**This paper is intended
to give the newcomer to RF terminology a brief overview of SWR, return
loss and reflection coefficient. Instead of concentrating on mathematical
derivations or formulas which can make simple ideas seem complicated, this
paper will endeavor to explain the fundamental principals and physical
relevance of the terms.**

**SWR, which stands for
standing wave ratio, may be illustrated by considering the voltage at various
points along a cable driving a poorly matched antenna. A mismatched antenna
reflects some of the incident power back toward the transmitter and since
this reflected wave is traveling in the opposite direction as the incident
wave, there will be some points along the cable where the two waves are
in phase and other points where the waves are out of phase (assuming a
sufficiently long cable). If one could attach an RF voltmeter at these
two points, the two voltages could be measured and their ratio would be
the SWR. Identical results would be obtained by measuring currents. By
convention, this ratio is calculated with the higher voltage or current
in the numerator so that the SWR is one or greater.**

**Here are two examples
to illustrate how the numbers work. Consider a 1 volt source driving a
cable with either a short or open on the end such that all of the power
is reflected. Since the reflected wave is as big as the incident wave there
will be points where the two voltages cancel completely and other places
where the voltage will be 2 volts. The ratio of 2/0 is infinity which is
as "bad" as the SWR can be. If, instead, the load were equal to the characteristic
impedance of the feed line, say 50 ohms, no power would be reflected and
only a constant incident wave would appear at all points along the cable.
The ratio of any two voltages would therefore be 1 which is as "good" as
the SWR can be. The SWR for terminations between these two extremes may
be calculated by considering the interaction of the reflected wave with
the incident wave to determine the minimum and maximum voltages. But, as
it turns out, the SWR is simply the ratio of the resistance of the termination
and the characteristic impedance of the line. For example, a 75 ohm load
will give an SWR of 1.5 when used to terminate a 50 ohm cable since 75/50
= 1.5. A 25 ohm resistor will give an SWR of 2 since 50/25 = 2. Note that
the larger resistance is always used in the numerator by convention.**

**Consider that the concept
of a reflected wave also works at "DC". Suppose that a long pair of superconducting
jumper cables are connected to a 12 volt car battery and the far end of
the cables are touched together. The battery will be "shorted out" as long
as the cables are touching: that is, the battery voltage will fall to zero
and the current will be limited only by the internal resistance of the
battery. Another way to describe what is happening is to say that 6 volts
travels down the cables where is encounters the short and is reflected
back inverted in "phase". This -6 volt reflected wave cancels the +6 volts
at all points on the cables. In this example, the characteristic impedance
of this system is the battery's internal resistance: if a resistor of the
same value is connected to the ends of the cable then the voltage will
drop to 6 volts and maximum power will be delivered to the resistor. When
the short is removed the 6 volts reflects off of the open circuit without
inversion and it adds constructively bringing the voltage on the cable
up to 12 volts. A 12 volt battery could be said to be a 6 volt source driving
a poorly matched load. The battery is a 6 volt source when it is loaded
by its characteristic impedance which rarely happens - most batteries couldn't
withstand a "good" match for very long! The point is that SWR, return loss,
etc. are valid concepts for long cables, short cables, no cables, or even
ideal non-dimensional parts. And perhaps more importantly, simple Ohm's
Law computations at DC will give the same results as the more mysterious
RF equations involving magically reflecting signals and characteristic
impedance.**

**For example, consider
a 2 volt battery with a 50 ohm internal resistance driving a 50 ohm load
through 50 ohm coax cable. (Follow along on a piece of scratch paper!)
The match is optimum and the maximum power of 20 mW is delivered to the
load. (1 volt squared / 50 ohms.) Now consider a 100 ohm load. The current
is 2/150 = 13.3ma and the resulting voltage across the 100 ohms is 1.33
volts. The power dissipated in the resistor is 1.33 x 13.3 ma = 17.8mw.
Since incident and reflected power concepts are valid at DC it could be
said that 20 mW arrives at the 100 ohm resistor which absorbs 17.8 mW and
reflects the remaining 2.2 mW. The reflected 2.2 mW has a voltage of 0.33
volts in the 50 ohm cable. This reflected voltage adds to the 1 volt incident
wave to give 1.33 volts. For a very low frequency there would also be a
point along a sufficiently long cable where the voltages would subtract
giving 0.67 volts. (As the frequency approaches DC, the required cable
length approaches infinity!) The SWR is therefore: 1.33/.67 = 2. It is
indeed easier to calculate the ratio of the resistors as mentioned earlier!
Obviously, at DC the wavelength is infinite and only the voltage addition
is observed. Note that the reflected wave is not inverted when the resistance
is greater than the characteristic impedance of the cable! (Here is a memory
aid: remember the DC example where a short reflected a canceling negative
voltage. Obviously, a lower resistance reflects an inverted wave.) Also,
notice that the voltage across the 100 ohm resistor (1.33 volts) is equal
to the voltage that would appear across a 50 ohm resistor (1 volt) added
to the reflected voltage (0.33 volts). Although this description may seem
like an artificial construction, consider what happens when the battery
is first connected. With a fast oscilloscope connected at a midpoint on
the cable, the 1 volt could be observed as it passes as a step increase.
When the 1 volt arrives at the load, 0.33 volts is reflected and is observed
a short time later bumping the 1 volt up to 1.33 volts where the scope
is connected. The voltage does not simply go up to 1.33 volts in one step!**

