Bi-Amplification
As you might expect, Bi-Amplification means two amplifiers. One amplifier is connected to the woofer section of a loudspeaker while the other is connected to the combined mid and tweeter section. The Bi-Wire loudspeaker connection makes the Bi-Amplification hookup very easy.

--------------------------------------------------------------------------------
 
Unfortunately, with the arrival of Bi-Wiring, the exact meaning of Bi-Amplification has become blurred. I prefer the old original meaning. The original concept places a crossover between the preamplifier and the power amplifiers. With this arrangement each amplifier operates over a restricted frequency range. This restricted range presents each amplifier with a much simpler job and each amplifier is less likely to injure the sound in some way. The newer Bi-Amp concept simply uses two power amplifiers without a crossover. In this arrangement each amplifier must still work with the full frequency range, even though output current will flow over a restricted range. Unless one uses an external crossover ahead of the amplifiers, we dont feel the benefit justifies the extra cost.
 
The crossover consists of a LPF (Low Pass Filter) and a HPF (High Pass Filter). As its name implies the LPF passes frequencies below a cutoff and rejects frequencies above the cutoff frequency. Likewise, the HPF passes frequencies above its cutoff. In the Bi-Amplification connection the external Crossover frequency is set to match the speaker requirements. 

--------------------------------------------------------------------------------
 
Not for novices
In spite of any initial trepidation, connection of a basic audio system is very simple. Conventional speaker designs, where there is only one connection for the amplifier, make connection a nearly errorless process. Other than causing a short circuit or intermittent connection, not much can go wrong while connecting a speaker. The big decision is whether the terminals twist or press before accepting the wire. Bi-Amplification is not so simple.
 
The speakers built-in crossover is designed to match the efficiency of all the individual drivers (tweeters, midranges, and woofers are often called drivers, much as you are sometimes referred to as people). When using the Bi-Amplifier connection you must directly deal with some of these issues.
Here are the steps to connect speakers in the Bi-Amplification mode.

Turn everything OFF and wait at least 30 seconds for the power amplifiers to shut down.
Set all the sections of your crossover to the frequency required for your speakers. The speaker owners manual will usually give the crossover frequencies. If your speaker is a three-way (woofer, midrange, tweeter) design, the Bi-Wire connection separates the woofer from the combined midrange and tweeter section. Therefore, you should use the lower crossover frequency specified by the speaker manufacturer.
Connect the preamp output to the electronic crossover. Y-cables may be necessary.
Connect each output of the crossover to its amplifier channel.
If present, remove the bi-wire links from each speaker.
Connect each amplifier channel to its respective speaker section. Make sure that the correct frequencies pass through from the crossover, to the amplifiers, then on to the speaker sections and that you observe proper phasing.
 
      
 
     
Set the level controls on the crossover and power amplifiers such that a fixed level signal at any frequency will arrive at all speaker terminals at the same level.
This is a very important point, lets clarify it: If a 1 Volt 100 Hz signal on the left channel input to the crossover causes a 2 Volt signal at the output terminals of the left low frequency amplifier; then a 1 volt 1000 Hz input to the right channel crossover should result in a right high frequency amplifier output of 2 Volts.

If your amplifiers are identical, it is usually sufficient to set all the amplifier level controls the same. Most crossovers also have level controls that can be set the same.

Above, weve shown our preferred setup using one stereo amplifier per speaker. This arrangement allows minimum speaker wire length. If your amplifiers are not identical, use the more powerful amplifier for the low sections and the cleaner (better sounding) amplifier for the high sections.

If you have sufficient will and the instrumentation to make these level measurements, avoid taking them at the crossover frequency. A good choice of frequencies would be half and double the crossover frequency. Please note that few consumer or professional grade digital voltmeters have a frequency response good enough for this task. Always check the meter specs before using your meter for audio. Most meters roll off beginning at 1000 Hz or have a frequency response of ±3 dB (or worse). 
 

--------------------------------------------------------------------------------
 
If you are an expert
In our opinion, the best method of connecting your speakers is to supply one amplifier per voice coil and eliminate the speakers built-in crossover. If your speaker is a three-way design, then you must Tri-Amplify your speaker.
 
This technique, however, is not for the feint of heart because you must be prepared to modify your speakers and take some measurements. Individual driver efficiency varies. The original speaker crossover equalized these variations. After eliminating the original crossover, these sensitivity variations must be accounted for by your crossover or amplifiers. Another loose end is the fact that some speaker designers deliberately connect the midrange out of phase.
 
For anyone willing to take the trouble to devote one amplifier to each voice coil, the sonic rewards are outstanding. We can recall an unforgettable lesson many years ago when a manufacturer had two versions of the same loudspeaker. One version used the traditional set-up, the other was Bi-Amplified using built-in amplifiers. Even though the amplifiers used for the Bi-Amplified version were nothing special, the self amplified version always sounded better than the passive version, even when driven by our best amplifier using our best speaker wire.
 
A word of caution: While we enjoy the results of this technique very much, you may not. There will be many obvious improvements in the sound, everything will be clearer and tighter. Everyone will appreciate these benefits. The possible down side is associated with the imaging characteristics of your speakers. Part of the physics of crossovers is a slight time delay as the signal travels through the frequency selective networks. Depending on the design of the original speaker crossover and the new external crossover, the relative time delays between drivers may change after the modification. Because of the change in relative delays, the imaging characteristic of your speaker may change slightly. Only you will know if the result is good, bad, or insignificant.