First published in WorldRadio, Oct 2005 - Jan 2006, and reproduced here with permission. (Revision History [10])

An Energy Analysis at an Impedance Discontinuity in an RF Transmission Line

Where Does the Power Go? [1] There continue to be many differing responses to the question within the amateur radio community and, so far, no one else has presented the facts of the physics of electromagnetic energy as understood from the field of optics. Those technical facts from optics have been known and understood for decades and are consistent with the laws of physics and the equations governing the behavior of RF transmission lines. Light and RF waves are both composed of electromagnetic energy. Most of the following information comes from Optics [2]. In the field of optics, irradiance is the same thing as the power flow vector in an RF transmission line. Irradiance, like a power flow vector, has the dimensions of energy per unit time per unit area. The 1/4 wavelength thin-film deposited on glass to obtain a non-reflective surface performs in a virtually identical way to a 1/4 wavelength series matching section in a transmission line. Single-source RF energy in a transmission line and laser light are both coherent electromagnetic energy waves that obey the laws of superposition, interference, conservation of energy, and conservation of momentum. The power density terms in the irradiance equation have been multiplied by the unit area of the transmission line to obtain the resulting power equation in watts.

My Historical Perspective

My first memories of the answer to "Where does the power go?" are articles published in QST written by Walter Maxwell, W2DU, some quarter of a century ago. Mr. Maxwell later compiled the information into a book titled, Reflections, which quickly became the bible for Amateur Radio applications involving stub matching, transmission lines, and forward and reflected energy flow. Mr. Maxwell coined the terms, "virtual short" and "virtual open", as a shorthand description of what rearward-traveling reflected energy encounters at a match point in a transmission line resulting in 100% re-reflection [10]. He also explained the function of destructive wave interference and constructive wave interference in achieving a match point on a transmission line [8] which is what a large part of this article is about.

Sometime after the publication of Reflections, some people questioned the validity of Mr. Maxwell's concepts. In particular, Dr. Steven Best, VE9SRB, took Mr. Maxwell to task in a series of articles published in QEX [3]. Simply put, Dr. Best disagreed with Mr. Maxwell that reflected power is 100% "re-reflected" in a matched system. Before publication of his Part 3 QEX article, Dr. Best sent up trial balloons for his ideas on the usenet newsgroup, My opinion was that Dr. Best's future article contained numerous errors which were pointed out to him. However, the article as published still contained the alleged errors. My determination to resolve the conflicts between the concepts presented by Walter Maxwell and the ones presented by Dr. Best culminated in this present article.

In a nutshell, Walter Maxwell's "virtual short" is a two step process. The reflected wave from the load encounters the impedance discontinuity at the match point. A re-reflection occurs that equals the incident reflected power multiplied by the power reflection coefficient at the match point (the square of the voltage reflection coefficient). This re-reflected energy joins the forward wave traveling toward the load. That first energy re-reflection is not the only energy that joins the forward wave. That fact is what Dr. Best missed in his article. Interference of any kind was never mentioned in Dr. Best's QEX article.

The part of the reflected wave that is not re-reflected is transmitted back through the impedance discontinuity at the match point and attempts to flow toward the source. We know the reflected energy doesn't make it to the source in a matched system, so where does it go? The answer is mentioned in Reflections II [8]. What Mr. Maxwell is describing is wave cancellation due to total destructive interference between two reflected waves. The first wave is the part of the source forward wave that is initially reflected back toward the source from the match point. The second wave is the part of the reflected wave from the load that is transmitted through the match point toward the source. These waves are equal in magnitude and opposite in phase so, as Mr. Maxwell asserts in Reflections II, the two wavefronts cancel to zero at the match point thus eliminating reflections between the match point and the source. The canceling of these two waves to zero is the second step in Mr. Maxwell's virtual short process of 100% "re-reflection" (actually reflection plus redistribution [10]).

