Reflections Revisited: W2DU, W8KHK and Modern Measurement Boundaries
Reflections Revisited: W2DU, W8KHK and Modern Measurement Boundaries
Walter Maxwell gave amateur radio an unusually clear way to reason about mismatched transmission lines. Rick Maxwell’s first-hand laboratory history helps us read that work in its real instrument and transmitter context.
M. Walter Maxwell, W2DU—not James Clerk Maxwell—made reflected-power arguments accessible to generations of radio amateurs. His motor-generator analogy, conjugate-match treatment and practical insistence that low SWR does not prove antenna efficiency are still worth studying. They become more useful, not less, when every conclusion is tied to its source model, reference plane, mode, loss and measurement uncertainty.
Joeri’s assessment: keep Maxwell’s current-and-wave intuition. Add modern reference-plane discipline. A reflected wave can be reflected again, a matched input can coexist with large internal standing waves, and forward-wave amplitude can rise through coherent addition. None of those facts creates energy or proves that a tuner, feed line, ground system or antenna is lossless.
The Story Has a Published Record and a Family Witness
ARRL’s account of Walt Maxwell’s life records that he was first licensed as W8KHK in 1933 at age 14, later held W8VJR and W2FCY, and used W2DU from 1968. It also records the assigned W4GWZ call during his early broadcast work. ARRL identifies Richard “Rick” Maxwell as one of Walt’s three sons and notes that Rick, then WB4GNR, later took W8KHK.
Rick’s already-published, permissioned first-hand account supplies the more personal layer: he is Walt’s second son; he also previously held WB2HKX and AFC2HKX; and he remembers the equipment Walt used as the laboratory developed. Those family and instrument details remain attributed to Rick where an independent record is not linked. They are not presented as a complete corporate inventory or as access to private correspondence.
| Record | What it establishes | Evidence boundary |
|---|---|---|
| ARRL public history | W8KHK in 1933, later calls, W2DU from 1968, QST and book chronology | Independent public organizational record |
| Rick Maxwell, W8KHK | Second-son context, previous calls and the evolving retirement laboratory | Attributed first-hand family recollection, published with permission |
| Reflections III | Maxwell’s own explanations, examples and stated assumptions | Primary technical text; each proposition keeps its original boundary |
Maxwell’s “Another Look at Reflections” appeared in seven QST parts from 1973 through 1976 and was first assembled as an ARRL book in 1990. ARRL’s series index identifies Part I in April 1973. The later Reflections III is the primary text assessed below.
How Far Does the Free-Space Analogy Go?
In Reflections III, Maxwell says propagation in space occurs in “precisely the same manner” as on a transmission line. That is a powerful teaching bridge when it is bounded. In a homogeneous far-field region, the electric and magnetic fields are locally transverse, their ratio is set by the medium’s wave impedance, and energy propagates away from the antenna. A uniform transmission line also supports travelling waves with related voltage and current.
The systems are not literally interchangeable. A line’s conductors and dielectric impose a mode, characteristic impedance and return-current geometry. Close to an antenna, reactive electric and magnetic energy and longitudinal field components can be important; the free-space far-field ratio of about 377 Ω is not a universal local impedance. IEEE 145 antenna terminology keeps near-field and far-field regions distinct. Use the analogy to follow waves, then use the actual geometry and field region for calculation or measurement.
What Does the “Reflection Generator” Metaphor Teach?
Maxwell’s motor-generator picture gives the reflected voltage or current a memorable cause. The measurable mechanism is the boundary condition at a discontinuity. For a uniform lossless line with real characteristic impedance Z0 and load ZL, the load reflection coefficient is:
ΓL = (ZL − Z0) / (ZL + Z0)
Voltage and current—or the corresponding modal fields—must satisfy the new termination. The reflected wave is the solution required by those conditions, not a literal extra generator hidden at the load. Maxwell’s image remains useful if it is treated as a model rather than a component.
What Does Source Re-Reflection Actually Do?
A wave returned by the load can encounter a non-zero source reflection coefficient ΓS and be reflected toward the load again. For a simple line of length l and propagation constant γ, one complete round trip multiplies a forward component by:
q = ΓSΓLe−2γl
If a0 is the initially launched forward wave at the declared source plane, then for |q| < 1 the steady-state forward wave there is a = a0(1 + q + q² + …) = a0/(1 − q).
