LC Resonance Calculator

An LC resonant circuit is formed whenever an inductor (L) and a capacitor (C) are connected together, either in series or in parallel. At the resonant frequency, the inductive reactance (XL = 2πfL) and capacitive reactance (XC = 1/2πfC) are equal in magnitude and cancel each other. In a series circuit this cancellation produces minimum impedance — a current maximum — while in a parallel circuit it produces maximum impedance — a current minimum and voltage maximum. This dual behavior is the foundation of nearly every frequency-selective circuit in amateur radio.

Antenna traps are the most visible application of LC resonance in HF amateur radio. A trap is a parallel LC circuit inserted in a dipole or vertical antenna at a specific point along the element. At the trap's resonant frequency, the parallel LC presents very high impedance, electrically isolating the outer section of the antenna and making the element behave as a shorter resonant antenna for that band. On lower frequencies, the trap falls off resonance and appears as an inductance, loading the now-shortened inner element and allowing it to resonate at a lower frequency. Multi-band trap dipoles and trap verticals use two, three, or four traps to cover multiple HF bands from 10m through 80m on a single antenna.

Antenna Tuning Units (ATUs) use variable LC networks — L-networks, T-networks, and pi-networks — to transform the feedpoint impedance of a non-resonant antenna to the 50 Ω required by the transceiver. Calculating the component values for a specific impedance transformation at a specific frequency requires knowing the LC resonance relationships. ATU designers also use the Q factor to predict insertion loss: a low-Q inductor in the ATU wastes power as heat, while a high-Q coil passes more energy to the antenna. Coil forms, wire gauge, and winding pitch all affect Q.

Loading coils for short antennas, crystal filter equivalent circuits, intermediate frequency (IF) filters in superheterodyne receivers, and RF chokes in bias tees all rely on precise LC resonance calculations. A 160 m mobile antenna that is physically only 2 m tall requires a series loading coil to resonate the shortened element at 1.85 MHz. The exact inductance depends on the antenna's natural capacitance and the target resonant frequency — the same calculation this tool performs. Understanding LC resonance at the component level is a core competency for building and optimising amateur radio circuits.

When building antenna traps for field use, use silver-mica or NP0/C0G ceramic capacitors rather than general-purpose disc ceramics or electrolytic capacitors. Silver-mica capacitors have excellent Q, negligible temperature coefficient, and stable capacitance under voltage and current stress — all critical for an antenna trap that may be at high voltage during transmit. Avoid polystyrene and polyester film capacitors in traps as they cannot handle the RF voltage across a high-Z parallel resonant circuit at QRO power levels.

Measure your coil's actual inductance with an LCR meter or an antenna analyser in reactance mode before calculating the required capacitance. Inductance depends on winding pitch, core permeability, and proximity to conductive materials — a coil wound on a PVC form inside an aluminium housing may have 15–20% different inductance from the same coil in free air. Recalculate the required capacitance from the measured L, then verify the resonant frequency with the analyser before installation.

Q factor degrades rapidly at VHF and above as skin depth in the wire decreases and distributed capacitance becomes significant. Inductors that perform well at 14 MHz with Q > 200 may drop to Q < 50 at 144 MHz. For 2 m and higher band LC circuits, use silver-plated wire, large-diameter low-turn coils, and air-core construction to maximise Q. At 432 MHz and above, cavity resonators and microstrip lines typically replace lumped-element LC circuits because achieving useful Q values with discrete coils becomes impractical.