Voltages can cancel and currents can cancel but energy cannot cancel. What happens to the energy that existed in the waves before they were cancelled? Since we know that all the energy in a matched system winds up flowing toward the load, the answer is a no-brainer. There are only two directions in a transmission line. If energy that was previously flowing toward the source isn't flowing toward the source anymore, it must necessarily be flowing toward the load. The conclusion is inescapable. Not only is 100% of the reflected energy redistributed back toward the load at the match point, but wave cancellation is the cause of part of that redistribution. This is a well understood phenomenon in the field of optics [9] but not well understood in the field of RF engineering.[10]

An RF engineer will tell us that there are three things that can cause 100% reflection. Those are a short-circuit, an open-circuit, or a purely reactive impedance. But there is another phenomenon that can cause the reflected energy to reverse direction and flow toward the load - wave cancellation. In general:

The destructive interference energy resulting from wave cancellation at an impedance discontinuity becomes an equal magnitude of constructive interference in the opposite direction. Since there are only two directions in a transmission line, wave cancellation redistributes the energy in the opposite direction. [9] This redistributed energy joins the forward wave just as the re-reflected energy does.

The General Case Qualitative Analysis

The following discussion of a generalized impedance discontinuity in an RF transmission line, operating under steady-state conditions, is not intended to replace a conventional quantitative voltage analysis. It is intended instead as a conceptual qualitative energy analysis that extends the voltage analysis and answers that original question: Where Does the Power Go?

The following diagram is of a generalized impedance discontinuity in a typical RF transmission line. Pfor1 is the forward power and Pref1 is the reflected power on the source side section of transmission line having a characteristic impedance of ZØ1. Likewise, Pfor2 is the forward power and Pref2 is the reflected power on the load side section of transmission line having a characteristic impedance of ZØ2.

Every power component has an associated voltage component (and an associated current component). For instance, Pfor1 is associated with the RMS values of Vfor1 (and Ifor1) in the following way:

Pfor1 = Vfor1 2 ÷ ZØ1 = Ifor12 (ZØ1) = Vfor1 (Ifor1)   and   Vfor1 ÷ Ifor1 = ZØ1

We will continue that wave reflection model convention for this paper. Thus for any wave(x) or component wave(x) in a transmission line, there exists Vx and Ix such that:

Px = Vx2 ÷ ZØx = Ix2(ZØx) = Vx(Ix)   and   Vx ÷ Ix = ZØx

In the following figure, every power or component power has an associated voltage (and current) obeying the above rules. The Greek letter 'θ' will be used in the following equations to represent the relative phase angle between the two voltages, V1 and V2. V1 is associated with P1 and V2 is associated with P2. For the purpose of this paper, we will consider powers to be scalar values without associated phase angles. When power expressions become a function of a phase angle, that phase angle will be taken as the relative phase angle between the corresponding voltage waves.
Figure 2 shows an imaginary transverse plane (viewed on edge) dividing the transmission line into two segments, each with its own characteristic impedance. On each side of that plane, there exists a relationship between the energy flows and the transmission line that are governed by the characteristic impedance on that particular side of the impedance discontinuity. However, the imaginary plane has no width, so in Figure 2, all energy flows coexist at that same transverse plane, i.e. all superposition happens at the plane, not some distance away from the plane.

The following equations govern the distribution of energy at the impedance discontinuity, which, of course, is constrained by the conservation of energy principle. The Greek letter, 'ρ', will be used to designate the voltage reflection coefficient.

Power Reflection Coefficient:   ρ2 = [(ZØ2 - ZØ1) ÷ (ZØ2 + ZØ1)]2

Power Transmission Coefficient = (1 - ρ2)

Note that 100 times the power reflection coefficient is the percentage of power that is reflected. Likewise, 100 times the power transmission coefficient is the percentage of power that is transmitted.

While the voltage reflection coefficients are of opposite signs on the two sides of the junction, the power reflection coefficient is always positive on either side of the junction. The same concept applies to the power transmission coefficient. Since the impedance discontinuity is an imaginary plane and contributes no losses, all the power that is not reflected at the impedance discontinuity plane is transmitted through the impedance discontinuity plane.

P1 = Pfor1(1 - ρ2)   and   P2 = Pref22)

P3 = Pref2(1 - ρ2)   and   P4 = Pfor12)

P1 + P4 = Pfor1   and   P2 + P3 = Pref2

So far, nothing has been presented that differs from the wealth of information available on reflections in a transmission line. Anyone who is confused at this point should review a good reference on the reflection model for RF transmission lines. The remainder of this paper will answer the question: "Where Does the Power Go?"

The following equations are paraphrased from similar relationships published in Optics. The symbol 'I' representing irradiance in a light wave has been replaced by the symbol 'P' representing the power flow vector in an RF wave (or RF wave component) in a transmission line. Note that these equations apply to coherent waves. V1 and V2 are superposed at the load side of the impedance discontinuity, using phasor math, to obtain Vfor2 where 'θ' is the relative phase angle between V1 and V2. Note that cos(θ) = cos(-θ), so for an energy analysis, it doesn't matter if V2 is leading or lagging V1.

