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  • added SPL by doubling drivers

    I understand that using 2 identical speakers in parallel will give a 6dB increase compared to the single speaker due to the doubled surface area and the resulting doubling of amp power. I also understand that using 2 speakers in series will give a 0dB increase compared to one speaker. Sigfried Linkwitz provides proof for this here: http://www.linkwitzlab.com/faq.htm#Q21. Unfortunately, his math is a little bit too vague for me to plug in some real world numbers and fully digest the equations. I'm hoping somebody can help me with this. There are generic rules of thumb out there (3dB for doubling cone area, 3dB for doubling power, etc), but I'm hoping to dig deeper into the physics behind these rules of thumb so that I can better understand it and how it would apply to different speaker configurations. I'm ok with the electrical side of things, but on the mechanical side of things, like the relationships of cone velocity with respect to voltage and current and the relationship to cone area and output, etc.

    Thanks for the help.

  • #2
    Re: added SPL by doubling drivers

    Check out page 78 of John Eargle's book Electroacoustical Reference Data *
    Under section 38: "Normalized Mutual Coupling For Multiple Pistons"
    The background and formula is listed there for determining coupling.

    * Use Google book preview
    Last edited by Sydney; 06-22-2011, 01:10 PM. Reason: Addition
    "Not a Speaker Designer - Not even on the Internet"
    “Pride is your greatest enemy, humility is your greatest friend.”
    "If the freedom of speech is taken away, then dumb and silent we may be led, like sheep to the slaughter."

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    • #3
      Re: added SPL by doubling drivers

      Thanks, but I don't have the book, and at $187, it's not likely that I'm going to in the future either.

      Comment


      • #4
        Re: added SPL by doubling drivers

        Apologies Jim:
        I failed to mention that part of the book can be accessed via Google Book preview with this string:
        "eargle mutual coupling"

        FYI: I set up a xls spreadsheet ( # of drivers vs CTC spacing ) as i found it handy
        "Not a Speaker Designer - Not even on the Internet"
        “Pride is your greatest enemy, humility is your greatest friend.”
        "If the freedom of speech is taken away, then dumb and silent we may be led, like sheep to the slaughter."

        Comment


        • #5
          Re: added SPL by doubling drivers

          Originally posted by jim85iroc View Post
          I understand that using 2 identical speakers in parallel will give a 6dB increase compared to the single speaker due to the doubled surface area and the resulting doubling of amp power. I also understand that using 2 speakers in series will give a 0dB increase compared to one speaker. Sigfried Linkwitz provides proof for this here: http://www.linkwitzlab.com/faq.htm#Q21. Unfortunately, his math is a little bit too vague for me to plug in some real world numbers and fully digest the equations. I'm hoping somebody can help me with this. There are generic rules of thumb out there (3dB for doubling cone area, 3dB for doubling power, etc), but I'm hoping to dig deeper into the physics behind these rules of thumb so that I can better understand it and how it would apply to different speaker configurations. I'm ok with the electrical side of things, but on the mechanical side of things, like the relationships of cone velocity with respect to voltage and current and the relationship to cone area and output, etc.

          Thanks for the help.
          It's a typically over complicated explanation. The fact is that for any two sources, regardless of size or input power, the radiated sound pressure adds vectorial. If the sources are closely spaced (correlated or spaced much less than a wave length) then they are in phase at all points in space and the sound pressure just adds everywhere. So if they each radiate a sound pressure of 1 independently then they sum to 2. Acostic power is the square of the pressure so power goes from 1 squared = 1, to 2 squared = 4. In dB, 10 log(4/1) = 6dB. So two sources which radiate the same sound pressure radiate 6dB more acoustic power when correlated. Now the electrical power into the sources is just the sum of the power delivered into each. Just add the power. If the drivers receive the same power it's 1 +1 = 2 which in dB is 3dB more power. So the two sources radiate 6dB more acoustic power with a 3dB increase in input power resulting in a 3dB increase in efficiency.

          If you make the drivers identical fine. But its the same if one driver is a 6" woofer and the second is a 10". And it carries over to drivers with different efficiency too. Lets say you have driver 1 which radiates a sound pressure of 1 with 1 watt in. Driver 2 radiates a sound pressure of 1.3 with an input power of 0.8 watt. Assume they are closely space, the net sound pressure of both is 2.3 for a 7.23 dB increase in radiated acoustic power, relative to driver 1 alone.. The input power is 1.8 watt or 2.55 dB greater than 1 watt. So relative to the first driver the system radiates 7.23 dB more acoustic power with 2.55 more input power or a gain in efficiency of 4.68 dB compared to the first driver. Or you can use a more appropriate reference for sound pressure if you like and have a more standard measure of the increase in efficiency.

          you can go through the arguments from first principles if you like, but it just make things less simple.


