Here are some simple truths that you probably knew before you got here, but when they are all put together, you will have 7 different things happening.

It is a little difficult to keep track of all 7 things that are happening, but this section will try to help you do that. Please go slow here. Take breaks if you would like to.

It helped me to draw diagrams of all this. Please feel free to stop and grab some paper to draw a diagram or two, or more.

This page is the most difficult page to understand of all the pages in this site. It uses high school algebra but I show you every move. Please feel free to skip all the math stuff, but please read the discussion parts so you can learn what is really going on.

OK, nothing is perfect, and there will be a very very small amount of resistance in the coil and capacitor in the tuner which will create a very small loss, but it is truly tiny. (0.01 dB is a good estimate) This is absolutely true, Honest!

* I need to interrupt this discussion to explain a bit about the term "re-reflection". This interruption has been added after receiving an email from Cecil, W5DXP. He is an absolute expert when it comes to energy moving from place to place in a coax or ladder line. He has both experience and education in this field. He wants you to know that the term "re-reflection" is not technically accurate. The reason it is not accurate is because the complete process in the tuner involves superposition, interference, and wave cancellation, and not simply re-reflection. I did not mention this in the first writing because I wanted to keep this as simple as possible. I am including this information now because Cecil, W5DXP is correct and if you understand those concepts, it may make understanding this material easier. It also may let other high power Ph.D folks know that I am trying to keep this as simple as possible while trying to be as correct as possible.You can look him up on Google or visit his web site information at

www.mellesgriot.com/products/optics/oc_2_1.htm

or at micro.magnet.fsu.edu/primer/java/scienceopticsu/interference/waveinteractions/index.html

_____ _______

__________ |SWR | |Antenna| ________

__|Transmitter|__

**Coax #1**

__|meter|__

__| tuner |__

**Coax #2**

__|Antenna|__

Coax #1 is usually quite short, and coax #2 is far longer because it goes from your desk up to the antenna.

L. B. Cebik, W4RNL (SK) who has written many articles for the ARRL on transmission lines and antenna tuners.

http://www.cebik.com and M. Walt Maxwell, W2DU who has written the book "Reflections:Transmission Lines and Antennas". This book was published by the ARRL. At the time of this writing (April 2010), Walt is 91 years old, and is still active and answers his email regularly.

While not a person, just as important is The ARRL Antenna Book, published by the ARRL.

Note from the author :This statement is not to imply that L. B. Cebik, W4RNLand M. Walt Maxwell, W2DU have read this web site and sent me a message telling me that they approve of what is written here. What it does mean is that nearly 100% of what is here comes from what they have written in books or on the interenet. I did not create these thoughts, but I report them in as simple a manner as I can. Naturally, I agree with them and believe them to be absolutely correct.

This is the last, but long, simple truth:The reason this is controversial is because so many people have been told a different story. When you hear any story over and over again, it becomes part of the "common knowledge" of the culture, and it tends to be condsidered the truth, even when it is clearly not true at all. That is what has happened here.

__re-reflected__at the antenna tuner. When the tuner is correctly tuned, no energy gets back into coax #1. An SWR meter is usually placed into coax #1 as a tuning aid, to measure the reflected energy. That meter will show an SWR of 1:1 when the reflected energy has been 100% re-reflected.

__add__to the transmitter energy output. It may seem strange that the system is resonant and still has reflections due to mismatched impedance, but the coax and antenna are not the same impedance.

Actually, except for the losses in the coax, 100% of the energy that leaves the transmitter will be radiated out of the antenna, no matter how high the SWR, because of the re-reflection. A high SWR will create a higher loss in the coax because a higher amount of energy travels backwards in the coax. This enegy going backwards is subject to the same losses as the forward moving energy.

This is a very sticky point. According to M. Walter Maxwell in his book

__Reflections:Transmission Lines and Antennas__, published by the ARRL, on Page 13 - 4, he says "

**The antenna tuner really does tune the antenna to resonance, in spite of opinions to the contrary of those who are unaware of the priciples of conjugate matching. The tuner obtains a match, by which all reactances throughout the entire antenna system are canceled, including that of the off-resonant antenna, thereby tuning it to resonance."**

An even better way to discribe what happens is to point out that the specific spot called the "matching point" is where the impedance is 50 Ohms with zero reactance and it exactly matches the impedance of coax #1

__at that point__. There is really no need to claim that coax #1 or coax #2 have been tuned, because it is the "matching

__point__" that is connected to coax #1, not the complete length of coax #2.

__Please be patient here.__This explaination has lots of steps, and each one is critical to understanding what really happens in the coax of an antenna system that is not perfectly matched.

