Resonant Frequency Calculator
Instantly convert resonant frequency with our free converter. See conversion tables, formulas, and step-by-step explanations.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Resonant Frequency Calculator
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Formula: f = 1 / (2 * pi * sqrt(L * C))
Worked example — 101.3 pF capacitor needed to resonate at 1 MHz with 250 uH
Formula
f = 1 / (2 * pi * sqrt(L * C))
The resonant frequency is calculated using the inductance (L) in henries and capacitance (C) in farads. Q factor = (1/R)*sqrt(L/C) for series RLC. Bandwidth = f/Q. Characteristic impedance = sqrt(L/C).
Worked Examples
Example 1: AM Radio Tuning Circuit
Problem:An AM radio uses a 250 uH inductor. What capacitance tunes to 1000 kHz?
Solution:f = 1 / (2*pi*sqrt(L*C)) Rearranging: C = 1 / (4*pi^2*f^2*L) C = 1 / (4 * 9.8696 * (1e6)^2 * 250e-6) C = 1.013e-10 F = 101.3 pF
Result:101.3 pF capacitor needed to resonate at 1 MHz with 250 uH
Example 2: Audio Crossover Filter
Problem:Design a resonant circuit at 3 kHz using a 10 mH inductor and find the Q with 50 ohm resistance.
Solution:f = 1/(2*pi*sqrt(L*C)), so C = 1/(4*pi^2*f^2*L) C = 1/(4*9.8696*9e6*0.01) = 2.814e-7 F = 281.4 nF Q = (1/50)*sqrt(0.01/2.814e-7) = 3.77
Result:C = 281.4 nF, Q = 3.77, BW = 796 Hz
Frequently Asked Questions
What is resonant frequency in an LC circuit?
Resonant frequency is the frequency at which an LC (inductor-capacitor) circuit naturally oscillates when energy is exchanged between the magnetic field of the inductor and the electric field of the capacitor. At resonance, the inductive reactance equals the capacitive reactance, and they cancel each other out. The formula is f = 1 / (2 * pi * sqrt(L * C)), where L is inductance in henries and C is capacitance in farads.
What is the quality factor (Q) and why does it matter?
The quality factor Q measures how underdamped a resonant circuit is, representing the ratio of energy stored to energy lost per cycle. A higher Q means sharper resonance with a narrower bandwidth and less energy loss. For a series RLC circuit, Q = (1/R) * sqrt(L/C). A circuit with Q of 100 has a bandwidth that is 1/100th of its resonant frequency. High-Q circuits are essential in radio receivers for selecting narrow frequency bands.
How does resistance affect resonant frequency?
In an ideal LC circuit with no resistance, the resonant frequency depends only on L and C. When resistance is added (RLC circuit), the undamped natural frequency remains the same, but the actual oscillation frequency (damped frequency) decreases slightly. The damping ratio determines whether the circuit oscillates (underdamped), critically damps, or overdamps. Resistance also broadens the bandwidth and reduces the Q factor.
Where are resonant circuits used in practice?
Resonant circuits are fundamental to radio tuning, where they select specific frequencies from the electromagnetic spectrum. They are used in bandpass filters, oscillators, impedance matching networks, wireless power transfer systems, and MRI machines. Crystal oscillators in computers use mechanical resonance of quartz crystals. Tesla coils use resonance to achieve extremely high voltages. Even musical instruments rely on acoustic resonance principles.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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