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Power amplifier limited SPL of a dipole woofer

Given two different 10" drivers, and power amplifiers of 60 W and 180 W capability into 8 ohm, what on-axis, free-space SPL can be expected at 1 m from a dipole woofer with D = 15" (380 mm) between its front and rear wave exits? 

To answer this question I used closed-box1.xls with the parameter values in the following two tables. The spreadsheet can be used for dipole speakers by setting the box volume Vb to a value much larger than Vas and specifying D.

Peerless and Seas drivers:

ATI power amplifiers:

For an estimate of the SPL level in the room add 6 dB to the free-space numbers in the graphs for 2p radiation, and another 6 dB for the use of two woofer cabinets. If two drivers are used in each cabinet, and each driver has its own amplifier, then add 6 dB more for a total of 18 dB. But, if the two drivers are connected in parallel and driven from a single amplifier, then you can add the last 6 dB only as long as the amplifier is not limited by its Imax. 

The first graph is for the 180 W amplifier and assumes that it can deliver almost twice its normal 8 ohm current of 6.7 A into a lower impedance load. At frequencies below 36 Hz the amplifier can easily drive the 10" XLS to its Xmax of 12.5 mm. Between 36 Hz and 88 Hz the SPL is limited by the 53.5 V peak swing of the amplifier, and above 88 Hz it is additionally limited by its 12 A maximum current capability. The W26 driver has 5.6 dB less volume displacement, Sd Xmax, than the 10" XLS. It also has a weaker motor, but that is compensated by lower moving mass and higher compliance. The result it that the SPL is now excursion limited to 66 Hz, albeit at less output than the XLS. Above 66 Hz the W26 motion is voltage limited. The current never comes up to its 12 A maximum. Note that above 66 Hz there is little difference in obtainable output from either driver when used with the 180 W amplifier.  

Using the 60 W amplifier with an estimated Imax = 7 A yields almost identical SPL from the two drivers above 44 Hz, but the level is about 5 dB = 10 log(180W/60W) lower than for the higher power amplifier. Only below 22 Hz is the SPL limited by Xmax for the 10" XLS driver. Above 22 Hz SPL becomes voltage limited up to 88 Hz and current limited above. The SPL from the W26, by comparison, is excursion limited below 44 Hz and voltage limited above. Again, as with the 180 W amplifier, the output never becomes current limited. So if you used the lower power amplifier, then the higher displacement 10" XLS has no SPL benefit above 44 Hz, but below 44 Hz it can provide up to 5.6 dB = 20 log(440cm³/231cm³) higher SPL. In the case of the 180 W amplifier the SPL advantage of the XLS over the W26 is below 66 Hz.

The relationship between SPL, driver parameters and amplifier parameters is complicated as these examples hopefully illustrated. Each combination of amplifiers and drivers must be analyzed to determine its sound level output potential. Equalization merely shapes the acoustic frequency response and gives full use of a driver's capability.

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