Resonance, Match, SWR and Efficiency: Four Different Questions

An antenna can be resonant and badly matched. It can be well matched and inefficient. It can be non-resonant yet radiate efficiently through a low-loss matching network. Those are not awkward exceptions; they follow from the definitions.

This is why I am looking closely at Greg Mihran, KJ6ER’s Antennas Primer 1: Antenna Fundamentals, July 2026 edition. Across its slides, resonance, impedance, SWR, matching-component loss, radiation efficiency and modelled gain appear side by side. Several individual formulas are useful. The trouble starts when a result for one quantity appears to settle a different question.

The clearest counterexample is already in Greg’s presentation: its resonant 2,450 Ω monopole is nowhere near a direct 50 Ω match. Its 99.8% figures beside SWR plots concern power acceptance, not radiation efficiency. We can follow those examples through the station and see exactly where the meanings separate.

The slide references below refer to that July 2026 edition, not to any later revision. This is a disagreement with specific engineering inferences, not a claim that the antennas cannot make good contacts.

The Four Questions

The ARRL glossary keeps resonance and SWR separate. The active IEEE 145-2025 antenna terminology standard supplies the current formal framework for antenna and antenna-system terms. A practical article should still state its exact numerator, denominator and reference plane rather than rely on the word “efficiency” alone.

Put the Reference Plane Before the Number

Consider the complete path:

A meter at the transmitter sees the impedance looking into everything downstream. A VNA calibrated at the antenna connector sees the load at that connector. A NEC source sees the model at its numerical source segment. The input and output of a transformer are different planes and normally present different impedances.

A complete result sounds like one of these:

• “49 + j2 Ω at the antenna-side connector after feedpoint calibration.”
• “1.10:1 SWR at the tuner input, referenced to 50 Ω.”
• “91% modelled structural radiation efficiency at the wire source, excluding the external transformer and feedline.”

Move the reference plane through a line or matching network and the displayed resistance, reactance and reflection coefficient can change. The physical radiator has not magically changed; the network between the plane and radiator has been included or excluded.

The Primer’s Own Resonant Counterexample

Slide 13 starts correctly with complex impedance, then gives 50 + j0 Ω as the desired condition for 50 Ω coax and identifies it as resonant. That example is valid: it is both resonant and matched. But the remaining resistance at resonance might instead be 10 Ω, 500 Ω or several thousand ohms. Zero reactance does not specify the resistance.

Now turn to slide 82. Its ideal-ground monopole example, attributed there to Steve Yates, AA5TB, marks a zero-reactance point near 0.47 wavelength and about 2,450 Ω. By the primer’s own definition, that point is resonant. Connected directly to an ideal 50 Ω line, however, 2,450 + j0 Ω gives approximately 49:1 SWR. No contradiction exists in the antenna; the contradiction appears only if resonance is used as shorthand for a 50 Ω match.

This also supplies a counterexample to slide 14’s general claim that antenna impedance reaches its minimum at resonance. The high-resistance zero-reactance point on slide 82 is not a minimum-impedance series resonance.

A series-RLC analogy describes one kind of resonance, not every distributed antenna. Real antennas can exhibit low-resistance series resonances, high-resistance parallel or antiresonant conditions and multiple zero-reactance frequencies. Zero reactance therefore does not universally mean minimum impedance magnitude.

More Current Is Not More Efficiency

Slide 14 goes further: it identifies efficiency with current in the circuit and says this is maximised at resonance. That is where a helpful circuit analogy becomes an incorrect efficiency definition.

For a fixed voltage applied to a simple series RLC circuit, current is largest when the reactances cancel and impedance magnitude is minimum. Radiation efficiency is not current amplitude:

In a linear system, raising drive scales radiation and dissipation together; it does not improve their ratio. Tuning out reactance can improve power transfer from a particular source. It does not prove that a larger fraction of accepted power becomes radiation.

