Off-Resonance Parallel-LC Trap Calculator

“Non-resonant trap” is convenient shorthand, but the LC network still resonates. The useful idea is to put that resonance away from either operating band, commonly between them, so the same trap is inductive on the lower frequency and capacitive on the higher frequency. That can help shape current in both wire sections. It does not calculate the antenna for us.

What the Calculator Actually Solves

For an ideal lossless inductor and capacitor connected in parallel, the two-terminal impedance is purely reactive away from resonance:

Below f₀, the ideal network is inductive. Above f₀, it is capacitive. The calculator solves the simultaneous equations X(f_low) = +X_low and X(f_high) = −X_high. With angular frequencies ω₁ and ω₂:

When the two requested magnitudes are equal, these equations reduce to f₀ = √(f_lowf_high). That symmetry is mathematically neat. It is not evidence that equal reactance or the geometric-mean resonance is optimal for the complete antenna.

Where the Required Reactances Come From

The trap sits between two parts of a radiator. Its required impedance depends on the conductor length on each side, its position, wire diameter, height, ground, feed arrangement and the intended resonance or match on both bands. An electromagnetic model can solve the complete geometry and report the series load needed at the chosen position. A measured prototype can also be adjusted iteratively with a characterized load.

The calculator cannot infer those reactances from the band names alone. A value of 120 Ω is therefore not a recommendation. It is merely the default input used to demonstrate the equations. If the antenna model requires +j496 Ω at the lower frequency and −j1249 Ω at the higher frequency, those are the values to enter.

For a symmetric centre-fed dipole, use matched traps in corresponding positions on both legs. An end-fed wire has a different current, voltage and return-path system. It may use a related loading idea, but values and positions cannot be transferred from the dipole without modelling that topology, its transformer or tuner and its intended return conductor.

The Wire-Length Output Is Only a Geometry Reference

The tool preserves two useful planning sketches from the original idea: a symmetric dipole with an inner quarter-wave reference on the upper band, and an end-fed wire with an inner half-wave reference. The displayed lengths are scaled free-space references:

• Symmetric dipole: each inner reference is the scaled upper-band quarter wavelength; each outer extension is the difference between the scaled lower- and upper-band quarter wavelengths.
• End-fed wire: the inner reference is the scaled upper-band half wavelength; the outer extension is the difference between the scaled lower- and upper-band half wavelengths.

Those dimensions deliberately do not include the calculated trap reactance. Once the trap is inserted, its loading changes the electrical length, current and terminal impedance. The “wire planning factor” is only a way to scale the unloaded sketch; it is not a coax velocity factor, dielectric certificate or prediction of the final cut. Model and tune the actual insulated wire, trap enclosure, height, bends and surroundings.

A Real Trap Is Not an Ideal Parallel LC

A real inductor has winding resistance, skin and proximity effects, lead inductance, distributed capacitance and self-resonance. A real capacitor has equivalent series resistance and inductance, dielectric loss, voltage coefficient, temperature coefficient and a finite current and voltage rating. Leads, mounting hardware and weatherproofing become part of the network.

Near parallel resonance, circulating current in L and C and the voltage across the network can greatly exceed the terminal current and voltage intuition suggested by a low-power antenna sweep. Finite Q limits the peak impedance and changes both reactance and loss. Parasitics move the measured resonance away from the ideal result.

Measure the assembled trap as a complex two-terminal impedance across and beyond both operating bands. Use a fixture whose open, short and load effects are corrected or de-embedded at the trap terminals. Record test level, temperature, lead geometry and uncertainty. Pair-match traps used in symmetric legs.

Do Not Read Performance from the Component Values

A trap can help create two useful antenna modes, but the calculated L and C do not guarantee resonance, 50 Ω, low SWR, bandwidth, radiation efficiency, gain or a particular pattern. The full wire and return-current distribution produces those results.

Low SWR can coexist with trap, conductor, ground, transformer or feedline loss. A high-Q trap can create substantial component stress. A lower-Q network can broaden the impedance curve by dissipating wanted power. Neither “sharp” nor “broad” is an efficiency verdict.

Use a calibrated VNA to save complex input impedance at a declared reference plane. Measure current magnitude and phase at repeatable positions on both sides of each trap and on the feedline exterior. Compare the installed pattern or field at equal accepted power. Then repeat the measurements after the antenna and traps have reached their operating temperature.

A Defensible Design Sequence

1. Fix the target geometry. Record total length, trap position, conductor diameter, height, ground, feedline and return-current boundary.
2. Solve the complete antenna. Obtain the required complex series impedance at the trap position on both operating bands.
3. Use the calculator for synthesis. Enter the positive lower-band inductive reactance and the magnitude of the upper-band capacitive reactance.
4. Select real components. Include tolerance, Q, self-resonance, ESR, ESL, voltage, RF current, temperature and enclosure effects.
5. Measure each assembled trap. Save R+jX over frequency at its actual terminals and match a pair where symmetry matters.
6. Put the measured network back into the model. Re-optimize wire lengths and trap positions using the real data.
7. Commission the installed antenna. Measure input impedance, conductor and feedline currents, loss or field result, pattern where required and thermal drift.
8. Repeat A/B/A. Restore the starting condition so weather, connector repeatability and cable movement cannot impersonate an improvement.

Primary and Authoritative Technical Sources

• David Birnbaum, K2LYV — Design of a Two-Band Loaded Dipole Antenna
• ARRL — HF Trap Antennas
• Keysight — Impedance Measurement Handbook
• Coilcraft — Testing Inductors at Application Frequencies
• Murata — Capacitor Impedance and ESR Frequency Characteristics
• Lawrence Livermore National Laboratory — Numerical Electromagnetic Code v5
• IEEE 149-2021 — Recommended Practice for Antenna Measurements
• ICNIRP — RF exposure guidelines from 100 kHz to 300 GHz

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