Resonant Frequency Calculator
Calculate the resonant frequency of an LC circuit from inductance and capacitance values. The resonant frequency is where inductive and capacitive reactances are equal and cancel each other. See also our RLC Circuit Calculator and Inductive Reactance Calculator.
How to Calculate Resonant Frequency
The resonant frequency of an LC circuit is the frequency at which the inductive reactance (XL = 2πfL) equals the capacitive reactance (XC = 1/(2πfC)). At this frequency, energy oscillates between the inductor's magnetic field and the capacitor's electric field with no net reactive power exchange with the source. The circuit appears purely resistive at resonance.
This principle is fundamental to radio communications, where LC circuits are tuned to select specific frequencies from the electromagnetic spectrum. By varying either L or C, the resonant frequency can be adjusted to receive different stations or transmit on different channels.
Resonant Frequency Formula
Resonant Frequency:
f₀ = 1 / (2π√(LC))
Angular Frequency:
ω₀ = 1 / √(LC) = 2πf₀
At Resonance:
XL = XC → 2πf₀L = 1/(2πf₀C)
Solving for L or C:
L = 1 / (4π²f₀²C)
C = 1 / (4π²f₀²L)
Period:
T = 1/f₀ = 2π√(LC)
Example Calculation
Find the resonant frequency of a circuit with L = 10mH and C = 100nF:
L = 10 mH = 0.01 H
C = 100 nF = 100 × 10⁻⁹ F = 10⁻⁷ F
LC = 0.01 × 10⁻⁷ = 10⁻⁹
√(LC) = √(10⁻⁹) = 31.62 × 10⁻⁶
f₀ = 1/(2π × 31.62×10⁻⁶) = 5,033 Hz ≈ 5.03 kHz
Verification:
XL = 2π × 5033 × 0.01 = 316.2 Ω
XC = 1/(2π × 5033 × 10⁻⁷) = 316.2 Ω ✓
Wavelength: λ = c/f = 3×10⁸/5033 = 59.6 km
LC Resonant Frequency Reference Table
| Inductance | Capacitance | Resonant Frequency |
|---|---|---|
| 1 mH | 1 µF | 5,033 Hz |
| 1 mH | 100 nF | 15,915 Hz |
| 1 mH | 10 nF | 50,330 Hz |
| 10 mH | 100 nF | 5,033 Hz |
| 100 µH | 100 pF | 1.592 MHz |
| 100 µH | 10 nF | 159.2 kHz |
| 10 µH | 100 pF | 5.033 MHz |
| 10 µH | 10 pF | 15.92 MHz |
| 1 µH | 100 pF | 15.92 MHz |
| 1 µH | 10 pF | 50.33 MHz |
| 100 nH | 10 pF | 159.2 MHz |
| 10 nH | 10 pF | 503.3 MHz |
Frequently Asked Questions
What is resonant frequency?
Resonant frequency is the natural oscillation frequency of an LC circuit where energy transfers back and forth between the inductor and capacitor with maximum efficiency. At this frequency, the circuit's impedance is purely resistive (reactive components cancel), and the amplitude of oscillation is maximum for a given energy input.
Does resistance affect resonant frequency?
For ideal series and parallel RLC circuits, resistance does not change the resonant frequency — it only affects the amplitude and bandwidth of the resonance. However, in practical circuits with lossy components, the actual peak response frequency can shift slightly from the ideal f₀ = 1/(2π√LC), especially for low-Q circuits (Q < 5).
How do I tune an LC circuit to a specific frequency?
Choose either L or C as fixed, then calculate the other: C = 1/(4π²f²L) or L = 1/(4π²f²C). For variable tuning, use a variable capacitor (varactor diode for electronic tuning, or air-variable capacitor for manual tuning). For example, to tune to 1 MHz with L=100µH: C = 1/(4π² × 10¹² × 10⁻⁴) = 253 pF.
What is the relationship between resonant frequency and wavelength?
For electromagnetic waves: wavelength λ = c/f, where c = 3×10⁸ m/s (speed of light). A 1 MHz resonant circuit corresponds to a 300m wavelength (AM radio band). A 100 MHz circuit corresponds to 3m (FM radio). A 2.4 GHz circuit corresponds to 12.5cm (WiFi). This relationship is crucial for antenna design, where antenna length is typically λ/4 or λ/2.
Why do LC circuits oscillate?
When a charged capacitor is connected to an inductor, the capacitor discharges through the inductor, converting electric field energy to magnetic field energy. When fully discharged, the inductor's collapsing magnetic field recharges the capacitor in the opposite polarity. This cycle repeats at the resonant frequency. Without resistance, oscillation continues indefinitely (ideal case).
What are common applications of resonant circuits?
Radio/TV tuners (frequency selection), oscillators (signal generation), filters (bandpass/notch), impedance matching networks, wireless power transfer, RFID systems, MRI machines (nuclear magnetic resonance), and metal detectors. Any application requiring frequency-selective behavior uses resonant circuits in some form.
Resonance in Different Circuit Configurations
While the basic resonant frequency formula f₀ = 1/(2π√LC) applies to both series and parallel LC circuits, their behavior at resonance differs significantly. A series LC circuit has minimum impedance at resonance (ideally zero), allowing maximum current flow — useful for bandpass filters. A parallel LC circuit has maximum impedance at resonance (ideally infinite), blocking current flow — useful for band-reject filters and tank circuits in oscillators. Understanding this duality is key to choosing the right topology for your application.
Practical Applications
- AM/FM radio: Variable capacitor tunes LC circuit to select broadcast frequency
- Crystal oscillators: Quartz crystal acts as very high-Q LC equivalent
- Antenna matching: LC networks match antenna impedance to transmitter output
- Wireless charging: Resonant coupling maximizes power transfer efficiency
- EMI filters: LC filters attenuate specific interference frequencies
- Induction heating: High-frequency resonant circuits generate eddy currents in metals