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 Robert Lay W9DMK Posts: n/a Additional Line Losses Due to SWR

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

 Richard Clark Posts: n/a Dave Posts: n/a Wes Stewart Posts: n/a 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

 Robert Lay W9DMK Posts: n/a On Fri, 26 Nov 2004 00:24:13 -0000, "Dave" wrote:

the 1/4 wave open end coax looks like a short circuit at the feed point. so

Dear Dave,

Yes, I believe it does - that is, it makes perfect sense to have a low
resistance and to have a near zero reactive component. What does not
make sense is that the high SWR is supposed to produce outrageous
losses. I don't see values that I can interpret as high losses - quite
the opposite. Maybe I just don't interpret it correctly, but I would
expect it to be several ohms - not 0.57 ohms.

In fact, and this is where it gets ridiculous, the examples in the
ARRL Antenna Book would lead me to believe that the above quarter wave
line would exhibit 20 dB of total losses. In order to get those
numbers the SWR at the load of say 8000 would have to decrease to
1.01:1 at the source end in order to account for 20 dB in losses. (See
the example on page 24-9 of the 17th Edition.)

Bob, W9DMK, Dahlgren, VA
http://www.qsl.net/w9dmk
 Robert Lay W9DMK Posts: n/a Dave Posts: n/a "Robert Lay W9DMK" wrote in message
...
On Fri, 26 Nov 2004 00:24:13 -0000, "Dave" wrote:

the 1/4 wave open end coax looks like a short circuit at the feed point.

so

Dear Dave,

Yes, I believe it does - that is, it makes perfect sense to have a low
resistance and to have a near zero reactive component. What does not
make sense is that the high SWR is supposed to produce outrageous
losses. I don't see values that I can interpret as high losses - quite
the opposite. Maybe I just don't interpret it correctly, but I would
expect it to be several ohms - not 0.57 ohms.

In fact, and this is where it gets ridiculous, the examples in the
ARRL Antenna Book would lead me to believe that the above quarter wave
line would exhibit 20 dB of total losses. In order to get those
numbers the SWR at the load of say 8000 would have to decrease to
1.01:1 at the source end in order to account for 20 dB in losses. (See
the example on page 24-9 of the 17th Edition.)

the cases they talk about in there are figuring the loss in power that you
resistance so it receives zero power which is what the arrl book says... in
this case all the power that is sent down the line is reflected back minus a
little bit of heating so the swr at the feedpoint should be near infinite,
but not quite. the actual loss in the wave going down and coming back is
very small hence the very low impedance. this is an effect that is used to
make coaxial stub filters and transformers.

 Robert Lay W9DMK Posts: n/a On Thu, 25 Nov 2004 20:51:16 -0700, Wes Stewart
wrote:

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

Dear Wes,

I hope that MacAlpine agrees with what Dave and Richard are telling
me, because their responses seem to be correct and are exactly what I
was afraid of - that I've been sucked into another example of the
strange terminology used to describe "losses".

I have always thought of "loss" as a conversion to another form of
energy (typically heat energy) which is lost from the system.
Apparently, the kind of "loss" being described in the example that I
gave is not a loss at all. It's more like "return loss", which is also
not a true "loss" in my thinking. In other words, it seems that the
"Additional Losses Due to SWR" are not losses at all, but are simply a
measure of the power that "could" have been delivered to the load were
it not for the mis-match.
Bob, W9DMK, Dahlgren, VA
http://www.qsl.net/w9dmk

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