f = 1 / (2 * π * √(L * C))
f = Frequency (Hz)
L = Inductance (H)
C = Capacitance (F)
π = 3.1415926535
Calculate the resonant frequency of an LC circuit — essential for filters, oscillators, and tuning circuits.
"The natural frequency at which an LC circuit stores and exchanges energy between magnetic and electric fields."
f0 = 1 / (2 π √LC)
Where:
f0: Resonant frequency (Hz)
L: Inductance (H)
C: Capacitance (F)
Note: This formula applies to both series and parallel LC circuits.
The value of inductance in the circuit, measured in henrys (H).
It represents the coil’s ability to store energy in a magnetic field.
Microhenry (μH) = 10⁻⁶ H
Millihenry (mH) = 10⁻³ H
Henry (H) – used for large inductors
Example: A ferrite core inductor may have 10 μH
The value of capacitance in the circuit, measured in farads (F).
It represents the capacitor’s ability to store charge.
Picofarad (pF) = 10⁻¹² F
Nanofarad (nF) = 10⁻⁹ F
Microfarad (μF) = 10⁻⁶ F
Farad (F) – rarely used in practice
Example: A ceramic capacitor may have 100 pF
At resonance:
1. Inductive reactance equals capacitive reactance (XL = XC)
2. The circuit oscillates naturally without external driving force
3. Solving for $ f $ gives the resonant frequency formula
In a series LC circuit:
Impedance is minimum → current is maximum
Used in band-pass filters and oscillators
In a parallel LC circuit:
Impedance is maximum → voltage is maximum
Used in tank circuits and antenna tuning
Energy continuously swaps between the inductor (magnetic field) and capacitor (electric field), creating sustained oscillations.
1. Tuning radio receivers to specific stations
2. Designing band-pass and band-stop filters
3. Building oscillators (e.g., crystal, Hartley, Colpitts)
4. Matching antennas to transmitter frequencies
5. Power electronics (resonant converters)
6. Teaching AC circuit theory in classrooms
The resonant frequency of an LC circuit is calculated using the formula: f₀ = 1 / (2π√LC). This formula applies to both series and parallel LC circuits.
At resonance, the inductive reactance (XL = 2πfL) equals the capacitive reactance (XC = 1/2πfC), causing them to cancel out.
The circuit then oscillates naturally, exchanging energy between the inductor's magnetic field and the capacitor's electric field.
While both share the same resonant frequency formula, their circuit behavior at resonance is opposite.
In a series LC circuit, impedance reaches its minimum (ideally zero) and current is at its maximum — making it ideal for band-pass filters and signal selection.
In a parallel LC circuit (also called a tank circuit), impedance reaches its maximum and voltage is at its peak — making it ideal for oscillators, RF amplifiers, and impedance matching networks.
In an ideal LC circuit (R = 0), the resonant frequency depends only on L and C. In real-world circuits, resistance from wire windings, core losses, and PCB traces causes the actual resonant peak to shift slightly lower than the theoretical value.
However, for most engineering applications, the formula f₀ = 1 / (2π√LC) remains an accurate and widely used approximation. The main impact of resistance is reducing the Q factor and broadening the resonance bandwidth, rather than significantly changing the frequency itself.
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