What Is the RLC Resonant Frequency, Bandwidth & Q-Factor Calculator?
An RLC circuit combines a resistor, an inductor, and a capacitor to create electrical harmonic resonance.
How Does the RLC Resonant Frequency, Bandwidth & Q-Factor Calculator Work?
Energy stored in the inductor magnetic field alternates cyclically with electric field energy in the capacitor.
RLC Resonant Frequency, Bandwidth & Q-Factor Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
f_0 = \frac{1}{2\pi \sqrt{L \cdot C}}, \quad Q = \frac{1}{R} \sqrt{\frac{L}{C}}, \quad \Delta f = \frac{f_0}{Q}
Resonant frequency f0 occurs when inductive and capacitive reactances are equal; Q factor dictates damping and bandwidth.
How to Use the RLC Resonant Frequency, Bandwidth & Q-Factor Calculator
- Specify inductance in millihenries (mH).
- Provide capacitance in microfarads (µF).
- Input series resistance in Ohms.
Step-by-Step Example Calculation
10 mH / 0.1 µF Radio Tuning Circuit
Input Values:
inductanceMh:10.0
capacitanceUf:0.1
resistanceOhms:50.0
Worked Steps: With 10 mH and 0.1 µF, the circuit resonates at 5.033 kHz (5033 Hz) with Q = 6.325 and a 3-dB bandwidth of 795.8 Hz.
Understanding Your Result
Resonant Frequency (f₀): Peak oscillation frequency in Hz and kHz.
Quality Factor (Q): Ratio of stored energy to dissipated energy per cycle.
Bandwidth (Δf): Frequency width where power remains within 50% (-3dB) of peak.
Factors That Affect the Result
- Inductance and capacitance set the frequency; series resistance sets peak sharpness and damping.
When Should You Use This Calculator?
- AM/FM radio receiver front-ends, induction heating coils, audio cross-over networks, and RFID tags.
Assumptions & Limitations
- Assumes linear passive components without frequency-dependent core eddy current saturation.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard electrical engineering alternating current formulation.