RLC Circuit Calculator
Use this RLC circuit calculator to find the resonant frequency, Q-factor, bandwidth, angular frequency, and other key characteristics of a series RLC circuit. Simply enter the inductance (L), capacitance (C), and resistance (R) to get instant results.
What is an RLC Circuit?
An RLC circuit is a fundamental building block of electronic engineering. It consists of three passive components connected in series:
- Resistance R — dissipates energy (measured in Ohms, Ω)
- Inductance L — stores energy in a magnetic field (measured in Henries, H)
- Capacitance C — stores energy in an electric field (measured in Farads, F)
RLC circuits are used in radio tuning circuits, filters, oscillators, and signal processing applications.
Resonant Frequency Formula
The resonant frequency of an RLC circuit is the natural frequency at which the circuit oscillates when energy is not dissipated. It is calculated using:
f = 1 / (2π × √(L × C))
Where:
- f — resonant frequency (Hz)
- L — inductance (H)
- C — capacitance (F)
Example: With L = 1 µH and C = 2 pF, the resonant frequency is: f = 1 / (2π × √(1×10⁻⁶ × 2×10⁻¹²)) ≈ 112.54 MHz — a typical VHF radio frequency.
Q-Factor of the RLC Circuit
The Q-factor (quality factor) measures how underdamped the circuit is, or the ratio of stored energy to energy dissipated per cycle:
Q = (1/R) × √(L/C) = Z₀ / R
- High Q → sharp resonance, narrow bandwidth, low energy loss
- Low Q → broad resonance, wide bandwidth, high energy loss
Q-factor is critical in filter design, antenna matching, and oscillator stability.
Other Key Parameters
| Parameter | Formula | Description |
|---|---|---|
| Angular Frequency (ω₀) | ω₀ = 1 / √(LC) | Frequency in radians per second |
| Period (T) | T = 1 / f | Time for one complete oscillation |
| Characteristic Impedance (Z₀) | Z₀ = √(L/C) | Impedance at resonance |
| Bandwidth (BW) | BW = R / (2πL) = f₀ / Q | Frequency range where power ≥ half maximum |
| Damping Coefficient (α) | α = R / (2L) | Rate of amplitude decay |
Unit Systems
This calculator supports both Metric (SI) and American engineering unit conventions:
- Metric (SI): H, mH, µH, nH for inductance; F, µF, nF, pF for capacitance; Ω, kΩ, MΩ for resistance
- American: Common RF engineering values — µH, nH for inductance; pF, nF for capacitance
Common Applications
- Tuning circuits — used in analog AM/FM radios to select a specific broadcast frequency
- Bandpass filters — pass only signals near the resonant frequency, blocking others
- Oscillators — generate stable AC signals (e.g., crystal oscillators in clocks and processors)
- Impedance matching — maximize power transfer in RF and audio circuits
- Signal processing — component of equalizers, crossover networks, and notch filters
FAQs
What happens at resonant frequency?
At resonance, inductive reactance (XL) equals capacitive reactance (XC), so they cancel each other.
The total impedance equals just the resistance R, and current reaches its maximum value.
What is the difference between series and parallel RLC?
In a series RLC circuit, all components share the same current. At resonance, impedance is minimum (= R).
In a parallel RLC circuit, all components share the same voltage. At resonance, impedance is maximum.
How does resistance affect the circuit?
Resistance R determines energy loss. Higher R → lower Q-factor → broader bandwidth → circuit reaches steady state faster.