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From: g.bold@auckland.ac.nz (Gary E. J. Bold)
Date: Tue, 9 Jun 1998 10:40:31 +1200
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 low-pass L 
are about

L = 1.1 uH, C = 2200 pF

The capacitor in particular is inconveniently large.   Now consider the 
high-pass Tee.  There are an infinite number of reactance combinations which, 
in principle, achieve the same match.  In particular, if Q = 100 again, the 

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 
MFJ-945D, built small for mobile operation.  This is a high-pass 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 high-pass Tees are 
common - they match, albeit with high losses, with convenient capacitor values.

As supplied, my MFJ-945D 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 non-conducting 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 Ten-Tec 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 "Break-In" 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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