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Audioholics Subwoofer Measurement Standard Part I

by March 05, 2008

When it comes time to size up a subwoofer's performance, the proof is in the measurement! Audioholics takes a hard look at the science of subwoofer measurements in a two-part series covering a broad spectrum of measurement methods, useful to both pro and enthusiast alike. Let the science begin!"

This article began life as an ongoing series of conversations, carried out over the past couple of years with Gene. He recognized Audioholics’ need to bring a degree of organization to its own in-house subwoofer measurement procedures. I was tasked with that challenge and present here Part I.

Part II, to be published later, will cover other topics such as linear & nonlinear distortion measurement, mechanical noise floor measurement, amplifier measurement and so forth. Part II will also include a collection of worked examples and conclude with a table summarizing all results.

Projects of this size are seldom a solo effort and this was no exception. To that end, a huge debt gratitude
is owed to Charlie Hughes, Jeff Szymanski, Siegfried Linkwitz, Don Keele, Neville Thiele and many others who contributed their time and expertise in helping me knock this manuscript into shape. Thank you, gentlemen! And of course, a big thanks to Gene as well for his almost supernatural patience as he waited for me to bring this to completion. Thanks, Gene!


The purpose of both documents is to present a set of measurement guidelines by which a comprehensive objective assessment of a subwoofer’s performance can be developed. Included within this document’s definition of a subwoofer are: single & multiple driver subwoofer systems; powered and passive systems; systems featuring vented or totally enclosed cabinets; along with less common items such as dipole subwoofers.

Though industry professionals can (and do) make use of the methods or approaches presented here, this document is intentionally structured and organized to make it particularly useful to the audio enthusiast. Given the particular type and/or characteristics of a sub you may be interested in measuring you may find it unnecessary to apply all the measurement procedures covered in Parts I & II. In any event, with the variety of software-based measurement tools currently available, it is now possible for the audio enthusiast to work up a collection of accurate measurements at very little expense. Certainly much less expensive than what it would have cost 20 or 30 years ago!

If you’ve spent any time at all contributing to the development of any sort of industrial standard, you’ll know the process tends to be evolutionary in nature. Similar in character to the more formal standards (AES, IEC, etc) from which parts of this work are drawn, nothing here is written in stone. As new research and/or measurement technologies/techniques appear on the horizon they will be included, whenever/wherever appropriate and/or applicable. This is a living document that will evolve over time and improve with age.

1a. System Impedance: Magnitude & Phase

Graphic 1.gif

Figure 1: System Impedance

Purpose: To determine: (1) the characteristics of the impedance load placed on a power amplifier by the system
across a defined frequency spectrum segment; (2) various system parameters; and (3) the identification of
any anomalies/pathologies that are reflected back to the electrical domain.

Value: Impedance curves provide an assessment of the impedance the system presents to the driving amplifier. When
presented with phase data it provides further insight into the ease or difficulty a given amp may face in driving
the system. Impedance curves also are useful in indicating system parameters such as resonance frequencies,
system rated or nominal impedance and so forth. In some cases, they can also provide evidence of a variety of
system anomalies/pathologies, such as pronounced standing-wave resonances arising within the air enclosed by the cabinet.

Method of Measurement: Measure the driver’s Revc and the system’s impedance (with driver still in cabinet & any
internal power amp and/or processors disconnected from the driver), then remove the driver from the cabinet and proceed to Section 2, Driver Impedance, Magnitude & Phase. Except where it is noted otherwise or simply not applicable, the suggested frequency spectrum is
10 Hz to 320 Hz.

finger.jpgFor maximum accuracy, remove test lead and/or amp-to-sub cable impedance from all measured driver/system impedance curves. One method of accomplishing this is by measuring each beforehand and subtracting them from the driver/system measured impedance curve. Also, impedance measurements should be done in an environment as noise & vibration free as possible. Prior to making any acoustical or electrical measurements of the system, be sure to inspect all fittings, fixtures, hardware, etc to be certain that all are bolted down securely: leaks, loose hardware and so forth can and will effect measurement data.

