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Working In Tandem: Combining Near And Far Field Measurements

Insights into overcoming the inaccuracy of quasi-anechoic techniques at low frequencies.

In addition to the overall 6 dB increase in the mean level, in the transition region between high and low frequencies, the baffle diffraction effect causes peaks and dips in the response curve that vary depending on the baffle shape and dimensions, and the position of the driver on the baffle. In a seminal paper on the subject published in 1951, Olsen [3] demonstrated measured diffraction response for 12 different enclosure shapes.

If enclosure diffraction effects are not accounted for, the near field/far field splice technique described above can cause errors in the estimated frequency response. Luckily, there are software tools available to simulate baffle diffraction.

For example, Figure 2 shows the baffle diffraction estimated with a program call the Edge, from Tolvan Data [4] for a rectangular loudspeaker enclosure with a 127 mm driver mounted in the middle of its 197 x 294 mm front baffle.

Figure 2. Estimated Diffraction effect for a closed box bookshelf speaker with 127 mm driver mounted in the center of a 197 x 294 mm rectangular baffle.

Figure 3a shows three frequency response curves for the same loudspeaker system – the measured near field response, the quasi anechoic far field response measured using a 5 ms time window, and the near field response combined with the simulated diffraction response shown in Figure 2.

Figure 3b shows the results of splicing the near field / far field response curves with and without the estimated diffraction response. Note that without the estimated diffraction (red trace in Figure 3b) the spliced curve is significantly off at low frequency.

Figure 3a. Relative response (left) of near field measurement, diffraction corrected near field measurement and far field measurement. Figure 3b shows combined near/far field response with and without diffraction correction.

Ground Plane Measurements

Another approach to approximating the free field response of a loudspeaker is the ground-plane measurement technique [5]. This technique takes advantage of the fact that the acoustic reflection from a loudspeaker placed directly on a hard, reflective surface is predictable.

Consider the sketch in Figure 4, showing a loudspeaker and microphone placed 1 m above a reflective surface. The microphone is positioned on-axis, 2 m away from the loudspeaker.

Figure 4. Sketch of a loudspeaker and microphone tested at 1m above a hard, reflective surface.

For this geometry, the difference in path length for the reflected sound and the direct sound is about 894 mm. At the speed of sound (343 m/s at room temperature), this represents a time difference of 2.61 ms. Hence, if a sinusoidal signal is generated by the loudspeaker, two sine signals of the same frequency and essentially the same amplitude will arrive at the microphone, but the reflected sound will be delayed by 2.61 ms.

This time delay represents a phase shift. At some frequencies, the signals will be 180 degrees out of phase and they will completely cancel out. At frequencies two times higher, the signals will be exactly in phase, and their combined amplitude will be twice that of the direct sound, or 6 dB higher in level. This causes a comb filter effect at the microphone position, as shown in Figure 5. For this geometry, the signals completely cancel out at multiples of 192 Hz, and they sum to twice the amplitude of the direct sound at multiples of 384 Hz.

Figure 5. The comb filter effect caused by interference between the reflected sound and direct sound for the geometry shown in Figure 4.

As the loudspeaker and measurement microphone are moved closer to the reflecting plane, the path length difference decreases, causing the notches of the comb filter to occur at higher frequencies. In the limiting case, the loudspeaker and the microphone are placed directly on the ground plane, and the speaker is tilted such that the reference axis points directly at the microphone.

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