How do you design an LC filter from a prototype?

From RF Design Wiki · By the RF Design Wiki editorial team · Published October 21, 2026 · Last reviewed October 21, 2026 · How we research

LC filter design starts from normalized low-pass prototype values g_k, then applies impedance scaling (multiply L by R₀, divide C by R₀) and frequency scaling (divide by ω_c). For a low-pass: L_k = g_kR₀/ω_c, C_k = g_k/(R₀ω_c). Band-pass filters replace each element with a resonator.^[1]

What is a worked low-pass example?

Third-order Butterworth, 50 Ω, f_c = 100 MHz, shunt-C first. g = 1, 2, 1. C₁ = C₃ = 1/(50·2π·10⁸) ≈ 31.8 pF; L₂ = 2·50/(2π·10⁸) ≈ 159 nH.

How is the band-pass transformation done?

With center ω₀ = √(ω₁ω₂) and fractional bandwidth Δ = (ω₂ − ω₁)/ω₀, each series inductor becomes a series LC with L = g·R₀/(ω₀Δ), C = Δ/(ω₀·g·R₀); each shunt capacitor becomes a parallel LC with C = g/(ω₀ΔR₀), L = ΔR₀/(ω₀g). Narrow bandwidths give impractical value spreads, which coupled-resonator topologies avoid.^[1]^[2]

What practical issues arise?

Choose components with self-resonant frequency well above the passband (for low-pass, above the stopband you must reject).
Use standard values and re-optimize; check sensitivity with Monte Carlo.
Pad and via parasitics shift response above a few hundred MHz; include them in simulation.
Shield or separate input and output to preserve stopband rejection.

Frequently asked questions

Shunt-first or series-first?

Both are valid duals; choose based on available values and termination needs.

What limits LC filter frequency?

Component self-resonance, Q and parasitics, practically a few GHz.

Why do narrow filters use coupled resonators?

Direct transformation yields extreme L and C ratios; coupled resonators keep values practical.

References

Online sources accessed October 21, 2026; printed works cited by edition. See all sources.

“Microwave Engineering, 4th ed.”. D. M. Pozar, Wiley. 2012.
“Microwave Filters, Impedance-Matching Networks, and Coupling Structures”. G. Matthaei, L. Young, E. M. T. Jones, McGraw-Hill / Artech House. 1964; Artech reprint 1980.

Categories: Filters and passives

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