On Wed, 28 Feb 2007 17:51:30 -0800, Richard Clark
wrote:

The load voltage is 84 volts (to sufficient accuracy). The voltage at
the source port is 84 volts (to sufficient accuracy). The line has
been defined to be lossless. The same potential at the same angle is
returned to the source through 360 degrees of travel and no loss
(analysis allows us to treat the load as a generator). That signal
applied to the transmitter finds there is no potential difference, and
thus there is no current flow. This variously describes either a
short or an open; and either way it represents an infinite mismatch -
ALL the reflected power is re-reflected to the load.


Hi All,

Well, in lieu of Owen providing his own solution, much less
fulminating against the BS provided by yours truly in the quote above
(how seductive is it to the rest of you?). The problem here arises
out of a mixture of models, but this topology is not my choice and it
is inclined to invite such problems.

We can look at the details provided to find a 600 Ohm line terminated
at both ends by 70 Ohm resistors (again, I am forced to the
presumption of the source resistance, but given the constraints it is
the only value available). The energy within the resonant line is
ringing (one reason why a mismatched line it is called resonant is
because of circulating energy - the allusion to ringing).

If we deposit ourselves in the line, within the fields of energy, it
would be like inhabiting a hall with two partial mirrors, one at each
end. To other descriptions, these partial mirrors are leaky
interfaces. Some of the energy is passed through, some is reflected.
The "some" can be rendered into an absolute through knowledge of the
degree of mismatch - it is already provided within the original post
as being 8.6:1 (to a sufficient accuracy). In this regard, the
resonant line has a poor Q, however "poor" is in the eye of the
beholder because a flat line has the poorest of Qs at 1 (or worse).

The topology, and the question, invited me to respond with both the
lumped equivalent (this topology is in the classic expectation of
repetition of the load, cast back identically through a lossless line
to its input) and a Thevenin analysis (200W of power applied to a
source that could only supply 100W). The topology here has the
classic expectation of 50% efficiency that only a 70 Ohm source can
provide. Given that there is special constraint of a very strongly
specified line length, that too invites an analysis (which then
corrupts the lumped equivalent analysis if they are not separated).

So, we have three avenues commingled here in pursuit of an answer as
to explaining the power. Let us return to that hall of mirrors and
traverse its length (and unfortunately it must violate another
expectation of steady state, but this topology, much less expectations
galore, was not my choice - but I wander into any discussion with so
many invitations).

The first pass of energy sees the partial mirror of the load
interface. Some energy passes, some reflects. That which passes
cannot supply the expected potential of 84 volts (to a sufficient
accuracy); that remains to be justified by further analysis. The
reflected energy approaches an IDENTICAL mirror at the source end. The
reflected energy is coherent to the source (this is enforced by the
topology) behind that mirror. However, and revealing my deception
above, the reflected energy is not the same amplitude. There are two
sources of energy now embracing the source resistance of 70 Ohms.
There is a potential difference across that source resistance that is
different from that of what would be a presumed steady state 84 volts
(to a sufficient accuracy). Others can provide that computation if
they wish as the magnitude is one of degree (pun intended).

We have COOLED the source resistance! But we have not provided the
full load (anyone want to bet we cooled it by an equal degree? - pun
intended again). And the 200W application must be accounted for
somewhere (this inclusion is, of course, a sham of moving between
topologies and expectations that are so inviting).

And so on, and so on, ad infinitum through the successive waves of
reflection and dissipation for this statistical curiosity for me to
once again conclude:
ALL the reflected power is re-reflected to the load.
which is to say, energy (through the corruption of terms that has been
generally allowed).

73's
Richard Clark, KB7QHC