Parallel Rlc Calculator

Analyze the behavior of a parallel RLC circuit by calculating its key electrical properties. Enter the component values and frequency below. Ensure you use base units (Hertz, Ohms, Henries, Farads).

Enter circuit parameters and click “Calculate RLC Properties”

Circuit Parameters
Frequency (f):		Hz
Resistance (R):		Ω (Ohms)
Inductance (L):		H (Henries)
Capacitance (C):		F (Farads)
Note: For Farads, 1µF = 1e-6 F, 1nF = 1e-9 F, 1pF = 1e-12 F. For Henries, 1mH = 1e-3 H.

Understanding Parallel RLC Circuits

A parallel RLC circuit consists of a resistor (R), an inductor (L), and a capacitor (C) connected in parallel. When an AC voltage source is applied, the circuit’s behavior is frequency-dependent due to the reactances of the inductor and capacitor.

Key Parameters:

• Inductive Reactance (X_L): The opposition offered by an inductor to alternating current. It increases with frequency.
  X_L = 2πfL
• Capacitive Reactance (X_C): The opposition offered by a capacitor to alternating current. It decreases with frequency.
  X_C = 1 / (2πfC)
• Impedance (Z): The total opposition to current flow in an AC circuit. For a parallel RLC circuit, it’s calculated using admittances (reciprocal of impedance).
  Conductance (G) = 1/R
  Inductive Susceptance (B_L) = 1/X_L
  Capacitive Susceptance (B_C) = 1/X_C
  Total Admittance (Y) = √(G² + (B_C – B_L)²)
  Total Impedance (Z) = 1/Y
  Phase Angle (θ) = arctan((B_C – B_L)/G) for Admittance Y. The impedance phase angle is -θ.
• Resonant Frequency (f_r): The frequency at which X_L = X_C. In a parallel RLC circuit, impedance is maximum at resonance.
  f_r = 1 / (2π√(LC))
• Quality Factor (Q): A measure of how underdamped an oscillator or resonator is. For a parallel RLC circuit at resonance, it relates the energy stored to the energy dissipated per cycle. A higher Q factor indicates a sharper resonance peak (narrower bandwidth).
  Q = R√(C/L) or Q = R / X_L(resonant) = R / X_C(resonant)
• Bandwidth (BW): The range of frequencies for which the circuit’s power is at least half its maximum power (at resonance).
  BW = f_r / Q

At resonance, the reactive components (B_L and B_C) cancel each other out, and the circuit appears purely resistive (impedance is maximum and equal to R if it’s an ideal parallel tank driven by a current source, or more complex if driven by a voltage source with series resistance). Below resonance, the circuit is predominantly inductive. Above resonance, it’s predominantly capacitive.

Electronics Resources

Parallel R-L-C Circuits (AllAboutCircuits) RLC Circuit – Parallel (Wikipedia) Parallel RLC Circuit (HyperPhysics)