A short loaded vertical can be resonant and matched while losing much of its accepted power in a coil, conductor and return path. A non-resonant full-size doublet can radiate efficiently when its feedline and matching network have low loss. Resonance is often convenient, but it is not an efficiency certificate.

For teaching, this distinction matters. Resonating a loaded antenna may let the transmitter deliver more power. Reducing coil or ground loss may make it radiate a larger fraction of the power it accepts. Those are two different improvements, and neither needs to be hidden inside the word “resonance.”

Matching Is an Impedance Relationship

For a real characteristic or reference impedance Z₀:

Zero reflection occurs when Z_L equals Z₀. For ordinary 50 Ω coax, the load at that plane must therefore be 50 + j0 Ω.

Slide 83 recognises the next design task: transforming the approximately 2,450 Ω end-fed impedance to something convenient for coax. A transformer or tuner changes the impedance presented at its input. That is its job.

The slide groups 49:1 and 56:1 ununs together as suitable matches. For an ideal fixed 2,450 Ω load, the arithmetic is more specific: a 49:1 impedance ratio produces 50 Ω; 56:1 produces 43.75 Ω, or about 1.14:1 SWR on an ideal 50 Ω line. A real complex antenna and non-ideal transformer may favour either ratio. But the two cannot both be the exact ideal transformation of the same fixed resistance.

The useful engineering choice is the ratio and network that gives acceptable power transfer with low loss and adequate operating margin for the actual load. A match alone does not answer that whole question. A lossless network can match an inefficient radiator without repairing its radiation efficiency. A lossy network can produce an excellent match while making complete-system efficiency worse.

This is why an antenna tuner normally does not make the remote radiator resonant. The ARRL tuner explanation draws the boundary correctly: the tuner can lower SWR on the radio side while the line between tuner and antenna retains its own standing waves.

The 99.8% Figure Is Match Acceptance

NIST Technical Note 1098 gives the standard relationships for a real line reference:

Slides 51, 104 and 109 put percentages beside the PERformer, Challenger and Dominator SWR sweeps. At 1.10:1, the displayed 99.8% is essentially correct rounding: about 99.77% of the incident power is accepted at that plane. At 1.50:1, the accepted fraction is 96.00%. The arithmetic is not the problem. Calling it radiation efficiency would be.

Slide 155 takes 1.50:1 SWR as implying 96% delivery to the antenna structure. That needs a boundary. If the meter is at the transmitter, the downstream network includes the feedline, matching hardware and antenna. Some accepted power becomes line or component heat before reaching the radiator. The 96% describes net acceptance at the meter’s plane, not a measurement of radiated watts.

Nor does that SWR threshold alone settle whether a tuner is useful. A tuner adds loss, while a particular transmitter may reduce output into a particular mismatch. Compare those effects in the actual station. There is no need to chase 1:1 for its own sake, but an SWR percentage is not a complete station power budget.

On a lossy line, the magnitude of the reflected wave is attenuated on its return trip, so transmitter-end SWR can look better than load-end SWR. The plane must accompany the value.

Minimum SWR Is Not Necessarily Resonance

The resonant frequency solves X(f) = 0. The minimum-SWR frequency minimises:

Because both resistance and reactance change with frequency, the closest approach to 50 Ω can occur where reactance is not zero. The two frequencies often lie close together in a simple adjusted antenna, but they do not have to coincide.

An SWR-only screenshot therefore cannot locate resonance. Complex impedance—or at least the reactance trace—is required. The primer’s field sweeps are useful match measurements; the bottom of each dip is not, by itself, a measurement of zero reactance.

