About

In Radio Frequency (RF) engineering and signal processing, the parallel RLC circuit is a fundamental building block used for tuning and filtering. This calculator determines the resonant frequency-the point where the inductive and capacitive reactances cancel each other out, resulting in purely resistive impedance. It also calculates the Quality Factor (Q), which defines the sharpness of the resonance peak, and the Bandwidth (BW).

Accurate tuning requires precise values. This tool accepts inputs with standard engineering prefixes (pico, nano, micro) to avoid manual conversion errors, which are common when dealing with high-frequency circuits. The results help in designing tank circuits for oscillators or band-pass filters.

Formulas

Resonant Frequency:

f_r = 12π√LC

Bandwidth:

BW = 12πRC

Reference Data

Parameter	Symbol	Formula	Description
Resonant Freq	f_r	1/(2π√LC)	Frequency of oscillation
Angular Freq	ω₀	1/√LC	Radians per second
Quality Factor	Q	R√C/L	Sharpness of the peak
Bandwidth	BW	f_r / Q	Frequency range at -3dB
Damping Factor	ζ	1/(2Q)	Rate of decay
Inductive Reactance	X_L	2πfL	Opposition to change in current
Capacitive Reactance	X_C	1/(2πfC)	Opposition to change in voltage
Impedance at Res.	Z_max	R	Maximum impedance (Parallel)

Frequently Asked Questions

In a Series RLC circuit, impedance is minimized at resonance (short circuit behavior). In a Parallel RLC circuit (tank circuit), impedance is maximized at resonance (open circuit behavior). This makes parallel circuits ideal for selecting specific frequencies while rejecting others.

A high Q-factor indicates a narrow bandwidth and a very sharp resonance peak, which is desirable for selectivity in radio tuners. A low Q-factor means a wide bandwidth, useful for broadband applications.

The calculator has built-in dropdowns for units. Internally: 1 uF (micro) = 10^-6, 1 nF (nano) = 10^-9, 1 pF (pico) = 10^-12. Always ensure units are consistent if doing manual calculation.

If the resistor is removed (open circuit), the parallel LC circuit is "ideal" and would theoretically oscillate forever. In reality, internal resistance in wires and components always provides some damping.