Subwoofer Measurement Tactics: Methods Continued Page 3

This approach places either a raw driver or the front panel of the loudspeaker system within and flush with a large baffle. The rationale often cited for making use of this approach is that in changing the domain space from 4π steradian (spherical) to 2π steradian (hemispherical) the resulting amplitude response measurements will more accurately portray the low frequency performance of the system within a typical listening environment.

In practice, the usual implementations of this approach make use of either a simple, large baffle, (as per IEC standard 268 -14) for driver testing, a hemi-anechoic chamber or simply burying the system in the ground (or other large flat surface, such as a roof) with the driver or the faceplate of a complete system positioned upward and flush with the test surface.

From a practical standpoint, digging a hole in the backyard to measure your sub’s amplitude response isn’t typically found in the list of items guaranteed to result in a positive SAF. Besides all that, what if your sub is a vented system with the ducts firing out any panel other than the one the driver(s) are bolted into - how are you going to bury that?

Modeling again in LEAP 5, the plots showing at above left are free-air (blue), half-space @ 2m (red) and half-space @ 1m (purple).

The near field approach, when done correctly is a simple, yet very effective means for capturing the direct sound amplitude response of your subwoofer. Where it comes to measuring subs, many of the practical limits or issues faced when employing some of the alternate approaches illustrated above are simply rendered moot at the frequencies of interest. If your only option is to measure your subwoofer indoors, this is probably the best – and easiest - approach to take.

From Eq 2:

Where:

p_n = peak pressure in the near field at the center of the piston (driver diaphragm)

r = distance from measuring point (mic position) to the center of the piston

a = piston radius

, peak axial pressure measured at a distance, r, in the far field of the piston

ρ_o = density of air, = 1.21 kg/m³ at 20^° C

U₀ = piston peak output volume velocity

k = wave number, = 2π/λ = ω/c

c= velocity of sound in air, = 343 m/s

We see that for those frequencies of interest (ka < 1), the near field sound pressure is directly proportional to far field sound pressure and the measurements made in the near field are basically independent of the space into which your subwoofer is firing; measuring “near” and scaling to “far” is valid & accurate. The upper frequency boundary for accurate near-field measurements is reached when a/λ ~ .26

In addition to being an effective means by which to measure a sub’s amplitude response, this technique (when done correctly) also allows for equally valid measurements of system distortion, efficiency and total acoustic power. It can be used to measure either closed or vented systems, powered or passive.

The near-field sound pressure measurement technique requires the measurement microphone be placed in a position centered on and normal to the driver’s dustcap and no further away from the center of the radiator than .11a (r ≤ .11a), assuming measurement data accurate to within 1dB or less is the goal. If you’re measuring a vented system, you’ll need to measure separately the acoustic output of the driver(s) and port(s). When measuring the latter, you’ll need to place the mic centered on & normal to the duct’s port, flush with the system’s faceplate.

Where there is only one radiator, such as a sub comprising a single radiator (driver) in a totally enclosed box, you need only measure the driver’s near-field output and scale the resulting data. If you’re measuring a vented system (or any system featuring more than one radiator, be it port(s), driver(s) or passive radiator(s)), then individual measurements are made of each radiator and the data are then combined to produce the total system amplitude response. Because all measurements are being taken near-field, the data should be scaled to an appropriate distance, commonly 1 or 2 meters. So how do you scale the nearfield measurement data to, say, 1m? To calculate the near-field scaling factor (1m, half-space) use:

FF_dB = NF_dB - 20 * Log(0.2821 * SQRT(Sd)) (dB) (3)

Where: Sd is the effective diameter of the radiator, m^2

(To calculate the 1m, full-space (anechoic), far-field equivalent, use the above equation and

subtract 6dB from the results).

Here are some alternate equations useful in scaling NF to FF measurement data:

FF_dB = NF_dB - 20 * Log(4d/r) dB, 4π-space (4a)

and

FF_dB = NF_dB - 20 * Log(2d/r) dB, 2π-space (4b)

Where:

FFdB = scaled far-field dB value

NFdB = near-field dB value

d = distance at which far-field values are to be calculated (eg: 1m)

r = effective radius of radiator

Note: units (m, in, cm, etc) must be the same for both d & r

Refer to the chart below for the Sd values for a variety of nominal driver sizes:

Should the distance between driver(s) and port(s) be significant in terms of the wavelengths of interest, the maths become a bit more complex if data of the highest quality is your requirement. Neville Thiele wrote a concise paper on the maths involved, referred to in the bibliography.

Before commencing any near-field measurements, be certain your measurement mic can handle the acoustic output dished out by the radiator(s) at close proximity. This holds especially true if you’re interested in doing max. dB spl output testing.

Also, when setting drive levels its best to do a number of test runs, working up each time to determine driver excursion so you don’t end up with the mic getting hit by the unit’s diaphragm when doing the actual measurements. As well, to ensure accurate port data, avoid using drive levels so high as to introduce turbulence in the port.

In this brief overview we’ve looked at a variety of approaches to subwoofer measurement. Each has its own set of strengths, weaknesses and limitations. Success in capturing accurate data depends on correctly understanding how to measure, how to interpret the results and above all remaining cognizant of the limitations inherent to whichever approach is used. And if all else fails, there’s not much a little 1/3^rd-octave smoothing won’t make look good.

As a handy reference, a graph featuring plots of a system modeled in the half-space, ground plane and free-air space domains, along with an accompanying table are included below.

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