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reflection loss formula
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by X-WB1AUW on July 4, 2005
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Recently, I began wondering how much of a signal is reflected when the antenna and line don't have the same impedance.
I found these formulas:
reflected loss=psquared
p=Zline-Zload/Zline+Zload
Given: Zline=50; Zload=25
25/75; 1/3=11%
SWR can be approximated by Zline/Zload? Is so then 50/25=2:1, an 11% reflected signal.
Did I get the correct formulas and correct conclusion?
73
Bob, AE7G
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RE: reflection loss formula
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by K7PEH on July 4, 2005
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They look OK but I am too lazy to go grab a book and check.
Howevever, to compute the total loss is more complicated than just plugging the values into this formula. The reason is that the reflected signal is reflected again and again.
Let's suppose that 10 percent of your signal is reflected, that means that 90 percent is transmitted (or heats the antenna and surroundings). But, that 10 percent does travel back down the transmission line to your transmitter or your tuner (whatever it sees first). There, it is reflected again back towards the antenna (with some loss of course). And, you get another chance to radiate some signal.
This continues until there is no signal left. But, each traversal of the transmission line eats away at the signal due to the line loss. This is where a coax, even low-loss, is not too good with high SWR. But, with low-loss ladder line or window line, this is not that bad of a thing to have a high SWR. In that case, most of your signal will still get radiated assuming you have a good antenna.
phil
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RE: reflection loss formula
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by X-WB1AUW on July 4, 2005
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Oooops. Forgot to indicate that 1/3 squared is 1/9, which equals 11%
Can't remember ever reading about how much signal is reflected; tons of info on line loss and extra line loss from the SWR because the voltage and current increase.
Bob
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RE: reflection loss formula
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by W9PMZ on July 5, 2005
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SWR = Zo / RL or SWR = RL / Zo (whichever is greater than unity and if ZL is purely resistive).
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RE: reflection loss formula
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by KA5N on July 5, 2005
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You ask if your conclusion is correct. What conclusion? You write down a couple of equations that are available in any antenna book and ask if they are the correct formulas and conclusion. What are you attempting to do? Is this going to be a weekly thing? First attenuation of a rf signal with distance and now reflected power, what's on for next week?
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RE: reflection loss formula
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by W9PMZ on July 5, 2005
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pp 81, Microwave Engineering, Passive Circuits; by Peter A. Rizzi
A very good book to have as a reference.
Another good book to have on the shelf is, Antenna Theory and Design; by Warren L. Stutzman and Gary A. Thiele
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RE: reflection loss formula
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by W9PMZ on July 5, 2005
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But to answer the question "reflection loss"
G is gamma, upside down L, reflection coefficient
RefL is reflection loss in dB
|G| = ( SWR - 1 ) / ( SWR + 1 )
RefL = 10 log ( ( 1 ) / ( 1 - |G| ) )
or
RefL = 10 log ( ( SWR + 1 )^2 / ( 4 * SWR ) )
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RE: reflection loss formula
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by W9OY on July 5, 2005
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I would look into the concept of return loss.
RL=20*log(reflection coefficient)
The relfection co-efficient (S11) is the ratio of a incident voltage (or current) divided by a reflected voltage (or current) measured at the same point. It has both magnitude and phase. It's magnitude is related to SWR.
SWR= 1+S11/1-S11
You can imagine that by massaging the SWR formula into impedance ratios, solving for S11 and substituting it into the return loss formula you get the Reflected loss formula.
Return loss is useful to characterize the efficiency of power transfer into a load, and as a tool to describe how a system behaves as it deviates from maximum power transfer, or from resonance. For example it is intersting to think about what happens at an antenna but is is also interesting to analyze what happens in the tank of an RF amplifier that is too lightly loaded in terms of return loss, and also to analyze what is going on at the plate end of the tank in terms of return loss.
Here are a couple articles about meters that have good dynamic range for meaasuring return loss that may be of interest. They are worth a look.
http://users.adelphia.net/~n2pk/RLPmtr/RLPv1c.pdf
http://www.telepostinc.com/n8lp.html#F
another interesting related article:
http://www.web-ee.com/primers/files/SmithCharts/smith_charts.htm
Here is a calculator that gives you some idea of how the magnitude of RL varies as a function of mismatch.
http://www.giangrandi.ch/electronics/anttool/swr.html
As RL approaches infinity maximum power transfer occurs. As RL approaches 0 power transfer approaches minimum. Play around with this calculator for various SWR's below 2:1 and above 2:1 and you will discover a lot of interesting things about wives tales regarding transmission lines. Like some how it doesn't matter how high the SWR is on an openwire line, but SWR is critical on coax.
73 W9OY
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RE: reflection loss formula
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by W5DXP on July 5, 2005
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>W9OY wrote: As RL approaches infinity maximum power transfer occurs.<
Hope that's a typo. Maximum power transfer occurs when a conjugate match exists. As RL approaches infinity, the SWR also approaches infinity, and power transfer approaches a minimum. If the source impedance is 50 ohms, the characteristic impedance is 50 ohms, and the load impedance is 50 ohms, maximum power transfer will occur. Instead of maximum power transfer, could you be instead talking about maximum efficiency? 73, Cecil, W5DXP
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RE: reflection loss formula
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by W9OY on July 5, 2005
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The return loss is a measure of how many DB down the the reflected wave is from the incident wave. A return loss of 100db is far better than a return loss of 2db.
Note the return loss is "20log(Vfor/Vref)". If Vref is very small a near perfect match exists, also if Vref is very small, (Vfor/Vref) is very large and a large return loss results according to the formula.
An SWR of 1.00001:1 yeilds a return loss of 106 DB Almost all the signal is admitted into the load and almost none is reflected back to the line.
An SWR of 1.5:1 yeilds a return loss of 14db
for 5 amps of current on a feed line 4 amps are admited to the load and 1 amp is reflected back to the feedline. 20% of the current or 4% of the power is reflected
An SWR of 10:1 yeilds a return loss of 1.74 db
for 5 amps of current 1 amp is admitted to the load and 4 amps are reflected.
An SWR of 1000:1 yeilds a return loss of .0174 db
Almost none of the signal is admitted to the load and almost all the signal is reflected back to the line.
VSWR and return loss are inversely related.
Play with the calculator to convince yourself.
www.giangrandi.ch/electronics/anttool/swr.html
73 W9OY
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