Frequency Means in Off-Resonance Trap Design

The attractive idea is simple: choose a trap frequency between two amateur bands, let the network look inductive on the lower band and capacitive on the upper band, then use those opposite reactances to shape the same wire into two useful radiators. The trap still has a resonance; it is merely kept away from the operating bands.

I use frequency means to organise that first calculation. I do not use them as substitutes for an antenna model or a measurement. A mean can centre two numbers according to one mathematical rule. It knows nothing about wire length, trap position, height, ground, current phase, component loss or the radiation pattern we actually want.

The Three Useful Means

Let the lower and upper design frequencies be f1 and f2, with both expressed in the same unit.

The arithmetic mean is centred by equal frequency offsets: fA − f1 = f2 − fA. The geometric mean is centred by equal frequency ratios: fG/f1 = f2/fG. The harmonic mean is the reciprocal-domain counterpart of the arithmetic mean and weights the result toward the lower frequency.

A “log midpoint” between two positive frequencies is simply their geometric mean. It is not a fourth independent choice.

Why the Geometric Mean Is Appealing

Amateur bands are commonly discussed by ratios and octaves. For two frequencies with a 2:1 ratio, the geometric mean lies at the same multiplicative distance from each one. That reciprocal symmetry makes it a natural initial trap-resonance candidate when the two bands are approximately octave related.

But equal ratios do not imply equal trap reactance. For an ideal lossless parallel LC network used as a two-terminal series element:

Below f0, the network is inductive. Above f0, it is capacitive. Its reactance is nonlinear with frequency, and a real network adds resistance, parasitic capacitance and self-resonance effects. Equal frequency ratios around f0 therefore do not guarantee equal reactance magnitudes or equal currents in the antenna sections.

What the Arithmetic Mean Can—and Cannot—Represent

The arithmetic mean is useful when equal linear frequency offsets are the relevant comparison or when exploring a geometry with a separate physical-symmetry constraint. It does not create physical symmetry. Equal wire lengths come from the geometry; equal and opposite currents come from the full electromagnetic system.

For widely separated frequencies, the arithmetic midpoint can sit far above the geometric midpoint. That changes the trap reactance on both bands and therefore changes the wire lengths required for the final solution. Neither midpoint is “more physical” without a declared objective.

As a deliberately stark example, the arithmetic mean of 3.6 and 28.5 MHz is 16.05 MHz. That calculation is correct, but it does not establish that a trap at 16.05 MHz will optimise an 80-to-10-metre vertical, split its conductors symmetrically in the electrical sense, or preserve a desired low-angle pattern. Those are antenna results, not properties of the averaging formula.

The Harmonic Mean Is Another Starting Coordinate

The harmonic mean can be helpful when a problem is naturally expressed through reciprocal quantities. It always lies below the geometric and arithmetic means for two unequal positive frequencies. That position may produce a useful pair of reactances in a particular antenna, but “impedance sensitive” is not a general proof for choosing it.

The honest comparison is to calculate or measure R + jX for each candidate network at both operating frequencies, insert those values into the same antenna geometry, and inspect the resulting currents, feed impedance, pattern and loss. A label on the mean does not predict that outcome.

Symmetry Has Several Meanings

Mechanical symmetry, geometric symmetry, feed-current balance, trap-pair matching and radiation-pattern symmetry are related but different. A centre-fed dipole may have equal-length legs while unequal surroundings drive common-mode current. Two traps may share a nominal resonance while component tolerances give different resistance and phase. A perfectly symmetric model can still develop multiple lobes when its conductors become electrically long.

For that reason, a frequency mean cannot “ensure current symmetry.” At most it can preserve one chosen frequency relationship in the initial design. Verify symmetry through current magnitude and phase on corresponding conductor positions, feed-line exterior current, and the installed azimuth and elevation patterns.