The explanations are below.

1) Reflections happen at the coax - antenna connection andThe last part of this statement seems to be missing from most discussions of SWR and mis-matched conditions. This is why a lot of people think that refelected power gets into the radio and does damage.they also happen at the coax - tuner connection.That does not happen!

** What does kill radios is explained at the very bottom of this page. **

2) These reflections do not cause energy loss.All losses are due to the coax itself.

3) Energy moving backwards in the coax is subject to the exact same losses as energy moving in the forward direction.

4) The amount of energy reflected at the coax - antenna connection depends on the amount of impedance mis-match (read SWR) between the antenna and the coax. The greater the mis-match, the greater the reflection.

5) The amount of energy re-reflected at the coax - tuner connection is 100% of the energy that gets there, but not all the energy that was originally reflected gets back to the coax - tuner connection.There will be losses in the coax.All the reflected energy that reaches the coax - tuner connection is re-reflected back into the coax headed for the antenna. (Yup, another lossy trip in the coax.)

6) The re-reflected energy will be in phase with the generator so the two signals will add. This can createmoreforward power in the coax than the transmitter is actually producing. It is possible to measure 125 Watts forward power from a 100 Watt transmitter because the re-reflected poweraddsto the transmitter power

7) Coax losses are the only losses in the whole system. These losses can be significant, but they are the ONLY losses in the antenna system. If you have been paying attention, you know that this last step is just a re-statment of other steps above.

##
Here come the details! Do not skip this section. It is full of math, but you

_{_____ }

can do it. Use a calculator that has X ^{2 }and √ X.

1) Reflections happen at the coax - antenna connection, and again at the coax - tuner connection.This means that energy will zoom up the coax between the antenna and the tuner and some of it will return down the coax. The "lost" energy is both lost in the coax, and radiated out into space by the antenna.2) These reflections do not cause energy loss.

Another detail must be intorduced here. Every time the signal is reflected ( or re-reflected) a 180 degree phase shift happens to the current. This means that the current turns around and goes the other way,and it also turns upside down.Both things happen at the reflection points.

Let me say this again. In the case where the impedance of the antenna is greater than the impedance of the coax, [ Z_{Antenna}> Z_{coax}] the reflected voltage will just turn around and go in the other direction, but the reflected current will become upside down as it also travels in reverse. This means that the forward voltage and reverse voltage are in phase with each other, but the forward current and reflected current are 180 degrees out of phase with each other. When the reverse ( and upside down ) current reaches the tuner, another 180 degree phase reversal and direction change will happen.

Now the re-reflected current is back in phase with the generator current, and the forward and reverse voltage are also in phase.This phase reversal is a good thing because it allows the forward and reverse current to ADD together when the re-reflection happens at the tuner. Try drawing a picture of this. Be patient. Go slow.

Energy losses are caused by heating ( I3) Energy moving in a coax^{2}* R ) or radiation, but not by reflection. The law of conservation of energy tells us that what ever goes into a reflection will come out if there is no radiation and no heating.

__will__have losses due to leakage and ( I

^{2}* R ) heating.

These losses are well documented by the companies that make the coax. One of my favorite places to find the losses in different kinds of coax ishttp://www.ocarc.ca/coax.htmThey have a calculator that will help you convert the dB losses into actual Watts for a better understanding of what is happening. You will find it about half way down the page.

Here is an example of a typical coax with its typical loss in an antenna system with a SWR of 1.4 to 1. Go to the web site listed directly above and scroll about half way down the page to the calculator. Press the little "down arrow" and pick Belden 9913 (RG-8). It is a high quality coax used by many amateurs. Do not change anything else yet. When you have chosen the Belden 9913 coax, press the "calculate" button. ## Follow the zig - zag path of power!

