Measurement Techniques for Crossover Design"
This second part of "Speaker Measurement Techniques for Crossover
Design," is to attempt to resolve some of the open-ended
issues described in the first presentation as well as to take a few steps
back and describe what our ultimate "goal" really is.
In a perfect world, a loudspeaker consists of a single driver/enclosure that can reproduce the entire audio spectrum, with no phase-shifting or time-delays at any given frequency. Unfortunately, we don't have the loudspeaker technology to be able to live in this perfect world, at least not yet. What we are left with is two or more drivers to design a loudspeaker capable of successfully reproducing the full audio spectrum.
I'm going to make a couple of assumptions at this point. The first is that my next example is going to assume the use of two loudspeaker drivers for a two-way design. The next assumption is that the job of picking the "brand and type" of loudspeaker driver has already been done.
Before two loudspeaker drivers can be placed on a baffle, we need to know exactly where to place them. In order to know where to place them, we need to know what their frequency and phase response characteristics are. As if this wasn't enough, we also need to know what their relative acoustic-centers are.
In order to answer these questions, I'm going to create what I like to call a "virtual design." This "virtual design" will enable computer simulation tools to determine the acoustic center of the two drivers, and allow for simulation of different crossover topologies before any enclosure/cabinet is created, or crossover is built. After the crossover topology is picked, and the relative acoustic-centers are found the actual enclosure can be used based off of this "virtual design," and the "actual crossover design" can be developed with outstanding accuracy.
A total of three measurements are taken at this point.
Note: The phase response for these three measurements are the actual phase responses, including all time-delays and offsets. If your loudspeaker measurement tools don't allow for actual phase measurements to be performed, you can't utilize this procedure.
Use Calsod or similar crossover development package to create a design that uses both the single tweeter and woofer responses. Then create another design that uses the response of both the tweeter and woofer combined. Remove as much of the phase response "lag" from the tweeter and woofer measurements as necessary to bring the phase response into a useable region. Note, the phase removed should be equal to both the tweeter and woofer responses, EXCEPT for the delta that can be measured (shown as d above). Use the Pythagorean theorem for finding the length of the hypotenuse and subtract 2 meters from this length. After adjusting the proper phase shifts for both the tweeter and woofer measurements, remove the same amount of phase "lag" from the combined response as you did for the tweeter response. Next, adjust the phase/delay of the woofer response (measurement #2) so that it combines with the tweeter response (measurement #1) to produce a plot that imitates the combined measured response (measurement #3). Concentrate around the crossover frequency of the tweeter and woofer. Since the actual frequency is not known yet, assume a couple of octaves (i.e. from 1kHz to 5kHz). The resulting delay is the offset "x," as shown above.