Pfor2 = P1 + P2 + 2[SQRT(P1 · P2)]cos(θ)       (Eq 1)

This equation is identical to Dr. Best's (Eq 12) [3], which was presented without any reference to interference in his QEX articles. From Optics, we can identify the third term in the equation as the interference term. [4] The interference term accounts for the fact that (V1+V2)2 is not equal to (V12 + V22), which, again, follows directly from the theory of superposition. These subjects are discussed in detail in Optics, chapters 7 and 9.

The following is the key equation that Dr. Best neglected to include in his QEX article. It is the other half of the energy equation and brings all of the energy into balance as required by the conservation of energy principle. It can be shown that the relative phase angle between V3 and V4 is (180 degrees minus θ) and since cos(θ) = -cos(180-θ), the following equation applies when V3 and V4 are superposed at the source side at the impedance discontinuity:

Pref1 = P3 + P4 + 2[SQRT(P3 · P4)]cos(180°-θ)

Pref1 = P3 + P4 - 2[SQRT(P3 · P4)]cos(θ)       (Eq 2)

Note the negative sign of the last term! Steady-state energy is supplied into the impedance discontinuity by two waves, one associated with Pfor1 (from the source) and the other associated with Pref2 (reflected from the load). Steady-state energy leaves the impedance discontinuity as two waves, one associated with Pfor2 (toward the load) and the other associated with Pref1 (toward the source). Anyone familiar with an S-parameter analysis will recognize those four terms. In fact, Eq 1 and Eq 2 can be independently developed from the S-parameter equations.[5] Since the power supplied to the impedance discontinuity is (Pfor1 + Pref2) and none of it is stored, (other than the energy being handed back and forth continuously between the electromagnetic and electrostatic fields), the power entering the impedance discontinuity must equal the power exiting the impedance discontinuity such that:

(Pfor1 + Pref2) = (Pfor2 + Pref1)

In a matched system, Pref1 equals zero but in a mismatched system, Pref1 can be any value between a small value and Pfor1. The conservation of energy principle requires that the total destructive interference energy equal the total constructive interference energy such that:

2[SQRT(P1 · P2)]cos(θ) + 2[SQRT(P3 · P4)]cos(180°-θ) = zero

2[SQRT(P1 · P2)]cos(θ) - 2[SQRT(P3 · P4)]cos(θ) = zero       (Eq 3)

This is the equation that explains everything about power at an impedance discontinuity in a transmission line. Note that there is a dotted line for interference energy in Figure 2. The destructive interference energy resulting from wave cancellation at the impedance discontinuity becomes an equal magnitude of constructive interference in the opposite direction. [6] This can happen in either direction in a mismatched system but will happen in only one direction in a matched system. The following cases are all the possibilities referenced to the relative phase angle, 'θ', between V1 and V2:

If ( 0 ≤ θ < 90 ) then there exists constructive interference between V1 and V2, i.e. cos(θ) is a positive value. Therefore there exists an equal magnitude of destructive interference between V3 and V4 where cos(180-θ) is a negative value. A positive sign on the interference term indicates constructive interference. A negative sign on the interference term indicates destructive interference.

If θ = 90 deg, then cos(θ) = 0, and there is no destructive/constructive interference between V1 and V2. There is also no destructive/constructive interference between V3 and V4. Any potential destructive/constructive interference between any two voltages is eliminated because θ = 90 deg, i.e. the voltages are superposed orthogonal to each other (almost as if they were not coherent).

If (90 < θ ≤ 180) then there exists destructive interference between V1 and V2, i.e. cos(θ) is a negative value. Therefore there exists an equal magnitude of constructive interference between V3 and V4 where cos(180-θ) is a positive value.

One note of importance is that, in the case of a mismatched impedance discontinuity, reflected power is not 100% re-reflected and redistributed. Dr. Best was right about that.

