance combinations which,
in principle, achieve the same match. In particular, if Q = 100 again, the
combination
C1 = 109 pF
C2 = 213 pF
L = 6.28 uH
achieves, nominally, the SAME match.
HOWEVER, the POWER loss in the inductor is now 24%.
These values are typical of matches achieved when using transmatches like my
MFJ945D, built small for mobile operation. This is a highpass Tee with
maximum capacitor values of 220 pF. With this match, if 100 watts is input to
the transmatch, about 580 V rms appears across the capacitors, and the current
through the inductor is about 4.2 Amp rms.
Nevertheless, the transmitter IS matched, and will at least NOT be working into
the wrong load. This is, I believe, the REAL reason why highpass Tees are
common  they match, albeit with high losses, with convenient capacitor values.
As supplied, my MFJ945D had another problem. The top aluminium panel got
quite warm after an extended CW QSO. The top of the vertically mounted tapped
inductor is only a few mm from this panel, and eddy currents in it cause
losses. On 80 meters, I measured the inductor Q at about 70 with the top
panel in place, rising to 130 when I removed it. I estimated that with 100
watts in, about 15 watts were lost in the transmatch, about 8 watts of which
were dissipated in the panel.
I've replaced the metal panel with a nonconducting one. As a result, the
matching settings became quite different on all bands. The difference in
signal level is (of course) undetectable, but I feel better about it.
I emailed MFJ for comment, but nothing came back.
I've never been rich enough to afford a TenTec transmatch (we pay roughly 3
times in ZL dollars what you do in US dollars) but I'm sure they don't have
such problems.
As an aside, the design equtions for L and Tee networks with LOSSLESS inductors
are well known, but there are no tractable equations for designing with LOSSY
inductors, and the reactance values needed can be appreciably different. But
it's relatively simple to write computer programs which find such matching
values iteratively, which is how I got the numbers above.
If the inductor losses are small (say less than 15%) there are relatively
simple equations for estimating power losses in Pi, Tee and L matching networks
by pertubation methods. These appear in a text I wrote, and also published in
the NZART Journal "BreakIn" in the 1980s.
If anyone is interested, email me for the computer program. I also have a PDF
file somewhere with all the equations and worked examples.
73, Gary ZL1AN.

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