LC Filter Resonance & Characteristic Impedance
Resonant (natural) frequency and characteristic impedance of an LC filter, computed in one step from the inductance L and capacitance C.
Worked example
Input: Inductance L 10 µH, Capacitance C 100 nF
Result: Natural (resonant) frequency f₀ 159.155 kHz, Characteristic impedance √(L/C) 10 Ω
Result: Natural (resonant) frequency f₀ 159.155 kHz, Characteristic impedance √(L/C) 10 Ω
Formula
f₀ = 1 / (2π·√(LC))
Z₀ = √(L / C)
How it works
The natural frequency of an LC low-pass filter is f₀ = 1/(2π√(LC)) and its characteristic impedance is √(L/C). Above f₀ it is a second-order filter and attenuates 40 dB per decade. Useful for first-pass design of DC-DC converter filters and mains EMI filters.
Practical tipf₀ is the natural (resonant) frequency; the −3 dB point depends on load and Q. Near resonance the filter amplifies (Q peaking) and can interact with the source impedance and become unstable. Compare the characteristic impedance with the load impedance and add damping resistance if needed.
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Results and summaries are for reference. For certification and test reports use the latest official standard text and calibrated instrument data. Last updated: 2026-10-10