When a single ferrite bead or capacitor isn't enough to clean up a noisy line, you reach for a Pi filter or T filter. These are two- and three-element networks that combine capacitors and inductors (or ferrites) into a lumped low-pass structure with much steeper rolloff than any single component can provide.

A Pi filter looks like the Greek letter π: capacitor to ground, series inductor, capacitor to ground. A T filter is the dual: series inductor, capacitor to ground, series inductor. Which one you pick depends on the source and load impedances:

• Pi filter works best when both source and load are high impedance. The shunt caps present a low impedance to noise, forcing it to ground rather than propagating.
• T filter works best when both source and load are low impedance. The series inductors block noise current from flowing through low-Z paths.
• L filter (asymmetric, one L and one C) is the choice when source and load impedances differ dramatically — put the shunt element on the high-Z side.

Get the impedance pairing wrong and you get reflection, not attenuation. A Pi filter driving a low-impedance load can actually resonate and amplify noise at the LC corner. This is why datasheets for USB, HDMI, and Ethernet common-mode chokes always specify the target impedance environment.

Real-world example: USB 2.0 power line filtering on a laptop dock. The 5V rail feeds a downstream device drawing ~500 mA, with switching noise from the upstream buck converter around 1–10 MHz. A typical Pi filter uses a 10 µF ceramic → 600Ω @ 100MHz ferrite bead → 10 µF ceramic. The caps handle low-frequency ripple; the ferrite dissipates high-frequency energy as heat. Combined attenuation exceeds 40 dB in the FM band, which keeps the dock from desensitizing the laptop's Wi-Fi radio.

Rule of thumb — cutoff frequency: For a symmetric Pi or T filter with inductance L and total shunt capacitance C, the -3 dB corner is:

f_c ≈ 1 / (2π√(LC))

Example: L = 1 µH, C = 10 nF → f_c ≈ 1.6 MHz. Above cutoff, attenuation rolls off at 40 dB/decade (Pi/T) versus 20 dB/decade for a single-pole RC. Place the cutoff at least a decade below your noise frequency and a decade above your signal bandwidth.

Watch out for self-resonance: real capacitors become inductive above ~10–100 MHz, and real inductors become capacitive. Combine a large electrolytic (bulk energy storage) with a small ceramic (high-frequency bypass) at each shunt node to cover a wider band.