Index LoudspeakersZobel Network

Zobel Network

Flatten the rising impedance of a voice coil with one resistor and one capacitor.

Zobel resistor7.75Ωnearest E12: 8.2 Ω

Zobel capacitor13.3µFnearest E12: 12 µF

Inductive above1.23kHz

Settles at7.75Ω

Impedance seen by the crossover

Driver alone
With Zobel

Circuit

The model covers the voice coil only. The bass resonance peak is left out; a Zobel does not affect it.

Input

Voice-coil resistance

R_e

Voice-coil inductance

L_e

Resistor rule

How it works

The problem

A voice coil is a resistor in series with an inductor. Above a few hundred hertz the inductance takes over and impedance climbs steadily:

\left|Z(f)\right| = \sqrt{R_e^{2} + (2\pi f L_e)^{2}}

A passive crossover is designed for a fixed load. If the load doubles by the crossover frequency, the filter no longer does what was calculated.

The fix

Otto Zobel's network places a resistor and capacitor in series across the driver. As frequency rises, the capacitor lets the resistor take over just as fast as the inductor shuts the coil off. Choosing equal time constants makes the combination resistive:

R_z = R_e

C_z = \frac{L_e}{R_e^{2}}

Real coils are lossy and their inductance falls with frequency, so the long-used practical rule raises the resistor by a quarter:

R_z = 1.25\,R_e

C_z = \frac{L_e}{R_z^{2}}

Switch between the two rules to compare. The exact rule gives a ruler-flat line for an ideal coil; the classic rule lets the impedance drift up to $1.25\,R_e$ , which better matches measured drivers.

Using it

Fit the Zobel directly across the woofer terminals, after the crossover. Then calculate the crossover using the flattened impedance. The resistor should be rated for a few watts; the capacitor should be a film or bipolar type.

References

O. J. Zobel, “Theory and Design of Uniform and Composite Electric Wave-filters,” Bell System Tech. J., vol. 2, no. 1, pp. 1–46, 1923. IEEE· Internet Archive