Impedance Compensation Circuits
by Isaac MCN
f4ier@hotmail.com 0. Introduction DIY loudspeaker beginners usually start off with offtheshelf crossovers. These are designed using equations from textbooks, which assume a resistive load. Loudspeakers are far from resistive! To the unsuspecting, untrained, listener the results of using textbook filters may sound OK, but it will be shown that such crossovers fail to do what they're supposed to do. 1. Textbook Crossovers  Some Basics Ohm's law states that voltage equals the product of current and resistance. Given the following circuit, <insert VR1R2 series circuit here> The current through the circuit is simply 2V / 2Ohms = 1A and the voltage across R1 is 1V = the voltage across R2 as well  the voltage was divided in half into the 2 resistors. If R1 where to be bypassed [0 resistance], then the full 2V will appear across R2. If, on the other hand, R2 were to be infinitely large [R2 is effectively disconnected], then no voltage would be measured across R2. These overservations hold for any frequency of the applied voltage because resistors are not reactive. If R1 were to be substituted with a fixed value inductor, which has a rising impedance with frequency, then the voltage division between both loads would varry with frequency. 1. OffTheShelf Crossovers Or Textbook Crossovers Circuit analysis books introduce filter design using examples with purely resistive loads. 1. The Electrodynamic Loudspeaker An electrodynamic loudspeaker has a vibrating cone  held in place by a spider and surround assembly  powered by a permanent magnetvoicecoil motor. The springiness of the suspension and mass of the cone form a 2ndorder resonant system. A typical electical impedance measurement looks like the following graph. where one can see a peak centered around the resonance frequency of the device under test and a rising impedance due to the voicecoil inductance. There is always a peak because a loudspeaker tends to vibrate more at its resonance frequency and this induces more opposing current through the voicecoil. 
IMPEDANCE COMPENSATION CIRCUITS by Isaac MCN
f4ier@hotmail.com 0. Introduction Often an available amplifier is more comfortable with flatimpedance loads. In reality a loudspeaker has a complex impedance. To compensate for this, circuits can be designed and implemented. Probably the most common impedance compensation circuit is the socalled Zobel network, which has a few derivatives the simplest being the capacitorresistor network. The full Zobel network would also compensate for the resonance impedance peak of the driver at the resonant frequency, Fs. 1. Woofer One of the most famous drivers in the DIY world is the Vifa P17WJ0008. Many builders use it because it has a smooth frequency response and resonable bandwidth. Because many constructors use it, the said driver was chosen to be modeled in this website. The following is a picture of the the driver unit along with its ThieleSmall Parameters.
