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Midwest Audio Fest

It’s that time audio enthusiasts! Registration for the 2019 Speaker Design Competition is now open! Visit midwestaudiofest.com for details and to list your speaker project. We are excited to see all returning participants, and look forward to meeting some new designers this year, as well! Be sure your plans include a visit to the Parts Express Tent Sale for the lowest prices of the year, and the Audio Swap Meet where you can buy and trade with other audio fans. We hope to see you this summer! Vivian and Jill
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Stupid question: Parallel driver gets +6dB?

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  • Stupid question: Parallel driver gets +6dB?

    Sorry for the stupid question (or possibly stupid person in my case), but I've always just accepted that when you parallel a pair of identical drivers that you gain +6dB of sensitivity. I've read the online explanations which repeat that you get +3dB from doubling the power (double current, halving resistance) and +3dB from the other driver. And Linkritz's page is far too mathematical and complex for my simpleton brain to grasp.

    So while staying up with my newborn until 3am last night, I was thinking about the +6dB and can't see where it comes from. To me, it seems that you're counting the extra driver twice. I understand that paralleling the drivers will halve your resistance and double the current for the same voltage, thus there's double the power available. Each driver sees the same power as it did individually in the system, so you get +3dB from the 2nd driver being driven at the same level as when there was only one. To me that accounts for both power doubling and the extra driver. My assumption though is that the extra driver only adds +3dB if it's driven at the same level as the single driver setup (hence both power and driver accounted for). If that's wrong and the extra driver adds +3dB regardless of the drive, then that could be where I'm not seeing this (though I don't see how a driver doubles output even when driven lower because displaced air shouldn't double unless the second driver moves the same amount as in the single driver setup).

    My apologies for the stupid question/person. Please help explain the +6dB gain in simpleton terms as I'm obviously the wooden spoon in the knife drawer.

    Thanks.
    Nichikuros - Peerless 831735 Nomex + Vifa NE25VTA
    Digger8 - Small compact 8" sub with F3 = 20Hz
    Madison-D and Madison-R - Tang Band W4-1720 + Vifa BC25SC06 or Beston RT003C (TM and MTM)
    Jeffrey - Tang Band W5-704D + Beston RT003C
    Jasmine - Fountek FW146 + Fountek NeoCD3.0 Ribbon in Pioneer BS21 Cabinet

  • #2
    Re: Stupid question: Parallel driver gets +6dB?

    +3dB for the extra power. +3dB for the added driver area. 6dB total, up to the frequency where the drivers are no longer correlated, and then it reverts to 3dB. The driver spacing determines the correlation point. That's for parallel drivers.

    Series drivers see no increase in sensitivity, because the power is halved, cancelling the radiation gain from the extra area.
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    • #3
      Re: Stupid question: Parallel driver gets +6dB?

      You're thinking about it the right way. You really are only gaining 3 dB in efficiency from adding the second driver (same Fs, same Qts, but twice the Vas), but now it's a 4 ohm system (assuming 8 ohms to begin with), so it will draw twice the power that a single one would have with a given voltage across the terminals, giving you another 3dB boost. This additional power draw needs to be accounted for when level matching to other drivers on the same circuit. If you put the drivers in series, you will get the same 3 dB increase in efficiency, but now you will have a 16 ohm system which will draw half the power, which will lower the SPL 3dB for a given voltage, giving you a net change of 0dB. Either way, the only real gain is the 3dB in efficiency, which you pay for with twice the box size - after that, the impedence based increases or decreases are just a matter of level matching with other drivers on the circuit.

      Dan
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      • #4
        Re: Stupid question: Parallel driver gets +6dB?

        Consider one driver with 1 watt input that output some pressure. Let's say the pressure is 1.

        Now add the second driver in parallel. Both drivers have the same voltage across them. Each driver has 1 watt input. Total power in = 2 watts.

        The second driver will also radiate a pressure of 1.

        The pressure fields of each driver add vectorially. At low frequency both drivers radiate with the same phase so the sum reduces to a scalar sum. The summed sound pressure is 1 + 1 = 2.

        SPL increase = 20 log (2/1) = +6dB.

        So at low frequency sound pressure in dB increases by 6dB.

        Voltage supplied across the driver is the same so there is a 6dB increase in voltage sensitivity.

        But power increased by 3 dB (Power increase = 10 Log (Power for 2/ Power for 1) = 10 Log (2) = 3dB

        Thus these is only a 3 dB increase in efficiency.

        Summary:

        Two drivers in parallel give

        a) 6dB increase in SPL at low frequency,

        b) 6dB increase in voltage sensitivity,

        c) 3 dB increase in efficiency.
        John k.... Music and Design NaO dsp Dipole Loudspeakers.

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        • #5
          Re: Stupid question: Parallel driver gets +6dB?

          Thanks guys. I think this equation SPL increase = 20 log (2/1) is where I was missing the understanding. I kepth looking at it as efficiency and not SPL. It makes sense to me now mathmatically with the equation johnk gave. Still fuzzy conceptually as the doubling the driver area only doubles the amount of air moved if the displacement is the same as a single driver which means each driver gets the same power as the single driver did which accounts for doubling the power. I can't conceptually separate the area and power since they seem to be tied together in order to produce double the volume of air moved. But at least I can now see the math better.
          Thanks!
          Nichikuros - Peerless 831735 Nomex + Vifa NE25VTA
          Digger8 - Small compact 8" sub with F3 = 20Hz
          Madison-D and Madison-R - Tang Band W4-1720 + Vifa BC25SC06 or Beston RT003C (TM and MTM)
          Jeffrey - Tang Band W5-704D + Beston RT003C
          Jasmine - Fountek FW146 + Fountek NeoCD3.0 Ribbon in Pioneer BS21 Cabinet

          Comment


          • #6
            Re: Stupid question: Parallel driver gets +6dB?

