Transmission Line Question

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ashart:
I'm perplexed!

Walt Maxwell, in his book Reflections II, extensively discusses transmission-line reflections.  In Appendix 7-1, discussing the transmission line conjugately driven by a matched source, [ eg: Z(source) = R + jX and Z(line) = R- jX ], but terminated by a mismatch, [ Z(load) and Z(line) not equal ], Maxwell states:

   “The reflection at the mismatch gives rise to a second wave that travels back to the input of the line with the magnitude determined by multiplying the magnitude of the initial wave by the magnitude of [the reflection coefficient] ρ.  On arriving at the line input it sees total reflection ρ = 1 at the matching point in the network that achieved the conjugate match.”

Now I’ve read this idea enough times, in enough places, by enough authors, in enough different wording, that it would seem foolhardy to disbelieve it.  But!  Back on page 3-1, Maxwell states in Eq.  3-1 that:
      
         ρ =  [ Z(load) - Z(line ] / [ Z(load) + Z(line) ]

I’ve also seen that equation in lots of places, and in a conjugate-matched system, this equation, I believe, ends up with a zero numerator, and thus equates to zero.

And if so, how do I correlate p = 0 here with Maxwell’s later statement that the conjugate match at a line input gives ρ = 1?  Was he lying in Chapter 3 or is he lying in Appendix 7?

Ok, ok, so Walt didn’t lie.  Where am I missing the boat?  How does a first reflection from a mismatched load, arriving at the conjugately-matched line input, get fully reflected?

-al hart,
al@w8vr.org

KA2DZT:
Without having read any of Maxwell's work, it seems p is a number between zero and one.  I concluded this from just what you say his equations are.

I think I see that with a perfect match p would be zero.

Probably not much help,

Fred

Just re-read your last question,  I'm not getting how the reflected wave reaching the matched input gets fully reflected (p=1).  I always thought it gets absorbed by the matched input.

Maybe I'm not understanding something.

I think I also see where p would be the absolute value because I think I see where p could be a negative number when Z(line) is greater than Z(load).
Been a while since I did any math with complex numbers.

R. Fry SWL:
RE:“... The reflection at the mismatch gives rise to a second wave that travels back to the input of the line with the magnitude determined by multiplying the magnitude of the initial wave by the magnitude of [the reflection coefficient] ρ.  On arriving at the line input it sees total reflection ρ = 1 at the matching point in the network that achieved the conjugate match.” ...

If this concept was universally true, there would be no need for the load SWR protection circuitry included in many transmitters.

Such reflected power can (and has) caused the destruction of r-f output stage components of a transmitter -- particularly where high incident power is involved, such as in the broadcast industry.

ashart:
Mr. Fry:

Thank you for your response.  I read Maxwell to opine that with a mismatched load, injury to a final amplifier caused by high line SWR is not caused by reflected power being dissipated by that amplifier per se, as so many do erroneously believe, but instead, is caused by excessive voltage or current at the antenna terminals resulting from a change in feedline impedance.

Supporting Maxwell, it seems reasonable to assume that phase-angle considerations (P = V I cos theta) might allow destructive voltages or currents to prevail even without the dissipation of any power.

73 de al hart
al@w8vr.org

wa1sth:
Reading this made my head hurt....

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