Rlc Series Resonant⚠ unverified
Electrical / Filters · Compute the resonant frequency of a series RLC circuit
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| f0 | f0 | Hz | 1.0 | Nominal/reference frequency |
| R | R | — | 1.0 | Resistance |
| L | L | H | 1.0 | Inductance |
| C | C | F | 1.0 | Capacitance |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | f0 | Hz | Resonant frequency, in hertz (Hz) |
The science & history
Understanding the Parameters
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$L$, $C$ — resonance depends only on their product. $R$ does not shift $f_0$; it sets how sharp the resonance is (see Q Factor, Rlc Bandwidth).
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$f_0$ — where the circuit looks purely resistive (voltage and current in phase, unity power factor).
Derivation (Approaching a Proof)
The series impedance is $Z = R + j\big(\omega L - \tfrac{1}{\omega C}\big)$ (see Impedance Inductor, Impedance Capacitor). Resonance is where the reactive part vanishes, so the two reactances are equal:
$$\omega_0 L = \frac{1}{\omega_0 C} \quad\Rightarrow\quad \omega_0^2 = \frac{1}{LC} \quad\Rightarrow\quad f_0 = \frac{1}{2\pi\sqrt{LC}}.$$
At $f_0$, $|Z| = R$ is minimal, so for a fixed drive the current is maximal — the circuit "selects" $f_0$. (Equivalently, energy oscillates freely between $L$ and $C$ at this frequency; see Resonance Frequency LC Circuit.)
History
Series and parallel resonance are the electrical heart of tuning — matching a circuit's $f_0$ to a desired signal — dating to the wireless work of the 1890s–1900s (Lodge's "syntony," Marconi, Tesla). The same $1/(2\pi\sqrt{LC})$ governs oscillators, IF strips, and RF matching to this day.
Related Concepts: Resonance Frequency LC Circuit, Q Factor, Rlc Bandwidth, Impedance Inductor, Impedance Capacitor
Notes: Registry calculator rlc-series-resonant (unverified; the card lists a spurious f0 input and
mislabels R — only $L$ and $C$ set $f_0$).