Siegfried Linkwitz:
Page 4 As I looked further into this issue, I realized that two principal things were not well-understood. First, very little was known at that time about the effects of diffraction from the cabinet edges. Second, and more importantly, very little was understood about how phase-shift with respect to the current passing through the voice-coils of different drivers affected the polar radiation pattern of a speaker. In other words, the interaction between the electrical side of a driver and the acoustical response was not clear at the time. For example, the phase-shift between the current in the tweeter and midrange voice-coils, relative to the placement of these drivers on the baffle, affects the speaker's radiation pattern.

Basically, since few drivers are really coaxial, with the difference in physical placement—that is, if the path lengths between the drivers and the listening point are different, or even if they are the same—you get a vector addition which is a function of the phase-shift between the different voice-coil currents and the distance between each driver and the listener. So Russ Riley and I began our work, in earnest, to be sure that the drivers were in-phase in the crossover region. This, in essence, is what the Linkwitz-Riley crossover is all about: making sure that you have the same acoustic phase between the midrange/woofer and the tweeter at the crossover.

Dickson: How about the phase relationship outside of the crossover region?

Linkwitz: As it turns out, that same phase relationship is maintained at other frequencies as well. This is very much in contrast to the classical Butterworth crossovers that people use in a number of speakers. An inherent property of the Butterworth design, whether these are first-order, third-order, fifth-order, etc., is that the crossovers are always in phase quadrature. In other words, the acoustical signals coming from the midrange and tweeter are phase-shifted by 90 degrees relative to each other. At its -3dB point, each driver has an amplitude of 0.7, and if you add two 90 degrees phase-shifted vectors of 0.7, you get unity—the outputs of the two drivers add to unity on-axis. However, as you move further away off-axis, one or the other driver will experience more phase-shift as the path length difference becomes longer, and you'll have either a dip or a peak in the amplitude response off-axis.

In any event, the true maximum output of the two drivers will occur someplace off-axis, and this is an audibly bad thing. The peak off-axis response can then reflect from the nearest boundary and combine with the direct sound as added coloration.

Now, a first-order crossover can be made phase-perfect at one point in space, but I feel quite strongly that you cannot just look at a speaker's performance at one single point in space. The off-axis response is also very important to a speaker's overall performance in a real room, because the radiation in these other directions will add, through reflected and reverberant interactions, to what you hear. Typically, we don't listen to speakers outdoors or in anechoic chambers.

For an ideal Linkwitz-Riley crossover, the amplitude is flat on-axis or at unity, just as it would be for an ideal Butterworth. However, the Butterworth response will have its peak off-axis. In contrast, the amplitude of the L-R crossover will be down in level off-axis, and will never be higher than the on-axis response. The crossover point of a Linkwitz-Riley will also be at the -6dB point, equivalent to an amplitude of 0.5, and only when you add vectors with amplitudes of 0.5 that are in phase will you get unity. If there is any phase angle between these half-amplitude vectors, their sum will be less than unity.

A very important point that people sometimes miss in this discussion is that when we are speaking of a given crossover, we are talking about an acoustic crossover, or what happens acoustically. Now, what I have to do electrically to achieve the correct acoustic response may not look anything at all like a textbook filter design. The actual filter often looks very little like the drawings I may show to explain any given example. This is also true for a Butterworth filter. It is highly unlikely that a textbook electrical Butterworth crossover will produce an acoustic Butterworth response, because the driver's response enters into the picture as well.

Dickson: There is a general misconception in some circles about differential vs absolute phase effects in speakers. Recently, I've heard about some well-meaning but misinformed retailers who arbitrarily reverse the polarity of either the tweeter or midrange hookup wires in all of the speakers they sell which are designed with high-order crossovers, in an attempt to make them "in-phase"—much to the horror of the original designer. Perhaps you could shed some light on this issue.

Linkwitz: If someone were to arbitrarily change the polarity between drivers in a good Linkwitz-Riley crossover, they should get a strong null at the crossover point on-axis. In fact, this is a test I use to see how well I have executed the acoustic crossover. However, making such a change with the idea of somehow making a "phase-coherent" speaker is not correct. It will certainly change the sound, mind you, but is definitely not recommended.

Dickson: The Dvorak and Vivaldi speakers represent a radical departure from your earlier philosophy. What inspired this change in direction and could you outline some of the primary goals you've tried to achieve with these new dynamic dipole designs?