Efficiency, Power Compression & Max SPL
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)
If 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
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
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.
Figure 5: Power compression, curves normalized to the reference curve.
Metric Specification: 6 dB compression at ABC db-SPL amplitude magnitude, re: XYZ db drive voltage /1m/4π/Znom, XX Hz to YY Hz
Σngineers
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
calculated.
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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