Impedance Compensation Circuits
by Isaac MCN
DIY loudspeaker beginners usually start off with off-the-shelf 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. Off-The-Shelf 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 magnet-voice-coil motor. The springiness of the suspension and mass of the cone form a 2nd-order 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 voice-coil 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 voice-coil.
IMPEDANCE COMPENSATION CIRCUITS
by Isaac MCN
Often an available amplifier is more comfortable with flat-impedance 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 so-called Zobel network, which has a few derivatives the simplest being the capacitor-resistor network. The full Zobel network would also compensate for the resonance impedance peak of the driver at the resonant frequency, Fs.
One of the most famous drivers in the DIY world is the Vifa P17WJ-00-08. 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 Thiele-Small Parameters.