Complex, On-axis Frequency Response

2. Axial, Polar & Power Frequency Response; Sensitivity; Efficiency; Group Delay; Effective Frequency Bandwidth; Power Compression; and Maximum System Sound Pressure Level

Figure 3: dB-SPL Plot

2a. Complex, On-axis frequency response.

Purpose: To determine the amplitude & phase response of the direct sound output of the subwoofer, across the frequency spectrum segment of interest.

Value: This gives us the actual amplitude & phase response of the subwoofer, free from the influence of the room. It’s a baseline that gives us a clear picture of the system’s actual performance.

For all measurements, use a calibrated microphone. Do not use sound level meters or an uncalibrated microphone. All other gear used in the test-signal chain should be calibrated as well or at the very least possess a known, constant amplitude response within +/- .5 dB in the relevant frequency range. All gear should present negligible non-linear distortion under normal test conditions.

Method of Measurement:

Near-field (Indoors): The measurement microphone should be placed such that it is centered on and normal to the dustcap. It should be positioned as close as possible to the surface of the dustcap, at its center point. This places the microphone at a reference point that is defined by the intersection of the reference axis and the reference plane. The axial amplitude-response measurement data produced by the microphone at this position is such that to all other frequency and directional-response amplitude response measurements are referred to it.

Keeping in mind the large displacements subwoofer driver diaphragms are capable of, the maximum excursion attainable should be determined beforehand, so as to prevent damage to either the driver or the microphone.

Figure 4a & b: Mic\Driver Disposition for NF Measurement. 4c: Mic\Port Disposition

Nearfield measurement can easily result in sound pressure levels in excess of that for which a particular measurement microphone might be rated. Prior to actual measurement, a series of test runs, using incrementally increasing drive levels, can be useful in establishing both driver excursion (as mentioned
above) & system sound pressure levels and how they relate to the measurement microphone’s rated SPL maximum. Overlaying a plot of the mic’s rated SPL maximum (red curve, above) prior to making any preliminary test measurements makes evaluation quick & easy. If measuring a ported system, establish maximum mic-safe system SPLs by measuring the port output first. And wear appropriate hearing protection!

Σngineers Note #2… Nearfield Measurement: accuracy & limits;

Helpful hints & Tips

1. Keeping the measurement distance, r < 0.11a, where a = effective diameter of the driver being measured, keeps measurement errors to less than 1 dB of the true nearfield dB spl.

2. The theoretical upper frequency (soft) limit for nearfield measurements is given by:
(“soft” as in various authorities quote either ka = 1 or ½; it can only be defined loosely.)

ka = 1
Where: k = wave number
a = effective driver radius

For radius, a, given in meters, the upper frequency limit is given by:

For radius given in cm, the upper frequency limit is given by:

And for radius, a, given in inches:

If the subwoofer features a vented cabinet, the output of the duct(s) must be measured as well. As with the NF driver spl measurements, the measurement microphone should be placed such that it is centered on and normal to the center point of the duct’s external vent (Figure 4c). The individual amplitude response curves of all ducts are then scaled and vector summed with that of the driver(s) and the resulting system curve is then scaled to 1 meter. If the system curve data are scaled to a distance other than 1m, that should noted.

Nearfield measurement typically obscures or minimizes any contribution made by the cabinet’s panels to the system’s total acoustic output. Ultimately, the relevance of any such acoustical contributions actually made by the panels depends on the degree to which they are audible.

Multiple Drivers and/or Ports

Where:
H_NF(f) = System near-field response, dB spl
H_D(f) = Driver near-field measured response, dB spl
S_P = Total effective radiating surface area of the port(s), m²
S_D = Total effective radiating surface area of the driver(s), m²
H_P(f) = Port near-field measured response, dB spl

Method of Measurement:

Ground Plane (Outdoors): The subwoofer is placed on a solid, smooth surface in a position located well away from any other reflective boundaries. To ensure minimal acoustic interference (< 1dB contribution to total pressure) from objects large enough to be reflective at the wavelength of interest, the subwoofer should be located at a distance from said object or boundary that is no less than 5x the mic-to-cabinet measurement distance. The cabinet panel containing the driver(s) is then pointed at the microphone, positioned flush with the ground and located 2 meters along an imaginary axis, drawn from the center of the driver (for single driver systems) or center of the panel (for multiple-driver systems).

