The LC tank circuit (resonant circuit) is the heart of RF oscillators, bandpass filters, wireless transmitters, and impedance matching networks. At resonance, inductive and capacitive reactances cancel (XL = XC), resulting in a purely resistive impedance. The fundamental formula is f₀ = 1 / (2π√(LC)). For example, L = 100 µH, C = 47 pF gives f₀ ≈ 2.32 MHz — widely used in FM receivers.
Quality factor Q determines selectivity: Q = (1/R)√(L/C) for series, Q = R / √(L/C) for parallel (with inductor ESR). Bandwidth BW = f₀ / Q. A high-Q circuit (e.g., Q=100) offers narrow bandwidth, ideal for channel selection; low-Q (Q<10) for wideband. Practical LC circuits appear in LC oscillators (Colpitts, Hartley), RF amplifiers, and harmonic filters. This calculator supports both topologies and bulk analysis for rapid design iteration.
Design example: For a parallel tank with L=10µH, C=100pF, R=5000Ω → f₀≈5.03MHz, Q≈159, BW≈31.6kHz — perfect for AM IF filtering. Always include parasitic resistance for accurate Q. Use our bulk upload to sweep component values and visualize resonant performance.