When I start a speaker design project, the first item on my list is the selection of the speaker. I select the speaker that I need to match my application and the selected amplifier and then build the cabinet to the speaker parameters. These applications are focused on a single cabinet providing a 15 or 18 inch cone speaker for a subwoofer or 10, 12 or 15 inch cone speaker for a two-way cabinets providing the low frequencies below 800 Hz for a point source or line array application.
My focus personally is on horn loaded designs but we will start with the basics and work our way to my applications. The first thing the selection of your raw speaker and then design around that. The reason for this is because you are looking for the most efficient speaker in your price range. To do this, we need three of the Thiele/Small loudspeaker parameter from the spec sheet.
The efficiency calculation requires the following parameters:
Fs – Resonant frequency of loudspeaker moving mass (in free air). Also known as Fo. The point at which moving parts are balanced. The goal is to prevent your enclosure from ‘ringing’. As a general rule of thumb:
Lower Fs indicates a woofer with lower low-frequency response
Higher Fs indicates a woofer with a higher low-frequency response
Vas represents the equivalent air volume of moving mass as to the compliance (springiness) as the driver’s suspension.
Qes is a measurement of the speaker’s electrical suspension system (the voice coil and magnet). Also described as the resonance characteristics of electrical factors of the loudspeaker.
The ȵ or No parameter is the electrical to acoustical conversion efficiency in percent. In most cases this parameter is not provided in the speaker specifications.
One equation for Efficiency1 (No) = (2.7*(10-8)*((Fs3)*Vas)/Qes)*100. With this algorithm, do not be surprised to only see 2 to 3%. Note: this algorithm agrees with the manufactures that provide this parameter.
Another equation for Efficiency2 (No) = ((157.75*Fs3*Vas)/(11303*Qes))*100. With this algorithm, values range from 6 to 15%.
Other parameters to consider:
Sensitivity (SPL) represents the efficiency and volume expectations at 1W/1M into 2.83V/8 ohms.
Qts is the resonance characteristics of the electrical and mechanical factors combined and is called the ‘Total Q’ of the driver and is derived from (Qes*Qms)/ (Qes+Qms).
As a general rule of thumb:
Qts of 0.4 or below indicates a transducer well suited to a vented enclosure.
Pe or PMax is the thermal power handling capacity of the driver in watts. This thermal capacity is related to coil temperature and the point where adhesives and coil insulation melt or changes shape. This parameter is to be used to match the amplifier output in watts.
EPB is the Efficiency Bandwidth Product which is a number that shows the trade-off between efficiency and bandwidth of a driver. Useful in determining driver loading for a sealed, vented enclosure or suited for horn loading. This is defined by EBP = fs / Qes. The common rule of thumb indicates the recommended cabinet loading includes:
EBP<50 indicates a sealed enclosure.
EBP>100 is perhaps best for a vented enclosure
EBP>50 but <100 would be effective in a sealed or vented enclosure
EBP>150 is suited for a horn loaded configuration
After a review of almost a hundred speaker and their parameters to match my requirement, I have finalized my selection.
Highlights on above table provide ideal choices for each parameter. Some compromise will be required for each of these parameters to finalize your selection. To explain this comprise, I will use the Peavey Sheffield Pro 1500. These details include:
- Lowest cost of the 4 available 15 inch speakers
- Maximum power with Pmax at 500 is good because my amplifier is 440Wx2@8Ω
- Highest sensitivity (SPL) at 98.0 dB is still good because I can provide 98 dB @ 50 feet with the above 440 Watt amplifier
- Lowest Fs for lowest frequency response that is 40 to 3k Hz
- Smallest Vas to minimize cabinet volume and this selection is 7.5 and resonable
- Lowest Qes and Qts with Qts < .4 with a .47 I will have to compromise
- Highest EBP at 85 where larger speakers are this low with a few exceptions
- Highest Eff1 of the 4 available and hoping to improve with the loading of this speaker into a cabinet that can increase this which will increase the SPL from the free air sensitivity (SPL) of 98.0 dB by 5 to 10 dB
Effects of Vas on Efficiency
The above graph is showing the effects of the parameter Vas on efficiency. For this example I am using the Peavey Sheffield Pro 1500 with an Fs of 42.7 Hz, Qes of .46 and a Vas of 7.5 Ft3. With these parameters, using the equation No = 2.70*10-8fs3Vas/Qes, with a Vas of 7.5 the efficiency is 3.15%. Looking at the speaker selection above this is one of the best results. If a cabinet was built with a smaller volume, the efficiency decreases. Now by increasing the internal damping material within the smaller cabinet an increased cabinet volume can be realized and increasing the efficiency.
Typical dimensions for minimum required to maintain free air efficiency
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