RLC Circuit Calculator

Calculate resonant frequency, Q-factor, impedance, and damping characteristics for RLC circuits

Calculate RLC Circuit Parameters

Resistance value in the RLC circuit

Inductance value of the inductor

Capacitance value of the capacitor

RLC Circuit Analysis Results

0.000 Hz
Resonant Frequency (f₀)
0.000
Q-Factor
0.000 Hz
Bandwidth (BW)
0.0000
Damping Factor (ζ)
0.00 Ω
Characteristic Impedance (Z₀)
0.000e+0
Angular Frequency (ω) rad/s

Resonant frequency: f₀ = 1 / (2π √(LC))

Q-factor: Q = (1/R) × √(L/C)

Input values: R = 0.00 Ω, L = 0.000e+0 H, C = 0.000e+0 F

Circuit Quality Analysis

Example Calculation

Radio Tuning Circuit

Application: AM radio tuning circuit

Resistance (R): 30 Ω (coil resistance)

Inductance (L): 25 mH (tuning coil)

Capacitance (C): 50 μF (variable capacitor)

Circuit Type: Series RLC for frequency selection

Calculation Results

f₀ = 1 / (2π √(LC))

f₀ = 1 / (2π √(0.025 × 0.000050))

f₀ = 1 / (2π √(1.25×10⁻⁶))

f₀ = 1 / (2π × 1.118×10⁻³)

f₀ = 142.35 Hz

Q = (1/30) × √(0.025/0.000050) = 0.745

RLC Circuit Applications

Radio Tuning

Variable capacitor circuits for selecting specific radio frequencies from the spectrum.

Frequency: AM (0.5-1.6 MHz), FM (88-108 MHz)

Audio Filters

Bandpass and notch filters in audio equipment and crossover networks.

Frequency: 20 Hz - 20 kHz (audio range)

Oscillators

LC tank circuits in radio transmitters and signal generators.

High Q required for stable oscillation

Q-Factor Guide

🔴

Q < 0.5

Overdamped - No oscillations

🟡

Q = 0.5

Critically damped - Fastest response

🔵

0.5 < Q < 1

Underdamped - Some overshoot

🟢

Q ≥ 1

Good quality - Suitable for resonant circuits

Quick Reference

Resonant Frequency:
f₀ = 1 / (2π√(LC))
Q-Factor:
Q = (1/R) × √(L/C)
Bandwidth:
BW = f₀ / Q
Damping Factor:
ζ = 1 / (2Q)

Understanding RLC Circuits

What is an RLC Circuit?

An RLC circuit is an electrical circuit consisting of a resistor (R), inductor (L), and capacitor (C) connected in series or parallel. These circuits are fundamental building blocks in electronics, exhibiting natural resonant behavior where energy oscillates between the magnetic field of the inductor and the electric field of the capacitor.

Key Characteristics

  • Resonant frequency depends only on L and C values
  • Quality factor Q determines circuit selectivity
  • Resistance R controls damping and bandwidth
  • Phase relationship between voltage and current varies with frequency

Circuit Behavior

At Resonance (f = f₀):
• Inductive and capacitive reactances cancel
• Impedance is minimum (series) or maximum (parallel)
• Current and voltage are in phase
• Maximum power transfer occurs

Design Considerations

  • Higher Q provides better frequency selectivity
  • Lower resistance increases Q-factor
  • Bandwidth is inversely proportional to Q
  • Component tolerances affect frequency accuracy

Series RLC Circuit

  • • Impedance Z = R + j(ωL - 1/ωC)
  • • Minimum impedance at resonance (Z = R)
  • • Maximum current at resonant frequency
  • • Voltage across L and C can exceed input voltage
  • • Used in bandpass filters and tuned amplifiers

Parallel RLC Circuit

  • • Admittance Y = G + j(ωC - 1/ωL)
  • • Maximum impedance at resonance
  • • Minimum current from source at resonance
  • • Current through L and C can exceed input current
  • • Used in tank circuits and oscillators