Neutralizing driver’s inductance effect with a Zobel network
 

A Zobel is a series resistor-capacitor (R-C) network that is connected in parallel with a loudspeaker driver in order to neutralize the effects of the driver’s voice coil inductance L(e). Figure 1 below shows a Zobel consisting of resistor R1 and capacitor C1.

Figure 1: A Zobel Network Consisting of R1 and C1

Because a loudspeaker’s voice coil is itself an inductor, the impedance of the driver increases with frequency much like an inductor. When a woofer is used with a passive crossover the driver’s L(e) has the effect of spoiling the crossover filter action. A Zobel can be used to restore the impedance of the driver to the nominal value in the high frequency range. This will allow the crossover filter to operate more effectively in the high frequency range where it is used to attenuate the highs going to the woofer.

Without a Zobel network the impedance of a typical woofer looks something like on Figure 2 below. Notice the rise in impedance to the right. The peak at the left is the resonance peak of the driver. If this were a tweeter we would want to neutralize the resonance peak. Since we are discussing woofers here, it is the rise in impedance through the crossover region that concerns us.

Figure 2: Impedance of a Driver without a Zobel

With the addition of a properly designed Zobel network the impedance will re-changed to look like on Figure 3 below. Now the woofer exhibits a flat (resistive) impedance through the crossover region in the midrange and high end.

Figure 3: Impedance of a Driver with a Zobel added

You can design a Zobel network for your woofer by starting with a resistor (at least 10 Watt) equal to the nominal impedance of the driver. For an 8 Ohm woofer you would use an 8 Ohm resistor, 4 Ohm woofer, 4 Ohm resistor, and so on. Next, calculate the value of the capacitor from the nominal impedance and the driver’s L(e) value. Use the following formula:

(where L is in Henrys and R is in Ohms, and C is in Farads)

Concerning component selection, just use the closest available 5% value. The more accurate the better, certainly, but 5% is usually plenty accurate for crossover components.

The power (wattage) rating requirement of a crossover resistor depends strongly on its location in the circuit. Your Zobel resistor can probably be rated as low as 10 or 20% of the power rating of your woofer. On the other hand, a tweeter attenuator resistor might need to be rated as high as 10 TIMES the power rating of the tweeter. If you need to be absolutely certain that you are staying within the power rating of your components, you will need to do a detailed power dissipation analysis of the crossover circuit.

Example:

Driver Nominal Impedance = 8 Ohms
Driver L(e) = 1 mH = .001 H

R = 8 Ohms (10 W minimum rating)
C = 15.6 micro Farads (film type capacitor preferred)

Listening Test

Try this test. Listen carefully to the woofer in your system with the crossover connected. Alternately connect the Zobel network in and out of the circuit. You should notice a reduction in the highs coming from the woofer when the Zobel is connected.

Summary

Adding a Zobel to a woofer will allow the passive crossover to work more effectively. The impedance of the woofer will also be restored to the driver’s nominal impedance throughout the high frequency range. This technique allows the use of crossovers designed for resistive loads to operate as intended.

Reference:

O. J. Zobel, "Theory and Design of Uniform and Composite Electric Wave Filters",
Bell Tel. Sys. Tech. J., vol. 2, pp. 1-46 (1923 Jan).