LC Resonance Frequency Calculator

Design and analyze precision constant current sources for LED drivers, battery charging, sensor excitation, and analog biasing. Compute output current, power loss, and compliance voltage with interactive schematic visualization.

Enter any positive inductance and capacitance. Default: 100 µH and 100 pF → ~1.59 MHz resonance.
? FM Radio (100 MHz) : 0.1 µH, 25 pF
? AM Radio (1 MHz) : 250 µH, 100 pF
? WiFi 2.4 GHz : 2.2 nH, 2 pF
? Audio Filter (1 kHz) : 100 mH, 0.253 µF
? IF Transformer (455 kHz) : 680 µH, 180 pF
Local & Private: All calculations run inside your browser. No data is uploaded or stored.

Fundamentals of LC Resonance

An LC circuit (also called a tank circuit, resonant circuit, or tuned circuit) consists of an inductor (L) and a capacitor (C) connected together. At the resonant frequency, the inductive reactance (XL = 2πfL) equals the capacitive reactance (XC = 1/(2πfC)), causing energy to oscillate between the magnetic field of the inductor and the electric field of the capacitor. This phenomenon is fundamental to radio transmitters, receivers, filters, and oscillators.

Thomson's Formula (Resonant frequency):

$$ f₀ = \frac{1}{2π \sqrt{LC}} $$

$$ ω₀ = 2πf₀ = \frac{1}{\sqrt{LC}} ,  T = 2π \sqrt{LC} ,  Z₀ = \sqrt{\frac{L}{C}} $$

Historical & Theoretical Background

The LC resonance principle was first mathematically described by Sir William Thomson (Lord Kelvin) and later refined by Heinrich Hertz and Nikola Tesla in the late 19th century. The formula f = 1/(2π√(LC)) became the cornerstone of wireless communication. In 1891, Tesla demonstrated resonant transformers, and by the early 1900s, LC circuits enabled the first radio receivers. Today, the same equation governs everything from smartphone RF front‑ends to MRI machines and particle accelerators.

Why Use an Interactive LC Calculator?

  • Rapid prototyping: Instantly find component values for desired frequency bands (AM/FM, Wi‑Fi, Bluetooth).
  • Educational tool: Visualize how changing L or C shifts the resonant peak; see reactance equality.
  • Filter design: Bandpass, bandstop, and impedance matching networks rely on accurate LC resonance.
  • Oscillator tuning: Design Colpitts, Hartley, or Clapp oscillators with precise frequency prediction.

Derivation & Calculation Methodology

Starting from Kirchhoff's voltage law in a series LC circuit: VL + VC = 0 → L·(d²q/dt²) + q/C = 0. This differential equation yields simple harmonic motion with angular frequency ω₀ = 1/√(LC). Converting to ordinary frequency: f₀ = ω₀/(2π) = 1/(2π√(LC)). For parallel LC, the same resonant condition occurs because the admittance becomes purely real at ω₀. The calculator uses double‑precision arithmetic to ensure high accuracy, with unit conversions handled internally (H, F base SI units). The characteristic impedance Z₀ = √(L/C) is also provided, useful for impedance matching and Q factor estimation.

Step‑by‑Step Calculation Guide

  1. Enter the inductance value and select its unit (H, mH, µH, nH).
  2. Enter the capacitance value and select its unit (F, mF, µF, nF, pF).
  3. Click 'Calculate Resonance' — the tool converts both to SI base units (Henries and Farads).
  4. The resonant frequency (f₀) is displayed, together with ω₀, period T, and Z₀.
  5. The included LC circuit diagram shows the inductor and capacitor symbolic representation and marks the calculated f₀.