If you have done this correctly, the calculator will tell you that Belden 9913 has a dB loss of only 0.388 dB and that calculates out to 91.461 Watts output from the coax if you put 100 Watts in to it.

Where did the rest of that power go?

It was lost to leakage inside the coax and to ( I^{2}* R ) heating.

How much of that 91.461 Watts will be used by the antenna and how much will be refelected?

The reflection coefficient is a number that tells you the percentage of reflection at the antenna - coax connection. The symbol "p" is used to represent this reflection coefficient. The math is easy to do.

This is the official end of the first cycle of the generator. This first cycle started with a 100 Watt signal leaving the generator, but only 88.921 Watts was transmitted. The total loss so far due to heating and leakage was

p = ( SWR -1 ) / ( SWR + 1 )We started by assuming that the SWR is 1.4 to 1. Use that 1.4 value to fill in the formula.

p = ( 1.4 - 1 ) / ( 1.4 + 1 ) = 0.4 / 2.4 =0.166

The reflection coefficient is used for voltage, currrent, and when squared, it is used for power.

Since the reflection coefficient is 0.166 in this example, the voltage reflected will be 16.6% of what arrives from the generator, and the current reflected will also be 16.6% of what arrives from the generator. The power that is reflected will be thesquare of the reflection coefficient.

To find out how much power is reflected, you will need to use the following formula.

Reflected Power = p^{2}times the Power available

Reflected Power = (.166)^{2}times 91.461 Watts.

Reflected Power = (0.02775) Times 91.461 Watts

Reflected Power = 2.54 Watts

This means that 2.54 Watts of the forward power will be reflected back down the coax toward the tuner, and the rest ( 91.461 W - 2.54 W = 88.921 Watts) 88.921 Watts will be used by the antenna and be radiated into space.

====================================

Try drawing a picture of this. Be patient. Go slow.

Is it break time yet?

====================================

The power that reached the coax - antenna connection was 91.461 Watts and 97.25% of that power will be radiated into space, leaving 2.75% to be reflected back down the coax. Both of these percentages come from the Reflection Coefficient that has been squared.

(Reflection Coefficient)^{2}= (0.166)^{2}= .0275, which means that 2.75 % will be reflected.

Power used by the antenna = 100% - 2.75 % = 97.25%

How much power will be radiated by the antenna?

The antenna will radiate 88.921 Watts into space.

This number will get slightly larger after the reflected power is returned to the antenna, but for now, during the first cycle, only 88.921 Watts are transmitted.

How much power is headed toward the tuner?

Only 91.461 Watts was available at the antenna - coax connection, and 2.75 percent of that will be reflected back down the coax toward the tuner.

( 91.461 Watts times 2.75% = 2.54 Watts ) 2.54 Watts will be returned to the coax to go back to the tuner.

How much power gets to the tuner?http://www.ocarc.ca/coax.htm

We must use the calculator again. Put 2.54 Watts in the place of the 100 Watts just above the "calculate" button. Press the "calculate" button.

Do it now please. Notice that 2.323 Watts gets to the tuner and the rest was lost to heat and leakage.

5) How much power is re-reflected at the tuner?

100 % of the reflected power that gets to the tuner will be re-reflected. In this case, the power that is re-reflected is 2.323 Watts. This 2.323 Watts now starts its way back to the antenna.

6) The re-reflected energy will be in phase with the generator so the two signals will add. [Note: If the two signals were not exactly in phase, the addition still happens, but the method is messy, and the result is not the same. This would be the case if the antenna was not exactly tuned to the operating frequency as it is in this example or if an antenna tuner was not correctly adjusted.]

The generator is producing 100 Watts and now it will have an additional 2.323 Watts added to it, for a total of 102.323 Watts heading for the antenna.

( 100W - 91.46 W = 8.55W ) 8.55 Watts on the trip up to the antenna, andThere are still 2.32 Watts stored in the coax( and tuner) about to be added to the generator power.

( 2.54 W - 2.32 W = 0.217 W ) 0.217 Watts loss on the way back down the coax.

This makes a total of ( 8.55 W + 0.217 W = 8.76 W ) 8.76 Watts actually lost in the form of heat and leakage.

All the power is accounted for. This is important because it helps you realize this explanation is correct.

