LC Resonant Frequency Calculator
Tank circuit resonant frequency
Required Parameters
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Quick Answer
Resonant frequency: f = 1 / (2π√(LC)). At resonance, inductive and capacitive reactances cancel, leaving only resistive impedance.
Design Notes
LC resonance is the foundation of radio tuning, oscillators, and impedance matching networks. The quality factor Q = (1/R)√(L/C) determines selectivity — high Q means narrow bandwidth. In practice, component parasitics (ESR, stray capacitance) shift the actual resonant frequency from the ideal calculation.
Common Mistakes
- 1
Ignoring parasitic capacitance of inductors, which creates a self-resonant frequency (SRF) above which the inductor behaves as a capacitor.
- 2
Not accounting for PCB trace inductance and pad capacitance at GHz frequencies.
- 3
Using the formula for series vs parallel LC without considering the topology difference.
Knowledge Base
What is LC resonance?
LC resonance occurs when inductive reactance (XL = 2πfL) equals capacitive reactance (Xc = 1/2πfC). At this frequency, energy oscillates between the inductor's magnetic field and capacitor's electric field. The resonant frequency is f = 1/(2π√LC). At resonance, impedance is purely resistive.
What is a tank circuit?
A tank circuit is a parallel LC circuit that stores energy by shuttling it between the inductor and capacitor. At resonance, it presents very high impedance (theoretically infinite for ideal components). Used in radio receivers to select one station frequency, oscillators, and bandpass filters.
How do I calculate resonant frequency?
f = 1 / (2π√(LC)). Example: L = 10µH, C = 100pF: f = 1 / (2π × √(10×10⁻⁶ × 100×10⁻¹²)) = 1 / (2π × √(10⁻¹⁵)) = 1 / (2π × 31.62×10⁻⁹) = 5.03 MHz. This is a typical FM radio tuning circuit.
What is the Q factor of an LC circuit?
Q (quality factor) measures selectivity: Q = (1/R)√(L/C) for a series RLC, or Q = R√(C/L) for parallel. Higher Q = narrower bandwidth = sharper tuning. Practical Q ranges: air-core inductors 50-200, ferrite toroids 100-500, crystal resonators 10,000-100,000.
Why doesn't my LC circuit resonate at the calculated frequency?
Common reasons: (1) Parasitic capacitance of the inductor (every inductor has a self-resonant frequency above which it acts as a capacitor). (2) PCB trace capacitance adds to C. (3) Component tolerances (±10-20% for common inductors). (4) Coupling to nearby conductors changes effective L and C.
What are practical applications of LC resonance?
Radio tuning (AM/FM receivers), antenna matching networks, crystal oscillator circuits, LC filters (bandpass/notch), wireless power transfer (Qi charging), RFID systems, MRI imaging coils, Tesla coils, and switched-mode power supply resonant converters (LLC topology).
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