Complete Guide to LC Resonance: Frequency, Q Factor, Bandwidth
The Resonance Frequency Calculator determines resonant frequency (f₀), Q factor, and bandwidth for series and parallel LC circuits. Essential for tuned circuits, filters, and oscillators.
What is Resonance?
Resonance occurs when inductive reactance (XL) equals capacitive reactance (XC). Energy oscillates between L and C with minimal loss.
- Series LC: Minimum impedance, maximum current
- Parallel LC: Maximum impedance, minimum current
Our Resonance Calculator uses standard formulas with optional resistance for real-world Q and bandwidth.
Resonant Frequency Formula
f₀ = 1 / (2π √(LC)) — same for series and parallel.
Q Factor (Quality Factor)
- Series: Q = (1/R) × √(L/C)
- Parallel: Q = R × √(C/L)
Higher Q → sharper peak, narrower bandwidth.
Bandwidth
BW = f₀ / Q — frequency range where power ≥ 50% of peak.
Why Use Resonance?
- Radio Tuning: Select station frequency
- Filters: Band-pass, band-stop
- Power Transfer: Maximum efficiency
- Oscillators: Crystal, LC tanks
Pair with Reactance and Impedance calculators.
Formulas Summary
| Parameter | Series | Parallel |
|---|---|---|
| f₀ | 1/(2π√(LC)) | |
| Q | (1/R)√(L/C) | R√(C/L) |
| BW | f₀/Q | |
| Impedance at f₀ | R | Very high |
Behavior at Resonance
- Series: Z = R, current max, voltage across L/C = Q × V_in
- Parallel: Z ≈ L/(R×C), current in tank high, total current min
Calculation Steps
- Convert Units: mH → H, μF → F
- Compute f₀: 1/(2π√(LC))
- If R given: Calculate Q and BW
- Verify: XL = XC at f₀
Example: L=10 mH, C=100 nF, R=5 Ω (Series)
- f₀ = 1/(2π√(0.01×100e-9)) ≈ 5033 Hz
- Q = (1/5) × √(0.01/100e-9) ≈ 200
- BW = 5033 / 200 ≈ 25 Hz
Component Selection
| Parameter | Typical Values |
|---|---|
| L | 1 μH – 100 mH |
| C | 1 pF – 100 μF |
| Q | 10–1000 (air core higher) |
Real-World Losses
- ESR (C): Increases series R
- Winding R (L): Reduces Q
- Stray C: Shifts f₀
Applications
- RF Tuners: AM/FM radios
- Wireless Charging: Resonant coupling
- Medical: MRI coils
- Power Electronics: LLC converters
Design Tips
- High Q: Use low-loss cores, silver mica caps
- Tuning: Variable C or L
- Impedance Matching: Q affects bandwidth
- Safety: High voltages in series at resonance
Common Mistakes
- Unit Errors: nF as μF
- Ignoring R: Q infinite unrealistic
- Parallel R: Not same as series
- DC Analysis: Resonance only in AC
Advanced Topics
- Damped Oscillation: Under/critically/overdamped
- Coupled Resonators: Band-pass filters
- Crystal Resonance: Piezoelectric Q > 10,000
- Temperature Drift: C0G/NP0 caps stable
FAQs
Is f₀ same for series and parallel? Yes — depends only on L and C.
Can Q be > 1000? Yes — quartz crystals, superconducting coils.
How to measure resonance? Sweep frequency, find peak current (series) or voltage (parallel).
Conclusion
LC resonance enables selective frequency circuits. Our Resonance Frequency Calculator delivers f₀, Q, and bandwidth instantly. Design precision filters and oscillators with Reactance, Impedance, and Construction tools. Innovate with 1000 Calculators.