          P.S. I have a paper on my web site addressing this from a very fundamental view.
          John k.... Music and Design NaO dsp Dipole Loudspeakers.

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          • #6
            Re: added SPL by doubling drivers

            John,
            The reason that I'm trying to understand the math behind it is so that I can experiment with changing different variables.

            Specifically, I want to be able to compare two speakers that perhaps have different areas, or different electrical impedances. Everything that I'm finding discusses the effect of adding another identical speaker in parallel or in series, but what if the situation isn't that clean? What if I replace a single 8 ohm driver with a pair of series-wired 16 ohm equivalents? What if I replace a single 10" driver with 2 8" drivers? etc, etc. I'm hoping to understand this well enough to be able to understand the relationship between those types of changes.

            Comment


            • #7
              Re: added SPL by doubling drivers

              The fact is that for any two sources, regardless of size or input power, the radiated sound pressure adds vectorial.
              This is the key for acoustic summation:
              If the SPL @ frequency vs angle data is know for the sources - Then the SPL levels at any position can be calculated.
              In the Pro-Sound industry: having this data available in forms such as CLF data; allows for venue sound mapping and cab placement planning.
              This is separate from the impact in the electrical part of the system: calculated with the impedance and electrical phase data for the sources.
              "Not a Speaker Designer - Not even on the Internet"
              “Pride is your greatest enemy, humility is your greatest friend.”
              "If the freedom of speech is taken away, then dumb and silent we may be led, like sheep to the slaughter."

              Comment


              • #8
                Re: added SPL by doubling drivers

                If I understand your question, here's how to look at it.

                Voltage sensitivity. Forget power.

                Use the voltage sensitivity for the driver(s). Use for example an 8 ohm 87 dB woofer.
                If you put 2.83 volts on it, it produces 87 dB SPL.

                Now wire a second one in parallel. Both drivers see 2.83 volts, and both produce 87 dB. So the SPL of the two together is 87dB + 6 dB = 93 dB

                That's 93 dB with 2.83 volts.

                If the two drivers are wired in series, each driver sees half of the 2.83 volts. In dBs, the half voltage output is -6 dB. So you get 81 dB from each driver. Then the two drivers combine as 81 dB + 6 dB = 87 dB.

                Notice that I've not mentioned power, or dB with one watt at one meter. That is not what you need to be looking at anyway, unless you are concerned about amplifier power requirements.




                Originally posted by jim85iroc View Post
                I understand that using 2 identical speakers in parallel will give a 6dB increase compared to the single speaker due to the doubled surface area and the resulting doubling of amp power. I also understand that using 2 speakers in series will give a 0dB increase compared to one speaker. Sigfried Linkwitz provides proof for this here: http://www.linkwitzlab.com/faq.htm#Q21. Unfortunately, his math is a little bit too vague for me to plug in some real world numbers and fully digest the equations. I'm hoping somebody can help me with this. There are generic rules of thumb out there (3dB for doubling cone area, 3dB for doubling power, etc), but I'm hoping to dig deeper into the physics behind these rules of thumb so that I can better understand it and how it would apply to different speaker configurations. I'm ok with the electrical side of things, but on the mechanical side of things, like the relationships of cone velocity with respect to voltage and current and the relationship to cone area and output, etc.

                Thanks for the help.

                Comment


                • #9
                  Re: added SPL by doubling drivers

                  Originally posted by rpb View Post
                  If I understand your question, here's how to look at it.

                  Voltage sensitivity. Forget power.

                  Use the voltage sensitivity for the driver(s). Use for example an 8 ohm 87 dB woofer.
                  If you put 2.83 volts on it, it produces 87 dB SPL.

                  Now wire a second one in parallel. Both drivers see 2.83 volts, and both produce 87 dB. So the SPL of the two together is 87dB + 6 dB = 93 dB

                  That's 93 dB with 2.83 volts.

                  If the two drivers are wired in series, each driver sees half of the 2.83 volts. In dBs, the half voltage output is -6 dB. So you get 81 dB from each driver. Then the two drivers combine as 81 dB + 6 dB = 87 dB.

                  Notice that I've not mentioned power, or dB with one watt at one meter. That is not what you need to be looking at anyway, unless you are concerned about amplifier power requirements.
                  Yes, all that is correct, but also when in parallel and both driver see 2.83V, the power input is doubled. That means a 6dB increase in acoustic power out for a 3dB increase in electrical power in. A 3dB increase in efficiency.

                  When in series there is no net increase is acoustic power ot but since each driver gets 1/2 of 2.83 V and since power goes like V^2 across the driver, the power delivered to each driver is 1/4 of what it was in parallel (Or alone) Thus the total power in is 1/2 or -3dB. Now there is no change in output acoustic power since it remains at 81dB, but the total electrical power in is -3dB. Again, there is a 3dB increase in efficiency.

