RF Passives › Distributed Filters

Stepped Impedance Lowpass Filter

Design stepped-impedance lowpass filters using alternating high/low impedance microstrip sections. Enter your substrate, cutoff frequency and prototype order — get exact PCB trace widths and lengths, a schematic and frequency response. No external tools needed.

// PCB Substrate Parameters
// Filter Specifications
MHz
Ω
Ω
Ω
Design rules: ZH ≥ 2×Z0 (approximate series L)  ·  ZL ≤ Z0/2 (approximate shunt C)
Typical: ZH=100–150Ω, ZL=10–20Ω. Wider ratio → better approximation → sharper cutoff for same order.
// Design Equations
Series L approximation (ZH section):
Electrical length: θH,k = arcsin(gk·Z0/ZH)
Approximate inductance: Lk = ZH·sin(θH,k) / ωc

Shunt C approximation (ZL section):
Electrical length: θL,k = arcsin(gk·ZL/Z0)
Approximate capacitance: Ck = sin(θL,k) / (ZL·ωc)

Physical length from θ:
l = θ·λg/(2π) = θ·c / (2π·fc·√εeff)
// Filter Schematic
ZH sections (inductive) ZL sections (capacitive)
// Frequency Response (Prototype Model)
SI-LPF response Ideal LC prototype
// PCB Layout Rules
① Abrupt width transitions. Keep the transition from ZH to ZL as abrupt as possible — avoid chamfering as that defeats the purpose. The impedance step is the design intent.

② Ground plane clearance. ZL (wide) sections need ≥3× section width of clearance from any top-layer copper to avoid coupling.

③ Via stitching alongside. Run a row of GND vias on each side of the filter to suppress surface wave modes — especially important above 3 GHz.

④ Keep filter in a straight line. Bends add parasitic reactance. If bends are necessary, use mitered or curved bends — not right-angle corners.

⑤ Stopband limitation. SI-LPF has a spurious passband near 2×fc due to the λ/2 resonance of sections. Use an absorptive resistive section or cavity after the filter if high stopband rejection is required.

Stepped Impedance Lowpass Filter — Design Guide

A stepped impedance lowpass filter (SI-LPF) is the simplest type of distributed microwave filter. It replaces the lumped inductors and capacitors of an LC prototype with alternating sections of high and low characteristic impedance microstrip lines. High impedance sections (narrow traces) approximate series inductors; low impedance sections (wide traces) approximate shunt capacitors.

Why Use Stepped Impedance Instead of Lumped LC?

At microwave frequencies above about 1 GHz, lumped components become impractical — inductors have self-resonant frequencies that limit their useful range, and capacitors become difficult to mount without adding parasitic inductance. SI-LPF sections have no self-resonance issue (they are purely distributed structures) and can be fabricated directly on PCB with no additional components. The design is also mechanically robust and repeatable.

Design Trade-offs

The approximation quality depends on the impedance ratio ZH/ZL. A wider ratio gives a better approximation to lumped elements and allows a higher-order filter in a given physical length. However, ZH is limited by the minimum manufacturable trace width (typically 0.1–0.2 mm), and ZL is limited by the maximum trace width that fits the board and stays below the surface wave threshold. On FR4 at 2.4 GHz: ZH=120Ω (W≈0.3 mm) and ZL=15Ω (W≈14 mm) are practical limits.

Spurious Passband

Unlike lumped LC filters, SI-LPF has a spurious passband that appears near 2×fc. This is because the distributed sections pass signals again when they become a half-wavelength long. If high stopband attenuation is required at multiples of the cutoff frequency, an additional lumped-element or cavity filter section must be cascaded.