Resonance, Matching, SWR and Efficiency Are Four Different Things

A foundational guide to four antenna properties that are repeatedly confused.

An antenna can be resonant and badly matched. It can be well matched and inefficient. It can have low SWR without being resonant. It can be non-resonant yet radiate efficiently through a low-loss matching network.

Those are not edge cases. They follow directly from the definitions.

Greg Mihran’s July 2026 antenna primer places resonance, impedance, SWR, “matching efficiency”, radiation efficiency and modelled gain beside one another across many slides. Some individual formulas are valid. The recurring problem is that proximity on a slide encourages one quantity to be treated as evidence for another.

A low analyser trace can confirm a match at its calibration plane. It cannot confirm the modelled efficiency printed elsewhere. A zero-reactance point can establish resonance at a stated port. It does not establish 50 Ω, maximum current, minimum impedance or maximum radiation efficiency. A matching transformer can make a transmitter see 50 + j0 Ω without changing where the accepted watts ultimately go.

The four questions

The ARRL glossary keeps the first and third definitions separate: antenna resonance is where feedpoint impedance contains only resistance, while SWR measures the impedance match between a feedline and its load. They can coincide in one well-designed antenna. That does not make them the same property.

Put the reference plane before the number

Every impedance, SWR and efficiency statement needs a boundary. Consider the complete power path:

A meter at the transmitter sees the system looking into the cable. A VNA calibrated at the antenna connector sees the load at that connector. A NEC source placed directly on a wire sees the model source port. A transformer’s input and output are different planes with different impedances.

Moving the plane can change the displayed resistance, reactance, reflection coefficient and SWR. It does not magically change the physical antenna. A meaningful statement therefore sounds like this:

• “The measured impedance is 49 + j2 Ω at the antenna-side connector after feedpoint calibration.”
• “The transmitter sees 1.1:1 SWR at the tuner input.”
• “The model predicts 91% radiation efficiency at its ideal source port, excluding the external transformer.”

Without the plane, each number is incomplete.

Resonance means X = 0—nothing more

Write the input impedance at the declared plane as:

Slide 13 of the primer writes impedance correctly as R ± jX, but then uses 50 + j0 Ω as the “perfect” impedance and calls this resonant. That example is both resonant and matched to a 50 Ω line. It is a special intersection of two conditions, not the definition of resonance.

The primer itself later supplies the counterexample. Slide 82 marks a 0.47-wavelength monopole as resonant because X = 0, while giving its resistive feedpoint impedance as approximately 2,450 Ω. That antenna is resonant but would have roughly 49:1 SWR if connected directly to an ideal 50 Ω line.

This also contradicts slide 14’s general statement that antenna impedance is at its minimum at resonance. A simple series RLC circuit has minimum impedance at its series resonance. An antenna is a distributed electromagnetic structure and can exhibit low-resistance series resonances, high-resistance antiresonances and multiple resonant points. One series-RLC sketch cannot be promoted into a universal antenna law.

Resonance does not maximise radiation efficiency

Slide 14 also says that “efficiency (current in the circuit)” is at its maximum at resonance. This combines a current-amplitude statement with an efficiency ratio.

For a fixed voltage applied to a simple series RLC circuit, current is highest when the net reactance cancels and the impedance magnitude is lowest. But radiation efficiency is not current. In a linear antenna:

If drive level doubles, radiated and dissipated powers both scale. The ratio does not become better merely because the current is larger. Tuning out reactance can improve power delivery from a particular source. It does not prove that a larger fraction of the accepted power becomes radiation.

A short loaded vertical can be resonated and matched while losing much of its accepted power in the loading coil and return path. A full-size but non-resonant doublet can be used efficiently through a low-loss matching network. Resonance is often convenient. It is not a certificate of efficiency.

Matching is impedance transformation

For a real line impedance Z0, the load reflection coefficient is:

A transformer or matching network changes the impedance presented at its input. That is exactly what it is supposed to do. Slide 83 recognises that the approximately 2,450 Ω end-fed half-wave point needs a large impedance transformation before it can be connected conveniently to 50 Ω coax.

The same slide says a 49:1 or 56:1 unun provides “optimal SWR” for that 2,450 Ω point. For an ideal fixed 2,450 Ω load, 49:1 transforms exactly to 50 Ω, while 56:1 transforms to 43.75 Ω. Either ratio may prove preferable with a real, complex, frequency-dependent antenna and a non-ideal transformer. They cannot both be the exact ideal transformation of the same fixed resistance. The installed impedance and transformer characteristics decide.