                  The point bening it really make no difference from an efficiency point of view whether you connect in series or parallel. But from a sensitivity point of view it does. Now ask, what do I have, an amp with low rated power (low voltage swing) but doubles power into 4 ohms, or do I have an amp with a very large voltage swing that does not like low impedance loads? The first case would suggest a parallel connection, the second a series.
                  John k.... Music and Design NaO dsp Dipole Loudspeakers.

                  Comment


                  • #10
                    Re: added SPL by doubling drivers

                    The simple answer (per Keele) is that doubling the number of drivers when spaced closer than 1/4 wavelength so that their outputs fully couple doubles the radiating efficiency. Double the efficiency=+3dB. The downside is that the upper corner frequency (Ka) is reduced by a factor of 0.7 for each doubling. Therefore you only get your +3dB up to that lowered Ka frequency. It also means that there is a finite limit to how many drivers may be added before you reach maximum system efficiency, with direct radiators about 25%. Beyond that you get no more mutual coupling gains, and any additional output is purely power related.
                    www.billfitzmaurice.com
                    www.billfitzmaurice.info/forum

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                    • #11
                      Re: added SPL by doubling drivers

                      Originally posted by billfitzmaurice View Post
                      The simple answer (per Keele) is that doubling the number of drivers when spaced closer than 1/4 wavelength so that their outputs fully couple doubles the radiating efficiency. Double the efficiency=+3dB. The downside is that the upper corner frequency (Ka) is reduced by a factor of 0.7 for each doubling. Therefore you only get your +3dB up to that lowered Ka frequency. It also means that there is a finite limit to how many drivers may be added before you reach maximum system efficiency, with direct radiators about 25%. Beyond that you get no more mutual coupling gains, and any additional output is purely power related.
                      The 1/4 wave length is just an approximation, like saying baffle step happens at X Hz. There is a transition between +3dB efficiency and no increase as wave length decreases compared to separation. It isn't even monotonic. It follows a curve similar to the center plot shown here:



                      6db at long wave length, 3dB as frequency rises, transition in between. Ignore the rest of the figures as they are not relevant to this discussion.
                      John k.... Music and Design NaO dsp Dipole Loudspeakers.

                      Comment


                      • #12
                        Re: added SPL by doubling drivers

                        Originally posted by johnk... View Post
                        Yes, all that is correct, but also when in parallel and both driver see 2.83V, the power input is doubled. That means a 6dB increase in acoustic power out for a 3dB increase in electrical power in. A 3dB increase in efficiency.

                        When in series there is no net increase is acoustic power ot but since each driver gets 1/2 of 2.83 V and since power goes like V^2 across the driver, the power delivered to each driver is 1/4 of what it was in parallel (Or alone) Thus the total power in is 1/2 or -3dB. Now there is no change in output acoustic power since it remains at 81dB, but the total electrical power in is -3dB. Again, there is a 3dB increase in efficiency.

                        The point bening it really make no difference from an efficiency point of view whether you connect in series or parallel. But from a sensitivity point of view it does. Now ask, what do I have, an amp with low rated power (low voltage swing) but doubles power into 4 ohms, or do I have an amp with a very large voltage swing that does not like low impedance loads? The first case would suggest a parallel connection, the second a series.
                        I think too, if sensitivity is already expressed in terms of Sound Pressure Level for a given input voltage, then understanding sensitivity increase works best when we throw out radiating area. For example, a 7" woofer and 1" dome tweeter, if in phase (correlated SPL) and rated at the same sensitivity, will still sum +6dB over that reference sensitivity - despite their vast differences in radiating area - thus the reason why a Linkwitz-Riley crossover is down 6dB at the crossover point.

                        If they are in parallel, and receiving the same voltage to each driver, then the voltage goes up by 2, and the SPL gain is 20 Log (2) = +6.02 dB.

                        Jeff
                        Click here for Jeff Bagby's Loudspeaker Design Software

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                        • #13
                          Re: added SPL by doubling drivers

                          Originally posted by Jeff B. View Post
                          I think too, if sensitivity is already expressed in terms of Sound Pressure Level for a given input voltage, then understanding sensitivity increase works best when we throw out radiating area. For example, a 7" woofer and 1" dome tweeter, if in phase (correlated SPL) and rated at the same sensitivity, will still sum +6dB over that reference sensitivity - despite their vast differences in radiating area - thus the reason why a Linkwitz-Riley crossover is down 6dB at the crossover point.

                          If they are in parallel, and receiving the same voltage to each driver, then the voltage goes up by 2, and the SPL gain is 20 Log (2) = +6.02 dB.

                          Jeff
                          Yep, and then it's not area, it's volume velocity. And it is really for simple sources, and uniform (omni) polar response, and...., and.....
                          John k.... Music and Design NaO dsp Dipole Loudspeakers.

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