Now we are in a position to discover something that falls out from the conservation of energy principle. A simple mathematical manipulation of equation 3 above will show that:

|(P1)(P2)| = |(P3)(P4)|

Therefore the power resulting from constructive interference is:

Pfor2 = P1 + P2 + 2[SQRT(P3 · P4)]cos(θ)       (Eq 4)

This equation tells us where the extra energy comes from that allows (V1+V2) to superpose to Pfor2 > |P1|+|P2| in a typical matched RF system. The destructive interference event (involving the superposition of V3 and V4) feeds energy into the constructive interference event (involving superposition of V1 and V2).[6]

Why not turn this qualitative analysis into a quantitative analysis? If we know the forward power and reflected power on each side of the impedance discontinuity and the reflection coefficient at the impedance discontinuity, we can certainly do a quantitative analysis. The only problem is that there are two solutions. Without additional information, one cannot tell whether V2 is leading or lagging V1 and therefore there exists two possible solutions. In order to confine the results to one unique solution, one would need to know the number of wavelengths between the discontinuity and the load and the reflection coefficient at the load. But as we shall discover in Part III: For a ZØ-matched system, the two-solution problem disappears because the phase angle between V1 and V2 is always zero degrees (ZØ2 > ZØ1) or 180 degrees (ZØ2 < ZØ1).

Note: It cannot be over-emphasized that "wave cancellation" does not imply energy cancellation. "Wave cancellation" refers to the cancellation of two coherent EM voltage/current waves traveling the same path in the same direction. The energy components in the cancelled waves cannot be destroyed so the energy must seek another path, i.e. it is redistributed in the opposite direction in a transmission line.

The Special Case ZØ-Matched Analysis

Someone might ask, why bother with a special case? As it happens, this special case applies to all matched systems for which Pref1 = 0, and is the most common case within amateur radio. One might say the matched case is not all that 'special'. Here's a diagram for the ZØ-matched system.

Note that interference energy flows in only one direction for a ZØ-matched system and that direction is always toward the load. When the system is matched, Pref1 equals zero, i.e. there are no reflections flowing toward the source and a quantitative analysis becomes possible. For a matched system, the phase angle between V1 and V2 is zero degrees and the phase angle between V3 and V4 is 180 degrees. In addition, the magnitudes of V3 and V4 are equal and therefore the magnitudes of P3 and P4 are equal. V1 is arbitrarily assigned a reference phase angle of zero degrees. V2 will therefore, possess a phase angle of zero degrees. For a positive ρ, V4 will be at zero degrees, and V3 will be at 180 degrees. If ρ is negative, V4 will be at 180 degrees and V3 will be at zero degrees. This is in agreement with the rules governing wave reflection.

When two coherent waves of equal magnitude and opposite phase encounter each other while moving in the same direction in a transmission line, complete cancellation of the two waves occurs. The total voltage goes to zero and the total current goes to zero in the direction of the canceled waves. Vref1 (and Iref1) go to zero at the match point. That's entirely logical since the reflected power flow vector toward the source equals zero in a matched system.

In a ZØ-matched system with reflections, total destructive interference occurs at the source side of the ZØ-match point and eliminates reflections toward the source. Following the principle of conservation of energy, the destructive interference energy previously associated with the two cancelled reflected waves becomes total constructive interference energy flowing toward the load as part of Pref2.

The energy equations governing the behavior of a ZØ-matched system are simplified because the phase angle between V1 and V2 is zero degrees for total constructive interference. The phase angle between V3 and V4 is 180 degrees for total destructive interference.

Pfor2 = P1 + P2 + 2·SQRT(P1·P2)         (Eq 5)

The constructive interference event of Eq 5 is called total constructive interference.[7]

Pref1 = P3 + P4 - 2·SQRT(P3·P4)         (Eq 6)

The destructive interference event of Eq 6 is called total destructive interference.[7]

For a ZØ-matched system, in which all reflections are cancelled toward the source, it is necessary for P3 to equal P4. From that fact and knowing that (P1)(P2) = (P3)(P4), it can be shown that, in a matched system:

|Pfor2| = |P1| + |P2| + |P3| + |P4|         and since

|P1| + |P4| = |Pfor1|         and         |P2| + |P3| = |Pref2|

We can conclude that:         |Pfor2| = |Pfor1| + |Pref2|

Which is what a lot of people have been saying for a lot of years.[8] Note: The absolute value marks are included to indicate that these powers are scalar values, not power flow vectors.

Conclusion: There are two steps leading to the total redistribution of reflected energy back toward the load in a ZØ-matched system.

1. P2 = Pref2 ( ρ2 ) is the first re-reflection event and occurs when the reflected wave associated with Pref2 encounters the impedance discontinuity.

