Calculator KB-31
Reactance and resonance calculator
A capacitor blocks low frequencies more effectively, while an inductor blocks high frequencies. Resonance occurs where their reactances are equal.
Result
In brief: Calculate the capacitive and inductive reactance, resonant frequency, and characteristic impedance of an LC circuit, with a frequency response graph. Example: Resonant frequency: 1.592 kHz.
Calculation example
| Frequency | 1 kHz |
|---|---|
| Capacity | 1 µF |
| Inductance | 10 mH |
| Resonant frequency | 1.592 kHz |
|---|---|
| Capacitive reactance XC | 159.2 Ω |
| Inductive reactance XL | 62.83 Ω |
| Series circuit at this frequency | 96.32 Ω |
| Characteristic impedance | 100 Ω |
How it is calculated
XL = 2π · f · L
f₀ = 1 / (2π · √(L · C))
Reactance doesn’t dissipate energy; it stores it and gives it back. At the resonant frequency, XL and XC are equal: a series circuit nearly shorts the signal, while a parallel circuit nearly opens it.
What to look for
- Real components aren’t ideal: a capacitor has ESR and lead inductance, so above its resonant frequency it behaves like an inductor.
- A 100 nF ceramic capacitor is often placed next to an electrolytic specifically to handle high frequencies.
Frequently asked questions
How do you calculate a capacitor's reactance at a given frequency?
Xc = 1 / (2π · f · C). A 1 µF capacitor has a reactance of 159 Ω at 1 kHz, and 3.18 kΩ at 50 Hz.
How do you find the resonant frequency of an LC circuit?
f₀ = 1 / (2π · √(L · C)). A 10 mH inductor and a 1 µF capacitor resonate at 1.59 kHz, with a characteristic impedance of 100 Ω.
Why does a capacitor stop working at high frequencies?
It has lead inductance. Above its self-resonant frequency, it behaves like an inductor, so a small-capacitance ceramic capacitor is placed nearby for high frequencies.