Signal Used: Constant voltage (preferred) or constant current, downward swept sine wave, MLS or impulse signal. Regarding the
swept sine wave, unless otherwise required, use as low a test signal drive level as possible that can
repeatedly produce clean data.

Metric Specification: Nominal or rated impedance (Znom): should be stated such that the minimum impedance is no
less than 80% of the stated nominal or rated impedance.

finger.jpgAs per IEC 60268-5 standard practice, the value of Znom is specified based on the minimum value of the system’s modulus of impedance (Zmin) such that Znom is no more than 1.25*Zmin. In practical terms this means a system with a Zmin value as low as 6.4 Ω could be considered an 8Ω system, systems with a Zmin value as low as 12.8Ω could be considered a 16Ω system, and systems with a Zmin as low as 3.2Ω could be considered a 4Ω systems.

Nominal System Impedance, (10 – 320 Hz): A.A Ohms
Local minimum(s): X.X Ohms (Mag. & Phase) @ Y.Y Hz
Local maximum(s): W.W Ohms (Mag. & Phase) @ Z.Z Hz

1b. Driver Impedance: Magnitude & Phase

Graphic 2.gif

Figure 2: Driver Impedance

Purpose: To determine: (1) various driver/system parameters, and (2) the identification of any driver anomalies/pathologies reflected back to the electrical domain.

Value: Driver impedance curves provide for a great deal of useful information, in addition to an assessment of the
impedance presented by the system’s raw driver. Driver impedance curves are useful for deriving Thiele-Small
parameters. In some cases, they can also provide evidence, as already mentioned of driver anomalies/pathologies or other noteworthy characteristics.

Method of Measurement: Measure the driver’s Revc and the diameter of the driver, including 1/3rd to ½ the surround.
With the driver out of the cabinet and secured in place or otherwise restrained from any possible movement, remeasure the impedance. This is the driver free-air impedance. Then using either the delta-mass (i.e., added-mass) or delta-compliance (i.e., added compliance) perturbation technique, remeasure the driver’s impedance. From this and the previously taken free-air impedance curve, derive the Thiele-Small parameter values. The change in mass or compliance should be large enough so that the driver’s resonance frequency is altered by at least 30%.

finger.jpgAs with the system impedance measurements outlined above, for maximum accuracy, remove test lead and amp-to-sub cable impedance (where applicable) from all measured driver impedance curves. Do this by measuring each beforehand and subtracting them from the driver’s measured impedance curve. Also, unless otherwise required, set the test voltage or current value to the lowest possible that still provides clean, repeatable measurement data.

Signal Used: Constant voltage (preferred) or constant current, downward swept sine wave, MLS or impulse signal. Unless otherwise required, use as low a test signal drive level as possible that can repeatedly produce clean
data. Driver impedance measurements are measurement signal-level dependent and the driver parameters derived from impedance measurements done at different test signal levels will show differences.

Metric Specification: Driver T/S Parameter Table (See below).

audioholics.jpgΣngineers Note #1 Determining Raw Driver Thiele/Small Parameters
From Measured Impedance Curves

As expertly demonstrated by Thiele, Small, Benson, Novak and others, a great deal of useful information can be derived from a driver’s impedance curve. Collectively, the information gleaned from the raw data are formulated as defined parameters, a subset of which is commonly known as the “Thiele/Small” (T/S) parameters. Working up a small table populated with various T/S parameter values helps to round out the objective portion of a subwoofer assessment and provide a check against other measurements to ensure all around accuracy.

At left is an example of a commercially available speaker parameter utility at work. Two further graphics are presented each illustrating how to mathematically derive an estimate of a driver’s parameters from impedance data if you don’t have access to a program such as that shown at left. (See Bibliography ref. #38 in Part II for an in-depth discussion of both techniques)

Graphic 3.gif Graphic 4.gif Graphic 5.gif

Revc (Ω) 3.225
fs (Hz) 29.11
Qts (-) 0.338
Vas (l) 88.46
Efficiency (%) .600
Sensitivity (dB/1W/1m)
To illustrate the utility of the parameter chart, we could now, for xample, check both the measured midband sensitivity of the system or work up an estimate of the system’s half-space max dB spl, at a given distance, given a particular wattage amplifier using the formula:

dB spl = dBW + Sensitivity (dB) – 20* Log(D2/1m)
Where dBW = 10 * Log(amplifier electric Watts out)
D2 = measurement distance, meters

