Reflected Power and Re-Reflection: Source, Load, Phase and Loss

“Reflected power bounces between the antenna and tuner until the antenna finally uses it” can describe a carefully chosen pulse example. It is not a universal account of a continuously driven RF system. In steady state, forward and reverse waves are complex amplitudes with phase; source and load boundaries determine them together, and real loss remains real.

Where the Bouncing-Watts Story Comes From

The familiar example starts with 100 W incident on a load that accepts 75 W and reflects 25 W. If the source end then reflects all 25 W back, the load accepts 75% of that encounter, reflects the rest, and so on:

That is valid energy bookkeeping for separated pulses when the line is lossless, the load always reflects 25% of incident power, and the source boundary fully reflects each returning pulse with the assumed phase behavior. It demonstrates one possible boundary condition. It does not prove that every transmitter or tuner returns every reverse wave to the antenna.

The story becomes false when it silently assumes all of the following:

• complete reflection at the source end;
• no attenuation on either journey;
• a fixed load coefficient;
• independent power packets even after they overlap;
• the necessary phase for reinforcement; and
• an unchanged original forward-meter reading while additional “returned watts” are counted again.

If a returning wave changes the source-boundary solution, the total forward and reverse waves at that plane change. One cannot keep an earlier 100 W reading and then append another 25 W as though the two measurements described the same state.

Start With Voltage and Current Waves

For a uniform transmission line, sinusoidal voltage and current can be decomposed into forward and reverse terms. With one common coordinate convention:

Here γ = α + jβ contains attenuation and phase constant. The minus sign in the reverse-current term is not optional: it is why forward and reverse powers subtract even though local voltage magnitudes may add.

At the load reference plane, the voltage reflection coefficient is:

For a passive load and a lossless line with real positive Z₀, the reflected-power fraction is |Γ_L|². The phase of Γ_L determines where voltage and current maxima occur; it cannot be recovered from SWR alone.

The Source End Has Its Own Reflection Coefficient

A reverse wave arriving at the source end does not remember that it was “reflected power.” It encounters the impedance looking into the complete source-side network. For a passive linear termination and real Z₀:

Thus “reflected power always re-reflects” and “the transmitter always absorbs reflected power” are both unjustified absolutes. Either behavior, or a mixture, can occur in a linear passive model. The actual boundary must be identified.

A Radio Is More Than Its 50 Ω Label

Between the antenna socket and the active transistor or valve there may be an output transformer, low-pass filter, matching network, directional coupler, relays, tuner, combiner or circulator. A reverse wave meets all of that hardware. Foldback or shutdown can change the forward source wave, while a circulator can route reverse power into a load rather than back into the PA.

A small-signal source-match measurement can characterize a linearized boundary at a stated frequency and operating condition. It must not be extrapolated automatically to a strongly driven nonlinear transmitter. Network-analyzer documentation calls source match an error because a DUT reflection can reflect again from the analyzer source and then return to the DUT. That is direct laboratory evidence that re-reflection is conditional on the source boundary.

Multiple Reflections: The Round-Trip Factor

In a linear source–line–load model, one complete down-and-back wave contribution is multiplied by:

The expression makes five facts explicit: neither end need reflect completely; the line attenuates both journeys; the line adds round-trip phase; later contributions can reinforce or oppose earlier ones; and line length matters through phase even when SWR magnitude is unchanged.

If |q| < 1 and the source launches the same linear contribution, the forward-voltage series converges:

There is an important edge case. With a strictly lossless line and two perfectly reflecting boundaries, |q| = 1 and the ordinary geometric sum does not converge. At phases that reinforce, an ideal continuously driven resonator has no finite steady-state amplitude without loss, source impedance, nonlinearity or some other limiting mechanism. That ideal problem must be treated as a transient or resonant system—not hidden inside a convergent “eventually all watts are used” story.

Pulse Echoes and Continuous-Wave Steady State

When a pulse is shorter than the line’s round-trip delay, individual echoes can be separated in time. Time-domain reflectometry uses precisely this idea: the timing and polarity of reflections locate and characterize impedance discontinuities. In that regime, drawing each journey is physically intuitive.

With a continuous carrier, the round trips overlap after the turn-on transient. The line then contains a sinusoidal steady-state solution. There are still forward and reverse waves, but there is no operational need to label an RF cycle as being on its third or seventh journey. All same-frequency contributions travelling in one direction have already combined into the total complex amplitude.

