####   Syllabus Sections:-

5d Return Loss and SWR

5d.1 Understand that the standing wave ratio (SWR) is a measure of the signal travelling back down the feeder expressed in terms of the standing waves caused by the reflected signal voltage (or current).

The formula is :-  When there is a mismatch between feeder and antenna we proved in the earlier section (click here to check back) that to satisfy some of the transmitted power is reflected, ie returned, to the transmitter. Moving back from the antenna we find that the reflected voltage is alternately in phase or out of phase with the transmitted wave.

When in phase the voltages ADD, when out of phase they subtract.

The highest voltage is VFORWARD + VREVERSE, and

the lowest voltage is VFORWARD - VREVERSE

These points of maximum and minimum are at steady positions along the feeder and are called STANDING WAVES.

The STANDING WAVE RATIO which is a measure of the mismatch is VMAX / VMIN which is (VFORWARD + VREVERSE) / (VFORWARD - VREVERSE) it is also incidentally equal to ANTENNA RESISTANCE / LINE CHARACTERISTIC RESISTANCE or to be more accurate, the impedances.

Effect of line loss.

Losses along the feeder reduce the voltages of the reflected wave as it travels towards the transmitter, which increases the VMIN and decreases the VMAX, so that the ratio VMAX / VMIN falls as it travels back to the transmitter, ie the Standing Wave ratio reduces.

So if you have a long feeder and a great deal of loss, the SWR at the transmitter might well look ok but in fact there could be a major mismatch at the antenna!!!!

5d.2 Recall that return loss is the ratio of the forward signal power to the return signal power; normally expressed in dB.

The equation given in the Equation Sheet for the exam does not take that statement at face value. Instead it takes it to mean

Return loss = Return Signal Power divided by Forward Signal Power

and the syllabus shows the equation as  we can show this as a diagram to further help explain it to you ... RETURN LOSS is really nothing more than another way of saying SWR.

A low RETURN LOSS result of the equation is actually a good thing, when using the equation on the equation sheet.

#### The lower the return loss or put it another way the "Greater the REDUCTION in power returning to the transmitter" the better the antenna is radiating.

We are considering the REFLECTED POWER with respect to the ARRIVING INCIDENT POWER, to determine how much power is reflected with respect to that which is arriving. Another way of putting it is to say "How much power is left of the INCIDENT POWER to be reflected after the power has been consumed by the load resistance. So if the incident power into the antenna is 100W and reflected power back to the transmitter as 1W, ignoring for a moment the dB equation and using simple maths, the RETURN LOSS is a ratio 1:100 = 1 / 100 = 0.01 a LOW RETURN LOSS.

AND if we have incident power into the antenna is 100w and 75 Reflected power back to the transmitter RETURN LOSS = 75 / 100 = 0.75 a HIGH RETURN LOSS.

So where does the equation given in the syllabus fit in. Well properly, loss quantities, when expressed in decibels, should be positive numbers. However, return loss has historically been expressed as a negative number, and this convention is still widely found in the literature and is where it is considered the Syllabus has used the equation but that equation taking the ratio of reflected to incident power results in a negative sign for return loss.

So when using the syllabus equation you will result in a NEGATIVE number rather than the positive and greater than 1 figure you would expect.

So to fully understand the next part you must adjust you brain to think that negative numbers are bigger than positive numbers but before moving on try out a few sums on your calculator and see the difference results for in the exam your will have to use the equation  Understand that a low SWR equates to a high return loss and a high SWR equates to a low return loss.

You are aware, or should be that a low SWR means that very little of your signal is being reflected by a mismatch in the antenna / feeder system and vice versa. So take a look at the following examples.

If the load is replaced by an open circuit, then no power is consumed and 100% of the INCIDENT POWER is reflected, and there is NO RETURN LOSS.

Let's look again at a diagram that you saw earlier in the section on SWR. Power arriving is 200v x 2 amps = 400 Watts

Power Reflected is 100V x 1 amp = 100 Watts

The reduction in the power arriving to the power reflected is 100 / 400 = 25% = 1/4 or we can say 6dBs, this is the return loss at SWR of 3:1

If we try Power Reflected / Power arriving as 16 / 400 we get 1/25 or 4% and the new RETURN LOSS becomes 14dBs and the SWR works out to be 1.5 :1, a better performance.

So from this you can see that a HIGH SWR and a LOW RETURN LOSS is BAD and a LOW SWR and a HIGH RETURN LOSS is GOOD. Seems a crazy way of looking at things but that what you have to learn !!!

AND LASTLY on Return loss the answer is normally expressed in dB but as you do not have to do any maths on this point just be aware that answer would be in dB and not as a unit mentioned above !!

So remember the Higher RETURN LOSS in dBs becomes, the better the performance of the feeder and aerial system.

#### SWR return loss and Reflected Coefficient

SWR return loss and Reflected Coefficient are all related functions, RETURN LOSS is much more convenient to use in assessing systems performance, as manipulation in dBs is simple and especially at microwave, power meters are much used.

NOTE: Reflected coefficient is the ratio on INCIDENT WAVE VOLTAGE (or CURRENT) to the REFLECTED WAVE VOLTAGE (or CURRENT).

It can be shown that it is equal to in our example above and that it is equal to = 1/2 ( or (300-100)/(300+100) = 1/2

5d.3 Understand that the feeder loss will reduce the SWR and increase the return loss at the transmitter.

Recall that Return Loss at transmitter = Return Loss at antenna + 2 x (feeder loss)

If we have a system where there is no feeder loss and the match is perfect then 100W from the TX will be 100W at the antenna.

But nothing is perfect so let's now assume that we have 100W from the TX and a mismatch so we have 10W reflected.

so from this equation :  RETURN LOSS at antenna = 10 log 10 / 100 = -10dB

But if the feeder has a loss of 6dB then :

RETURN LOSS at TX = -10 + (2 x -6 ) = -22dB which appears to make the antenna not so bad !!!  