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


Graphic 6.gif

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.

finger.jpgFor 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

finger.jpgGraphic 10.gifNearfield 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.

finger.jpgNearfield 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

In the case where the system features multiple drivers and/or ports, the Near-field approach can be used. In this case, the complex (magnitude & phase) response of the driver(s) and/or port(s) should be measured individually, then vector summed to give the overall Near-field system response, using the following formula:

HNF(f) = System near-field response, dB spl
HD(f) = Driver near-field measured response, dB spl
SP = Total effective radiating surface area of the port(s), m2
SD = Total effective radiating surface area of the driver(s), m2
HP(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).




finger.jpgOwing 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.

finger.jpgBe 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.

finger.jpgTo 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.

Graphic 12.gifSample 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 dBLF HF : 20 – 83 Hz
-6 dBLF HF : 18 – 90 Hz
-10 dBLF HF : 16 – 98 Hz

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

finger.jpgWhichever 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.

audioholics.jpgΣngineers 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.

2b. Polar response, Beamwidth, Directivity & Q.

Graphic 13.gif

Figure 6: Polar response

Purpose: To determine the amplitude response of the subwoofer at various angles along a common plane, referenced to the on-axis amplitude response and measurement position.

Value: In addition to providing a wealth of information regarding the off-axis amplitude response characteristics of the subwoofer a variety of other performance specifications can be derived from the measurement data, such as beam width (BW), Q, directivity index (DI) and power response. Note that Q for directivity bears no relation to the quality factors Qms, Qes, and Qts. mentioned in Section 1b.

Method of Measurement: Ground-plane measurement lends itself particularly well to collecting polar response data as it requires only a bare minimum of hardware resources. Essentially, the sub is set up as for a standard on-axis measurement session. The reference point is established (the point of intersection between the reference axis with the reference plane) and the on-axis measurement is made. (If it is practical to raise the sub above the ground any response plot discrepancies owing to mutual coupling or baffle-size increase owing to actual-virtual system interaction can be minimized, however minimal they may be). The sub is then rotated, in angular increments, typically on the order of 5°, 10° or 15°. Below left shows a collection of such plots, in this case the measurements were made at 15° increments.

Once all the measurements have been collected, the curves are then normalized to the 0°on-axis curve by dividing each curve into the 0°on-axis curve. In doing so, the resulting plotted response at each point along the measurement path is relative to the on-axis response. Below right shows the result of normalizing the data plots at left. Though the data curves presented below right are normalized polar amplitude response curves, they are not usually presented in Cartesian format. Rather, they are more commonly seen as presented above in Figure 6.

Graphic 14.gif Graphic 15.gif

finger.jpgRegardless of how or where you locate your reference measurement point, for polar response measurement purposes, the reference point and the point of rotation must be one and the same. As such, it is essential to keep the distance from the reference or rotation point to the measurement microphone identical at each angular position used during the measurement sequence. Keep in mind, too, that holding the sub in one position and moving the microphone from measurement point to point produces results just as valid as rotating the sub and holding the measurement mic in one position. Marking the rotation point and drawing radii of equivalent length from it to each angular measurement position with a piece of chalk is a dirt-cheap way to set up for the polar amplitude response measurement sequence. Once your artwork is complete all you need do is place the sub so that the reference measurement point intersects an imaginary axis (shown in blue in the graphic below), normal to the ground, and drawn through the previously marked point of rotation. You’re now ready to measure! (If your initial measurement set was taken in the horizontal plane, vertical plane measurements can be subsequently be taken by tipping the sub on its side and repeating the sequence.

Graphic 16.gif

Figure 7: Horizontal plane polar response plot measurement layout

2b.II: Beam width (BW), Q, Directivity index (DI) and Power Response

Referring now to Figure 6, Beamwidth (also referred to as “coverage angle”) is that angle formed by drawing 2 radii, located either side of the reference axis, where the amplitude response, for a given frequency has decreased by 6dB, with respect to the 0° on-axis reference value. In Figure 6, the BW at 320 Hz is 180°.

