LC Circuit Resonant Frequency Calculator
Calculate the resonant frequency of an LC circuit (inductor-capacitor tank circuit).
Essential for radio tuning, filter design, and oscillator circuits.
How It Works
An LC circuit (also called a tank circuit or tuned circuit) consists of an inductor (L) and a capacitor (C) connected together. At a specific frequency called the resonant frequency, the circuit oscillates — energy swings back and forth between the magnetic field of the inductor and the electric field of the capacitor.
The resonant frequency formula:
f = 1 / (2π × √(L × C))
Where:
- f = resonant frequency in Hertz (Hz)
- L = inductance in Henries (H)
- C = capacitance in Farads (F)
- π ≈ 3.14159
Angular (radian) frequency:
ω₀ = 1 / √(L × C) (in radians per second)
Characteristic impedance:
Z₀ = √(L / C) (in Ohms)
Unit conversions used in this calculator:
| Inductance | Value |
|---|---|
| 1 H | 1 Henry |
| 1 mH | 0.001 H |
| 1 µH | 0.000001 H |
| 1 nH | 0.000000001 H |
| Capacitance | Value |
|---|---|
| 1 F | 1 Farad |
| 1 mF | 0.001 F |
| 1 µF | 0.000001 F |
| 1 nF | 0.000000001 F |
| 1 pF | 0.000000000001 F |
Series vs. Parallel LC circuits:
In a series LC circuit, impedance is minimum at resonance (close to zero) — the circuit passes the resonant frequency easily. Used in bandpass filters and series resonant traps.
In a parallel LC circuit (tank circuit), impedance is maximum at resonance — the circuit blocks the resonant frequency from passing through. Used in oscillators, AM radio tuning circuits, and bandstop filters.
Real-world applications by frequency band:
| Application | Frequency | Typical Component Values |
|---|---|---|
| AM Radio Tuning | 535–1,605 kHz | L=250µH, C=25–350pF |
| FM Radio Tuning | 88–108 MHz | L=100nH, C=2–5pF |
| Wi-Fi 2.4 GHz | 2,400 MHz | L=1nH, C=4.4pF |
| Power factor correction | 50–60 Hz | L=10mH, C=100µF |
Quality Factor (Q): The Q factor describes how sharp the resonance peak is. High Q = narrow, sharp resonance (selective filters). Low Q = broad, gentle resonance (wideband). Q is determined by the resistance in the circuit — this calculator assumes an ideal lossless LC circuit (Q = ∞). In real circuits, inductor winding resistance and capacitor ESR reduce Q.
Worked example: L = 100 µH, C = 100 pF f = 1 / (2π × √(0.0001 × 0.0000000001)) = 1 / (2π × 0.0000000031623) ≈ 1.592 MHz This is in the AM broadcast band — a classic tuning circuit value.