**In cases involving RF
signals, some time will pass during the 'round trip of the reflected energy
and the phase of the reflection will also depend upon this length of time.
Imagine that a resistor in a black box is at the end of a length of cable.
From the outside world this length of cable will give the reflection from
the resistor a phase shift since the signal must make a round trip through
the length. If a 100 ohm resistor has an SWR of 2, a cable long enough
to invert the signal after the round trip will make it look like a 25 ohm
resistor, also with an SWR of 2 but with inversion (a cable with a multiple
of 1/4 wavelength would do the trick). Since the impedance looking into
this black box is a function of the SWR and the cable length, it can be
seen that intentionally mismatched lines can be used to transform one impedance
into another. Notice that the 1/4 wave cable inverts the impedance and
preserves the SWR. This impedance inversion may be used to match two impedances
at a particular frequency by connecting them with a 1/4 wave cable with
an impedance equal to the geometric mean of the two impedances. (The geometric
mean is the square-root of their product.) A 50 ohm, 1/4 wave cable will
match a 25 ohm source to a 100 ohm load : sqrt(25 x 100) = 50. Of course,
it is not always easy to find the desired impedance cable!**

**Multiples of 1/2 wavelength
will give enough delay that the reflection is not inverted and the impedance
will be the same as the load. Such cables may be used to transfer the load
impedance to a remote location without changing its value (at one frequency).**

**Other cable lengths will
transform an impedance which differs from the cable's impedance with a
reactive component. If the load is a lower impedance than the cable, a
length below 1/4 wave will have an inductive component and above 1/4 (but
below 1/2) wave a capacitive component. If the load is a higher impedance
than the cable, the reverse is true. Above 1/2 wavelength, the reactance
will alternately look capacitive and inductive in 1/4 wave multiples. This
reactance will combine with the load's reactance and offers the possibility
of resonating the reactive component of the load. Therefore, a cable with
the "right" length and impedance can match a source and load with different
resistance and reactance values. Obviously, these calculations can become
quite involved and most engineers resort to a Smith chart, a computer program
or perhaps the most common method, trial and error with a SWR meter or
return loss bridge! In most cases, it is most desirable to match every
component of a system to the chosen system impedance so that device matching
is not frequency sensitive and critically dependent upon the cable lengths.**

**SWR is a useful number
for evaluating the actual voltages and currents present along transmission
lines and SWR can be directly measured in many cases but it is often more
convenient to work with other, equivalent measures. For example, the voltage
reflection coefficient is the fraction of the incident voltage that is
reflected. If 0.2 volts reflects from a load with a 1 volt incident wave
then the reflection coefficient is 0.2. This number conveys the same information
as the SWR but is often more easily calculated and observed. And the terms
'power transmitted', 'transmission loss' and 'power reflected' need no
explanation beyond explaining that they are usually percentages. The return
loss is simply the amount of power that is "lost" to the load and does
not return as a reflection. Clearly, high return loss is usually desired
even though "loss" has negative connotations. Return loss is commonly expressed
in decibels. If one-half of the power does not reflect from the load, the
return loss is 3 dB.**

**Return loss is a convenient
way to characterize the input and output of signal sources. For example,
it is desireable to drive a power splitter with its characteristic impedance
for maximum port-to-port isolation and , therefore, it may be desireable
to check the output return loss of an oscillator or other source. Theoutput
return loss is measured by applying a test signal to the oscillator through
a directional coupler or circulator:**

** **

**Any reflected energy appears
at the test port and will be x dB below the input. This dB drop is the
return loss (after correcting for the coupler's loss). The test signal
frequency is swept through or adjusted to be near the oscillator's output
frequency. A spectrum analyzer connected to the test port of the coupler
will display the output of the oscillator and the reflected test signal.
The dB drop in the reflected test signal below the applied level is the
output return loss. The baseline is easily determined by disconnecting
the oscillator so that nothing is connected to the coupler's test port.
Since there is no load all of the energy will reflect and a 0 dB return
loss reference may be established. In situations where an open is unacceptable
due to high power levels an intentional mismatch will provide a known return
loss. For example, a 75 ohm resistor will exhibit a 14 dB return loss in
a 50 ohm system while reflecting only 4% of the test power.**

**An isolator is a seemingly
magical device which allows energy to flow in only one direction so reflected
energy from a load at the test port does not return to the signal generator
but is passed on to the output port regardless of the impedance at any
of the ports! This "magic" defies linear "common sense" for passive networks
but isolators are highly non-linear devices employing special ferrite in
powerful magnetic fields. Engineers who design circuits and systems operating
above 500 MHz enjoy the utility of the ferrite isolator but these marvelous
devices become impractical below about 200 MHz. Circuits are available
in the technical library which simulates the ferrite isolator for frequencies
below 300 MHz. The RF op-amps can handle signals approaching 12 dBm so
this isolator is only suitable for bench testing low-power RF devices.
The attenuation through a directional coupler or return loss bridge can
make measurements difficult when the return loss is high and the test signal
is small but the isolator has no "loss" and will work well with very small
signals. It is also desirable to use small signals when testing antennas
for obvious reasons. The isolator exhibits a good output return loss at
its test impedance and its good input return loss provides an excellent
termination for a long cable from a generator with a questionable SWR.**