LC Resonant Frequency Calculator
What This LC Resonant Frequency Calculator Does
An LC resonant circuit combines an inductor (L) and a capacitor (C) so that energy oscillates back and forth between magnetic and electric fields. This calculator helps you find the resonant frequency f of that oscillation from the inductance and capacitance values you choose.
Resonant LC circuits are fundamental building blocks in radios, filters, oscillators, and impedance-matching networks. By choosing L and C carefully, you can tune a circuit to respond strongly at one frequency and reject others.
Resonant Frequency Formula
The ideal resonant frequency of a simple LC circuit is given by:
f = 1 / (2π√(LC))
where:
- f is the resonant frequency in hertz (Hz)
- L is the inductance in henries (H)
- C is the capacitance in farads (F)
In mathematical notation, the relationship can be written as:
This formula applies to both series and parallel LC configurations when you are only interested in the ideal resonant frequency and you ignore all resistance and parasitic elements.
How to Use This Calculator
To compute the resonant frequency of your LC circuit:
- Enter the inductance L in henries (H). You can also enter values using decimal forms of common prefixes, for example:
- 1 mH = 0.001 H
- 10 µH = 0.00001 H
- Enter the capacitance C in farads (F). Typical design values are very small, for example:
- 100 nF = 100 × 10−9 F = 0.0000001 F
- 10 pF = 10 × 10−12 F = 0.00000000001 F
- Optionally, enter the series resistance R in ohms (Ω). The simple LC resonance formula does not depend on R, but resistance affects the circuit quality factor (Q) and bandwidth. The calculator may show R alongside the result to remind you that real-world components are not ideal.
- Submit the form to compute the resonant frequency. The result is calculated in hertz (Hz) and can also be interpreted in kHz, MHz, or GHz depending on the magnitude.
If you see very large or very small numbers, check that you converted your milli (m), micro (µ), nano (n), and pico (p) prefixes correctly into base SI units.
Interpreting the Result
The computed value of f is the frequency at which the inductor and capacitor exchange energy most efficiently. Around this frequency:
- A series LC circuit tends to have a very low impedance.
- A parallel LC circuit tends to have a very high impedance.
Typical frequency ranges and where they often appear include:
- Audio band (20 Hz – 20 kHz): tone generators, basic audio filters, some power applications.
- kHz range: switching power supplies, low-frequency communication links, RFID systems.
- MHz range: AM/FM radio, many RF filters, oscillators, and antenna matching networks.
- GHz range: microwave links, radar, high-frequency wireless communication.
If your computed frequency falls far outside the band you expect, verify that both L and C are in the correct units and that you did not confuse, for example, nF with pF or mH with µH.
Worked Example
Suppose you are designing a simple tuned circuit for a 10 MHz RF application and you want to know the resonant frequency of a particular inductor–capacitor combination. Assume:
- L = 1 µH = 1 × 10−6 H
- C = 250 pF = 250 × 10−12 F
Step 1: Multiply L and C.
L × C = (1 × 10−6) × (250 × 10−12) = 250 × 10−18 = 2.5 × 10−16
Step 2: Take the square root.
√(LC) = √(2.5 × 10−16) ≈ 5 × 10−8
Step 3: Multiply by 2π.
2π√(LC) ≈ 2 × 3.1416 × 5 × 10−8 ≈ 3.1416 × 10−7
Step 4: Take the reciprocal to find f.
f = 1 / (2π√(LC)) ≈ 1 / (3.1416 × 10−7) ≈ 3.18 × 106 Hz
So the resonant frequency is about 3.18 MHz. If your target is 10 MHz, you would need to adjust either L, C, or both. For example, you could reduce the inductance, reduce the capacitance, or do both in a way that makes LC smaller so that the frequency increases.
Using the Calculator in Design
Here are some common ways this LC resonant frequency calculator ties into real design tasks.
Tuning Radio Receivers
In many radio receivers, an LC resonant tank is used at the front end to select a narrow band of frequencies and reject others. By adjusting C with a variable capacitor (or adjusting L with a tunable inductor), you shift the resonant frequency to tune different stations. Enter your chosen L and C values into the calculator to see which frequency band the circuit will favor.