###
That's a lot of information. What is the actual result ?

What's the Score?

Belden 9913 Belden 8216Input Power - - - - - - - - - - - - - - - - - - - - - - - - - 100 WThis shows where the power is lost, and what is radiated. This is far too much information, but it is necessary to tell the whole story truthfully.

Loss of power going up the Coax- - - - - - - - - - - - -8.55 W

Power reaching the Antenna - - - - - - - - - - - - - - - 91.46 W

Power Radiated by the Antenna- - - - - - - - - - - - - 88.91 W

Reflected Power returned to the Coax- - - - - - - - - 2.54 W

Loss of Power going back down the Coax - - - - - - -0.217 W

Power that arrives at the Tuner - - - - - - - - - - - - - - 2.32 W

Radiated power evenually evens out to - - - - - - - - 91 W.

(after about 5 cycles)

As you know, this is only the first cycle.Make a diagram of all this information so you can see where all these numbers fit in. That will help you understand this.

The power that is still in the coax (and tuner) will add to the generator power which will add a little to the output and add to the losses. This will continue for a few cycles until the system settles out to finally produce 91 Watts radiated power.

## Finally, take a look at what happens when the SWR is high and what happens when the coax loss is great.

First, lets look at what happens when the SWR is high (SWR = 3)

This uses the same 50 Ω coax as before.

SWR = 1.4 SWR = 3

Input Power - - - - - - - - - - - - - - - - - - -------- - - - - - - - 100 W 100 W

Loss of power going up the Coax - - - - - - - - - - - - - -8.55 W8.55 W

Power reaching the Antenna- - - - - - - - -- - - - - - - - - 91.46 W 91.46 W

Power Radiated by the Antenna - - - - -- - - - - - - - - - 88.91 W 68.59 W ←

Reflected Power returned to the Coax - - - - ---- - - - - - 2.6 W 22.86 W

Loss of Power going back down the Coax - - - - - - - -0.217 W1.95 W

Power that arrives at the Tuner - - - - - - - - - - ---- - - - - 2.32 W 20.9 W

Radiated power eventually settles out at - - --- - - - - - - 91.0 W 86.7 W←Even when there is a high SWR, the final power output is nearly the same.

## SWR is not a killer at all.

This is the same SWR = 1.4, but the COAX now has a loss of 2.5 dB (Belden 8216) which is Rg - 174.

Coax loss = .388 dB Coax loss = 2.5 dB

Input Power- - - - - - - - - - - - - - - - - - - - - - - - - - 100 W 100 W

Loss of power going up the Coax- - - - - - - - - - - - - -

**8.55 W**

**43.7 W**

Power reaching the Antenna - - - - - - - - - - - - - - - - 91.46 W 56.2 W

Power Radiated by the Antenna- - - - - - - - - - - - - - 88.91 W 54.6 W

Reflected Power returned to the Coax- - - - - - - - - - 2.54 W 1.56 W

Loss of Power going back down the Coax- - - - - - - -

**0.217 W**

**0.68 W**

Power that arrives at the Tuner- - - - - - - - - - - - - - - 2.32 W .87 W

Radiated power eventually settles out at- - - - - - - - - 91 W

**55.1 W**

### These losses are terrible! The coax losses have ruined the output power!!

### So, why do people think they can blow up their rigs or linear amplifiers when there is a high SWR on the antenna?

There is a totally different reason.

A high SWR on an antenna probably means that the antenna is not tuned to the frequency that is being used. This, in turn, means that the antenna has some inductive or capacitive reactance that is de-tuning the final amplifier. De-tuned final amplifiers draw far too much current and can burn up. The rig or linear amplifier will have to be re-tuned to avoid creating too much heat.

Many linears and nearly all tube amplifiers have some tuning knobs that allow you to "dip the plate current" or adjust the SWR by adjusting something on the front of the device.

Transistor rigs usually do not have any tuning adjustments. To avoid the extra heat created when running a de-tuned amplifier, there is a protection circuit that will significantly reduce the output power if the SWR is high.

**.**

*The conclusion section*- - -unless - - -

• you are not using a tuner and

• there is a circuit inside the rig that shuts down power when it sees a high SWR.

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