You've met the Zobel network already — the RC series pair across an amplifier output that flattens a speaker's rising voice-coil impedance. But real loudspeaker loads punish amplifiers in two distinct ways, and a Zobel only fixes one of them. The other fix is the Thiele network, and understanding when to reach for each keeps your amp stable, cool, and unconditionally happy.

The two problems:

• Rising impedance with frequency (voice-coil inductance): the load looks increasingly inductive above a few kHz. This causes phase margin erosion inside the amplifier's feedback loop. → Zobel/Boucherot cell fixes this by presenting a resistive load at HF.
• Capacitive loading from long speaker cables (especially electrostatic speakers or shielded cables — 100 pF/ft adds up): this creates a pole with the amplifier's output impedance that eats phase margin and can cause outright oscillation. → Thiele network (a parallel L||R placed in series with the output) fixes this by isolating the amp from the cable capacitance at high frequencies.

The Thiele network is deceptively simple: a small air-core inductor (typically 1–5 µH) with a damping resistor (typically 5–10 Ω) wired in parallel across it, placed in series between the amp output and the speaker terminal. At audio frequencies the inductor is a short (fraction of an ohm) so signal passes through. At RF, the inductor becomes high-impedance and the resistor dominates, decoupling the amp's feedback node from whatever nastiness the cable is doing.

Rule of thumb sizing: Pick L so that ωL equals the damping resistor R at roughly the amplifier's unity-gain crossover frequency. For a typical 500 kHz crossover and R = 6.8 Ω: L = R/(2πf) = 6.8/(2π × 500k) ≈ 2.2 µH. Wind about 15 turns of 18 AWG on a 12 mm form and you're within 20%.

Real-world example: The Bryston 4B professional amplifier uses both networks at each output: a Zobel (10 Ω + 0.1 µF) directly across the binding posts, and a Thiele (2 µH air-core with 4.7 Ω in parallel) in series with the hot terminal. Similar topology appears in nearly every serious hi-fi amp — Krell, McIntosh, Hafler — and in every well-designed pro-audio power amp intended for long XLR-to-speakon runs.

Layout warning: the Thiele inductor must be air-core or a very-low-permeability ferrite. Iron cores saturate under bass transients and create audible intermodulation. Keep it physically away from the input stage — even 2 µH radiates enough magnetic field at 100 W to couple into a nearby feedback trace and turn your amp into an oscillator.