RLC Resonance Calculator – Calculate Resonant Frequency

Calculate resonant frequency, quality factor, and bandwidth for RLC circuits. Essential for filter and oscillator design.

Inductance L (H)

Capacitance C (F)

Resistance R (Ω)

How to Use This RLC Resonance Calculator

Enter inductance value

Input the inductance in henries (H). This is the L component in your RLC circuit.

Enter capacitance value

Input the capacitance in farads (F). Common values are in microfarads or picofarads.

Enter resistance and calculate

Input resistance in ohms for Q factor and bandwidth calculations. Click Calculate to see resonant frequency and circuit characteristics.

RLC Circuit Formulas Reference

Parameter	Formula	Units
Resonant Frequency	f₀ = 1/(2π√LC)	Hz
Angular Frequency	ω₀ = 2πf₀	rad/s
Quality Factor (Series)	Q = (1/R)√(L/C)	Dimensionless
Bandwidth	BW = f₀/Q	Hz
Characteristic Impedance	Z₀ = √(L/C)	Ω

Understanding RLC Resonance

An RLC circuit contains resistance (R), inductance (L), and capacitance (C). At resonance, the inductive and capacitive reactances cancel each other out. The circuit behaves purely resistive, and current reaches its maximum value for a given voltage.

The resonant frequency depends only on L and C — resistance doesn't affect where resonance occurs, only how sharp the resonance peak is. This is why radio tuners use variable capacitors: changing C shifts the resonant frequency to select different stations.

Quality factor Q measures how "selective" the circuit is. High Q means a narrow bandwidth — the circuit responds strongly only near resonance. Low Q means broader response. Q is essentially the ratio of stored energy to energy lost per cycle.

Key insight: At resonance, voltage across L or C can be Q times the source voltage. In a high-Q circuit (Q=100), a 1V input can produce 100V across the capacitor — useful for voltage multiplication but potentially destructive.

RLC Circuit Applications

Radio Tuners

AM/FM radios use RLC circuits to select specific frequencies from the antenna signal. Variable capacitors or inductors tune the resonant frequency to match the desired station.

Bandpass Filters

RLC circuits pass frequencies near resonance while attenuating others. Used in audio crossovers, communication systems, and signal processing to isolate specific frequency bands.

Impedance Matching

At resonance, the circuit presents purely resistive impedance. This property matches antennas to transmitters, speakers to amplifiers, and maximizes power transfer.

Oscillators

RLC tanks form the frequency-determining element in many oscillator circuits. The natural resonant frequency sets the oscillation frequency for RF generators and clock circuits.

Frequently Asked Questions

What's the difference between series and parallel resonance?

Series RLC has minimum impedance at resonance (current maximum). Parallel RLC has maximum impedance at resonance (current minimum). Series is used for signal selection; parallel for tank circuits and oscillators.

How does resistance affect resonance?

Resistance doesn't change the resonant frequency but affects Q factor and bandwidth. Higher R in series RLC means lower Q (broader response). Higher R in parallel RLC means higher Q (sharper response).

What is bandwidth in an RLC circuit?

Bandwidth is the frequency range where response is within 3dB (70.7%) of maximum. BW = f₀/Q. A 1 MHz circuit with Q=50 has 20 kHz bandwidth — it responds to frequencies from 990 kHz to 1010 kHz.

Can Q be less than 1?

Yes, but it indicates heavy damping. Q < 0.5 means the circuit is overdamped — no oscillation occurs. The response is sluggish with no resonance peak. Most practical resonant circuits have Q > 5.

What happens if I use real components?

Real inductors have series resistance; capacitors have equivalent series resistance (ESR). These reduce Q from ideal calculations. At high frequencies, parasitic capacitance and inductance also affect behavior.

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