LC / RLC Circuit Analysis

Resonance Frequency Calculator

Calculate the resonant frequency of an LC circuit from inductance and capacitance. Enter component values in common engineering units and instantly calculate frequency in Hz, kHz or MHz.

Resonance Frequency Tool

Calculate the natural resonance frequency of an ideal LC circuit using inductance and capacitance.

Resonant Components
Ω
Resistance is not included in the ideal resonance frequency equation. It primarily affects damping, bandwidth and Q factor.
Resonance Frequency
159.155
kHz
Frequency 159.155 kHz
Period 6.283 µs
Angular Frequency 1.000 Mrad/s
Circuit Series RLC
f₀ = 1 / (2π√LC)

Resonant frequency depends on inductance and capacitance.

RLC Resonant Network
Core Equations

Resonance frequency formulas

The fundamental LC resonance equation is determined by the product of inductance and capacitance.

Resonant Frequency
f₀ = 1 / (2π√LC)
Frequency in hertz when L is in henries and C is in farads.
Angular Frequency
ω₀ = 1 / √LC
Angular frequency is expressed in radians per second.
Period
T = 1 / f₀
The period is the time required for one complete oscillation.

Inductive Reactance

The reactance of an ideal inductor increases with frequency according to:

XL = 2πfL

Higher frequency produces higher inductive reactance.

At the resonance frequency, the inductive reactance has the same magnitude as the capacitive reactance.

Capacitive Reactance

The reactance of an ideal capacitor decreases with frequency:

XC = 1 / (2πfC)

Higher frequency produces lower capacitive reactance.

At resonance, XL and XC are equal in magnitude and opposite in phase.

Series vs. parallel resonance

Both circuit arrangements can resonate, but their impedance and current behavior around resonance differ.

Series RLC

In a series RLC circuit, the resistor, inductor and capacitor are connected in series.

  • At resonance, XL = XC.
  • The reactive voltages cancel in the ideal model.
  • The impedance reaches a minimum near resonance.
  • Circuit current can reach a maximum.
  • Resistance affects the peak current and bandwidth.
Z = R + j(XL − XC)

Parallel Resonance

A parallel resonant circuit places reactive elements in parallel. Practical circuits can have more complex equivalent models due to component losses.

  • Inductive and capacitive susceptances cancel near resonance.
  • Input impedance can become high near resonance.
  • Source current can reach a minimum.
  • Component currents can circulate internally.
  • Losses and topology affect the practical resonant behavior.
f₀ ≈ 1 / (2π√LC)

Worked resonance frequency examples

These examples show how inductance and capacitance determine the resonant frequency.

Inductance Capacitance Calculation Resonance
10 µH 100 pF 1 / (2π√LC) 5.033 MHz
10 µH 1 nF 1 / (2π√LC) 1.592 MHz
100 µH 100 nF 1 / (2π√LC) 50.33 kHz
1 mH 1 µF 1 / (2π√LC) 5.033 kHz

Resonance and Q factor

The resonant frequency tells you where the circuit resonates. The quality factor describes how sharply the circuit responds around that frequency.

For a simple series RLC circuit, an idealized quality factor can be expressed as:

Q = ω₀L / R

Higher Q generally corresponds to a narrower resonance bandwidth in the idealized series model.

Why Q matters

  • High-Q circuits have a sharper resonance.
  • Low-Q circuits have a broader response.
  • Component resistance and losses reduce Q.
  • Filters and resonators often use Q as a key design parameter.
  • Real inductors and capacitors have parasitic effects.

Where resonance frequency is used

LC and RLC resonance is fundamental to many electronic and RF systems.

RF Circuits

Tune antennas, matching networks and RF resonators to desired operating frequencies.

Filters

Design band-pass, band-stop and tuned LC networks around a target frequency.

Oscillators

LC networks provide frequency-selective behavior in oscillator and timing circuits.

Signal Processing

Resonant networks are used for frequency selection and impedance transformation.

Practical resonance design notes

  • Use SI units internally: henries for inductance and farads for capacitance.
  • The ideal resonance formula is f₀ = 1/(2π√LC).
  • Real capacitors have ESR, ESL and tolerance.
  • Real inductors have winding resistance, parasitic capacitance and tolerance.
  • PCB traces and component placement can introduce additional parasitic inductance and capacitance.
  • Resistance affects damping and Q factor even when it does not appear in the ideal LC frequency equation.
  • The measured resonant frequency can differ from the ideal calculated value because of parasitic components, loading and component tolerances.
  • For high-frequency designs, the self-resonant frequency of real components should also be considered.

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Frequently Asked Questions

Common questions about LC and RLC resonance frequency calculations.

Resonance frequency is the frequency at which the inductive and capacitive reactances of an LC circuit are equal in magnitude and opposite in phase. In an ideal LC circuit, the resonant frequency is f₀ = 1/(2π√LC).

For an ideal LC circuit, the resonant frequency is f₀ = 1/(2π√LC), where L is inductance in henries and C is capacitance in farads. The result is in hertz.

For the ideal series or parallel LC resonance equation, resistance does not appear in the basic formula. In practical circuits, losses, parasitic components, loading and circuit topology can influence the measured resonant behavior and quality factor.

At resonance, the magnitudes of inductive and capacitive reactance are equal. In a series RLC circuit, these reactive components cancel and the impedance reaches its minimum value, ideally leaving the resistance as the dominant impedance.

A series RLC circuit generally has minimum impedance at its resonant frequency, while a parallel resonant circuit generally has maximum input impedance near resonance. The exact behavior depends on the circuit topology and losses.

Inductance should ultimately be converted to henries and capacitance to farads. This calculator accepts nH, µH, mH and H for inductance and pF, nF, µF, mF and F for capacitance.

Angular resonance frequency is expressed in radians per second and is given by ω₀ = 1/√(LC). The ordinary frequency in hertz is f₀ = ω₀/(2π).