Thus, when using loudspeakers that see the same phase and amplitude signal, we cannot use a -3 dB down point, as it would yield +3 dB; thus, we need a -6 dB attenuation at the crossover frequency in order to ensure a flat frequency response. The same phase is the key point here. If a Butterworth second or fourth or sixth order crossover is used, the frequency response will display a bump at the crossover frequency. On the other hand, using a Linkwitz-Riley 2nd or fourth order crossover will yield a flat frequency response at the crossover frequency.
    Well at least that is the theory. Complications arise: the distance between drivers, the frequency response of each driver, the front-to-back spacing of the driver's voicecoils. If the distance between drivers exceeds the wavelength of the crossover frequency, or if one or both drivers droop at the crossover frequency, or if the tweeter acoustic center is substantially in front of the woofers, then the Butterworth aligned crossover might actually prove flatter.
    Do not falsely imagine that an even order crossover is phase flat; it isn't. The actual phase relation between 2nd order lowpass and highpass filters is a constant 180 degrees phase difference, which when one driver's connection is inverted, yields a constant phase relation between drivers, but not a flat phase response.

A Phase Flat Loudspeaker
    One interesting loudspeaker configuration was created by Philips. An ostensibly two-way loudspeaker was designed using a second order Butterworth crossover, but without the tweeter's phase reversal. Yes this resulted in a deep suck-out. The suck-out was then filled in by using a bandpass filter (-6 dB slopes) feeding a full-range driver. This extra speaker saw only the crossover frequency unattenuated, as all the frequencies below or above this frequency were attenuated at -6 dB per octave. The sum of all three driver's output equaled a phase-coherent flat frequency response. In this speaker system, the woofer was prevented from going too high, while the tweeter is protected from low frequencies, while fullrange driver filled in the hole. Unfortunately, this solution, like most speaker innovations, disappeared long ago.

Crossover Testing
    Evaluating active crossovers under actual use is difficult. Which component is making the biggest difference? The active crossover itself or the extra amplifiers and speaker cables? A listening test I have used is to take a pair of fullrange conventional loudspeakers and apply the crossover under test using my present amplifier and cables. This means there is no worry about relative efficiencies and frequency response limitations.
    The procedure is simple enough; place one speaker on top of the other and set the crossover frequency to some value between 300-700 Hz (too high a frequency will result in lobbing effects due to greater than wavelength spacing between drivers). This test requires a mono signal source and I recommend any of the mono Verve recordings of Ella Fitzgerald.

Fc/10                          Fc                         10xFc

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