What is the formula for Parallel (Tank) Resonant Frequency?

The Parallel (Tank) Resonant Frequency formula is f = (1/2π) × √(1/(LC) − R²/L²), where f—Parallel resonant frequency (Hz); L—Inductance (H); C—Capacitance (F); R—Series resistance of the coil (Ω).

What does f mean in the Parallel (Tank) Resonant Frequency formula?

f is Parallel resonant frequency (Hz).

Parallel (Tank) Resonant Frequency

Q: How do you calculate Parallel (Tank) Resonant Frequency?

Use the formula f = (1/2π) × √(1/(LC) − R²/L²). A real parallel LC "tank" circuit resonates slightly below the ideal 1/(2π√LC) because the coil’s series resistance shifts the resonant frequency. Enter the values you know in the calculator above and it solves for the remaining variable.

f = (1/2π)·√(1/LC − R²/L²)

Calculator

Resonant Frequency

Inductance

Capacitance

Coil Resistance

Result

—

Formula

f = (1/2π) × √(1/(LC) − R²/L²)

Description

A real parallel LC "tank" circuit resonates slightly below the ideal 1/(2π√LC) because the coil’s series resistance shifts the resonant frequency. At resonance the tank impedance is maximum (anti-resonance), which is why parallel resonant circuits are used as frequency-selective loads in oscillators, RF amplifiers, and traps. When R is small the correction term is negligible.

Variables

f — Parallel resonant frequency (Hz)
L — Inductance (H)
C — Capacitance (F)
R — Series resistance of the coil (Ω)

Practical Notes

For a high-Q coil (small R) this reduces to the familiar f = 1/(2π√LC). The term R²/L² must stay below 1/LC or the circuit is overdamped and does not resonate.

Related Concepts

All AC Circuits formulas →

Resonant Frequency Impedance (RLC Series) Quality Factor (Bandwidth) Quality Factor (RLC) Power Factor Apparent Power Reactive Power RLC Circuit Bandwidth

Need more features?

Save calculations, import telemetry data, simulate battery discharge, and collaborate with your team.

Try the App