Q is the numerical expression of the directionality of a system’s response. Strictly speaking, directivity is the ratio of axial intensity of the actual source to the intensity that would be produced by a point source emitting an equivalent amount of power. A source with equal output at a given frequency in every direction would have a Q = 1. With increasing directionality the Q value increases. A quick, first-order approximation of Q at a particular frequency (assuming axial symmetry) can be had by the following formula:

Q = 360°/BW°
where BW is specified in degrees.

The Directivity Index is simply the Q value specified above, expressed in dB. Specifically:

DI = 10 * Log (Q) (dB)

finger.jpgJust as with on-axis measurements, polar response data should be presented with information such as drive level, measurement distance, etc, providing sufficient detail depth & breadth to allow the measurement sequence to be reproduced by anyone wishing to do so.

2c. Power response.

Graphic 17.gif

Figure 8: Red curve: system on-axis response; blue curve: system power response

Purpose: To determine a subwoofer’s power response, expressed in dB spl.

Value: The axial amplitude response measurement, illustrated in Section 2a, has traditionally been a mainstay of the objective assessment process. However, as important as it is, it does not provide -in and of itself - sufficient information to convey as complete a picture as is needed in working up an objective assessment of a subwoofer. Where the axial amplitude response measurement resents a view of the sub’s direct sound response characteristics as measured at a single point in space, the power response gives an overall view of the amplitude response characteristics of the sound field generated by the sub, as measured at several points in space.

Method of Measurement: The approach here is similar to that for capturing polar response data (see section 2b). And just as with polar response measurement, groundplane measurement lends itself nicely to the power response measurement process.

Common practice is to take measurements at 15° intervals, in both the horizontal (below, left) and vertical plane (below, right). (A common alternate is 15° intervals in the forward hemisphere, 30° intervals for the rear hemisphere; various factors may dictate less or more widely spaced intervals and measurement at intermediate angles). The resultant plots are then averaged to produce a good approximation of what is commonly referred to as the power response of the system.

Graphic 18.gif Graphic 19.gif

finger.jpgJust as with on-axis & and polar amplitude vs. angle measurements power response data should be presented with information such as drive level, measurement distance,etc, providing sufficient detail depth & breadth to allow the measurement sequence to be reproduced by anyone wishing to do so.

2d. Sensitivity

Graphic 20.gif

Figure 2: Sensitivity

Purpose: To determine the sound pressure level produced at 1m, on-axis, when 1 watt (power sensitivity) or 2.828 Vrms (voltage sensitivity) is applied to the subwoofer.

Value: Indicates the actual acoustical output, in terms of sound pressure level, that will be produced by a subwoofer, given an electrical input signal of a specified voltage or wattage, the latter determined by the nominal system impedance value (1W = V^2/Znom). Knowing a system’s sensitivity assists in matching multiple systems. Also, dB-SPL acoustical output can be calculated given a known amplifier wattage.Graphic 21.gif

Approach: Sensitivity can be either measured or calculated (See Engineers Note #1 for the latter or graphic at right).

Signal Used: 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. Subsequently scaling the amplitude response plots to 1m, the sensitivity of the system can then be determined.

Metric specification: XY dB spl, X-Oct averaged SAS, 1W or 2.828 Vrms/1m/4π/Znom

Σngineers Note #4…
How do I calculate the mid-band acoustic output of a sub if I know the sensitivity of the unit, given a known electrical input, in Watts?

dB-SPL Out = Sensitivity + 10*Log(W)


dB-SPL Out = Mid-band, On-axis, acoustical output at 1m (dB-SPL)
Sensitivity = Measured or calculated sensitivity of the device (dB-SPL)
W = Input electrical power (Watts)

Worked Example

The 1m, on-axis, sensitivity of a subwoofer is 87 dB - spl. The sub is a powered system and features an amplifier rated at 300 Watts. What is the mid-band, on-axis dB-SPL this sub can theoretically produce at 1m when fed an input at 300W?

dB-SPL Out = 87.50 dB-spl + 10 * Log(300.0)
dB-SPL Out = 112.1 dB-SPL, at 1m, On-axis, 2 –π SR

finger.jpgWhen calculating efficiency, sensitivity and so forth, indicate if the values calculated are for a 2 or 4π-SR environment. “SR” stands for “steradian”, the mathematical expression for a solid angle. 4π or 2π -SR is thus the mathematical expression for full or half-space, respectively. 4π or 2π –SR is also sometimes expressed as simply “4π” or “2π”.

