LC Resonance Cheat Sheet
LC resonant frequency formulas, series vs parallel resonance, Q factor.
Reference
Core formulas
- Resonant frequency
- f_r = 1 / (2π √(L · C))
- Quality factor
- Q = ω₀·L / R = 1 / (ω₀·R·C) = (1/R) · √(L/C)
- Bandwidth
- Δf = f_r / Q
- Damping
- ζ = R / (2√(L/C)) = 1/(2Q)
- Characteristic Z
- = √(L/C)
Series LC (trap)
- Impedance minimum at resonance — Z ≈ 0 ideally.
- Used as a notch filter to reject one frequency.
- Antenna tuners, crystal filters.
Parallel LC (tank)
- Impedance maximum at resonance — ideally infinite.
- Used as a selective filter — RF tuning, oscillators.
- Current circulates between L and C at resonance.
Common f_r values
| L | C | f_r |
|---|---|---|
| 1 µH | 100 pF | 15.9 MHz |
| 1 µH | 1 nF | 5.03 MHz |
| 10 µH | 10 nF | 503 kHz |
| 100 µH | 100 nF | 50.3 kHz |
| 1 mH | 1 µF | 5.03 kHz |
| 1 mH | 10 µF | 1.59 kHz |
| 100 mH | 1 µF | 503 Hz |
Notes
- Real inductors have series resistance (DCR) that limits Q. Air-core is highest Q but lowest L.
- At RF (>100 MHz), parasitic capacitance of the inductor (SRF) limits useful range.
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