LC Resonance Circuit Calculator
Design and analysis of series, parallel, tapped and link-coupled LC circuits
Modes: Design (f₀,Q → L,C from E-series) | Design with known C (f₀,Q,C → L) | Design with known L
(f₀,Q,L → C) | Analysis (L,C → f₀,Q,BW) | Tuning (sweep)
Step 1: Circuit Configuration
Step 2: Input Parameters
Resonant frequency: f₀ = 1 / (2π√LC)
Impedance at resonance: Z_series(f₀) = Rs (resistive only)
Quality factor: Q = ωL / Rs = 1 / (ωCRs)
Bandwidth: BW = f₀ / Q
Cutoff frequencies: f_low = f₀ - BW/2, f_high = f₀ + BW/2
Reactances: XL = ωL, XC = 1/(ωC)
Impedance at resonance: Z_series(f₀) = Rs (resistive only)
Quality factor: Q = ωL / Rs = 1 / (ωCRs)
Bandwidth: BW = f₀ / Q
Cutoff frequencies: f_low = f₀ - BW/2, f_high = f₀ + BW/2
Reactances: XL = ωL, XC = 1/(ωC)
Series LC circuit has minimum impedance equal to Rs at resonance. Used in band-pass filters (BPF) and amplifier inputs.
Resonant frequency: f₀ = 1 / (2π√LC)
Impedance at resonance: Z_parallel(f₀) = Rp (high impedance)
Quality factor: Q = Rp / (ωL) = ωCRp
Bandwidth: BW = f₀ / Q
Alternatively: Z_parallel ≈ Q² × Rs (for high Q)
Impedance at resonance: Z_parallel(f₀) = Rp (high impedance)
Quality factor: Q = Rp / (ωL) = ωCRp
Bandwidth: BW = f₀ / Q
Alternatively: Z_parallel ≈ Q² × Rs (for high Q)
Parallel LC circuit has maximum impedance at resonance. Used in oscillators (VFO), notch filters and resonant amplifiers.
Transformation ratio: n² = Z_out / Z_in
Optimal tap: N_tap / N_total = √(Z_in / Z_out)
Input impedance: Z_in = Z_resonator / n²
Inductance at tap: L_tap = L_total × (N_tap / N_total)²
Optimal tap: N_tap / N_total = √(Z_in / Z_out)
Input impedance: Z_in = Z_resonator / n²
Inductance at tap: L_tap = L_total × (N_tap / N_total)²
Tapped circuit allows impedance matching via tap on the inductor. Often used in antenna tuners and PA output networks.
Coupling coefficient: k = M / √(L₁L₂)
Loaded Q: Q_L = Q_unloaded / (1 + k²Q²)
Critical coupling: k_critical = 1 / Q
Bandwidth: BW_loaded = f₀ / Q_L
Loaded Q: Q_L = Q_unloaded / (1 + k²Q²)
Critical coupling: k_critical = 1 / Q
Bandwidth: BW_loaded = f₀ / Q_L
Link coupling provides galvanic isolation between stages via mutual inductance M. Used between PA and ATU, in IF filters and input/output coupling.
E12: ±10% tolerance (10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82)
E24: ±5% tolerance (10, 11, 12, 13, 15, 16, 18, 20, 22, 24, 27, 30, 33, 36, 39, 43, 47, 51, 56, 62, 68, 75, 82, 91)
E96: ±1% tolerance (100 values per decade)
Frequency error (RSS): Δf/f₀ ≈ 0.5 × √(tol_L² + tol_C²)
Worst-case error: Δf/f₀ ≈ 0.5 × (tol_L + tol_C)
E24: ±5% tolerance (10, 11, 12, 13, 15, 16, 18, 20, 22, 24, 27, 30, 33, 36, 39, 43, 47, 51, 56, 62, 68, 75, 82, 91)
E96: ±1% tolerance (100 values per decade)
Frequency error (RSS): Δf/f₀ ≈ 0.5 × √(tol_L² + tol_C²)
Worst-case error: Δf/f₀ ≈ 0.5 × (tol_L + tol_C)
Temperature drift: Δf/f₀ [ppm/°C] = -0.5 × (TC_L + TC_C)
C0G/NP0: 0 ppm/°C (most stable)
X7R: -750 ppm/°C
Air coil: -50 ppm/°C
Ferrite core: -2000 ppm/°C
Coil DCR: ≈ 0.01-0.05 Ω/µH (depends on construction)
Capacitor ESR: ≈ 0.005-0.05 Ω (HF applications)
C0G/NP0: 0 ppm/°C (most stable)
X7R: -750 ppm/°C
Air coil: -50 ppm/°C
Ferrite core: -2000 ppm/°C
Coil DCR: ≈ 0.01-0.05 Ω/µH (depends on construction)
Capacitor ESR: ≈ 0.005-0.05 Ω (HF applications)
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