2e. Efficiency

Purpose: To determine the ratio of the acoustic power radiated by a subwoofer, PA, to the applied electrical power, PE.

Value: Electroacoustical efficiency indicates how much of the electrical power fed in to a subwoofer is converted into acoustical power radiated out. Usually expressed in % or dB, this metric is valid for the piston-band segment of the system’s pass band. It is a function of various T/S parameters and relates to sensitivity:

SP = 112.1 + 10*Log(η0) (dB SPL)

Approach : The subwoofers midband efficiency can calculated directly from the T/S parameters derived from the impedance measurements presented earlier. This equation assumes a radiation load of 2π-SR, free-field.

η0 = 100*(4π2/c2 * fs3Vas/Qes) (%)
η0 = 10*Log(4π2/c2 * fs3Vas/Qes) (dB)

finger.jpgIf the T/S parameters of the driver are based on free-air vs. Infinite baffle measurement, this equation will generate results slightly in error, typically a small fraction of a decibel.

Metric specification: Efficiency (Half-space) = X.Y% or XX.Y dB

2f. Group Delay

Graphic 22.gif

Figure 3: Group Delay

Purpose: To determine frequency-specific delay magnitude in terms of time for a given acoustic frequency band of interest.

Value: Group delay is the rate of change of the total phase shift with respect to angular frequency (the negative derivative of the phase function). Mathematically, it is expressed as:

In order that signal waveform fidelity may be preserved as it transits a given system, phase must change linearly with frequency response. Where phase nonlinearity exists, group delay exists.

Conversely, in a system where all frequencies transit in the same amount of time (or alternatively, transit with equal delay) no group delay exists. Time vs frequency Group delay plots indicate the degree of signal delay at any particular frequency.

Method of Measurement: Group delay is mathematically derived from the sub’s phase response by taking the negative derivative of the sub’s phase response with respect to frequency.

2g. Effective Frequency Bandwidth

Purpose: To determine the lower & upper frequency -3, -6, & -10 dB points, referenced to the subwoofers passband average dB SPL levels obtaining in the device’s maximum sensitivity zone.

Value: The EFB is useful for determining the passband of a device. The -3dB limits are given for comparative purposes, consistent with other published reviews. The -6dB limits are given to indicate the half-power points. The -10dB limits are chosen as they represent thedrop in dB spl levels sufficient to cause a perceived halving of the system’s output.

Approach: -3 dBLF HF , -6 dBLF HF , -10 dBLF HF points are located with reference to the mid-band sensitivity level determined earlier. They are found at those frequency points at or external to the system’s passband. (See side graphics in Section 2a or 2b).

Metric specification: -3 dBLF HF : AA – BB Hz, re: mid-band sensitivity, XY dB
-6 dBLF HF : CC – DD Hz “ “

-10 dBLF HF : EE – FF Hz “ “

[Presentation: -3 dBLF HF, -6 dBLF HF, -10 dBLF HF == or == -3dBlf/hf, -6dBlf/hf, -10dBlf/hf]

2h. Power Compression

Graphic 23.gif

Figure 4: Power Compression

Purpose: To determine the degree to which a subwoofer’s otherwise linear input-output fundamental amplitude transfer characteristic becomes non-linear at increasing drive levels.

Value: Thermal effects (voice coil heating and a concomitant increase in voice coil resistance) along with various other driver nonlinearities seen arising in Bl(x), Le(x) and Cms(x) (force factor, inductance and compliance, respectively) and, of course, mechanical limitations all contrive to limit the acoustic output in such a way that it does not grow linearly with an increase in electrical input. Bl(x), Le(x) and Cms(x) are parameters treated, not as constants as when they are treated as small signal parameters but as quantities that vary with the excursion (x) of the voice coil from its rest position.