The Model Tables Are Not 50 Ω Analyser Readings

The Challenger and Dominator tables make the reference-impedance issue concrete:

• Slide 95, Challenger, 20 m: the model lists 193 − j1.78 Ω and SWR 1.04. Calculating the reflection gives about 1.037:1 against 200 Ω, consistent with a 200 Ω reference before a nominal 4:1 transformer—not a direct 50 Ω match.
• Slide 96, Dominator, 17 m: the model lists 2,442 − j3.33 Ω and SWR 1.00. Against 2,450 Ω this gives about 1.0035:1, consistent with the displayed rounded value—not a direct 50 Ω match.
• Slides 104 and 109: the field analyser measures the assembled antenna through its matching hardware. That is a different port from the model’s high-impedance source.

The reference impedances above are inferred from the displayed arithmetic; they should be stated explicitly with the model results. Changing the SWR reference is legitimate. Comparing results without naming it is where readers lose the thread.

A good model match at 200 Ω or 2,450 Ω does not measure physical transformer loss. A good field match after the transformer does not validate modelled radiation efficiency. Likewise, the low SWR and average 90.8% efficiency in the PERformer model table on slide 42 are separate model outputs; the field sweeps on slide 51 cannot turn both into measured facts.

The Loss Budget Changes the Comparison

Greg does list matching-component losses separately on slide 91. That is useful, because the matching hardware is not lossless decoration. The Challenger’s 94.3% and Dominator’s 99.5% average structural figures on slides 95 and 96 are therefore not the efficiencies of the complete fed systems.

Here is an illustrative cascade using the primer’s own stated numbers. Assume the structural averages and slide 91’s aggregate attenuation apply at compatible operating conditions and boundaries. Multiplying by 10^−L/10, with L the positive attenuation in dB, gives:

These are not new measurements or a band-by-band ranking. The model averages cover different band sets, and the component losses need compatible frequency, load, power, temperature and port conditions before they can form a real system result. The calculation shows why the omitted boundary matters: under those assumptions, the smaller structural-efficiency figure can beat the larger one once feed-network loss is included. A structural percentage alone cannot choose the better station.

Slides 87 and 91 also give different LDG and Palomar 4:1 attenuation figures: 0.50 versus 0.34 dB, and 0.15 versus 0.24 dB. Different tests, conditions or hardware revisions could explain that. The slides do not make the distinction clear enough to carry those figures into one measured comparison. Keep the useful disclosure of loss; do not promote unmatched entries into precision that the record does not establish.

Radiation Efficiency Starts After Acceptance

The NIST work by Holloway and colleagues on radiation and total efficiency keeps accepted power separate from the upstream power available to the antenna. For incident and accepted travelling-wave powers at a port with a real reference impedance, use:

For a deliberately extreme arithmetic example, an antenna that accepts only 5% of incident power and radiates half of that accepted power has 50% radiation efficiency but only 2.5% total efficiency relative to incident power. Neither result is wrong. They answer different questions.

If the boundary moves upstream, define it explicitly:

That result can include mismatch, tuner, feedline, transformer, choke, conductor and ground losses. “Efficiency” without a numerator, denominator and boundary is incomplete.

Identical SWR Can Hide Opposite Antennas

A one-port VNA sees the total impedance. Radiation and heat both contribute to its real part. These hypothetical antennas have identical impedance, Γ, return loss and SWR, yet their accepted watts go to different destinations. A dummy load is the limiting example, which is why the ARRL warns that 1:1 SWR does not establish antenna efficiency.

Loss Can Make the SWR Curve Look Better

Suppose an idealised resonant radiator presents 10 Ω radiation resistance and negligible loss. Directly on a 50 Ω line it has 5:1 SWR but nearly 100% radiation efficiency for the power it accepts. Add 40 Ω series loss:

• input impedance becomes 50 + j0 Ω;
• SWR improves from 5:1 to 1:1; and
• radiation efficiency falls to 20%.

Real broadband antennas are more complex, but the principle is fundamental. Dissipation damps resonance and can broaden a low-SWR curve. Wide bandwidth may come from a genuinely broadband structure, loss, or both. SWR bandwidth is not an efficiency measurement.

