Parallel (Tank) Resonant Frequency
f = (1/2π)·√(1/LC − R²/L²)
Quick answer
This calculator solves f = (1/2π) × √(1/(LC) − R²/L²) for Resonant Frequency. With Inductance 10 µH, Capacitance 100 pF, Coil Resistance 0.47 Ω, the result is 5.033 MHz. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
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.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| f | Resonant Frequency | kHz | Hz, kHz, MHz, GHz |
| L | Inductance | mH | nH, µH, mH, H |
| C | Capacitance | nF | pF, nF, µF, mF, F |
| R | Coil Resistance | Ω | mΩ, Ω, kΩ, MΩ |
Step by step
- 1. What you know: Inductance 10 µH, Capacitance 100 pF, Coil Resistance 0.47 Ω
- 2. The relation: f = (1/2π) × √(1/(LC) − R²/L²)
- 3. Substitute: L = 10 µH, C = 100 pF, R = 0.47 Ω
- 4. Result: Resonant Frequency = 5.033 MHz
Worked examples
Minimum range
Given: Inductance 100 µH, Capacitance 100 pF, Coil Resistance 1 Ω
Result: Resonant Frequency = 1.592 MHz
Low range
Given: Inductance 1 mH, Capacitance 1 nF, Coil Resistance 10 Ω
Result: Resonant Frequency = 0.1591 MHz
Typical
Given: Inductance 10 µH, Capacitance 100 pF, Coil Resistance 0.47 Ω
Result: Resonant Frequency = 5.033 MHz
High range
Given: Inductance 100 µH, Capacitance 1 nF, Coil Resistance 4.7 Ω
Result: Resonant Frequency = 0.5032 MHz
Maximum range
Given: Inductance 1 mH, Capacitance 10 nF, Coil Resistance 47 Ω
Result: Resonant Frequency = 49.77 kHz
Solving for each variable
Solve for Resonant Frequency
Inductance 100 µH, Capacitance 100 pF, Coil Resistance 1 Ω → 1.592 MHz
Solve for Capacitance
Resonant Frequency 100 Hz, Inductance 100 µH, Coil Resistance 1 Ω → 99.61 µF
How Resonant Frequency changes with Inductance
| Inductance (input) | Resonant Frequency (result) |
|---|---|
| 1 µH | 15.92 MHz |
| 2.5 µH | 10.07 MHz |
| 5 µH | 7.118 MHz |
| 7.5 µH | 5.812 MHz |
| 10 µH | 5.033 MHz |
| 15 µH | 4.109 MHz |
| 20 µH | 3.559 MHz |
| 40 µH | 2.516 MHz |
| 70 µH | 1.902 MHz |
| 100 µH | 1.592 MHz |
The same result in other units
| Unit | Value |
|---|---|
| Hz | 5033000 |
| kHz | 5033 |
| MHz | 5.033 |
| GHz | 0.005033 |
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<p><a href="https://vbatpower.com/formulas/parallel-resonance/">Parallel (Tank) Resonant Frequency</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Parallel (Tank) Resonant Frequency?
Use f = (1/2π) × √(1/(LC) − R²/L²). With Inductance 10 µH, Capacitance 100 pF, Coil Resistance 0.47 Ω, Resonant Frequency works out to 5.033 MHz.
How do you calculate ideal resonant tank?
Rearrange for Resonant Frequency: with Inductance 1 mH, Capacitance 1 nF, Coil Resistance 10 Ω, Resonant Frequency is 0.1591 MHz.
How do you calculate parallel resonance?
Rearrange for Resonant Frequency: with Inductance 10 µH, Capacitance 100 pF, Coil Resistance 0.47 Ω, Resonant Frequency is 5.033 MHz.
What is the formula for Parallel (Tank) Resonant Frequency?
The formula is 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.
How do you find Capacitance when you know the other values?
Rearrange for Capacitance: with Resonant Frequency 100 Hz, Inductance 100 µH, Coil Resistance 1 Ω, Capacitance is 99.61 µF.
What units does Parallel (Tank) Resonant Frequency use?
Resonant Frequency is shown in Hz, kHz, MHz, GHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All AC Circuits formulas →Need more features?
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