Practical Engineering Examples

Application Frequency Inductor (L) Capacitor (C) Z₀ (Ω)
Medium Wave AM Radio 1 MHz 250 µH 101 pF 1573 Ω
FM Broadcast (88–108 MHz) 100 MHz 100 nH 25.3 pF 62.8 Ω
2.4 GHz Wi‑Fi / Bluetooth 2.45 GHz 2.2 nH 1.9 pF 34.0 Ω
455 kHz IF Transformer 455 kHz 680 µH 180 pF 1944 Ω
Low‑frequency Audio Filter 1 kHz 100 mH 253 nF 628 Ω
Case Study: FM Radio Tuner Front‑End

A typical FM radio receiver uses a variable capacitor (15–30 pF) and a fixed inductor (around 100 nH) to tune the 88–108 MHz band. Using the LC resonance formula: with L = 100 nH, C = 25 pF yields f₀ ≈ 100.7 MHz. By adjusting C from 22 pF to 30 pF the circuit covers the full FM band. This calculator allows rapid verification of tuning range, essential for RF design engineers. The characteristic impedance Z₀ also helps in matching the 50 Ω antenna system, ensuring maximum power transfer.

Beyond Ideal Resonance: Real‑World Effects

Real inductors have series resistance (ESR) and parasitic capacitance; capacitors have equivalent series inductance (ESL). These parasitics cause self‑resonance and alter the effective frequency. The calculator provides ideal resonant frequency, which is accurate for most discrete components up to several hundred MHz. For high‑precision RF work, consider component datasheet specifications. Nevertheless, the Thomson formula remains the fundamental design starting point. Additionally, the Q‑factor (quality factor) can be derived as Q = Z₀ / Rseries for series RLC, influencing bandwidth.

Common Misconceptions & Clarifications

  • Higher L or C always lowers frequency: True: f₀ ∝ 1/√(LC), increasing either component reduces resonant frequency.
  • Resonance exists only in series LC: False: Both series and parallel LC circuits resonate at the same frequency; only the impedance at resonance differs (minimum for series, maximum for parallel).
  • The formula requires ideal components: For most practical circuits, the formula yields excellent approximation if the operating frequency is well below self‑resonance of each component.

Applications Across Disciplines

  • RF & Wireless: Oscillators, mixers, band‑pass filters, antenna matching.
  • Power Electronics: Resonant converters (LLC, Class‑E) for efficient DC‑DC conversion.
  • Medical Devices: MRI RF coils use LC resonance at Larmor frequency.
  • Scientific Instruments: Cavity resonators, NMR spectrometers.

Trusted Electrical Engineering Reference – This tool implements the canonical Thomson formula verified against ARRL Handbook, IEEE standards, and classical electromagnetism texts (J.D. Jackson, “Classical Electrodynamics”; Hayt & Buck, “Engineering Electromagnetics”). Validated with hardware LC measurements. Reviewed by GetZenQuery electronics team, updated April 2026.

Frequently Asked Questions

Both types resonate at the same frequency f₀ = 1/(2π√(LC)). In series resonance, impedance is minimum (ideally zero). In parallel resonance, impedance is maximum (ideally infinite). The calculator gives the resonant frequency valid for both topologies.

Component tolerances (±5%, ±10%) directly shift f₀. For example, if L and C both have +5% error, f₀ shifts approximately -5%. Use precision components (1% or better) for critical RF designs.

The formula works theoretically, but parasitic effects dominate at microwaves. For mm‑wave, use distributed element models (transmission line resonators). However, for many PCB RF designs up to 3‑5 GHz, discrete LC modeling is reasonable.

Z₀ = √(L/C) defines the impedance magnitude at resonance for parallel tank circuits and determines the loaded Q when external resistance is added. It also appears in filter design (Butterworth, Chebyshev).

This calculator assumes ideal components as the fundamental LC resonance. For parasitic effects, advanced simulators (SPICE) are recommended. However, the tool is accurate for initial design and educational purposes.
References & Further Reading: Wikipedia LC Circuit; ARRL Handbook for Radio Communications; Horowitz & Hill, "The Art of Electronics" (3rd Ed.); All About Circuits – Resonance.