📻 Electrical Engineering & RF Oscillators
LC & RLC Resonant Frequency Calculator
Compute the natural resonant frequency ($f_0 = \frac{1}{2\pi\sqrt{LC}}$), Quality Factor ($Q$), 3dB bandwidth ($BW$), and characteristic tank impedance ($Z_0 = \sqrt{L/C}$).
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Component Values
Ω (Ohms)
Resonant Frequency (f₀)
1.0066 MHz
Quality Factor ($Q$)
126.5
3dB Bandwidth ($\Delta f$)
7.96 kHz
Characteristic $Z_0$
632.5 Ω
💡 Reactance Equality at Resonance:
$$X_L = 2\pi f_0 L = 632.5\,\Omega = X_C = \frac{1}{2\pi f_0 C} \implies X_L - X_C = 0\,\Omega$$
The Physics of LC Electrical Resonance
In an LC circuit, energy oscillates between the inductor's magnetic field and the capacitor's electric field:
- Resonance Condition: Occurs when inductive reactance equals capacitive reactance ($X_L = X_C \iff \omega L = \frac{1}{\omega C}$).
- Natural Frequency: $$f_0 = \frac{1}{2\pi\sqrt{LC}}, \quad \omega_0 = 2\pi f_0 = \frac{1}{\sqrt{LC}}$$
- Series Quality Factor ($Q$): $$Q = \frac{\omega_0 L}{R} = \frac{1}{R}\sqrt{\frac{L}{C}}$$
- Bandwidth ($BW$): $$BW = \frac{f_0}{Q} = \frac{R}{2\pi L}$$