WHITEPAPER

By Richard A. Scholl of Advanced Energy Industries, Inc. FORWARD AND

REFLECTED POWERS.
Measurements made in the RF domain are steeped in tradition. Like most WHAT DO THEY MEAN?
traditions, RF concepts are passed on by word of mouth as well as by written
legend. Also like most traditions, the concepts are imperfectly understood by many
who need to know better. In particular, the concept of reflected power is often
misunderstood. Most users have the impression that its presence is bad and so it
should be minimized. This paper is intended to help understanding and to dispel
myths surrounding RF measurements and practice.

ORIGINS directional wattmeter,

The use of radio frequencies in the first half and more of which he can place at
this century was centered on radio communication, as the any convenient point in
very name implies. In a radio station, power is generated by the cable. This device
a transmitter, usually housed comfortably in a shack, and the measures the voltage,
RF power is led to the (usually) remote antenna by a cable, or current, and their relative
transmission line, which in short wave stations can be several phase. It reports on its dials
wavelengths long. An antenna tuner is generally placed at quantities called forward power
the antenna end of this line. The function of this circuit and reflected power. Where do
is to match the antenna, which means that the complex such terms come from, and what
impedance represented by the antenna is transformed by this do they mean?
circuit to a fixed real impedance. This is desirable for two
reasons; the first relates to the transmitter and the second FORWARD AND REFLECTED POWER
to the line. A standing wave on a
transmission line can be thought of
Firstly, every transmitter has some impedance into
as being composed of two traveling
which it can deliver the most real power (usually set by design
waves, one moving toward the load
to 50 Ω). If the antenna’s impedance is different from this
(the forward wave) and one moving
ideal value, more voltage and/or current will be required of
in the opposite direction (the reflected
the transmitter to get a given radiated power than if the load
wave). These waves, moving through
was matched to the transmitter. This limits the maximum
the transmission line, interfere with one
power of the transmitter.
another to produce the standing wave.
Secondly, if a line is terminated in its characteristic Each of these waves have a voltage
impedance (also usually 50 Ω), the RF voltage along that line amplitude––the forward voltage Vf and the
will be uniform. If it is not so terminated, a standing wave will reflected voltage Vr. The conceptual problem
be set up along the line. A standing wave is a distribution comes from the dials of the directional
of RF voltage that rises and falls along the line. This can wattmeter, which are not calibrated in volts but
stress the line because the voltage peaks for a given power are rather in watts. How do we get watts from volts?
higher than the voltage on a matched line and the line could
The coupler (or wattmeter) assumes that the
arc over at these voltage maxima. A standing wave of current
forward wave is terminated in a 50 Ω resistor,
also exists along the line. This can result in overheating, or
calculates |Vf|2/50, and presents the result as forward
hot spots in the cable, at places where the current is at a
power. Similarly, it assumes the reflected wave is also
maximum.
terminated in a 50 Ω resistor, calculates |Vr|2/50, and
So for both reasons, the radio engineer matches the presents the result as reflected power. This can cause
antenna, meaning that he adjusts the antenna tuner until serious confusion because usually the waves are not
the transformed impedance is equal to the line impedance, impressed on any such resistor.
which is generally also the transmitter’s ideal load resistance.
If the antenna and tuner are replaced by a 50 Ω resistor,
To detect when the antenna is matched, he does not
then the forward wave is terminated in this resistor, and the
physically walk along the line to measure the actual standing
indicated forward power actually will be the power dissipated
wave. Rather more conveniently, he uses a device known as a
in the load resistor. Because the 50 Ω line is terminated in its

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FORWARD AND REFLECTED POWERS. WHAT DO THEY MEAN?

characteristic impedance, there will be no reflected wave resistor if the forward and reflected waves were impressed
and no standing wave, because the line is matched, and Vr upon it. Since there is no such resistor, there is no such
and the reflected power are zero. (If the tuner is adjusted to power.
transform the antenna impedance to exactly 50 Ω, the same
Let’s recap. What can be inferred from the forward and
thing occurs, except that the power is radiated from the
reflected power readings on our directional wattmeter and
antenna instead of being dissipated in a resistor.)
what cannot?
If the load at the end of the line is not equal to 50 Ω,
1. If the reflected power is zero, there will be no standing
then there will be a standing wave, and so a reflected wave.
wave on the line and no excess stresses on it.
Since the forward power is defined as the power in a 50 Ω
load, and since the load is no longer 50 Ω, the forward 2. If the reflected power is zero, the generator can deliver its
power no longer represents the load power. What about maximum rated power into the load.
the reflected power? What does it represent? 3. The difference between the forward and reflected powers is
One very common misconception is that the reflected the real power delivered to the load, but:
power represents the power that must be absorbed by the 4. the generator does not actually generate a power equal to
generator. That this is not the case can be easily seen, if one the forward power, and
looks at an extreme case. Suppose a lossless line is terminated
by a pure open circuit, and suppose that the line is exactly 5. the reflected power figure is not absorbed by the generator.
one wavelength long at the operating frequency. In this case If number 5 above is true, then why are generators rated
the current at the generator will be zero, and so the current to handle some maximum reflected power? The answer
in its internal impedance will be zero, so there is no power relates to the maximum voltage and current the generator can
dissipated in it. Yet there is a standing wave on the line, deliver. If a generator is rated to deliver, say, 1000 watts, this
so there are forward and reflected waves. The directional does not mean that it can do so into any load. As the load
wattmeter will show a forward and reflected power, and in resistance is increased, to get 1000 W, one needs more and
fact they will be equal to one another, and equal to the power more voltage (P=V2/R, so V=√PR) and sooner or later the
which would be dissipated in a 50 Ω resistor if the voltage at generator has produced all the voltage it can, and the power
the generator were impressed upon it. But there is no such is limited. Similarly, as the load resistance is decreased, the
resistor and so there is no power lost anywhere (again current goes up (P=I2R, so I=√P/R). Sooner or later the
assuming no line loss). generator cannot deliver any more current. In Appendix A,
Is there any measure of sense that we can get from the we indicate that the reflected voltage is defined as
forward and reflected power readings? What do they really
mean, anyway, if forward power doesn’t represent the power V – Z0 • I
delivered to the load and reflected power doesn’t represent Vr =
power absorbed by the transmitter? 2

