Owen Duffy wrote:
"Sal M. Onella" wrote in
:

I mistakenly put a 2m antenna on my dual band HT and tried to use it
for a short QSO on a nearby 440 repeater. The other ham said I was
barely making the repeater, while my poor HT got so hot that I could
barely hold it after a minute's use.

The antenna was wrong and the heat was real -- whatever the theory
behind it.

Let the anecodotes flow...

Your FM HT is a classic case than can be adequately represented by a steady
state analysis. Your HT was operating into a load that increased its
dissipation, but there would be almost certainly be other mismatched loads
that would decrease its dissipation.

The transmitter gets hot because it is operating into an incorrect load
impedance, not the 50-ohm load for which it was designed. As far as the
transmitter is concerned, that is the only problem.

What caused that incorrect load impedance is a totally different topic.

If you measured the impedance of that incorrect antenna, and then
replaced the antenna with a dummy load of the same impedance (a resistor
of the correct value, in series with an inductor/capacitor of the
correct value) then your transmitter will not know the difference. The
same value of load impedance will cause it to behave in exactly the same
way.

There are many different physical types of loads that could present
exactly the same impedance to the transmitter. These include antennas,
dummy loads and various combinations, with or without some length of
transmission line involved. So long as the load impedance presented to
the transmitter is exactly the same in all cases, the transmitter
behaves exactly the same (once it has reached steady state, after the
first few cycles of RF... more about that later).

The amount of power that the transmitter can deliver into that incorrect
load will depend on the transmitter circuit and on the value of the load
impedance - but NOT on the physical type of load.

You can measure the impedance of the load by disconnecting it from the
transmitter and connecting it to an impedance meter. (Seems obvious?
Think again - every time you make an impedance measurement, you are
using the principle that impedances of the same value are
interchangeable with no effect on steady-state operation.) If the load
happens to be an antenna and transmission line, you can use programs
like NEC and established transmission line theory to make an accurate
prediction of the load impedance. If the system happens to include an
ATU, that is just another device that modifies the load impedance
presented to the transmitter.

At that point, you're finished with antennas, transmission lines and
ATUs - once you know the load impedance they present to the transmitter,
everything else depends on the transmitter alone.

In other words, the antenna/transmission-line/ATU system can - and
wherever possible, SHOULD - be cleanly separated from transmitter
design. The separation interface is the output connector at the rear of
the transmitter.

In the huge majority of applications, both amateur and professional, it
IS possible to separate those two topics cleanly and completely. It
seems perverse to tangle them together unnecessarily.


All the above refers to the steady state, where the signal level is
constant; and if a transmission line is involved, the pattern of
standing waves is established and unchanging. For completeness, we now
need to check if anything was different during the few moments after
switch-on, while the steady-state pattern of standing waves was becoming
established. Starting from switch-on, we need to look at each of the
successive reflections and re-reflections along the transmission line,
and see how the steady state came to be.

The first thing to notice is that with the types of signals and lengths
of transmission line that we amateurs use, the steady state is
established within the first few cycles of RF, ie it all happens over
timescales much shorter than the signal's own envelope rise/decay time.
This means it is 'nice to know', but will seldom be of practical
importance.

A detailed analysis of the buildup of reflections along a transmission
line will be forced to consider reflections at the transmitter as well
as at the load - in other words, we have to specify a reflection
coefficient at *both* ends of the line. Chipman's book [1] gives a very
detailed analysis of this, and shows how the addition of voltages over
multiple reflections gives rise to a standing wave. The amplitude of the
standing wave builds up as mathematical series, in which each successive
reflection and re-reflection contribute an additional term. Some terms
add to the total while others subtract, and each successive term makes a
smaller contribution than the one before, so the series will converge
towards a constant value which represents the steady state. It should be
absolutely no surprise that, when summed to an infinite number of terms,
this series produces exactly the same results as the steady-state model
- exactly the same pattern of standing waves, and exactly the same load
impedance presented to the transmitter.

The important conclusion from this more detailed time-dependent analysis
is that re-reflections at the transmitter have NO effect on the final
steady-state pattern of standing waves. The ONLY effect of
re-reflections at the transmitter end was on the time-dependent details
of how that pattern built up, and on the final steady-state signal
levels. The magnitude of the standing waves depends on the transmitter
characteristics (in other words, on the 'signal level') but the shape of
the standing waves and their location along the transmission line
depends only on the line and the load. There are no special cases he
the same conclusion holds for all values of reflection coefficient at
the transmitter end, including 1 and 0.

Thus, even a detailed time-dependent analysis confirms that, once we
have reached the steady state, we can indeed make a clean separation
between the transmitter and its load. And since we can, we should.



[1] R A Chipman, 'Theory and Problems of Transmission Lines, Schaum's
Outline Series', McGraw-Hill. ISBN 0-07-010747-5. (Chipman isn't an
easy read, because he is Mr Meticulous who wants to tell you everything;
but you can rely on him not to cut corners.)


I await the inevitable photon explanation.

None needed. If anyone wishes to introduce additional complications
where none are necessary, then of course they're at liberty to do so.
But when invited to join in, everyone else is at liberty to decline.



--

73 from Ian GM3SEK 'In Practice' columnist for RadCom (RSGB)
http://www.ifwtech.co.uk/g3sek