This is coherent complex addition. The phases matter; component powers cannot be added as unrelated scalars. With a real power-wave normalization, net power through one reference plane is |a|² − |b|². If ΓS = 0, the returned wave is absorbed at that source plane and there is no source re-reflection. Kurokawa’s power-wave formulation and Keysight’s RF signal-flow treatment provide the formal and practical versions of that accounting.
A tuner, line and load can present Γin ≈ 0 at the rig reference plane while reflected waves remain inside the line or network. Under the same port normalization, that is the composite input S11, not an unconditional statement that the tuner alone has S11 = 0. Reference plane, termination and mode belong in the sentence.
When Is Conjugate Matching the Right Model?
For a linear Thevenin source with fixed impedance ZS, maximum available power is delivered to a load whose input impedance is ZS*. A passive, ideally lossless matching network can transform a different physical load into that input condition. This is not the same as making every junction equal to 50 Ω, and it is not a promise that every watt accepted by the network reaches the intended load.
NBS Monograph 137 treats conjugate match and mismatch within declared source and load conditions. In a real tuner or feed system, conductor, dielectric, core, contact and radiation losses change the delivered-power optimum. A perfect input match can therefore be an excellent operating condition and still be a poor efficiency measurement.
What Changes with Switched-Mode and Controlled PAs?
Conjugate-match theory remains exact inside its linear source model. It should not be promoted into a universal large-signal PA rule. In Class-E and Class-F operation, device voltage and current waveforms, output capacitance, network harmonics and switching conditions help define the required load. Protection loops, compression, filtering and supply limits can move the installed optimum again.
Nathan and Alan Sokal’s 1975 Class-E paper is a useful historical marker: switched-mode theory is not a consequence of SDR. A digital or software-defined exciter does not by itself identify the final amplifier class. For a modern PA, calibrated load-pull and ruggedness measurements can map power, efficiency, compression and stress over reflection magnitude and phase.
What Could W2DU’s Instruments Establish?
Rick recalls an early bench with directional couplers, bridges, generators and a slotted line, followed later by an HP 8640A generator, HP 8405A vector voltmeter with directional couplers, HP 4815A vector impedance meter, and a Tektronix spectrum analyser with tracking generator. He also explains that Walt did not have retirement-laboratory access to the automated HP vector network analysers used at RCA Astro-Electronics.
The HP 8405A manual describes relative RF magnitude and phase measurements. The HP 4815A manual describes direct complex-impedance measurements. With calibrated generators, couplers, fixtures and careful plane control, those instruments can establish vector relationships one frequency and configuration at a time and support manual Smith-chart work.
That is capable vector measurement, but “equivalent to a modern VNA” needs a method and uncertainty budget. A calibrated VNA separates incident and reflected waves, sweeps frequency, measures multiport S-parameters and applies systematic error correction. Directivity, source match, tracking, cable movement, connector repeatability and fixture models limit both old and new methods. IEEE 370-2020 is a modern reference for plane and fixture discipline.
What Survives from the 0.4λ and Radial Discussion?
Reflections III presents a “squashed hemisphere” extending a little beyond 0.4λ and recommends roughly 90–100 buried radials reaching that distance. Preserve that as Maxwell’s installation model, not a universal optimum. The original Brown, Lewis and Epstein vertical-antenna experiments compared particular radiator, radial and ground arrangements; they do not turn one geometry into a law for every site.
Buried radials are distributed, coupled and lossy current collectors, not isolated lossless wires whose free-space resonance alone sets performance. The useful count and length depend on frequency, soil conductivity and permittivity, burial or elevation, radial diameter, radiator height, feed geometry and the target metric. ITU-R BS.705 explicitly parameterises earth-system radius, radial count, conductor dimensions and ground constants. Measure field strength, feed loss and current distribution before declaring diminishing returns. A ground rod may serve protective-earthing or lightning functions, but it is not automatically a low-loss HF radial system.
Can Forward-Wave Power Exceed the Initially Launched Wave?
Yes, at a declared plane and in a declared steady-state wave decomposition. Maxwell’s worked examples show a forward component that grows through constructive re-reflection. The result is compatible with conservation of energy because the source continues supplying energy while the steady state develops, and reactive elements store and return energy each cycle.