First of all, the difference between the forward and

reflected power has a concrete meaning: it is the power This quantity increases as V differs from Z0I, and the
delivered to the load (proof of this is given in Appendix A). difference is limited by the maximum voltage and current the
In this sense, one can imagine that the forward power is being generator can create.
impressed upon the load, which is rejecting the reflected part Finally, it is remembered by those who used to work with
and absorbing the balance. We have to be careful not to take tube-type generators that a mismatched load can cause the
this imagery too far. It must not be inferred, for example, that plate of the tube to glow red. Does this not mean that excess
the generator actually has to generate the forward power. power is being dissipated there, and doesn’t this indicate that
The generator has to produce the power lost in the load, the reflected power is being absorbed by the tube?
line, and its internal impedance, and no more, because any
power produced must be delivered somewhere, and these are Certainly the higher temperature of the anode indicated
the only places for it to be lost. In the case of the open that the plate power was increased, but this does not mean
lossless line, there is no power lost in the load, line, or the that the reason was absorption of some kind of power coming
generator, and so there is no real power lost anywhere, but in from the outside. In a tube-type transmitter, the tube has a
there are forward and reflected power figures. These powers substantial voltage across it during conduction, resulting in
are not real energy flows, but rather are calculated figures large conduction losses. The actual losses depend upon the
which represent the power that would be generated in a 50 Ω design mode (A, AB, B, C, etc.) but can easily be larger than,
and are rarely less than 1/3 of, the output power. To achieve

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FORWARD AND REFLECTED POWERS. WHAT DO THEY MEAN?

high efficiency the tube must be biased well beyond cutoff wave on the line, Z0 must be equal to the characteristic
and must be operated on a tight load line. If there is reflected impedance of the transmission line. The directional
power as a result of a reactive load, the load line becomes an wattmeter must assume a value for Z0 and so is calibrated
open curve. This means that for a portion of the cycle, for use at only one impedance level.
substantial voltage exists across the tube at the same time
Voltage and current exist in a circuit with no
high current is being drawn through it. This results in the
transmission line, of course, and equations (1) and (2) may
large plate dissipation.
still be used to calculate a forward voltage and a reflected
In the case of modern FET amplifiers, the output voltage, even though there is no line to have a standing wave.
field effect transistors are operated as switches. The FET, These figures then represent the amplitudes of waves that
operated as a switch, is nearly an ideal one, with typical would exist on a line of impedance Z0 if it did exist in the
"on" resistance of considerably less than 1 Ω, and properly circuit.
designed amplifiers of this type have losses well under 10%
Let’s assume we are using a 50 Ω coupler. If we look
of the output power. These losses can increase or decrease,
closely at equation (2) we see that, the reflected voltage is
depending upon the load impedance, and in some cases the
zero if the voltage is exactly fifty times the current (and in
presence of reflected power can even result in decreased
phase with it). Zero reflected voltage means no reflected
dissipation. Modern protection circuits for such amplifiers
power, since the reflected power is defined as:
look only at the power lost in the output device and the
voltage across it, and reflected power is not measured.
|Vr|2
(3) Pr = ,
APPENDIX A Z0
The directional coupler samples the voltage and current
at the point in the line where it is inserted and produces from which is zero when Vr=0 (i.e., when V = Z0I).
them two quantities called the forward and reflected voltages,
which are the amplitudes of the two traveling waves which The forward power is similarly defined, as Pf = |Vf 2|/Z0,
make up the standing wave on the line. These are defined and the difference between the two powers is the load power:
as follows:
V + Z0 • I (4) Pload = Pf – Pr.
(1) V = for the forward voltage, and
f 2
This can be shown by substituting the defining equations
V – Z0 • I (1) and (2) for Vf and Vr into equation (4), yielding:
(2) Vr = for the reflected voltage
2 |Vf|2 |Vr|2

Here the voltages and currents are in bold print to

[ Z0 Z0 ]
1
Pload = –––– – –––– = –– [Vf •Vf – Vr •Vr ]=V•I=
Z0

emphasize that they are vectors (i.e., they have a phase angle) |V|•I• cosθ ,
and the addition and subtraction must be done with vector, or
complex algebra. The quantity Z0 is arbitrary; if there is a which is the true power in the load. Here • is indicating the
transmission line and if the voltages are to represent the "vector dot product" of the voltage and current vectors.
amplitudes of the traveling waves that make up the standing

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FORWARD AND REFLECTED POWERS. WHAT DO THEY MEAN?

Advanced Energy Industries, Inc.

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