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General

LC Resonance Calculator

Calculate the resonant frequency, characteristic impedance, Q factor, and bandwidth of a series or parallel LC tank circuit. Enter inductance, capacitance, and optional series resistance.

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Formula

f0=12πLC,Z0=LC,Q=Z0Rf_0 = \frac{1}{2\pi\sqrt{LC}}, \quad Z_0 = \sqrt{\frac{L}{C}}, \quad Q = \frac{Z_0}{R}

Reference: Terman, Radio Engineers' Handbook, McGraw-Hill, 1943

f₀— Resonant frequency (Hz)
L— Inductance (H)
C— Capacitance (F)
Z₀— Characteristic impedance (Ω)
Q— Quality factor
R— Series resistance (Ω)
BW— −3 dB bandwidth = f₀ / Q (Hz)

How It Works

LC resonance calculator computes the natural frequency f₀ = 1/(2π√LC) — essential for filter design, oscillators, and impedance matching networks. RF engineers, filter designers, and communication system engineers use this to design bandpass filters, tank circuits, and antenna matching networks. Per Pozar 'Microwave Engineering' (4th ed., Ch.6), at resonance the inductive and capacitive reactances cancel (X_L = X_C), creating either maximum impedance (parallel LC) or minimum impedance (series LC). The characteristic impedance Z₀ = √(L/C) determines loaded Q-factor and bandwidth: BW = f₀/Q. For 915 MHz ISM band filters, typical component values are L = 10-50nH and C = 1-10pF; at 2.4 GHz, values shrink to L = 2-10nH and C = 0.5-2pF due to parasitic limits.

Worked Example

Design a 915 MHz bandpass filter for LoRa receiver front-end with 50Ω system impedance and 26 MHz bandwidth (Q ≈ 35). Required: f₀ = 915 MHz, Q = 35. For a parallel LC tank: L = Q × Z₀ / (2πf₀) = 35 × 50 / (2π × 915MHz) = 305nH. C = 1 / (4π²f₀²L) = 1 / (4π² × (915MHz)² × 305nH) = 0.099pF. These values are impractical — use a coupled-resonator topology instead. Practical design: L = 27nH (Coilcraft 0402HP series, Q = 45 at 900MHz), C = 1.1pF (Murata GRM series, ±0.1pF tolerance). f₀ = 1/(2π√(27nH × 1.1pF)) = 923 MHz — add 0.15pF trimmer for tuning to exact 915 MHz.

Practical Tips

  • ✓For RF filters above 100MHz, use 0402 or smaller components to minimize parasitic inductance (0.5nH per mm lead length per Murata application notes)
  • ✓Measure actual component values with a VNA — inductor tolerance of ±20% causes 10% frequency shift; capacitor tolerance of ±5% causes 2.5% shift
  • ✓Temperature-compensate with NP0/C0G capacitors (±30ppm/°C) and air-core inductors; ferrite-core inductors drift 200-1000 ppm/°C

Common Mistakes

  • ✗Ignoring component self-resonant frequency (SRF) — a 27nH inductor with 3GHz SRF behaves capacitively above 3GHz; use components with SRF > 3× operating frequency
  • ✗Neglecting parasitic capacitance from PCB traces — 1mm of microstrip adds ~0.1pF at 1GHz, shifting resonance by 5-10% per IPC-2251 calculations
  • ✗Using NP0/C0G capacitors only at RF — X7R capacitors have piezoelectric effects causing 1-5% capacitance variation with applied voltage

Frequently Asked Questions

Q = f₀/BW = (1/R)√(L/C) measures selectivity. Higher Q means narrower bandwidth: Q = 100 at 1GHz gives BW = 10MHz. Practical LC filters achieve Q = 20-100; for Q > 100, use crystal or SAW filters (Q = 10,000-100,000).
Temperature shifts component values: ceramic capacitors drift ±30 to ±10,000 ppm/°C depending on dielectric (NP0 vs. Y5V). Ferrite inductors drift 200-1000 ppm/°C. A ±500 ppm/°C shift causes 50 kHz drift at 100 MHz over 100°C range — significant for narrowband applications.
Yes — LC resonance is fundamental to all passive filter topologies. Butterworth requires Q = 0.707 per stage; Chebyshev uses higher Q for sharper cutoff. Per Zverev 'Handbook of Filter Synthesis', a 3-pole Butterworth at 10MHz needs three LC tanks with Q = 1.0, 2.0, and 1.0.
Audio (20Hz-20kHz): L = 1-100mH, C = 0.1-100μF. RF (1-1000MHz): L = 10nH-10μH, C = 1pF-1nF. Microwave (1-10GHz): L = 0.5-10nH, C = 0.1-5pF. Above 10GHz, distributed elements (transmission lines) replace lumped LC per Pozar Ch.8.
Use high-Q inductors (Q > 50 at operating frequency) and NP0/C0G capacitors (Q > 1000). PCB layout: minimize trace length, use ground pour, avoid sharp bends. For Q > 100, consider silver-plated wire-wound inductors (Q = 200-400 at HF) or helical resonators.
f₀ = 1/(2π√LC). For L = 100nH, C = 100pF: f₀ = 1/(2π√(10⁻⁷ × 10⁻¹⁰)) = 1/(2π × 10⁻⁸·⁵) = 50.3 MHz. Allow ±10-20% margin for component tolerance — actual resonance of ±5% parts falls within 47.8-52.9 MHz.
Common causes: (1) Inductor SRF below target — every inductor has parasitic capacitance creating SRF; use inductors with SRF > 3× f₀. (2) PCB parasitics — 10mm trace adds ~1nH inductance and 0.5pF capacitance. (3) Component tolerance — 10% L and 5% C yields 7.5% frequency error. Use VNA to measure actual resonance and trim with variable capacitor.

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