RLC Impedance Calculator

Calculate complex impedance, phase angle, and AC circuit parameters for series and parallel RLC circuits

Calculate RLC Circuit Impedance

Resistance value in the RLC circuit

Inductance value of the inductor

Capacitance value of the capacitor

Operating frequency of the AC signal

RLC Impedance Analysis Results

0.00 Ω
Total Impedance (|Z|)
0.0°
Phase Angle (φ)
0.000
Q-Factor
0.00 Ω
Inductive Reactance (XL)
0.00 Ω
Capacitive Reactance (XC)
0.000 Hz
Resonant Frequency (f₀)

Series RLC Circuit:

Impedance: Z = √(R² + (ωL - 1/ωC)²)

Phase angle: φ = arctan((ωL - 1/ωC)/R)

Angular frequency: ω = 0.00 rad/s

Impedance Characteristics

Example Calculation

Audio Crossover Network

Application: Audio speaker crossover at 1 kHz

Resistance (R): 8 Ω (speaker impedance)

Inductance (L): 2 mH (tweeter protection)

Capacitance (C): 10 μF (woofer coupling)

Frequency: 1 kHz (crossover frequency)

Circuit Type: Series RLC for frequency filtering

Calculation Results

ω = 2π × 1000 = 6283.18 rad/s

XL = ωL = 6283.18 × 0.002 = 12.57 Ω

XC = 1/(ωC) = 1/(6283.18 × 10×10⁻⁶) = 15.92 Ω

X = XL - XC = 12.57 - 15.92 = -3.35 Ω

Z = √(8² + (-3.35)²) = √(64 + 11.22) = 8.67 Ω

φ = arctan(-3.35/8) = -22.7° (capacitive)

Impedance Components

Resistance (R)

Real component that dissipates energy as heat. Independent of frequency.

Unit: Ohms (Ω)

Inductive Reactance (XL)

Reactive component from inductors. XL = ωL, increases with frequency.

Causes current to lag voltage

Capacitive Reactance (XC)

Reactive component from capacitors. XC = 1/(ωC), decreases with frequency.

Causes current to lead voltage

Phase Angle Guide

🟢

φ = 0°

Purely resistive - V and I in phase

🔵

φ > 0°

Inductive - voltage leads current

🔴

φ < 0°

Capacitive - voltage lags current

🟣

φ = ±90°

Purely reactive - no power dissipation

Quick Reference

Series RLC:
Z = √(R² + (XL - XC)²)
Parallel RLC:
Z = 1/√(1/R² + (1/XL - YC)²)
Phase Angle:
φ = arctan(X/R)
Reactances:
XL = ωL, XC = 1/(ωC)

Understanding RLC Circuit Impedance

What is Impedance?

Impedance is the total opposition to current flow in an AC circuit, combining both resistance (real part) and reactance (imaginary part). Unlike resistance, impedance varies with frequency and can be represented as a complex number with both magnitude and phase components.

Complex Impedance

  • Z = R + jX (rectangular form)
  • |Z| = √(R² + X²) (magnitude)
  • φ = arctan(X/R) (phase angle)
  • X = XL - XC (net reactance)

Frequency Response

At Low Frequencies (f << f₀):
• XC >> XL, circuit is capacitive
• Impedance decreases with frequency
• Phase angle is negative (leading)
At Resonance (f = f₀):
• XL = XC, reactances cancel
• Impedance = R (minimum for series)
• Phase angle = 0° (resistive)
At High Frequencies (f >> f₀):
• XL >> XC, circuit is inductive
• Impedance increases with frequency
• Phase angle is positive (lagging)

Series RLC Circuit

  • • Same current flows through all components
  • • Voltages add: V = VR + VL + VC
  • • Impedance: Z = R + j(XL - XC)
  • • Minimum impedance at resonance
  • • Used in bandpass filters and tuned circuits

Parallel RLC Circuit

  • • Same voltage across all components
  • • Currents add: I = IR + IL + IC
  • • Admittance: Y = G + j(BC - BL)
  • • Maximum impedance at resonance
  • • Used in tank circuits and oscillators