Active Crossovers and Filters

Bi-Ampping Psycho-Acoustics
   An added advantage is a psycho-acoustic phenomena wherein bi-ampped systems seem more powerful than the sum of the amplifier wattages, e.g. two 36 watt amplifiers sound much more powerful than a 72 watt amplifier. 
    How is that possible? Half of the answer lies in the output voltage adding together rather than the wattages adding together. Wattage is based on the voltage squared. For example, 24 peak volts of output signal equals 36 RMS watts, but 48 peak volts of output signal equals 144 RMS watts. In other words,  doubling the voltage quadruples the wattage; tripling, increases the wattage by ninefold.

   What are active crossovers? In short, they electronic circuits that divide the audio spectrum up into discrete bands of frequencies and they function in place the passive crossovers found in loudspeakers. The underlying motivation for the switch to an active crossover is the improved accuracy and flexibility of the active crossover holds over the passive crossover.
   Loudspeakers represent truly complex impedances, which only an equally complex passive crossovers can match. Thus deriving the required crossover frequency and slope is difficult with a passive crossover and changing a preexisting passive crossover frequency is anything but easy.  Active crossovers, on the other hand, remove the large passive components that make up the passive crossover. This is for the good, as the hundred feet of magnet wire that makes up the inductors and the two back-to-back electrolytic capacitors that make up most crossover non-polarized capacitors are not missed: these components are far from ideal. And the power amplifier, once freed from having to work through this dreck, exercises a better control of the loudspeaker drivers. For example, a damping factor of 100 means little, if the passive crossover adds 1 ohm of DC resistance to the mix, thereby decreasing the effective damping ratio to 8. 
    Active crossovers also allow for a frequency tailoring that would be altogether impossible or at least incur efficiency penalties with a passive crossover. For example, with a network designed by Linkwitz, we can effectively shift the resonant frequency and Q of a loudspeaker driver. Furthermore, a high Q crossover can boost a drooping low frequency response of a low Q speaker while filtering away sub-sonic garbage, such as record warp.

200 Hz + 2 kHz added together

    Let's imagine a crossover point of 500 Hz. If a 144 watt amplifier is presented with a signal of two 24 volt tones, say 100 Hz and 2 kHz, the signal will trace a 2 kHz sine wave superimposed on a 100 Hz wave. The total peak voltage is 48 volts, which equals 144 RMS watts. Remember that a given instant the amplifier's output is at only one specific voltage. (The plate cannot be at +24 and at -12 volts at the same time. We are dealing with cooper wire and voltage, not fiber optics and light.) A passive crossover splits these two frequencies from the output from a 144 watt amplifier into two 24 volt signals. The active crossover also separates the two frequencies so that two 36 watt amplifiers can play these two tones at the same volume as the single 144 watt amplifier can, i.e. 24 volts at 100 Hz and 24 volts at 2 kHz.

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