LC Resonant Frequency
Calculate the resonant frequency of an LC circuit.
Used in radio tuning, filters, and oscillator design.
The Formula
f = 1 / (2π√(LC))
An LC circuit oscillates at its natural resonant frequency. At this frequency, energy swings back and forth between the inductor's magnetic field and the capacitor's electric field.
Variables
| Symbol | Meaning |
|---|---|
| f | Resonant frequency (Hz) |
| L | Inductance (Henrys, H) |
| C | Capacitance (Farads, F) |
| π | Pi (approximately 3.14159) |
Example 1
L = 10 mH, C = 100 nF. Find the resonant frequency.
f = 1 / (2π√(0.01 × 10⁻⁷))
f = 1 / (2π√(10⁻⁹)) = 1 / (2π × 3.162 × 10⁻⁵)
f ≈ 5,033 Hz ≈ 5.03 kHz
Example 2
Design an FM radio tuner for 100 MHz with L = 0.1 μH. What capacitance is needed?
C = 1 / (4π²f²L)
C = 1 / (4 × 9.87 × (10⁸)² × 10⁻⁷)
C ≈ 25.3 pF (picofarads)
When to Use It
Use the LC resonant frequency formula when:
- Tuning radio receivers and transmitters
- Designing bandpass and notch filters
- Building oscillator circuits
- Selecting components for a specific operating frequency