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Z = √(R² + (XL - XC)²)
Series Impedance
f₀ = 1 / (2π√LC)
Resonant Frequency
XL = 2πfL
Inductive Reactance
XC = 1 / (2πfC)
Capacitive Reactance
RLC impedance is the total opposition that a circuit containing a resistor (R), inductor (L), and capacitor (C) offers to alternating current (AC). Unlike pure resistance, impedance accounts for both energy dissipation (through resistance) and energy storage (through reactance). The impedance magnitude is calculated as Z = √(R² + (XL − XC)²), where XL is inductive reactance and XC is capacitive reactance. At the resonant frequency, XL equals XC, causing the reactive components to cancel and impedance to reach its minimum value equal to R alone. Understanding RLC impedance is essential for designing filters, tuning circuits, and analyzing AC power systems.
Identify the resistance (R in ohms), inductance (L in henries), capacitance (C in farads), and the operating frequency (f in hertz) of your circuit.
Compute XL = 2πfL. This represents the opposition to current flow from the inductor, which increases with frequency.
Compute XC = 1 / (2πfC). This represents the opposition to current flow from the capacitor, which decreases with frequency.
For a series RLC circuit, use Z = √(R² + (XL − XC)²). The phase angle is θ = arctan((XL − XC) / R), which indicates whether the circuit is inductive or capacitive.
RLC circuits form the foundation of bandpass, low-pass, high-pass, and band-stop filters used in audio equipment, radio receivers, and signal processing systems. The impedance characteristics determine the filter's cutoff frequencies and selectivity.
At the resonant frequency, the circuit impedance is minimized (series) or maximized (parallel), enabling applications in radio tuning, wireless power transfer, and oscillator circuits where frequency selectivity is critical.
Understanding impedance helps engineers analyze power factor, harmonic distortion, and voltage regulation in electrical distribution systems. Proper impedance matching maximizes power transfer efficiency.
| Application | R (Ω) | L | C | f₀ (Resonant) |
|---|---|---|---|---|
| AM Radio Tuner | 10 | 250 μH | 100 pF | 1.007 MHz |
| Audio Crossover (Low-pass) | 8 | 1.2 mH | 22 μF | 980 Hz |
| Power Line Filter (60 Hz) | 1 | 10 mH | 680 μF | 61 Hz |
| RF Matching Network | 50 | 100 nH | 10 pF | 159 MHz |
| EMI Suppression | 100 | 470 μH | 100 nF | 23.2 kHz |
| Wireless Charging (Qi) | 0.5 | 24 μH | 200 nF | 72.7 kHz |
Resistance opposes current flow and dissipates energy as heat, while impedance is the total opposition to AC current that includes both resistance and reactance. Impedance is a complex quantity with magnitude and phase, whereas resistance is purely real. In a DC circuit, impedance reduces to just resistance since reactance only exists with changing currents.
At resonance, the inductive reactance (XL) equals the capacitive reactance (XC), so they cancel each other out. In a series RLC circuit, impedance drops to its minimum value (equal to R), allowing maximum current to flow. In a parallel RLC circuit, impedance reaches its maximum value, minimizing current draw from the source.
The quality factor Q = (1/R) × √(L/C) measures how sharply the circuit resonates. A higher Q means a narrower bandwidth and more selective frequency response. Low-Q circuits have broad, gentle impedance curves while high-Q circuits have sharp, peaked responses ideal for precise frequency selection.
In a series RLC circuit, all components share the same current, and impedance is minimized at resonance. In a parallel RLC circuit, all components share the same voltage, and impedance is maximized at resonance. Series circuits act as bandpass filters for current, while parallel circuits act as bandpass filters for voltage.
This calculator is designed for single-frequency sinusoidal analysis. For non-sinusoidal waveforms (square, triangle, sawtooth), you would need to decompose the signal into its Fourier series harmonics and calculate the impedance at each harmonic frequency separately, then apply superposition to find the total response.
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