Resonance Frequency Calculator
Resonance frequency is the natural frequency at which a circuit or system oscillates with maximum amplitude. In an LC circuit, it's the frequency where the inductive reactance (Xʟ = 2πfL) equals the capacitive reactance (Xᴄ = 1/(2πfC)). At this point, energy oscillates between the inductor's magnetic field and the capacitor's electric field, and the circuit exhibits special impedance characteristics depending on configuration.
Resonance enables selective frequency response in electronic circuits. It's fundamental to radio receivers (tuning to specific stations), oscillators (generating precise frequencies), filters (passing or blocking certain frequencies), and many wireless systems. Understanding resonance allows engineers to design circuits that efficiently transfer energy at desired frequencies.
Key resonance concepts:
- Resonant frequency: f₀ = 1/(2π√(LC))
- Angular frequency: ω₀ = 1/√(LC) rad/s
- Impedance at resonance: Series: Z = R (minimum), Parallel: Z = L/(RC) (maximum)
- Bandwidth: Δf = f₀/Q, where Q = quality factor
- Selectivity: Ability to discriminate between close frequencies
This calculator solves for any parameter in the LC resonance equation:
- Find Frequency: Enter L and C → Get resonant frequency f₀
- Find Inductance: Enter f₀ and C → Get required inductance L
- Find Capacitance: Enter f₀ and L → Get required capacitance C
The calculator provides:
- Complete resonant parameters: Frequency, angular frequency, period, reactance
- Multiple unit support: L (H, mH, µH, nH), C (F, µF, nF, pF), f (Hz, kHz, MHz, GHz)
- Common circuit presets: AM/FM radio, WiFi, crystal radio, audio filters
- Impedance analysis: Calculates reactance at resonance for series/parallel understanding
- Educational insights: Explains circuit behavior at resonance
Typical inductance and capacitance values and their resonant frequencies:
| Application | Inductance (L) | Capacitance (C) | Resonant Frequency | Band |
|---|---|---|---|---|
| AM Radio (low end) | 100 µH | 365 pF | 530 kHz | Medium Wave |
| AM Radio (high end) | 100 µH | 100 pF | 1590 kHz | Medium Wave |
| FM Radio (88 MHz) | 0.1 µH | 32 pF | 88 MHz | VHF |
| FM Radio (108 MHz) | 0.1 µH | 22 pF | 108 MHz | VHF |
| WiFi 2.4 GHz | 2 nH | 1.8 pF | 2.4 GHz | UHF/SHF |
| WiFi 5 GHz | 1 nH | 1 pF | 5.0 GHz | SHF |
| Crystal Radio | 500 µH | 365 pF | 370 kHz | Long Wave |
| Audio Filter | 100 mH | 0.1 µF | 1.59 kHz | Audio |
| Induction Heating | 10 µH | 0.1 µF | 159 kHz | Medium Frequency |
| Tesla Coil (primary) | 100 µH | 0.1 µF | 50 kHz | Low Frequency |
Audio (20 Hz - 20 kHz): Large L and C values (mH, µF)
Radio Frequency (100 kHz - 100 MHz): µH and pF combinations
VHF/UHF (100 MHz - 3 GHz): nH and pF (stray capacitance matters)
Microwave (>3 GHz): Distributed elements, not lumped LC
Below are answers to frequently asked questions about resonance frequency:
Use the formula f = 1 / (2π√(LC)).
Given: L = 100 µH = 100×10⁻⁶ H, C = 100 pF = 100×10⁻¹² F
LC = 100×10⁻⁶ × 100×10⁻¹² = 1×10⁻¹⁴
√(LC) = √(1×10⁻¹⁴) = 1×10⁻⁷
2π√(LC) = 2π × 1×10⁻⁷ ≈ 6.2832×10⁻⁷
f = 1 / (6.2832×10⁻⁷) ≈ 1.59×10⁶ Hz = 1.59 MHz
Quick approximation: For L in µH and C in pF, f (MHz) ≈ 159.15 / √(L_µH × C_pF).
Real circuits have parasitic capacitance and inductance that shift resonance:
- PCB traces: Add small inductance (~1 nH/mm) and capacitance (~0.2 pF/mm)
- Component leads: Inductance ~1 nH/mm, capacitance ~0.5 pF
- Adjacent conductors: Increase capacitance
- Dielectric materials: Change effective capacitance
Correction: f_actual = 1/(2π√((L+L_parasitic)(C+C_parasitic)))
At high frequencies (>100 MHz), these effects dominate. Use simulation or measurement.
LC tank circuits store energy and oscillate at their resonant frequency, used in oscillators to generate sine waves:
| Component | Role in Oscillator | Example Circuit |
|---|---|---|
| LC Tank | Determines oscillation frequency | Colpitts, Hartley oscillators |
| Amplifier | Compensates for losses (provides negative resistance) | Transistor, op-amp |
| Feedback | Sustains oscillations | Capacitive or inductive divider |
| Start-up condition | Loop gain >1 initially | Biasing network |
Example Colpitts: Two capacitors in series with inductor across them. Frequency = 1/(2π√(L×(C₁C₂/(C₁+C₂)))).
Wireless power uses resonant inductive coupling at the same frequency:
- Choose frequency: Typically 100-200 kHz for Qi standard, 6.78 MHz for AirFuel
- Design coils: Self-inductance L₁ and L₂ based on size and turns
- Add capacitors: Choose C₁ and C₂ so that f₀ = 1/(2π√(L₁C₁)) = 1/(2π√(L₂C₂))
- Match impedance: Use series or parallel resonance to optimize power transfer
- Consider coupling coefficient k: Changes effective inductance, may need tuning
Example: f₀=100kHz, L=100µH → C = 1/((2π×100e3)² × 100e-6) ≈ 25 nF.
Quality factor Q measures the sharpness of resonance and energy efficiency:
| Parameter | Formula | Meaning |
|---|---|---|
| Q (series RLC) | Q = ω₀L / R = 1/(ω₀CR) | Higher Q → lower loss, sharper peak |
| Q (parallel RLC) | Q = R / (ω₀L) = ω₀CR | Higher Q → higher impedance at resonance |
| Bandwidth (Δf) | Δf = f₀ / Q | Frequency range where power > half |
| Energy relationship | Q = 2π × (energy stored / energy lost per cycle) | Measure of damping |
Practical Q values: Air-core coils Q ≈ 50-200, ferrite-core Q ≈ 20-100, quartz crystal Q ≈ 10⁴-10⁶. High-Q circuits used in filters, oscillators for stability.
Mechanical resonance is analogous to electrical resonance:
| Electrical | Mechanical Equivalent |
|---|---|
| Inductance L | Mass (inertia) |
| Capacitance C | Compliance (spring constant inverse) |
| Resistance R | Damping (friction) |
| Resonant frequency f = 1/(2π√(LC)) | f = 1/(2π√(m/k)) (spring-mass system) |
| Voltage across capacitor | Displacement of mass |
| Current through inductor | Velocity of mass |
Examples: Pendulum, bridge vibrations, tuning forks, musical instruments. At resonance, amplitude increases dramatically, can cause structural failure (Tacoma Narrows Bridge).