Power compression measurements give an assessment of the degree to which this nonlinearity presents itself, given a particular drive level. It also gives an indication of how well a subwoofer will accurately reproduce dynamic source material. Note: powered subwoofer systems often have limiter/compressor functions built into their processor algorithms to protect the driver(s) from possible damage. The effects of these limiter/compressor functions can appear similar in measurement to the results seen with a driver being driven hard enough for various nonlinearities to appear.

Approach: Near-field Approach (Indoors) or Ground Plane Approach (Outdoors)

Suggested 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 and charting amplitude response. Beginning with a voltage drive level of 2.828 Vrms (or that calculated using 1W = V^2/Znom) the reference dB Spl curve is produced. The sweep is repeated, each time the input drive voltage is stepped in 1, 3, or 10 dB increments. Increase the drive voltage until 3dB worth of compression is noted. The resulting data can be displayed as either discrete curves (Figure 4) or if desired the curves can be normalized and scaled to the reference curve (Figure 5). Note: the slower the sweep the more noticeable will be thermal effects. An alternate signal useful for such testing is shaped pink noise as per IEC 268-1.

Graphic 24.gif

Figure 5: Power compression, curves normalized to the reference curve.

finger.jpgPower compression testing makes use of high input drive level voltages; minimize the risk of damaging the subwoofer by running a few test curves, slowly increasing voltage drive levels at each run to check driver excursion (and the measurement microphone’s max.dB SPL) limits are not exceeded. See the “Engineers Notes” Below for a handy device useful in gauging displacement amplitudes. Above all, do not exceed the subwoofers rated input capacity for whichever electrical test signal is used. This is not testing to failure.

Metric Specification: 6 dB compression at ABC db-SPL amplitude magnitude, re: XYZ db drive voltage /1m/4π/Znom, XX Hz to YY Hz

audioholics.jpgΣngineers Note #5 Homemade Wedge Micrometer

If you don’t want to rely on your powers of estimation to size up maximum driver diaphragm displacement, a quick means to determine maximum excursion is by use of a wedge micrometer.


2i. Maximum Sound Pressure Level

Purpose: To determine the maximum dB spl levels for which the device is capable, given power handling capabilities and system sensitivity. A calculated datum approximation that does not take into account power compression. Because it is based on the average passband sensitivity of the device, maximum dB spl is also an average value. For a measurement-based approach see CEA 2010 “ Standard Method of Measurement for Powered Subwoofers.”

Value: Useful for determining upper system output performance limits.

Approach: Given power capacity and average system sensitivity, maximum sound pressure can be

dB-SPL Out = Sensitivity + 10*Log(W) (dB-SPL)

Metric specification: dB-SPLMAX @ Rated Capacity (W or Vrms), 1m/Xπ-SR

Conclusion for Part I

Here in Part I of the Audioholics Subwoofer Measurement Protocol we’ve looked at a variety of measurements that, taken together, provide a good deal of insight regarding the performance characteristics of a subwoofer. Though the various topics presented illustrate a significant portion of the typical measurements approaches used today, the picture, nevertheless, remains incomplete. More information is needed to form an opinion of what any particular subwoofer will sound like than can be gleaned from the information presented by the various measurements illustrated in Part I.

In Part II we’ll take a look at things such as linear distortion, nonlinear distortion, mechanical noise, power amp performance characteristics (where applicable) and so forth. Ideally, with the objective data provided by the various measurement outlined in both Part I & 2, a reasonably accurate opinion of the subjective sonic qualities of the subwoofer can be formed.

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About the author:

Mark's audio career, began in 1981 when he designed his first loudspeaker system for a client who had grown disenchanted with the off-the-shelf products then populating local audio emporiums. Since then, he has designed over 100 systems, now found in homes, studios, theaters and dance clubs in north America & Asia. Mark has done detailed analysis and reviews and tech articles related to loudspeakers and subwoofers for Audioholics.

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