Natural circuit oscillation
What is resonant frequency?
Resonant frequency is the natural frequency at which energy moves repeatedly between the magnetic field of an inductor and the electric field of a capacitor.
In an ideal LC circuit, resonance occurs when inductive reactance and capacitive reactance have equal magnitudes.
Standard resonance equation
Resonant frequency formula
Resonant frequencyf₀ = 1 ÷ (2π√LC)
- f₀ is resonant frequency in hertz.
- L is inductance in henries.
- C is capacitance in farads.
- π is the mathematical constant pi.
Worked LC circuit example
Calculate resonant frequency
Suppose an LC circuit has an inductance of 0.01 H and a capacitance of 0.000001 F.
- Use f₀ = 1 ÷ (2π√LC).
- Multiply L and C: 0.01 × 0.000001 = 0.00000001.
- Take the square root: √0.00000001 = 0.0001.
- Calculate 2π × 0.0001.
- The resonant frequency is about 1591.55 Hz.
Balanced circuit reactance
Inductive and capacitive reactance at resonance
Inductive reactance increases with frequency, while capacitive reactance decreases with frequency. At the resonant frequency, their magnitudes are equal.
Resonance conditionXₗ = Xc
Because the reactances act in opposite directions, they cancel each other in an ideal series RLC circuit.
Series circuit behavior
Series RLC resonance
In an ideal series RLC circuit at resonance, net reactance becomes zero. Total impedance therefore equals the resistance of the circuit.
For a fixed supply voltage, this produces the maximum circuit current. Real circuits remain affected by resistance, component tolerances, and parasitic effects.
Parallel circuit behavior
Parallel RLC resonance
Parallel RLC circuits also exhibit resonance, although their current and impedance behavior differs from the series case.
In a practical parallel resonant circuit, input impedance can become very high near resonance while the branch currents may remain large.
Rearranged equations
Solving for inductance or capacitance
InductanceL = 1 ÷ (4π²f₀²C)
CapacitanceC = 1 ÷ (4π²f₀²L)
These rearranged equations are useful when designing a circuit for a target resonant frequency.
Component relationships
How inductance and capacitance affect resonance
- Increasing inductance lowers the resonant frequency.
- Increasing capacitance lowers the resonant frequency.
- Decreasing either component raises the resonant frequency.
- Frequency changes according to the inverse square root of LC.
SI unit guidance
Resonant frequency units
- Frequency: hertz (Hz).
- Angular frequency: radians per second (rad/s).
- Inductance: henries (H).
- Capacitance: farads (F).
Convert millihenries, microhenries, microfarads, nanofarads, or picofarads into base SI units before entering them into this calculator.
Engineering applications
Where resonant frequency is used
- Radio transmitters and receivers.
- Frequency-selective filters.
- Oscillator and timing circuits.
- Wireless power systems.
- Antenna tuning networks.
- Audio and signal-processing circuits.
Model assumptions
Calculator limitations
This calculator uses the ideal LC resonance equation. Real components include resistance, tolerances, dielectric losses, winding losses, and parasitic capacitance or inductance.
At high frequencies, physical layout and component construction can also shift the measured resonant frequency away from the ideal result.
Common questions
Resonant frequency FAQ
What formula does the resonant frequency calculator use?
It uses f₀ = 1/(2π√LC), where f₀ is resonant frequency, L is inductance, and C is capacitance.
What units should I use for inductance and capacitance?
Enter inductance in henries and capacitance in farads to obtain resonant frequency in hertz.
What happens at resonance in a series RLC circuit?
At resonance, inductive reactance equals capacitive reactance, so the net reactance becomes zero and ideal circuit impedance equals resistance.
Does resistance affect the ideal resonant frequency?
The standard ideal formula depends only on inductance and capacitance. Resistance affects damping, bandwidth, and quality factor, but not the ideal resonance value.
Can this calculator solve for inductance or capacitance?
Yes. Provide resonant frequency and one component value to calculate the missing inductance or capacitance.