Richard Fry wrote:
Ian White wrote:
The so-called SWR meter is a steady-state instrument, so it always makes
sense to use that quicker, easier way of thinking. Since you're the one
who chooses to think of this particular situation in terms of multiple
reflections, any difficulties you encounter are entirely yours.
This reads to me as though you know they are there, but choose to
ignore them...?
Oh no, quite the opposite - but since these difficulties are entirely of
your own making, you get to do the work :-)
If you ever see a conflict between two different theories that explain
the same observed facts, then there's an error somewhere.
We agree on the subject of conflict resolution, but apparently not on
the location of the error.
Thank you for the more detailed explanation below... which, sure enough,
revealed where the error is.
If the multiple-reflection theory is extrapolated to infinite time, so
that it calculates results for the steady state, it *must* give identical
results to the steady-state theory. But whenever the steady-state
theory can be used, it will always get you there much more quickly.
This is true only to the extent that all the power ever generated by
the transmitter eventually either is radiated by the antenna or is
dissipated by losses somewhere.
That is exactly true in the steady state.
For simplicity, let's assume a tx with a source impedance of zero ohms
feeds a lossless transmission line of uniform impedance throughout its
length to a mismatch at the far end. The mismatch reflects a
percentage of the incident power back down the line to the tx, and
continues to do so as long as the transmitter generates power. The tx
will re-reflect the reflected power back to the far end -- in this case
all of the reflected power it ever sees, in fact. To this easily-seen,
real-world reality you agreed above ("Yes, that is a true observation, ...").
The re-reflections combine with the power generated by the tx at that
instant to create a vector sum at the sample point used by the meter.
There's the error: you can't "combine... power" in that way. You can
only create vector sums of voltage; and separately, vector sums of
current.
To make the multiple-reflection theory work correctly, you have to do
two separate vector sums at output port of the transmitter. First you
add all the voltage vectors: the 1st (original) forward, the 1st
reflected, the 2nd forward (re-reflected), 2nd reflected... and so on,
summed to infinity to give the correct result for the steady state.
Then you do the exactly same for all the forward and reflected current
vectors.
In order to account for reflection from the transmitter, you have to
assume some value of source impedance. Any value will do, for reasons
we'll see in a moment.
Now you can calculate two things: the vector ratio, which is the complex
impedance that the transmitter sees as a load; and the scalar product,
which is the power the transmitter can deliver into that load.
If you vary the source impedance of the transmitter, it will change all
the summed voltage vectors and all the summed current vectors - but each
voltage term in the sum will be changed by exactly the same factor as
its corresponding current term. Certainly the product (the output
power) will change, but the ratio (the load impedance) will not.
So, when correctly worked out, the load impedance is *not* a function of
the transmitter output impedance or the output power. Likewise, the
indication of the SWR meter is not a function of either the transmitter
output impedance or the output power - this last one being a well-known
fact.
--
73 from Ian G3SEK 'In Practice' columnist for RadCom (RSGB)
http://www.ifwtech.co.uk/g3sek