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

There are myriads of different techniques to measure raw speaker drivers for the design of a loudspeaker and its associated crossover. Measurements include magnitude & phase Frequency response, and Impedance magnitude & phase response. The ideal situation would be to perform the frequency response measurements in an Anechoic chamber, but if you're like the rest of us and don't have access to one, you must make these measurements via the Far-field and Near-field measurement method, or by the Ground-plane measurement method.

The Far-field measurement method requires the measurement microphone to be located a minimum distance of 1 meter from the driver and for the Near-field response the microphone is located as close to the driver as possible.

The Ground-plane measurement method requires the micropone and driver to be located on a concrete surface a minimum of 1 meter apart.

These two measurement methods require there to be no objects within the vacinity of the driver/microphone up to the lowest frequency that is intended to be measured, otherwise there will be unwanted reflections in the impulse response. For example, if your closest object is 5 feet from the microphone, the lowest frequency that can be measured is found by using the formula: t = d / C, where t=time, d=distance in inches, C=speed of sound in air in inches/second. Therefore, t = ( 5 feet x 12 inches ) / 13560 inches/second = 4.4 ms, or 226 Hz. You could then use the Near-field measured frequency response and splice the two pieces of data together. The problem with this is with the shelving and the phase responses (to be discussed later). Measurements can be made outdoors but care must be taken to avoid external noise sources from contaminating the data. Another aspect to be discussed is whether to perform the driver measurements with the driver in the intended enclosure or by mounting the driver a very large baffle instead. There has been some discussions on whether a driver still remains minimum phase if there is baffle diffraction within the frequency response.

I'll list several approaches here, one recommended from LinearX Systems, and the others from Speaker Builder articles. I'll then comment on these approaches.

As suggested by Linearx's LEAP program application guide (my interpretation): The following should be performed to sucessfully design a loudspeaker and crossover.

  • Measure SPL and Impedance, the drivers mounted in the loudspeaker enclosure, using the Ground-plane measurement method,
  • Taper the measured SPL data on both ends, at least an octave above and below the frequency range of interest so that the measured data is monotonic,
  • Perform a Hilbert transform on the data,
  • Import the data into LEAP (or other software, of course),
  • Add time delays to the woofer/mids relative to the front-baffle (zero delay plane) by physically measuring the drivers, with a caliper?
I don't feel that this method follows good design practices. While I agree that careful consideration should be taken when performing the Hilbert transform on the measured data, I do not agree on determining the time delay by measuring voice coil distances with a measuring device (horizontal offset). I also don't agree on using only the loudspeaker cabinet in performing the measurements for this stage, (i.e. crossover design), of the design. This method also doesn't take the driver distance to the listening axis into account. Yes, the time-of-flight is removed because of the Hilbert transform, but the distance of vertical offset is not taken into account (or re-added). For example, if you're measuring with respect to the tweeter's access, and the woofer/mid resides a distance "d" below the tweeter, the woofer/mid's path length to the measuring mic is longer than the tweeter's distance to the measuring mic. After the Hilbert transform is performed, ALL time-delays are removed. The Leap approach only adds back in the horizontal delay (i.e. the driver's voice coil distance to the baffle). What happens to the extra distance due to "d?" It is lost and all phase data becomes useless.

GR. Koonce's approach as written in Speaker Builder issues 6/98 & 8/98:

  • Similar approach as above with adding or entering a horizontal offset for each driver to correct for the relative acoustic-center position (or zero delay plane).
  • He also recommends that knowledge of only what the system acoustic response does on-axis is not sufficient to produce a good crossover design (i.e. you MUST consider what the speaker is doing off-axis to produce a good design). I couldn't agree more.
  • Doesn't recommend testing the drivers in the intended cabinet because the inclusion of enclosure effects may cause the assumption of each driver being a minimum phase network to be violated (therefore the Hilbert transform cannot be used to predict the phase response). Also, an un-expected rise in the system response, (up to 6dB), is possible if a narrow front baffle is used.
  • Recommends mouting the driver on a large round test baffle and test/measure at 1 meter from the test baffle.
  • Use a crossover modelling program that allows modelling the system response at your intended listening position/distance.
  • "A major hurdle was identifying the proper horizontal offset for each driver." He empirically developed equations for computing the offset based on the driver's physical measurement. Interesting.
I agree with what's stated here although I'd like to see clarification on these empirically developed equations, as well as what he thinks should be done with the driver's vertical offsets.

Linkwitz, in Speaker Builder issue 6/97:

  • Recommends measuring the frequency response with the drivers mounted on a baffle so its response contains the effects of diffraction from the baffle edges.
I agree that this should be done at some point but I feel for the crossover design stage that this will cause problems with getting an accurate phase response.

David Ralph, in Speaker Builder issue 1/00: Finding the relative acoustic-center offset between (two) drivers.

  • Make a raw measurement of both drivers combined from the same microphone position (doesn't specify if in the intended cabinet or both drivers located on a large baffle). This data will include the acoustic offset of both drivers. Then a way of adjusting the time-delay of one driver relative to the other for that specific mic position is necessary.
  • Next take measurements of each driver individually without moving the microphone.
  • Then import each measurement into a Calsodand use its capability of combining driver responses to compre the result against the combined raw measurement.
  • After the data is imported into Calsod, model the data and then create a single file containing the two driver models.
  • Use the combined raw measurement as the reference against which the resultant Calsod combined (system) result is compared.
  • Perform measurements on the tweeter axis.
  • Leave the tweeter offset at 0. Then modify the woofer offset repeatedly until the combined result from Calsod matches the measured result as closely as possible, with the emphasis on the area of the target crossover frequency. Use 1/6 octave smoothing in your measurement program before exporting the data file.
  • It's important to note that you MUST enter the vertical offsets as well as any horizontal (lateral) offsets. (yeah! someone gets it right!)

I like David's approach on finding the relative speaker offsets and I'm going to apply it in one of my designs. Although it's not mentioned in the article, I think that the combined raw data must have the time-of-flight delay included in the measured data and the raw driver responses have their time-of-flight delay removed (i.e. Hilbert transformed).