Owing to mutual coupling between source & image and a virtual doubling of the size of the front panel of the subwoofer there can arise slight differences between ground plane measurements and true free field, anechoic measurements. Raising the sub off the ground, while maintaining correct orientation and distance from the mic as well as keeping the mic flush with the ground can minimize or altogether eliminate this problem.

Figure 5: Ground Plane Measurement

In this arrangement, the microphone is measuring the combined amplitude response of the actual sub and a virtual or mirror image of the sub. In effect, the microphone is measuring the output of two identical sources, vibrating in phase and equal in strength - in a free field. With the mic sitting on the axis bisecting the sources, the on-axis pressure is doubled, the power generated has doubled, intensity has quadrupled and the sound pressure level is 6 dB up, compared to a sub measured free-field at the same distance.

If the system is driven with a 2.828 Vrms signal and measured at 2m using the ground plane approach, the resulting amplitude response plot will be virtually equivalent to that generated by the sub, at 1m, under free-field conditions, such as that obtaining at the top of a 100’ tower. System sensitivity can be determined from this plot and no magnitude scaling is required.

Be aware of the effects temperature, humidity and so forth can have on your measurements. Doing so can alter the actual performance of the sub as well as that of the measurement microphone. If background noise of a random nature affects the measurement process, make several measurements and use complex averaging to minimize the effect of the noise as well as increase the signal-to-noise ratio. For further insight regarding appropriate measurement conditions please see ANSI S12.18.

Suggested Nearfield & Groundplane Test Signal: Swept sine wave (320 Hz to 10 Hz), capturing sufficient data points to ensure post-processing accuracy, displayed on a semi-log plot, charting both magnitude and phase. The test signal is delivered at a pre-determined voltage, typically 2.828Vrms or calculated using 1W = V^2/Znom. For nearfield measurements, scaling the amplitude response plots to 1m, the sensitivity of the system can then be determined.

To avoid ambiguity or the possibility of data misinterpretation, the dB – SPL specification should be written out in its entirety. Essentially, it should provide enough information to allow the measurement sequence to be reproduced by anyone wishing to do so.

Sample complete dB – SPL Metric specification, without Sensitivity Analysis Segment (SAS).

87.5 dB SPL, ± .5 dB, 10 Hz to 320 Hz, 2.828Vrms/1m, re: 20 μPa, Near-field, On-axis, Scaled to 1m, No Smoothing, Swept Sine wave

-3dB lf/hf points: 20 – 83 Hz
-6dB lf/hf points: 18 – 90 Hz
-10dB lf/hf points: 16 – 98 Hz

Max. deviation within -3 dB lf/hf points: +x, -y dB

== or ==

Complete dB – SPL Metric specification (with SAS)

87.5 dB SPL, ± .50 dB, 20 – 80 Hz, 2.828Vrms/1m,
re: 20 μPa, Near-field, On-axis, Scaled to 1m,
No Smoothing, Swept Sine Wave
(3-Oct. /S.A.S)

-3 dB_{LF – HF} : 20 – 83 Hz
-6 dB_{LF – HF} : 18 – 90 Hz
-10 dB_{LF – HF} : 16 – 98 Hz

Max. deviation within -3 dB lf/hf points: +x, -y dB

Whichever dB – SPL metric specification is used, if sensitivity is measured using a drive voltage calculated by taking into account the nominal or rated impedance of the system (and is stated as such), substitute 1W (power sensitivity) for 2.828 Vrms (voltage sensitivity). Common practice, however, is to use voltage sensitivity.

Σngineers Note #3… The far field: Where is it? How do I know when my Mic is in it?
Key to any discussion concerning the ground plane technique is the “far field” concept and how it applies to microphone placement when measuring a subwoofer’s amplitude response.

In the far field of a subwoofer system, the subwoofer appears as a point source and sound pressure level varies inversely with distance, decreasing by 6 dB with each doubling of distance, or conversely, increasing by 6dB with each halving of distance.

Keeping this all this in mind, an expedient way to determine when a microphone has been placed in the far field is to simply run a series of amplitude response measurements, doubling the distance between the measurement mic and driver’s acoustic center (or other convenient reference point) and noting when the magnitude difference between plots, mid-band, reaches 6dB.

An old rule of thumb for estimating the far field boundary distance is to multiply the largest dimension of the source by 3. Note that with ground plane measurement, the “source” includes both actual and virtual sub.