RLC Circuit Solver
Add a resistor to an LC tank and you get the full second-order resonator: it still resonates at f₀ = 1/(2π√(LC)), but now the resistance sets the quality factor Q, the −3 dB bandwidth, and how the circuit rings when disturbed. This tool takes R, L and C for either a series or a parallel RLC circuit and returns the resonance, Q, bandwidth, characteristic impedance, damping factor, damping regime, and the damped natural frequency.
Equations & Parameters ▸
\(\omega_0=\dfrac{1}{\sqrt{LC}},\quad Z_0=\sqrt{\dfrac{L}{C}},\quad BW=\dfrac{f_0}{Q}\)
series: \(Q=\dfrac{\omega_0 L}{R}=\dfrac{Z_0}{R},\ \alpha=\dfrac{R}{2L}\); parallel: \(Q=\dfrac{R}{\omega_0 L}=\dfrac{R}{Z_0},\ \alpha=\dfrac{1}{2RC}\)
\(\zeta=\dfrac{\alpha}{\omega_0}=\dfrac{1}{2Q},\qquad \omega_d=\sqrt{\omega_0^2-\alpha^2}\ \ (\zeta<1)\)
series: \(Q=\dfrac{\omega_0 L}{R}=\dfrac{Z_0}{R},\ \alpha=\dfrac{R}{2L}\); parallel: \(Q=\dfrac{R}{\omega_0 L}=\dfrac{R}{Z_0},\ \alpha=\dfrac{1}{2RC}\)
\(\zeta=\dfrac{\alpha}{\omega_0}=\dfrac{1}{2Q},\qquad \omega_d=\sqrt{\omega_0^2-\alpha^2}\ \ (\zeta<1)\)
| Topology | Series (R, L, C in a loop) or parallel (R, L, C across a node). |
| R | Resistance (Ω). For parallel, this is the shunt/loss resistance. |
| L, C | Inductance and capacitance. |
Reference: Standard circuit theory; see Hayt & Kemmerly, Engineering Circuit Analysis, ch. 9.
Inputs
RLC form
Ω
Loss/dampingCoil
Cap
Results
Resonance
Resonant f₀—
Angular ω₀—
Characteristic Z₀ = √(L/C)—
Selectivity
Quality factor Q—
Bandwidth (−3 dB)—
Half-power f₁ / f₂—
Damping / transient
Damping factor ζ—
Attenuation α—
Regime—
Damped f_d—
Circuit