RLC Resonance Calculator | Resonant Frequency

📖 RLC Resonance Calculator

Resonance occurs in an RLC circuit when the inductive reactance equals the capacitive reactance, resulting in maximum current flow. The resonant frequency (f0) is determined by the inductance (L) and capacitance (C). This calculator computes the resonant frequency, bandwidth (BW), quality factor (Q), and cutoff frequencies. Essential for filter design, tuned circuits, and oscillator circuits.

📐 RLC Resonance Formulas

Resonant Frequency: f0 = 1 / (2π × √(L × C)) (Hz)
Bandwidth: BW = R / (2π × L) (Hz)
Quality Factor: Q = f0 / BW = (1/R) × √(L/C)
Cutoff Frequencies: f1 = f0 - BW/2 f2 = f0 + BW/2

Where:
L = Inductance (H) C = Capacitance (F)
R = Resistance (Ω) f0 = Resonant Frequency (Hz)
BW = Bandwidth (Hz) Q = Quality Factor

📊 RLC Resonance Reference

R (Ω)	L (mH)	C (µF)	f0 (Hz)	BW (Hz)	Q
10	1	0.1	15915	1591	10.0
100	10	1	1591	1591	1.0
1000	100	10	159	1591	0.1
50	5	0.5	3183	1591	2.0
100	1	1	5033	15915	0.32
1	10	0.1	5033	159	31.6

📌 Quality Factor (Q) Interpretation

Q > 10: High Q circuit - narrow bandwidth, sharp resonance
Q = 1-10: Medium Q circuit - moderate bandwidth
Q < 1: Low Q circuit - wide bandwidth, dull resonance
Q = f0 / BW: Higher Q = more selective circuit

💡 Applications of RLC Resonance

Radio Tuners: Selecting specific radio stations from the spectrum
Bandpass Filters: Allowing only a specific range of frequencies
Oscillators: Generating stable sine waves
Induction Heating: Using resonance for efficient power transfer
Wireless Power Transfer: Resonant inductive coupling
Impedance Matching: Maximizing power transfer between stages

❓ Frequently Asked Questions (FAQ)

❓ What is resonant frequency in an RLC circuit? ▼

Resonant frequency (f0) is the frequency at which inductive reactance equals capacitive reactance, resulting in maximum current. It is calculated as f0 = 1 / (2π × √(L × C)).

❓ What is bandwidth in an RLC circuit? ▼

Bandwidth (BW) is the range of frequencies between the two cutoff frequencies (f1 and f2) where the output is at least 70.7% of the peak output. BW = R / (2π × L).

❓ What is quality factor (Q) in an RLC circuit? ▼

Quality factor (Q) is a measure of how sharp the resonance is. Q = f0 / BW = (1/R) × √(L/C). Higher Q means narrower bandwidth and more selective circuit.

❓ What happens at resonance in a series RLC circuit? ▼

At resonance, impedance is minimum (equal to R), current is maximum, and voltage across L and C are equal and opposite, canceling each other.

❓ What is the phase angle at resonance? ▼

At resonance, the phase angle between voltage and current is 0° (unity power factor). The circuit behaves as a purely resistive load.

❓ What are the cutoff frequencies? ▼

Cutoff frequencies (f1 and f2) are the frequencies where output drops to 70.7% of the peak output. f1 = f0 - BW/2 and f2 = f0 + BW/2.