What is an LC Circuit (Tank Circuit)?
An LC circuit (also called a resonant circuit, tank circuit, or tuned circuit) is an idealized electrical circuit containing only an inductor (L) and a capacitor (C) connected together — either in series or in parallel. In an ideal LC circuit, there is zero resistance, so energy oscillates endlessly between the magnetic field of the inductor and the electric field of the capacitor.
LC circuits are widely used in electronics as signal generators and bandpass filters — they select a signal at a particular frequency from a more complex signal. You can find LC circuits in amplifiers, oscillators, tuners, radio transmitters, and receivers.
What is Resonant Frequency?
The resonant frequency (f₀) is the natural, undamped frequency at which an LC circuit oscillates. At this frequency, the inductive reactance (XL) and the capacitive reactance (XC) are equal and cancel each other out, causing the circuit to oscillate with maximum amplitude.
- At resonance: XL = XC
- Below resonance: the circuit behaves capacitively
- Above resonance: the circuit behaves inductively
Types of resonance include mechanical and acoustic, electrical, optical, orbital, and molecular. This calculator focuses on electrical resonance in LC circuits.
How to Calculate Resonant Frequency of an LC Circuit
The resonant frequency formula is derived from equating the inductive and capacitive reactances:
Where:
- f — resonant frequency in Hertz (Hz)
- L — inductance in Henries (H)
- C — capacitance in Farads (F)
- π ≈ 3.14159...
The angular frequency (ω, omega) is related to the resonant frequency by:
How to Use the Resonant Frequency Calculator
- Select your unit system: Choose Metric for SI prefixes (mH, µF) or American for common engineering prefixes used in American electronics practice (µH, nF).
- Enter inductance (L): Input the inductance value and select the unit — H (henries), mH (millihenries), µH (microhenries), or nH (nanohenries).
- Enter capacitance (C): Input the capacitance value and select the unit — F (farads), mF (millifarads), µF (microfarads), nF (nanofarads), or pF (picofarads).
- Click Calculate: The calculator instantly shows the resonant frequency, angular frequency, oscillation period, and reactance at resonance.
Unit Systems
Metric (SI) System
The metric system uses the International System of Units (SI). Inductance is measured in Henries (H) and capacitance in Farads (F). Common prefixes:
- Inductance: H, mH (10⁻³ H), µH (10⁻⁶ H), nH (10⁻⁹ H)
- Capacitance: F, mF (10⁻³ F), µF (10⁻⁶ F), nF (10⁻⁹ F), pF (10⁻¹² F)
American Engineering System
In American electronics practice, the most commonly encountered values use microhenries (µH) for RF inductors and nanofarads (nF) or picofarads (pF) for high-frequency capacitors. The same SI formulas apply — only the typical value ranges differ by convention.
FAQs
What happens at resonant frequency?
At resonant frequency, the LC circuit oscillates with maximum amplitude. The inductive and capacitive reactances are equal (XL = XC), and the circuit impedance is at its minimum (for series) or maximum (for parallel) configuration. Energy oscillates between the inductor's magnetic field and the capacitor's electric field.
What is angular frequency and how does it differ from resonant frequency?
The resonant frequency (f) is measured in Hertz (cycles per second), while the angular frequency (ω) is measured in radians per second. They are related by ω = 2π × f. Angular frequency is convenient in mathematical analysis of AC circuits.
Can I calculate frequency if I know only one component?
No. The resonant frequency depends on both inductance (L) and capacitance (C). You need both values to calculate f. However, you can rearrange the formula to find either L or C if you know the desired frequency and one component value.
What is the difference between series and parallel LC circuits?
Both types have the same resonant frequency formula f = 1/(2π√LC). The difference is in impedance behavior at resonance: a series LC circuit has minimum impedance (acts as a short circuit) at resonance, while a parallel LC circuit (tank circuit) has maximum impedance at resonance.
Why are LC circuits important in radio?
LC circuits are used in radio tuners to select a specific broadcast frequency. By adjusting the capacitor (variable capacitor), you can change the resonant frequency of the circuit, allowing you to tune in to different radio stations. The circuit passes signals at the resonant frequency while filtering out others.
What is Q factor?
The Quality factor (Q) measures how well the LC circuit stores energy relative to how much it dissipates. A higher Q means a sharper, more selective resonance peak. In ideal LC circuits (zero resistance), Q is theoretically infinite. In real circuits with resistance, Q = (1/R) × √(L/C) for series circuits.