2. P3 and P4 are associated with two waves involved in total destructive interference. Since the related voltages, V3 and V4, are equal in magnitude and 180 degrees out of phase, the energy components in P3 and P4 cease to exist on the source side of the impedance discontinuity, and instead are redistributed toward the load as total constructive interference. P3 and P4 are power flow vectors associated with two reflected waves that cancel, so according to the principle of conservation of energy, their combined energy (and momentum) must change direction. Since P3 and P4 are reflected energy components that end up flowing toward the load, the interference event can be considered to be a redistribution [9] of reflected energy. Combining steps 1 and 2 above, it is apparent that 100% of the reflected energy is re-reflected and redistributed in a matched system. P2, P3, and P4 are all reflected wave components.

Note that the author previously used the word "reflection" for both actions involving a single wave and the interaction between two waves. Now the word "reflected" is being used only for single waves and the word "redistributed" is being used for the two wave interference scenario.

Step 2 above, is a somewhat new concept in the field of RF engineering although it has existed for decades in the field of optics.[9] We amateur radio operators can add an item to the list of things that can cause a redistribution of the energy in incident waves: 1. Short-circuit, 2. Open-circuit, 3. Pure reactance, 4. Wave cancellation.[10] Wave cancellation cannot occur at a single load fed by a single source through a single transmission line but it can occur in a transmission line when waves are incident upon an impedance discontinuity from both directions. Although harder to understand and prove, wave cancellation (and therefore 100% redistribution of canceled wave energy) can also occur at (or inside) a source when RF energy is coming from both directions. For instance, reflected wave cancellation will occur in a tube-type final amp when the pi-network is tuned for system resonance. In that case, the reflected wave cancellation point would be the Zg-match point inside the transmitter.

Note: The steady-state existence of the P3 wave can be inferred from P3 = Pref2(1- ρ2) where Pref2 and (1-ρ2) do exist. Given that the P3 wave exists, then the existence of the P4 wave is necessary for wave cancellation. Unfortunately, superposition happens faster than humans can observe, even with their fastest instruments.

And that is where the power goes; (actually, it is the energy that does the "going").

A Simple Example

Consider the following lossless system with a 1:1 choke at point 'x':

100W XMTR---50 ohm coax---x---300 ohm twinlead---load
		Pfor1-->	Pfor2-->
		<--Pref1	<--Pref2
The source is supplying 100 watts. The SWR meter reads 1:1 on the coax. With the information given, can we calculate the forward power, reflected power, and SWR on the twinlead? How about voltages and currents on the twinlead?

The power reflection coefficient is [(300 - 50)/(300 + 50)]2 = 0.51 and the power transmission coefficient is (1 - 0.51) = 0.49. For the system to be matched, these coefficients must also exist at the load. So the forward power on the twinlead must be 100W/0.49 = 204.1 watts. That makes the reflected power on the twinlead equal to (204.1 - 100) = 104.1 watts. From these two power values, we can calculate Vfor2 = 247.4V, Ifor2 = 0.825A, Vref2 = 176.7V, Iref2 = 0.589A , SWR(300) = 6:1

The SWR can be calculated in any number of ways. VSWR(300) = (Vfor2 + Vref2)/(Vfor2 - Vref2)

If we know the physical length and velocity factor of the 300 ohm twinlead, we can actually calculate the feedpoint impedance of the load (antenna).

The author has endeavored to satisfy the purists in this series of articles. The term "power flow" has been avoided in favor of "energy flow". Power is a measure of that energy flow per unit time through a plane. Likewise, the EM fields in the waves do the interfering. Powers, treated as scalars, are incapable of interference. Any sign associated with a power in this paper is the sign of the cosine of the phase angle between two voltage phasors. A plus sign indicates constructive interference (or energy flow toward the load) and a minus sign indicates destructive interference (or energy flow toward the source).

I would like to thank Mr. Robert E. Lay, W9DMK, for his substantial contributions to this article.


[1] Bloom, Jon, "Where Does the Power Go?", QEX, Dec. 1994

[2] Hecht, Eugene, Optics, Fourth Edition, (c)Aug. 2001, Addison-Wesley, ISBN 0805385665

[3] Best, Steven R., "Wave Mechanics of Transmission Lines, Part 3", QEX, Nov/Dec 2001

[4] "Interference term", Optics, Eugene Hecht, Fourth Edition

Section 7.1 The Addition of Waves of the Same Frequency: It follows ... that the resultant flux density is not simply the sum of the component flux densities; there is an additional contribution 2E01E02cos(α12), known as the interference term.