Designing Filters
LC resonant circuits can form the core of band-pass and band-stop filters. The resonant frequency sets the center of the passband or stopband. Designers may start with a target center frequency, then use this formula to back-calculate combinations of L and C that achieve the desired resonance. After that, more detailed filter synthesis tools refine component values and add damping resistors.
Antenna Matching Networks
For antennas, impedance matching is critical to transfer power efficiently between a transmitter (or receiver) and the antenna. LC networks, such as L-matches, Pi networks, and T networks, are commonly used. They rely on resonance at the operating frequency to transform impedances. Once you know your operating frequency and load impedance, you can choose candidate L and C values, then verify the resulting resonance using the calculator.
Comparison: Series vs Parallel LC Circuits
The basic LC resonance formula is the same for ideal series and parallel circuits, but their behavior in a larger system differs. The following table summarizes key differences.
| Feature | Series LC Circuit | Parallel LC Circuit |
|---|---|---|
| Impedance at resonance | Minimum (ideally near zero) | Maximum (ideally very high) |
| Typical use | Series-resonant filters, impedance matching in some RF stages | Tank circuits, oscillators, band-pass or notch filters |
| Current behavior | Current peaks at resonance for a given applied voltage | Circulating currents within the LC branch can be large, but line current can be small |
| Voltage behavior | Component voltages can be higher than source voltage at resonance due to high circulating current | Voltages across L and C can be large even when input current is small |
| Effect of added resistance | Reduces peak current and widens the resonance curve (lower Q) | Reduces impedance at resonance and broadens the resonance curve (lower Q) |
| Common frequency range | From audio to high RF, depending on component values and losses | Commonly used in RF, oscillators, and tuned amplifiers |
Assumptions and Limitations
The LC resonant frequency formula is powerful but rests on several simplifying assumptions. When you apply the calculator’s results to real hardware, keep the following in mind:
- Ideal components: The formula assumes perfect inductors and capacitors with no series resistance, core losses, dielectric losses, or parasitic elements.
- No parasitic capacitance or inductance: Real circuits include stray capacitance between traces and wires, lead inductance, and coupling to nearby components. These parasitics can shift the actual resonant frequency.
- Linear behavior: The calculation assumes the inductor and capacitor remain linear over the applied voltage and current range. Core saturation, dielectric nonlinearity, and temperature effects are ignored.
- Single-frequency analysis: The formula only gives the principal resonance. In complex networks, additional resonances and anti-resonances can appear.
- Resistance and Q factor: Resistance does not change the basic resonance formula, but it strongly affects the quality factor (Q), bandwidth, and peak currents or voltages. The calculator’s frequency result is best viewed as an ideal center point.
Because of these limitations, treat the calculated resonant frequency as an estimate and starting point. For precision work, designers typically:
- Model the full circuit in a SPICE or RF simulation tool that includes parasitics and losses.
- Measure real prototypes with instruments such as network analyzers or impedance analyzers.
- Fine-tune component values based on measurements to achieve the exact target frequency.
This calculator is most useful for learning, quick design estimates, and early-stage what-if analysis, rather than final verification of a critical RF design.
Next Steps and Related Topics
Once you are comfortable with LC resonance, you may want to explore related concepts such as RLC circuits, quality factor (Q), bandwidth, and impedance matching networks. Many of these extend the same basic ideas you see in the LC resonant frequency formula while adding resistance, multiple reactive elements, and more realistic loss models.
Resonance Hunter
The calculator tells you the frequency. The game lets you feel it. Hunt for signal frequencies drifting across the electromagnetic spectrum by tuning your LC circuit in real-time. Energy pulses between your inductor and capacitor—match the resonance, lock the signal, chase the combo.
Tip: Larger L or C values lower the frequency (f = 1/(2π√LC)). Energy oscillates between the magnetic field in your inductor coil and the electric field in your capacitor plates. When you match a signal's frequency, you've found resonance—the circuit rings in harmony.