Reflections Revisited — What’s True and What’s Been Refined Since W2DU
Updated October 2025
Walter Maxwell (W2DU) — not James Clerk Maxwell — wrote one of ham radio’s most influential books on transmission lines and matching networks. It’s still sold by the ARRL and cited widely. Much of it derived from QST-era articles of the 1970s, before the wide availability of VNAs and advanced EM simulators.
We continue to value the book for its insight and intuition, but many readers sense that certain explanations should be read with a modern lens. Below we cover the most frequent follow-up questions, with corrections or clarifications based on 21st-century RF and network theory.
Q 1 — Did Maxwell really mean that radio waves propagate just like current in a coax line?
In Reflections III, he states that propagation in space occurs “in precisely the same manner” as on a transmission line, and that E and H are always perpendicular. That is a very effective teaching analogy for the far field (where the wave is TEM) but not a universally accurate statement. Near an antenna you have reactive fields; the fixed E/H = 377 Ω relationship does not strictly hold everywhere; and transmission lines enforce boundary conditions via conductors. So: correct in spirit for the far field, but not a literal equivalence everywhere.
Q 2 — What is the “reflection generator” metaphor?
Maxwell repeatedly explains a mismatch as a motor–generator that creates a reflected voltage or current. Modern network and field theory dispenses with that imagery: at a discontinuity, boundary conditions (voltage and current continuity, field continuity) impose that part of the incident wave is reflected with coefficient Γ = (ZL – Z0)/(ZL + Z0). There is no literal new generator at the load. The “generator” phrase is pedagogical, not physical.
Q 3 — Does “total re-reflection” *cause* a match?
Maxwell argues that a tuner or network must totally re-reflect the mismatch so that no reverse wave remains toward the source. In modern scattering-parameter language, the goal is S11 = 0 at the transmitter port: the net reflected wave cancels exactly. Whether you call it “total reflection” or “vector cancellation” doesn’t change the physics. In real-world tuners (with loss), the cancellation is approximate, but the operational result is the same: no reverse power seen at the rig end when a match is achieved.
Q 4 — Is conjugate matching universally valid for PAs?
Maxwell applies the conjugate-match theorem broadly, saying that real tuning networks can achieve it even in loaded systems. That holds for linear sources and small-signal amplifiers, but many modern high-efficiency PAs (e.g. Class E, F, switched-mode types) are non-linear, and their optimum load (for efficiency, output power, linearity) is determined via load-pull rather than strict conjugate matching. For tube or small-signal amplifiers, the conjugate-match principle is still a useful guideline.
Q 5 — Do we still accept the 0.4 λ “hemisphere” and 90–100 radials rule?
Maxwell’s model of near-field displacement current as a “squashed hemisphere” with a ground radius of ~0.4 λ, and his recommendation of 90–100 ground radials to that distance, is a valuable rule-of-thumb — but not a one-size-fits-all prescription. Modern EM modeling, field measurements, and real-world installations show that diminishing returns often set in with fewer radials or shorter lengths, depending heavily on soil conductivity, topology, and installation constraints. Elevated radials may require far fewer conductors if properly resonant. However, Maxwell’s admonitions remain valid: radials are not resonant circuits when buried, and ground rods cannot substitute for a proper radial system in HF vertical installations.
Q 6 — What about “forward power increase” via matching?
Maxwell’s derivation shows that through constructive interference (re-reflection), the forward wave can exceed the source’s incident wave — which is correct in steady-state RF theory. In modern terms, we view this through power-wave and S-parameter formalism: energy is exchanged reactively until a new steady-state amplitudes set in. The numeric results align; the key difference is using clearer, standardized terminology.
What Maxwell Got Spot-On
- The behavior of reflections at open or shorted ends (standing wave descriptions) — still textbook correct.
- The clear statement that buried radials are not resonant — still a vital practical insight.
- The warning that low SWR does not guarantee high radiated efficiency — an evergreen caution in HF verticals.
Takeaway
W2DU’s Reflections remains a bridge between ham practice and electromagnetic theory. Just read it with a modern lens:
| Maxwell’s phrasing | Modern equivalent / refinement |
|---|---|
| “Re-reflection causes the match.” | S11 = 0 — net reverse wave cancellation. |
| “Reflection generator.” | Boundary-condition reflection (Γ) rather than an internal source. |
| “Space and line propagation identical.” | Far-field TEM behavior is analogous; near-field differs. |
| “Conjugate match everywhere.” | Optimum load (often via load-pull), not always conjugate in non-linear PAs. |
| “0.4 λ radial hemisphere.” | Empirical guideline; real radial systems depend on soil and layout. |
Keep quoting Maxwell — he’s brilliant. But supplement it with scattering-parameter thinking, field-solver insight, and load-pull awareness.
Technical Sidebar: Maxwell’s Re-Reflection vs Modern S-Parameter View
Here’s a side-by-side conceptual mapping:
- Maxwell’s phrase: “The tuner totally re-reflects the mismatched wave so that no reverse wave remains toward the source.”
- Scattering-matrix equivalent: At Port 1, the reflection coefficient S11 = 0, meaning the vector sum of incident and reflected waves at that port is zero. The network cancels the reflected component by introducing a compensating wave (through its internal reactive structure), not by a new “generator.”
- Energy flow perspective: The mismatch-generated reflected wave does exist initially, but the matching network’s impedance transformation introduces a counter-wave that destructively interferes, leaving no net reverse flow back toward the rig. The “re-reflection” terminology is effectively the network’s internal reactive structure redirecting energy, not mechanically generating it.
- Lossy / non-ideal networks: In practice, internal dissipation means not all reflected energy is redirected—some is dissipated, so S11 never reaches exactly zero. Maxwell’s “total re-reflection” is thus an idealization.
Mini-FAQ
- Is Reflections III still worthwhile? Absolutely — the measurement techniques, intuitive exposition, and tuner behavior remain deeply educational. Just pair it with a modern S-parameter treatment.
- Did Maxwell use network analyzers? No — his era used couplers, SWR bridges, directional couplers, and oscilloscopes. His conclusions were impressively accurate given those constraints.
- How does this apply in SDR / modern transceiver setups? The wave physics is the same. Today we observe reflections, match behavior, and vector cancellation on a VNA or in digital signal-processing systems rather than with slotted lines.
Have feedback, corrections, or installation notes to share? Please contact RF.Guru. For new deep-dive articles and lab notes, subscribe to our updates.