1.591549
MHz
10,000,000
rad/s
1,000
Ω
628.3185
ns
188.4956
m
1.591549
MHz
10,000,000
rad/s
1,000
Ω
628.3185
ns
188.4956
m
The LC circuit calculator determines the resonant frequency, angular frequency, characteristic impedance, and free-space wavelength of an inductor-capacitor (LC) tank circuit. LC circuits — also called resonant circuits, tank circuits, or tuned circuits — are the fundamental building blocks of radio frequency (RF) engineering, oscillators, filters, and impedance matching networks.
At the heart of LC circuit behavior is electromagnetic resonance. When energy is supplied to an LC circuit, it oscillates between the electric field of the capacitor and the magnetic field of the inductor at a specific natural frequency. The resonant frequency, fr = 1 / (2π√(LC)), is the frequency at which this lossless energy exchange occurs. In practice, real LC circuits have some resistance causing damping, but the resonant frequency remains essentially the same for high-Q circuits.
LC circuits are the foundation of AM and FM radio tuners. By varying the capacitance (with a variable capacitor) or inductance, the resonant frequency shifts to select different radio stations. Similarly, LC oscillators in transmitters generate stable carrier frequencies. Crystal oscillators are refined LC circuits using the piezoelectric effect for extreme frequency stability.
The characteristic impedance Z₀ = √(L/C) is a critical parameter for impedance matching in RF circuits. When the source and load impedances match Z₀, maximum power transfer occurs. This parameter also determines the voltage and current magnification at resonance in series and parallel LC circuits respectively.
The free-space wavelength λ = c/fr (where c = 3×10⁸ m/s) relates the resonant frequency to the electromagnetic wavelength in free space. This is particularly useful in antenna design and transmission line matching, where antennas must be sized relative to the wavelength of the signal they are designed to receive or transmit.
This calculator accepts inductance in microhenries (µH) and capacitance in picofarads (pF) — the units most common in RF circuit design. For audio frequency LC circuits, enter inductance in µH and scale capacitance accordingly.
Key applications include: RF bandpass and bandstop filters, impedance matching networks, switching power supply resonant converters, induction heating systems, wireless charging (WPT) systems, crystal oscillator circuits, and notch filters for EMI suppression.
Resonant frequency: fr = 1/(2π√(LC)) in Hz, converted to MHz. L is in µH (×10⁻⁶) and C in pF (×10⁻¹²). Angular frequency: ω₀ = 2πfr = 1/√(LC) in rad/s. Characteristic impedance: Z₀ = √(L/C) in ohms — analogous to the surge impedance of a transmission line. Wavelength: λ = c/fr where c = 3×10⁸ m/s is the speed of light.
Higher inductance or larger capacitance lowers the resonant frequency. The characteristic impedance Z₀ helps with impedance matching — if your circuit impedance is 50 Ω, choose L and C such that √(L/C) = 50 Ω while maintaining the desired fr. Free-space wavelength is useful for antenna sizing: a half-wave dipole antenna is λ/2 in length at the operating frequency.
Inputs
Results
L = 0.318 µH and C = 12.5 pF gives fr ≈ 80 MHz, within the FM band (87.5–108 MHz). Tune C to select different stations.
Inputs
Results
L = 50 µH and C = 507 pF gives fr ≈ 1 MHz, commonly used in wireless charging and induction heating systems.
The resonant frequency fr = 1/(2π√(LC)) is the frequency at which inductive and capacitive reactances are equal and opposite (XL = XC), resulting in maximum energy exchange and minimum impedance (series) or maximum impedance (parallel).
In a series LC circuit, resonance produces minimum impedance (short circuit behavior). In a parallel LC circuit (tank circuit), resonance produces maximum impedance. Both resonate at the same fr = 1/(2π√(LC)).
Q (quality factor) = fr / Δf = ω₀L / R = 1 / (ω₀RC), where Δf is the bandwidth. Higher Q means sharper resonance and lower energy loss. Practical LC circuits have Q values from a few (RF chokes) to several hundred (quartz crystals).
The wavelength λ = c/fr determines the physical size of antennas and transmission line stubs. A quarter-wave resonant stub at fr is λ/4 long. This is essential in RF design and microwave engineering.
Z₀ = √(L/C) is the impedance at which an LC circuit stores equal energy in L and C. It is used for impedance matching in RF networks. For a 50 Ω system, choose L and C so that √(L/C) = 50 Ω.
Yes. Resonant converters (LLC, LCC topologies) use LC tank circuits to achieve zero-voltage or zero-current switching. The resonant frequency sets the optimal switching frequency for maximum efficiency.
1 µH = 10⁻⁶ H; 1 pF = 10⁻¹² F; 1 nF = 10⁻⁹ F; 1 mH = 10⁻³ H. This calculator handles the unit conversion internally.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
How helpful was this calculator?
Be the first to rate!
Parallel Resistance Calculator
Circuit Analysis Calculators
Series Resistance Calculator
Circuit Analysis Calculators
Parallel Capacitance Calculator
Circuit Analysis Calculators
Series Capacitance Calculator
Circuit Analysis Calculators
Parallel Inductance Calculator
Circuit Analysis Calculators
Series Inductance Calculator
Circuit Analysis Calculators
