Calculate Resonance Frequency

Calculator and formulas for calculating the resonance frequency of an oscillating circuit

LC Resonance Calculator

LC Oscillating Circuit

On this page you can calculate the resonance frequency, the inductance of a coil or the capacitance of a capacitor of an oscillating circuit. Two of the values must be known to calculate the third.

Results
Capacitance:
Inductance:
Resonance frequency:

LC Oscillating Circuit

Resonance Frequency

In theoretical systems without damping, the resonance frequency is equal to the undamped natural frequency f₀. In damped systems, the frequency at which the maximum amplitude occurs is always smaller than the undamped natural frequency.

Basic Formula
\[f_0 = \frac{1}{2\pi\sqrt{LC}}\]

Resonance frequency of an LC oscillating circuit.

Rearrangements
\[L = \frac{1}{(2\pi f_0)^2 C}\]
\[C = \frac{1}{(2\pi f_0)^2 L}\]

Calculation of L or C for a given resonance frequency.

LC Oscillating Circuit - Theory and Formulas

What is an LC Oscillating Circuit?

An LC oscillating circuit consists of an inductance (coil) and a capacitance (capacitor). At the resonance frequency, the inductive reactance XL equals the capacitive reactance XC. The following description shows the calculation of the resonance frequencies of an LC oscillating circuit.

Calculation Formulas

Resonance Frequency
\[f_0 = \frac{1}{2\pi\sqrt{LC}}\]

The frequency is calculated from inductance L and capacitance C.

Inductance
\[L = \frac{1}{(2\pi f_0)^2 C}\]

The inductance is calculated from frequency f₀ and capacitance C.

Capacitance
\[C = \frac{1}{(2\pi f_0)^2 L}\]

The capacitance follows from frequency f₀ and inductance L.

Resonance Properties

At Resonance
  • XL = XC: Reactances are equal
  • Z minimal: Impedance is minimal (series resonant circuit)
  • Z maximal: Impedance is maximal (parallel resonant circuit)
  • Phase angle = 0°: Current and voltage in phase
Energy Exchange
  • Magnetic field ↔ Electric field: Energy oscillation
  • Coil stores: Magnetic energy
  • Capacitor stores: Electric energy
  • Lossless: With ideal components

Practical Applications

Oscillators:
• LC oscillators
• Frequency generators
• VCOs
• Crystal oscillators
Filters:
• Bandpass filters
• Bandstop filters
• Crossover networks
• Antenna filters
Tuning circuits:
• Radio receivers
• Antenna couplers
• Transmitter amplifiers
• Impedance matching

Quality Factor and Damping

Oscillating Circuit Properties
  • Quality factor Q: Q = ω₀L/R = 1/(ω₀RC) - determines bandwidth
  • Damping: Real losses in R reduce the amplitude
  • Bandwidth: B = f₀/Q - frequency range around f₀
  • Resonance sharpness: Higher Q = sharper resonance
  • Settling time: Lower damping = longer settling time

Design Guidelines

Important Design Aspects
  • Component selection: Precise L and C values for accurate frequency
  • Minimize losses: High Q through low resistance
  • Temperature stability: Use NP0/C0G capacitors
  • Parasitic effects: Consider self-resonances of components
  • Loading: External circuit affects the resonance
  • Tuning: Variable capacitors for frequency adjustment

Mathematical Relationships

Angular Frequency
\[\omega_0 = 2\pi f_0 = \frac{1}{\sqrt{LC}}\]

Alternative representation with angular frequency ω₀

Thomson Formula
\[T = 2\pi\sqrt{LC}\]

Period of the free oscillation


Other LC calculators

Resonant frequency f0 calculator  •  Resistors-capacitors-inductors series circuit  •  Resistors-capacitors-inductors parallel circuit  •  Resonance of RCL parallel circuit  •  Resonance of RCL series circuit  •