But the match says nothing by itself about transformer loss, antenna loss or radiation pattern. A lossless transformer can produce a perfect match without changing the radiator’s radiation efficiency. A lossy transformer can also produce a perfect match while reducing complete-system efficiency.

This is why a tuner does not generally “make the antenna resonant”. It creates the required input impedance at the tuner’s radio-facing port. The antenna and the line on the far side retain their own impedance and standing-wave conditions. The ARRL tuner explanation makes the boundary explicit: lowering SWR at the radio does not change the SWR between tuner and antenna.

A conjugate match for maximum available power from a complex source is another matching problem. It should not be silently equated with a zero-reflection 50 Ω travelling-wave match.

SWR is a reflection number

SWR is calculated from the magnitude of the reflection coefficient:

These standard relationships are given in NIST Technical Note 1098. They explain the percentages printed beside the analyser sweeps on primer slides 51, 104 and 109.

Slide 51 calls 1.10:1 “99.8%” and 1.50:1 “96.0%”. The arithmetic is essentially correct for the fraction of incident power accepted at the measurement plane. It is mismatch efficiency, not radiation efficiency.

Slide 155 similarly says that SWR at or below 1.50:1 implies 96% power delivered to the antenna structure. More precisely, it means 96% of incident power is accepted at the stated port under the single-port relationship. If the meter is at the transmitter and the intervening feedline is lossy, that plane is not the physical antenna terminal, and line attenuation can make the transmitter-end SWR look better.

Minimum SWR is not necessarily resonance

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

Both resistance and reactance change with frequency. The closest approach to 50 Ω can therefore occur where reactance is not zero. The two frequencies often sit near one another in a simple, well-adjusted antenna, but they need not coincide.

An SWR-only screenshot cannot locate resonance unless the complex impedance or reactance is also shown. Calling the bottom of every SWR dip “resonance” discards half of the impedance measurement.

Reference impedance matters: the primer proves it

Slides 95 and 96 are especially useful because they expose a reference-plane issue numerically.

• Slide 95 gives the Challenger model an average impedance near 193 Ω and SWR 1.04. That SWR is evidently referenced to approximately 200 Ω, before its 4:1 impedance transformation.
• Slide 96 gives the Dominator model approximately 2,442 − j3 Ω on 17 metres and SWR 1.00. That SWR is evidently referenced to approximately 2,450 Ω, before its 49:1 or 56:1 transformer.
• Slides 104 and 109 show field SWR measured by a 50 Ω analyser after the physical matching hardware.

All are legitimate quantities if labelled with their reference impedance and plane. They are not interchangeable validations. A good model match at 200 or 2,450 Ω does not measure the physical transformer’s loss. A good 50 Ω field match after the transformer does not validate the modelled radiation efficiency.

Slide 91 separately lists transformer and choke losses. That is useful information. To obtain complete-system efficiency, compatible efficiencies must be combined across a clearly defined path rather than placed in separate columns and left for the reader to conflate. Using slide 91’s own aggregate component losses, simple compatible multiplication would place the Challenger near 85–87% and the Dominator near 78–88% before feedline and mismatch loss—not at their respective 94.3% and 99.5% structural figures.

There is also an unresolved documentation issue: slides 87 and 91 quote different loss values for the same LDG and Palomar 4:1 products. That may reflect different frequencies, revisions or methods. The primer does not identify the reason. A loss number needs frequency, power, fixture, termination and measurement method before it can be carried into a system budget.

Radiation efficiency begins after power is accepted

The NIST efficiency paper explains the IEEE distinction directly. Radiation efficiency uses accepted power as its denominator:

NIST gives a deliberately extreme example: an antenna accepts only 5% of incident power, then radiates half of what it accepts. Its radiation efficiency is 50%, while its total efficiency relative to incident power is 2.5%. Neither number is wrong. They answer different questions.

If the boundary moves upstream to include feedline, tuner, transformer and connector loss, define a complete-system efficiency:

The word “efficiency” without numerator, denominator and reference plane is not a complete engineering specification.

Two identical SWR readings can hide opposite antennas

A one-port VNA sees total input impedance. Radiation and heat both appear in the real part. Consider two hypothetical antennas, each adjusted to 50 + j0 Ω:

Their one-port impedance, reflection coefficient, return loss and SWR are identical. The accepted watts go to very different destinations. A 50 Ω dummy load is the limiting demonstration: an excellent match and almost no intended radiation.

This is why the ARRL warns explicitly that 1:1 SWR does not establish antenna efficiency.

