Resonant Frequency Calculator
Calculate the resonant frequency of an LC circuit from inductance and capacitance.
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An LC circuit (also called a tank circuit or tuned circuit) resonates at a specific frequency determined by the inductance and capacitance values. This calculator finds that frequency using the standard formula.
- Enter inductance. Enter the inductance value and select the unit (H, mH, or µH). RF coils are typically in the µH range; audio and power supply inductors in the mH to H range.
- Enter capacitance. Enter the capacitance value and select the unit (F, mF, µF, nF, or pF). RF tuning capacitors are typically 10 to 500 pF; audio coupling capacitors in the nF to µF range.
- Read the results. The resonant frequency in Hz (or kHz, MHz, GHz as appropriate) and the resonant period.
About LC Resonant Frequency
The resonant frequency formula is f = 1 / (2π × √(L × C)), where L is in henries and C is in farads. At resonance, the inductive reactance (XL = 2πfL) equals the capacitive reactance (XC = 1/(2πfC)), and they cancel each other. In a series LC circuit, impedance is minimum at resonance. In a parallel LC circuit (tank), impedance is maximum.
This property makes LC circuits useful for radio tuning, bandpass filters, impedance matching, and oscillator frequency control. AM radio uses LC circuits tuned to specific carrier frequencies. Variable capacitors allow tuning across a range of frequencies.
Frequently Asked Questions
What is the formula for LC resonant frequency?
The resonant frequency is f = 1 / (2π × √(L × C)), where L is inductance in henries and C is capacitance in farads. For example, a 10 mH inductor with a 100 nF capacitor resonates at 1 / (2π × √(0.01 × 1e-7)) = approximately 5033 Hz (5 kHz).
What happens at resonance in an LC circuit?
At resonance, the inductive and capacitive reactances are equal and opposite, so they cancel. In a series LC circuit, this creates a short circuit for signals at the resonant frequency (minimum impedance). In a parallel LC circuit (tank circuit), this creates an open circuit (maximum impedance). Energy oscillates between the inductor's magnetic field and the capacitor's electric field with no net energy consumed (in an ideal lossless circuit).
How do I tune an LC circuit to a specific frequency?
To target a specific frequency, choose one component value and solve for the other. For a 1 MHz resonance with a 100 µH inductor, C = 1 / ((2πf)² × L) = 1 / ((2π × 1e6)² × 1e-4) ≈ 253 pF. Use a variable capacitor (trimmer) to fine-tune. For wider tuning ranges, switched inductor banks or variable inductors (variometers) allow broad coverage.
What is the Q factor of a resonant circuit?
Q (quality factor) measures how selective a resonant circuit is. A high Q means the circuit responds sharply to signals near its resonant frequency and rejects others. Q = f₀ / bandwidth, or Q = (1/R) × √(L/C) for a parallel circuit. High-Q circuits (Q > 100) are used in radio receivers for channel selectivity. Low-Q circuits are used in audio crossovers where a broader response is needed.