Why woofer impedance rises
A moving-coil woofer or mid-bass driver is not a fixed resistor. After the impedance dip near the voice-coil DC resistance (Re), the curve climbs again as frequency rises. Rod Elliott of Elliott Sound Products (ESP) puts the cause on the voice coil’s semi-inductance, Le: without correction, impedance rises with frequency and upsets a passive crossover that was designed for a resistive load. How to read that curve is covered in speaker impedance curves, explained. A Zobel is the fix on the woofer side: a simple series resistor and capacitor across the driver. ESP’s crossover tables say the same for a two-way: the mid-bass or woofer will almost always need a Zobel network to correct the rise from Le. The tweeter’s resonant peak is a different problem (a notch filter), and tweeter level is an L-pad (how to pad a tweeter with an L-pad). Slope choice stays on first- vs second-order crossovers.
What a Zobel is
For a woofer or mid-bass, ESP’s Zobel is a series R-C network placed in parallel with the driver, after the crossover network. ESP’s wording: it is designed to prevent the impedance from rising at high frequencies. Adding it does not change the driver’s acoustic performance; it changes the load the crossover sees. ESP’s target band is practical: once compensation is in, keep impedance flat across the crossover region for at least about ±1 octave, and preferably ±2. With a 3 kHz crossover, that means roughly 1.5 kHz to 6 kHz as a minimum window, and 750 Hz to 12 kHz if you can get it.
Starting values
ESP’s preferred starting formulas (as printed):
Rz = Re × 1.1Cz = Le / Rz²
where Rz is the Zobel resistor and Cz is the Zobel capacitor. Worked example (ESP’s own sample mid-bass, not a recommendation). ESP’s sample mid-bass uses Re = 5.637 Ω and Le = 901 µH. That yields Rz ≈ 6.2 Ω and Cz ≈ 23.47 µF. ESP’s simulation flattened well with about 22 µF; his test-box optimum on that driver was 22 µF in series with 6.9 Ω. Your drivers will differ. Vance Dickason’s alternative, as ESP cites it from the Loudspeaker Design Cookbook:
Rz = Re × 1.25Cz = Le / Rz²
On ESP’s same example numbers, that gives about 7.0 Ω and 18 µF. ESP notes that Dickason’s resistance lined up better with the test box on that driver, while the capacitance came out low. ESP’s preferred method remains empirical: a speaker test box beats calculation when Le is uncertain.
Why you measure anyway
ESP is blunt that measurement systems often get Le wrong (on his example drivers, the measured Le did not match the impedance curve), because the coil is a semi-inductance and hard to model. Datasheet Le is therefore a starting guess, not a final part value. ESP’s Project 82 test box is the practical path: put a selectable R-C across the driver, sweep, and find the combination that flattens the rise above resonance. ESP also shows how to read the real equalized impedance (not the “8 ohm” label) once the network is in, and to design the crossover for that measured value. For the measurement loop itself, see REW basics. ESP’s design order is fixed: finish impedance compensation first, then design the crossover for the corrected resistive load. Calculators that assume a flat resistor only work after the Zobel (and any tweeter notch) are in.
Power rating of the resistor
The Zobel resistor dissipates real power. ESP’s Project 82 note: with a reasonably powerful amplifier (about 50-100 W), expect to use at least a 20 W resistor, and more with a bigger amp. Size for heat, not for the smallest part that fits the board.
When you don’t need one
ESP says none of this impedance compensation is necessary if you use an active crossover, because the speaker’s impedance cannot pull the filter around. ESP’s crossover tables repeat it: none of these networks are required with an active system. A series-connected first-order passive two-way is ESP’s noted exception on the passive side (it does not need the same compensation as a parallel higher-order network); that topology is a crossover layout choice, not a substitute for understanding the woofer’s rise.