Loss can improve the SWR curve

Suppose an idealised resonant radiator presents 10 Ω of radiation resistance and negligible loss. Connected directly to 50 Ω line, it has 5:1 SWR but nearly 100% radiation efficiency for the power it accepts. Add 40 Ω of series loss and the input becomes 50 + j0 Ω:

• SWR improves from 5:1 to 1:1.
• Radiation efficiency falls from nearly 100% to 20%.
• The analyser trace looks better while the antenna radiates a smaller fraction of its accepted power.

Real antennas are more complicated than this thought experiment, but the principle is fundamental. Dissipation damps resonances and often broadens a low-SWR curve. Wide SWR bandwidth may result from a well-designed broadband radiator, from loss, or from both. Bandwidth is not an efficiency measurement.

The resistance formula is conditional, not a VNA trick

Slide 15 gives the familiar series-equivalent expression:

That bookkeeping is valid when both equivalent resistances are known for the exact system and referred to the same current. The feedpoint measurement supplies only their sum. It does not label one portion “radiation” and the other “ground”.

Slide 15 also describes radiation resistance as “the total power radiated”. The units expose the error: radiation resistance is measured in ohms; radiated power is measured in watts. Radiation resistance is an equivalent quantity defined through a specified reference current, for example Rrad = Prad / Iref2 with RMS current. Move the current reference to a lower-current point and the numerical resistance can become much larger without creating extra radiated power.

Slide 17 nevertheless calculates ground loss by subtracting a fixed 37 Ω from measured feedpoint resistance. Slide 85 similarly treats an approximately 2,450 Ω end-fed input value as radiation resistance and combines it with an assumed 12 Ω loss to obtain 99.5%.

A large port-referred radiation resistance is therefore not automatically “better resistance”. Efficiency depends on the correctly referred ratio of radiated power to total accepted power. The approximately 2,450 Ω end-feed value occurs at a low-current, high-voltage point; its size alone cannot prove superior efficiency.

Those results require the actual radiation resistance and all loss terms to have been established independently. Input resistance alone does not do that. Rudy Severns addresses the quarter-wave shortcut directly in Ground-System Performance Part 4: radiation resistance changes with the radial system, so subtracting a fixed ideal value from a limited real installation should not be assumed valid.

What the primer’s evidence actually supports

The issue is not that SWR, resonance or modelling are unimportant. Each is useful evidence when attached to the claim it can actually support.

The field minima also differ from some model target frequencies: slide 42 models 14.250, 21.350 and 51.000 MHz, while slide 51 shows minima near 14.235, 21.245 and 52.050 MHz. That is not unusual and does not condemn the antenna. It demonstrates why the field traces are independent match measurements rather than experimental confirmation of every modelled quantity.

Four counterexamples worth remembering

Use the measurement that answers the claim

How to write the conclusion correctly

• Write “resonant at 14.20 MHz” only when X = 0 is shown at the stated plane.
• Write “matched to 50 Ω at the transformer input” when that is what the measurement establishes.
• Write “measured SWR is 1.12:1” without translating it into radiation efficiency.
• Write “the model predicts 91% structural radiation efficiency” when it is a numerical result with stated exclusions.
• Write “measured radiation efficiency” only when an appropriate efficiency measurement and uncertainty are supplied.
• Write “complete-system efficiency” only after defining the starting connector and including feed-network losses.

Takeaways you can trust

• Resonance means zero net reactance at a stated reference plane.
• A resonant resistance does not have to be 50 Ω.
• A matching network changes the impedance presented at its input.
• SWR describes mismatch relative to a stated line impedance.
• The 99.8% and 96.0% values beside the primer’s SWR plots are accepted-power percentages, not radiation efficiencies.
• Radiation efficiency is radiated power divided by accepted power.
• Total antenna-port efficiency can include mismatch; complete-system efficiency can additionally include feedline and matching loss.
• A one-port VNA cannot separate radiation resistance from loss resistance.
• Loss can flatten and broaden an SWR curve.
• Low SWR is valuable operational evidence, but it is not a measurement of gain or efficiency.

In Summary

The primer’s most useful starting point is its own impedance expression: Z = R + jX. The trouble begins when four different questions are compressed into one story.

Resonance asks whether X is zero. Matching asks how that complex impedance relates to a source or line. SWR converts reflection magnitude into a convenient ratio. Radiation efficiency asks what happens only after power has crossed the antenna-port boundary.

The primer’s slides actually contain the evidence needed to see the distinction. Its resonant 2,450 Ω monopole is not a direct 50 Ω match. Its 200 Ω and 2,450 Ω model SWRs are not the later 50 Ω analyser measurements. Its SWR-derived 99.8% is mismatch acceptance, not its separate 90.8%, 94.3% or 99.5% modelled structural efficiency.

Keep the definitions, reference planes and power denominators visible. Many apparent antenna mysteries disappear immediately.

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