Section 9.1 General Considerations: The 'interference term' becomes I12 = 2*SQRT[(I1)(I2)]cos(σ)
(where 'SQRT' replaces the square root sign.)

[5] S-Parameter Techniques, Hewlett Packard Application Note 95-1, available on the web. The S-Parameter normalized voltage equations are:

b1 = (s11)(a1) + (s12)(a2) and b2 = (s21)(a1) + (s22)(a2)

The squares of all those terms are related to power as explained in the application note. It is left as an exercise for the reader to square both sides of both equations above and observe that the resulting equations contain the interference term that agrees with Eq 1 and Eq 2 in the body of this paper.

[6] Optics, Eugene Hecht, Fourth Edition

Section 3.3 Energy and Momentum, "One of the most significant properties of the electromagnetic wave is that it transports energy and momentum." [Note from W5DXP: Energy and momentum must be conserved. The direction of the energy and momentum associated with reflected waves must be reversed for a match to occur.]

Section 4.11 Photons, Waves and Probability, "The principle of conservation of energy makes it clear that if there is constructive interference at one point, the 'extra' energy at that location must have come from somewhere else. There must therefore be destructive interference somewhere else. "If two or more electromagnetic waves arrive at point P out-of-phase and cancel, 'What does that mean as far as their energy is concerned?' Energy can be distributed, but it doesn't cancel out."

Section 7.1 The Addition of Waves of the Same Frequency, "The superposition of coherent waves generally has the effect of altering the spatial distribution of the energy but not the total amount (of energy) present."

[7] Optics, Eugene Hecht, Fourth Edition

Section 9.1 General Considerations, "A maximum irradiance (power) is obtained when cos(σ) = 1. ... In this case of total constructive interference, the phase difference between the two waves is an integer multiple of 2π, and the disturbances are in-phase. ... A minimum irradiance (power) results when the waves are 180 degrees out-of-phase, ... cos(σ) = -1, ... and is referred to as total destructive interference."

[8] Maxwell, Walter, Reflections II, (c) 2001 Worldradio Books, ISBN 0-9705206-0-3 page 4-3, "The destructive wave interference between these two complementary waves ... causes a complete cancellation of energy flow in the direction toward the generator. Conversely, the constructive wave interference produces an energy maximum in the direction toward the load, ..." page 23-9, "Consequently, all corresponding voltage and current phasors are 180 degrees out of phase at the matching point. ... With equal magnitudes and opposite phase at the same point (point A, the matching point), the sum of the two (reflected) waves is zero."

[9] Quotes from two web pages from the field of optical engineering:

"Clearly, if the wavelength of the incident light and the thickness of the film are such that a phase difference exists between reflections of p, then reflected wavefronts interfere destructively, and overall reflected intensity is a minimum. If the two reflections are of equal amplitude, then this amplitude (and hence intensity) minimum will be zero." (Referring to 1/4 wavelength thin films.)

"In the absence of absorption or scatter, the principle of conservation of energy indicates all 'lost' reflected intensity will appear as enhanced intensity in the transmitted beam. The sum of the reflected and transmitted beam intensities is always equal to the incident intensity. This important fact has been confirmed experimentally."

"... when two waves of equal amplitude and wavelength that are 180-degrees ... out of phase with each other meet, they are not actually annihilated, ... All of the photon energy present in these waves must somehow be recovered or redistributed in a new direction, according to the law of energy conservation ... Instead, upon meeting, the photons are redistributed to regions that permit constructive interference, so the effect should be considered as a redistribution of light waves and photon energy rather than the spontaneous construction or destruction of light."

Note from W5DXP: In an RF transmission line, since there are only two possible directions, the only "regions that permit constructive interference" at an impedance discontinuity is the opposite direction from the direction of destructive interference.

[10] Revision 1.1, Feb. 20, 2008 - In the original version, the redistribution of energy due to wave cancellation was called a "reflection", a common practice in amateur radio circles. W5DXP has changed that description in favor of a "redistribution" as described by the FSU web page. The word "reflection" is reserved for describing the event when a single wave encounters an impedance discontinuity. This is accordance with The IEEE Dictionary definition of "reflected wave". The word "redistribution" of energy is adopted for describing what happens to the energy when two or more waves interact. In like manner, since interference can occur with or without permanent wave interaction, interference alone is necessary but not sufficient to correspond to the permanent redistribution of energy.