A swept-frequency VNA and a time-domain transformation are two views of the same linear network. Keysight’s time-domain documentation explicitly relates the Fourier transform of frequency-domain reflection coefficient to reflection versus time. “Bounce” and “phasor” descriptions are not rival physics; they are different representations suited to different questions.

Add Complex Amplitudes Before Calculating Power

If two coherent forward contributions occupy the same frequency and mode:

The cross-term contains phase. The contributions may reinforce, partially cancel or oppose each other. Adding their separate wattages discards that information and is generally wrong for coherent steady-state waves.

This is also why advanced microwave work distinguishes voltage waves, pseudo-waves and power waves when reference impedances are complex. Kurokawa’s classic power-wave paper shows that the familiar simple power interpretation depends on the wave definition and reference impedance. For ordinary amateur calculations on a low-loss 50 Ω line, real Z₀ is usually a good approximation; it should still be stated.

The 100 W Forward, 25 W Reverse Example

Suppose a properly calibrated directional instrument at one plane on a real-Z₀ line indicates:

The 25 W reverse component is already included in that electromagnetic state. It cannot be “sent forward again” while the measured 100 W forward component remains fixed unless the source or boundary conditions change. After any source-side interaction, the meter reads the new total forward and reverse waves.

If an ideal lossless tuner is arranged so that 100 W of net average power crosses into an antenna-side line whose reflected-power fraction is 25%, the steady-state directional components at that plane can instead be:

This does not mean the transmitter independently generates 133.3 W and receives 33.3 W of free power. It means the travelling-wave decomposition contains larger counter-propagating components whose difference is the net transfer. A directional meter counts each total component once; it does not assign trip numbers to individual watts.

Reflection Is Not Dissipation; Extra Travel Adds Real Loss

An ideal impedance discontinuity can reflect energy without dissipating it. Real coax, tuners and antennas are not ideal. Conductor and dielectric loss act on each pass. Inductor resistance, capacitor ESR, relay and connector resistance, transformer loss, ferrite heating, loading-coil loss and antenna ground loss all convert some RF energy into heat.

Accordingly, “it is not lost because it will be re-reflected” fails twice: the source boundary may not re-reflect it, and any additional travel that does occur adds loss. High SWR does not create dissipation by itself, but it raises voltage and current maxima and increases loss in a real line relative to the same net transfer on a matched line.

What an Antenna Tuner Actually Changes

A tuner is an impedance-transforming network. At the shack it can present the PA with a suitable input impedance while the line between tuner and antenna remains mismatched. The antenna-side line can still contain substantial forward and reverse waves.

Describing an ideal tuner as “re-reflecting returned energy” can be one travelling-wave interpretation of the completed steady-state solution. It is not a licence to add the reverse meter reading to an unchanged transmitter output. The precise partition of an incident reverse wave between transmission toward the source and reflection back toward the load follows the tuner’s two-port scattering behavior and its termination.

A tuner does not:

• create energy from a reverse wave;
• erase feedline attenuation;
• make the antenna-side SWR 1:1 when located at the shack;
• guarantee that accepted antenna power becomes radiation; or
• protect components from high internal voltage or current automatically.

A real tuner also dissipates power. The practical test is not merely whether the transmitter sees a match, but insertion loss, component temperature, voltage and current stress, and delivered power across the required frequencies and loads.

A Better Diagnostic Checklist

At a defined plane, ask:

1. What is the reference impedance and is it sufficiently real?
2. What are the total complex forward and reverse wave amplitudes?
3. What are Γ_L and the effective source-side boundary?
4. What attenuation and phase does each line section add?
5. Is the problem a turn-on transient, a pulse echo or sinusoidal steady state?
6. Where is average power generated, dissipated, delivered or radiated?
7. Are the coupler’s directivity and calibration adequate for the claimed difference?

For a low-loss line with real Z₀, the local net average power relation is:

That is complete bookkeeping at the stated plane. Loss between planes changes the travelling components, so a meter at the transmitter and a meter at the antenna need not report identical values.

The Practical Verdict

Reflected RF can be reflected again. It is not automatically re-reflected, completely re-reflected or absorbed. The result depends on the impedance and phase presented by the source-side network, and a driven transmitter may not behave like a passive resistor.

Multiple reflections are real and especially intuitive as separated pulse echoes. In continuous-wave steady state, however, the wave contributions overlap coherently. Add complex amplitudes with phase, then compute power. Do not add forward and returned watt readings from incompatible states.

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