On Thu, 25 Nov 2004 20:20:32 GMT, (Robert Lay
W9DMK) wrote:

Bob,

You might want to look at this paper:

http://users.triconet.org/wesandlinda/AIEE_High_Swr.pdf



|Various authors provide curves or formula for computing the "total
|loss" in transmission lines, as opposed to the "matched-line" loss.
|Specifically, The ARRL Antenna Book gives an equation in Chapter 24
|that seems to give results consistent with other sources (See the
|details at the end of this posting). However, there seems to be a
|fundamental flaw in the way in which the equation is applied.
|
|In essence, the equation provides a loss factor which is a function of
|the matched-loss attenuation and the absolute reflection coefficient.
|The matched-loss attenuation is the value normally expressed in dB per
|100 ft. and shown in tables or shown in logarithmic plots as a
|function of frequency. The reflection coefficient is introduced into
|the expression in order to increase the total losses as the SWR on the
|line increases.
|
|After calculating a total loss factor it is applied to lines of any
|length based on the reflection coefficient at the load. In my opinion,
|it makes no sense whatsoever to provide an expression that is to
|determine the losses per unit length on a line and have it based on
|the reflection coefficient at the end of the line. If there is a
|mismatched load, and if the line has losses, then it follows that the
|SWR will become lower and lower the further we are from the
|termination. That being the case, would it not make more sense to say
|that the "additional" losses would be much higher at the load end of
|the line, where the SWR is high, than at great distance from the load,
|where the SWR is significantly lower? In fact, if the line is long
|enough, we know that the SWR approaches 1:1, and in a line with an SWR
|of 1:1 there should be no additional losses above the matched-line
|losses.
|
|Nonetheless, with that non-sensical approach, the numerical examples
|shown at the referenced page and also in a later article on the
|subject of Highly Reactive Loads makes it quite clear that the loss
|factor is applied uniformly to the entire length of line.
|
|If we take the expression for the total loss and apply it to small
|increments of line wherein the SWR is relatively constant, then it not
|only makes more sense, but it also predicts noticeably less total loss
|in longer lines.
|
|I have embarked on careful measurements of lines severely mismatched
|(quarter wave open circuit stubs), and I can find no correlation
|between my measurements and the values predicted by the "total loss"
|equation. My measurements always show very low losses in comparison to
|the model.
|
|I would be interested in corresponding with anyone who has other
|models for line losses, or anyone who has made measurements on
|quarter-wave stubs.
|
|##########Equation and data taken directly from The ARRL Antenna Book,
|17th Ed., page 24-9 ###############
|(Eq 10) Total Loss (dB) = 10 log [ {(Alpha * Alpha - (AbsRho *
|AbsRho)} / {Alpha * (1- (AbsRho * AbsRho)) } ]
|
|where
|
| Alpha = 10^(ML/10) = matched-line loss ratio
|
| AbsRho = (SWR - 1) / (SWR + 1)
|
|where
| ML = the matched-line loss for particular length of line, in
|dB
|
| SWR = SWR at load end of line
|
|The text then goes on with a numeric example using a 150 ft. length of
|RG-213 coax that is terminated in a 4:1 mismatch (SWR = 4:1, AbsRho =
|0.6) at 14.2 MHz. The calculations for total line loss, per the above
|equation, results in a total line loss of 2.107 dB.
|
|
|
|
|Bob, W9DMK, Dahlgren, VA
|http://www.qsl.net/w9dmk