The phrase “forward power increased” is incomplete without saying whether the baseline is available source power, the initially launched component, the final forward component or net accepted power. The safe accounting is complex first, power second. Add same-direction wave amplitudes coherently; then calculate |a|². At one real-normalised plane, subtract the reverse power |b|² to obtain net power flow. Do not use Pforward = Psource + Preflected as a universal scalar identity.
What Does the Lossless Assumption Prove?
An ideal lossless line or matching network isolates the reflection mechanics. It lets us track voltage, current, phase and conserved net power without also solving conductor and dielectric heating. That is why it is valuable.
A physical input match proves only that the measured same-mode reverse wave is small at that reference plane under those conditions. It does not prove that internal reflections vanished, that the matching network has zero insertion loss, that common-mode or harmonic power is absent, or that accepted power is radiated. Those claims require transmission, thermal, modal and radiation evidence. NBS Monograph 82 is a useful primary reference for the impedance and reflection measurements on which such distinctions rest.
| Maxwell’s teaching phrase | Useful physical meaning | Required boundary |
|---|---|---|
| Space behaves like a line | Travelling electric and magnetic fields carry energy | Field region, mode, medium and conductor geometry |
| Reflection generator | A mismatch produces a reflected wave | Boundary-condition solution, not a literal generator |
| Total re-reflection | Returned waves can reflect again and cancel at an input plane | Complex phase, source/load Γ, propagation and reference plane |
| Conjugate match | Maximum available power for a stated linear source model | Operating point, network loss and actual delivered-power objective |
| Forward-power increase | Coherent components establish a new steady-state amplitude | Declared baseline; no scalar power addition or energy creation |
| Lossless network | An ideal model that isolates wave mechanics | Real efficiency still needs loss, mode and radiation evidence |
Joeri’s Bottom Line
Read Reflections III because Maxwell made difficult transmission-line behaviour visible. Read Rick W8KHK’s laboratory history because it prevents an equally misleading simplification: Walt’s later work was not limited to a crude SWR bridge. Then carry both stories into a modern measurement practice that names the source model, operating state, mode, reference impedance, reference plane, phase and uncertainty.
The best tribute to a strong engineering teacher is neither automatic agreement nor casual dismissal. It is to reproduce the proposition, preserve the assumptions, measure the actual system and say exactly what the result proves.
Primary and authoritative references
- M. Walter Maxwell, W2DU — Reflections III
- ARRL — Walt Maxwell, W2DU, biography, calls and publication history
- ARRL — “Another Look at Reflections” QST series index
- K. Kurokawa — Power Waves and the Scattering Matrix
- NBS Monograph 137 — Scattering parameters, conjugate match and mismatch
- Keysight — RF power signal flow and mismatch
- Hewlett-Packard — 8405A Vector Voltmeter manual
- Hewlett-Packard — 4815A Vector Impedance Meter manual
- Nathan O. Sokal and Alan D. Sokal — Class-E switching-mode amplifier
- Brown, Lewis and Epstein — Ground systems as a factor in antenna efficiency
- ITU-R BS.705 — HF transmitting vertical-monopole characteristics
- IEEE 370-2020 — Interconnect measurement quality and de-embedding
Mini-FAQ
- Who were W2DU and W8KHK? M. Walter Maxwell, W2DU, first held W8KHK in 1933. His second son Richard “Rick” Maxwell later took W8KHK and supplied the attributed first-hand laboratory history used here.
- Is free-space propagation identical to a transmission line? No. The far-field travelling-wave analogy is useful, but conductors, modes, characteristic impedance and reactive near fields make the systems physically distinct.
- Does re-reflection create extra energy? No. Incident, reflected and re-reflected wave amplitudes add coherently while the source supplies energy and reactive elements store and return it.
- Does zero input reflection prove an efficient antenna system? No. It describes one mode at one reference plane; tuner, line, ground and antenna losses can still absorb accepted power.
- Does a conjugate match describe every RF power amplifier? No. It is exact for its stated linear source model. Switched and compressed PAs require large-signal load, harmonic, control and stress boundaries.
- Did W2DU use a modern automated VNA at home? Rick says no. Walt’s later retirement bench could measure vector magnitude, phase and impedance sequentially, but a VNA adds calibrated incident/reflected-wave separation, sweeping, multiport data and error correction.