Choose the Objective Before the Mean

There is no single scalar called antenna performance. Before changing the trap frequency, decide what the design must protect:

• Current use: whether the outer sections should carry substantial current on one or both bands.
• Pattern: azimuth and elevation shape, nulls, lobe count and takeoff-angle region at the installed height.
• Efficiency: accepted power converted to radiation rather than heat in the trap, conductors, ground and matching network.
• Match: complex feedpoint impedance across a stated band and at a declared reference plane.
• Stress: coil and capacitor current, voltage, temperature, corona clearance and drift at a stated waveform, power and duty cycle.
• Robustness: sensitivity to component tolerance, geometry, nearby objects, soil and wet weather.

A design can improve one objective while making another worse. A lower SWR can accompany greater loss. Current continuing past a trap can add radiation in one direction and cancellation in another. A broad impedance response can coexist with a pattern that changes rapidly across the band.

Model the Network as It Will Be Built

Begin with the arithmetic, geometric and harmonic candidates and calculate LC values for each. Do not stop at the ideal resonance equation. Measure the actual two-terminal complex impedance over all target bands with a suitable fixture and calibration or de-embedding. Pair-match the two networks when the antenna uses one in each leg.

In a NEC-class antenna model, divide the conductor at the physical trap position and insert the measured frequency-dependent impedance. Inspect current magnitude and phase along the full conductor, not only feedpoint SWR. Sweep dimensions and trap frequency together, because changing one alters the impedance seen by the other.

An ideal lumped load is a useful first comparison when the trap is electrically small. Coaxial, transformer-coupled or distributed structures may need a more complete equivalent circuit or measured network data. Leads, enclosure capacitance, coil proximity, conductor diameter and weatherproofing can be part of the RF component.

Turn a Promising Model into Evidence

• Characterise the trap pair. Save complex impedance, resonance, resistance, Q and pair mismatch across both bands.
• Freeze the installation. Record conductor dimensions, trap positions, height, ground model, feed line, common-mode control and nearby structures.
• Measure the antenna plane. Save calibrated complex impedance rather than only an SWR screenshot.
• Map current. Compare corresponding positions on both legs and measure the feed-line exterior.
• Separate loss from match. Estimate or measure component dissipation, accepted power, gain or efficiency with a stated method and uncertainty.
• Verify the pattern. Compare modelled and measured azimuth and elevation behaviour; do not infer takeoff angle from SWR.
• Test stress and weather. Record waveform, duty cycle, time, temperature and impedance drift in dry and wet conditions.

Primary and Authoritative Technical Sources

• ARRL, HF Trap Antennas—parallel-tuned traps, between-band design and practical component considerations.
• David Birnbaum, K2LYV, Design of a Two-Band Loaded Dipole Antenna—parallel-LC behaviour below, at and above resonance in a complete radiator.
• Lawrence Livermore National Laboratory, Numerical Electromagnetic Code v5—wire, load, ground, current and pattern modelling.
• IEEE Std 149-2021, Recommended Practice for Antenna Measurements—impedance, pattern, gain, efficiency, site and uncertainty practice.
• Keysight, Impedance Measurement Handbook—complex impedance, component models, fixtures and calibration.
• Coilcraft, Testing Inductors at Application Frequencies—frequency-dependent inductance, Q, loss and self-resonance.
• Murata, Capacitor Impedance and ESR Frequency Characteristics—ESR, ESL, dielectric loss and self-resonance in real capacitors.

Joeri’s Bottom Line

The frequency-mean idea is valuable because it replaces blind trial and error with three explicit starting hypotheses. For octave-related bands I usually examine the geometric mean first. When equal frequency offsets or a physical layout suggest another starting point, I examine the arithmetic or harmonic candidate as well.

Then I stop admiring the midpoint and look at the antenna. The useful trap frequency is the one that survives the complete model and the measurements: current where it helps, loss and stress within limits, a pattern worth using, and acceptable behaviour across both bands.

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