"Speaker Measurement Techniques for Crossover Design"
"The most critical but confusing aspect of loudspeaker design"

Part 2

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.

• Step 1 of the "virtual design" is to measure the on-axis response of both drivers and remove all acoustic delays by using the Hilbert transform (shown below).  The results are saved for later development.

TWEETER MEASUREMENT

WOOFER MEASUREMENT

• Step 2 of the "virtual design" is to determine the acoustic centers (or horizontal offset) of the woofer and tweeter.  Refer to the following image.

A total of three measurements are taken at this point.

1. Tweeter response is taken on its axis.
2. The woofer response is taken on the tweeters axix.  It's important to note that neither the panel or mic locations can be moved between all three of these measurements.  The only thing that is changed are the electrical connections.
3. Both the tweeter and woofer measurements are taken at the same time.

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.

• Step 3 of the "virtual design" is take the offset "x," found above, and the measurement results from Step 1 to create a "virtual design" that will enable you to experiment with different crossover topologies as well as different vertical offsets between the two drivers.

• Step 4 is to take the results from the "virtual design," build an enclosure, and re-measure the tweeter and woofer responses with the actual phase responses.  This data can then be used with the preliminary crossover design that was developed with the "virtual design." The "actual crossover design" can then be created with good confidence that the distance between the tweeter and woofer has been optimized to achieve the best possible result.