### THE DESIGN PROTOCOL: PART 3a,CROSSOVERS - MEASUREMENT FILES AND SIMULATION SOFTWARE

In a previous tutorial article we discussed the issue of using lab equipment to take loudspeaker measurements. In this part of the design process we have to make it happen so that our speaker project finds the necessary data to go on successfully.

-What sort of measurements are necessary for crossover network design ?

 There are different practices but the usual approach is to get the (complex) anechoic transfer function of each loudspeaker (ie. the Amplitude or SPL and Phase response) for 2.83Vrms input and at a distance of 1m across the tweeter axis (common microphone position for all driver measurements) and all driver (complex again) impedances in the range 5Hz-40kHz. Lab equipment is capable of exporting these two measurements (transfer function and impedance) as text files having as many rows as the measured frequency points. Each row usually bears three numbers: the first is that of frequency and the other two define the complex number which is the result of the measurement at this frequency point.

For example in such an SPL measurement for a SEAS 27TDC tweeter the first row of the respective measurement file exported by a PRAXIS measuring system was :

2.0000E+02   6.8831E+01   1.6335E+02

which corresponds to 200Hz, 68.8dB SPL, +163.35 degrees. The complex transfer function value is described by a {modulus,argument} pair of numbers. The last line of the same file is simply:

4.0000E+04   8.2324E+01   1.2252E+02

which corresponds to 40000Hz, 82.3dB SPL, +122.52 degrees. 'E' is the notation of the power of 10; the exponent being the integer following E. Thus E+02 stands for 10 raised to +2 which gives 100 (1.2252 times 100 equals 122.52).

We prefer having measurements well outside the audible spectrum because this allows for a detailed design as will be explained in the following text. However it is rarely feasible for anyone to have anechoic SPL measurements in the range 5-20000Hz or to have a measuring system operating above 22kHz.  The former is usually accepted by common practise as will be shown later on while the latter can be and should be resolved through a better measuring device.

Not knowing the SPL and phase responses of our drivers below 200-300 Hz has little to do with crossover design. Impedance is a different situation. Generally speaking we should have a picture of what is going on with our speaker as an electrical load in the range DC to 40kHz. This task can only be predicted (simulated) if we have measurements of our drivers in the same frequency range.

-Any special instructions concerning the required measurements ?

Measuring devices are capable of exporting text files with thousands of frequency points (typical 64K = 65536 points). Though it generally depends to our simulation software, it is usually necessary to restrict the simulation process to a few hundreds of points in whatever frequency range we choose. This speeds up calculations and helps these programs run effectively. The following table summarizes the required specifications:

### Measurement Files for Crossover Design

Baffle Object Type of Measurement Specifications
Woofer/Midrange SPL and Phase Responses  250Hz to 10000Hz min, as many points as imposed by software
Impulse Response anechoic segment of more than 8msec measured on Tweeter Axis at 1m distance
No smoothing
16 cycles averaging minimum
Phase delay due to tweeter flight time removed
Impedance  5Hz to 40000Hz, as many points as imposed by software
16 cycles averaging minimum
Checked against voice coil resistance
Tweeter SPL and Phase Responses  250Hz to 40000Hz min, as many points as imposed by software
Impulse Response anechoic segment of more than 8msec measured on Tweeter Axis at 1m distance
No smoothing
16 cycles averaging minimum
Phase delay due to tweeter flight time removed
Impedance  5Hz to 40000Hz, as many points as imposed by software
16 cycles averaging minimum
Checked against voice coil resistance

SPL/Phase Responses are derived by measured Impulse Responses as already explained in a previous tutorial. In order to have an anechoic measurement file (reflection-free) it is essential to have an anechoic or a quasi-anechoic impulse response segment (ie. a segment with a weak reflection starting at its 'tail'). To get a valid SPL/Phase Response value at 250Hz we need at least 8msec segment duration. This is generally easy in the case of a tweeter for which it is quite easy to suppress the very first strong reflection. It is not easy for woofers or midranges.

Averaging has also been mentioned before. 16 measurement repetitions (cycles) usually furnish robust results.

If we manage to have only one very weak reflection in our IR segment our SPL/Phase Responses will be smooth and adequately accurate. Further smoothing will only straighten out the curves hiding resonances that we should take care of.

-What exactly is 'checking against voice coil resistance'?

When we measure loudspeaker impedance, the electric circuit used comprises several sources of erroneous resistance. In theory these errors are swept way but in some cases we may end up with absolutely rational impedance curves that include a small resistance offset of 0.3-1.0 Ohms. Such an error is not detectable when impedance values are associated with frequencies for which no reference value is available for comparison. Instead we could use the voice coil dc resistance as a reference but is only valid at frequencies very close to dc (0Hz). Thus it is a good idea to always get impedance measurements beginning with extremely low frequencies like 5Hz or less. On the other hand giving our simulation software information on driver impedance at extremely low frequencies will allow for complete printouts of speaker impedance when our crossover has been designed and finalized.

-Why do we have to remove a phase delay term from our Phase Response measurements?

We have already proved that the Phase Response of a loudspeaker is a very abrupt curve swinging rapidly between -180 and +180 degrees. Its use is essential for a crossover simulation software. We have already said that such programs usually exploit only a sparsely aligned set of frequency points. A typical Phase Response would fail to be imported in such a program with only 100-500 points. Several +180 to -180 'jumps' would be shown as a smooth curve. Fortunately the mathematical foundation of Linear and Time Invariant Systems states that we can remove a phase term (proportional to frequency value) without affecting the information carried by the Phase Response of a System.

For this reason we assign the task of removing a phase delay term to our measurement device (or software) prior to saving and exporting the measurement file to our computers hard disk.

We choose to remove the phase delay term which corresponds to the flight time of the soundwave starting from the driver's emitting diaphragm and arriving at the microphone position. However for our Phase Responses to be useful we need to have the same phase term removed. We choose this term to be the shortest one ie. of the tweeter's flight time.

-What sort of simulation software will be used in this article ?

For historical reasons we chose to use the very first 'Computer Aided Loudspeaker System Optimization and Design' software by AudioSoft (CALSOD, Witold Waldman, Australia) which can only be executed in DOS window (under MS Windows XP) and which -to my knowledge- is no longer available for purchase. CALSOD has been extensively used by speaker industry and audio enthusiasts as well. Needless to say that modern software can and should be used instead. Current software operates in the same way so there is not going to be problem with our examples.

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