The Resistance Formula Needs the Same Current Reference

Slide 15 gives the familiar resistance-ratio formula. It is useful bookkeeping, not a way to make a VNA separate heat from radiation:

This expression is valid only when both equivalent resistances describe the same system and are referred to the same RMS current. A feedpoint measurement supplies their sum; it does not label which ohms represent radiation and which represent ground, coil or conductor heat.

Slide 15’s description also equates radiation resistance with radiated power. The units expose the problem: resistance is measured in ohms; power is measured in watts. Radiation resistance is an equivalent quantity defined by R_rad,ref = P_rad/I_ref² for RMS reference current. Move that reference to a lower-current point and the numerical resistance can become much larger without creating more radiated power.

That is the missing condition in slide 85’s 2,450/(2,450 + 12) calculation. Its 99.5% arithmetic is correct if both values are independently established equivalent resistances referred to the same current for the complete system. A high end-feed resistance and an assumed counterpoise loss do not establish those conditions by themselves. The distinction is developed further in EFHW efficiency and the high-feedpoint-resistance argument.

Slide 17 similarly subtracts a fixed 37 Ω radiation resistance to build its surface-radial loss comparison. Rudy Severns, N6LF, explains the limitation directly in Ground-System Performance, Part 4: radiation resistance itself changes with the radial and ground system. The fixed-ideal-value subtraction can be a useful approximation for a sufficiently large ground system; it is not a universal loss meter for small amateur installations.

What the Primer Demonstrates—and What It Does Not

The July primer contains useful impedance examples, models and field sweeps. My objection is to the jump between them. A low-SWR field result establishes a useful match; it does not measure the structural efficiency printed in a model table. A model efficiency is a result for its assumptions; it does not automatically include the external matching hardware.

That is also why a field SWR minimum need not land exactly at a model’s target frequency. For example, slide 42 targets 14.250, 21.350 and 51.000 MHz, while slide 51 shows minima near 14.235, 21.245 and 52.050 MHz. Installation differences are expected. They neither condemn the antenna nor validate every other model output.

Use the evidence that actually answers each claim:

A VNA can participate in several sophisticated efficiency methods. The boundary is precise: one-port S11 or SWR alone cannot separate radiation from dissipation or establish absolute efficiency.

Takeaways You Can Trust

• Resonance means zero net reactance at a stated plane.
• A resonant resistance does not have to be 50 Ω.
• A network can match a non-resonant load without changing the remote radiator’s resonance.
• SWR describes reflection relative to a stated line impedance and plane.
• 1 − |Γ|² is the accepted fraction at that plane—not radiation efficiency.
• Radiation efficiency is radiated power divided by accepted antenna-port power.
• A one-port VNA measurement cannot separate radiation resistance from loss resistance.
• Loss can flatten and broaden an SWR curve.
• Low transmitter-side SWR does not prove low voltage, current or loss elsewhere in the system.

The Useful Conclusion

The best starting point is Greg’s own Z = R + jX expression. The primer’s later examples then show why resonance, a 50 Ω match, low SWR and radiation efficiency must remain separate. Its resonant 2,450 Ω point is not a direct coax match. Its model SWRs use different impedance references from the field analyser. Its 99.8% beside an SWR trace is not a measurement of radiated power.

For a real station, I would choose the arrangement that delivers the required radiation pattern with the lowest practical complete-path loss—not the one with the prettiest isolated SWR or structural-efficiency number. A low-loss matching system can make a non-resonant radiator an excellent choice. A high-efficiency wire model can lose its apparent advantage in the transformer and feedline.

That is the engineering disagreement: the July 2026 primer’s match measurements and structural model percentages do not, by themselves, establish the complete-system efficiency comparison. Keep the source planes, the loss mechanisms and the power denominators attached to the numbers. Then the antenna can be judged for what it actually does, not for what a neighbouring percentage seems to promise.

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