            SPL goes like volume velocity squared. That is why SPL goes like 20 log (p2/p1) or 10 Log ( (p2/p1)^2). The "squared" comes out of the Log.

            Log(X^2) = 2 Log X.
            John k.... Music and Design NaO dsp Dipole Loudspeakers.

            Comment


            • #7
              Re: Stupid question: Parallel driver gets +6dB?

              Originally posted by jsr View Post
              Thanks guys. I think this equation SPL increase = 20 log (2/1) is where I was missing the understanding. I kepth looking at it as efficiency and not SPL. It makes sense to me now mathmatically with the equation johnk gave. Still fuzzy conceptually as the doubling the driver area only doubles the amount of air moved if the displacement is the same as a single driver which means each driver gets the same power as the single driver did which accounts for doubling the power. I can't conceptually separate the area and power since they seem to be tied together in order to produce double the volume of air moved. But at least I can now see the math better.
              Thanks!
              John covered it, but let me simplify it a bit more. In my opinion, the use of the term power and looking at if from a power point of view is what is tripping you up. Forget power for a minute.

              When we work with speakers we need to work with voltage sensitivity since the vast majority of our amplifiers are constant voltage sources. When we try to match woofers and tweeters we compare them in terms of their sensitivity at a fixed voltage drive (usually 2.83V), this keeps everything apples to apples.

              When you put two woofers in parallel, like anything else in parallel, both units will recieve the same voltage. If you are driving with 2.83V, then both woofers will be driven by that voltage and the increase will be 20 Log(2) or a +6.02 dB gain.

              Of course, as noted the power is not constant with the voltage because the impedance has changed - but again, voltage sensitivity is what we are really looking for here.

              This is really no different than when we are working with a woofer and a tweeter and we cross them over in phase with each other as in an LR4 crossover. Both drivers are at -6dB at the crossover point but sum to 0 dB ( whatever the reference level is). So, in this case both the woofer and tweeter are being driven with the same voltage and sum +6db from where they are at the crossover point. It's the same principle.

              You can define all of this in terms of power too, but that get's confusing in keeping it apples to apples since the impedance changes from one side of the equation to the other.

              Jeff B.
              Click here for Jeff Bagby's Loudspeaker Design Software

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              • #8
                Re: Stupid question: Parallel driver gets +6dB?

                Thank you Jeff and John. I think I finally see it now. I couldn't stop looking at it as power. Thanks again!
                Nichikuros - Peerless 831735 Nomex + Vifa NE25VTA
                Digger8 - Small compact 8" sub with F3 = 20Hz
                Madison-D and Madison-R - Tang Band W4-1720 + Vifa BC25SC06 or Beston RT003C (TM and MTM)
                Jeffrey - Tang Band W5-704D + Beston RT003C
                Jasmine - Fountek FW146 + Fountek NeoCD3.0 Ribbon in Pioneer BS21 Cabinet

                Comment


                • #9
                  Re: Stupid question: Parallel driver gets +6dB?

                  +3dB for the extra power. +3dB for the added driver area. 6dB total, up to the frequency where the drivers are no longer correlated, and then it reverts to 3dB. The driver spacing determines the correlation point. That's for parallel drivers.

                  Series drivers see no increase in sensitivity, because the power is halved, cancelling the radiation gain from the extra area.
                  Good points as they apply to a parallel hookup. However, what about the correlation issue as it relates to drivers wired in series. You noted that with a series hookup the power is halved, which nulls out the additional doubled radiating area. This works when the driver spacing allows for correlated support. However, with wider spacing that support would be gone, and you would get a net loss in output of 3 dB.

                  I might be wrong here, and if I am I would like to know where I miscalculated.

                  Howard Ferstler

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                  • #10
                    Re: Stupid question: Parallel driver gets +6dB?

                    Originally posted by Jeff B. View Post
                    John covered it, but let me simplify it a bit more. In my opinion, the use of the term power and looking at if from a power point of view is what is tripping you up. Forget power for a minute.

                    When we work with speakers we need to work with voltage sensitivity since the vast majority of our amplifiers are constant voltage sources. When we try to match woofers and tweeters we compare them in terms of their sensitivity at a fixed voltage drive (usually 2.83V), this keeps everything apples to apples.

                    When you put two woofers in parallel, like anything else in parallel, both units will recieve the same voltage. If you are driving with 2.83V, then both woofers will be driven by that voltage and the increase will be 20 Log(2) or a +6.02 dB gain.

                    Of course, as noted the power is not constant with the voltage because the impedance has changed - but again, voltage sensitivity is what we are really looking for here.

                    This is really no different than when we are working with a woofer and a tweeter and we cross them over in phase with each other as in an LR4 crossover. Both drivers are at -6dB at the crossover point but sum to 0 dB ( whatever the reference level is). So, in this case both the woofer and tweeter are being driven with the same voltage and sum +6db from where they are at the crossover point. It's the same principle.

                    You can define all of this in terms of power too, but that get's confusing in keeping it apples to apples since the impedance changes from one side of the equation to the other.

                    Jeff B.
                    Good points. However, regarding your comments when matching woofers and tweeters in terms of sensitivity (and this obviously will apply to midrange drivers, too), I would like to interject a comment. I believe that things can get complicated when trying to get a good level match between woofers, mids, and tweeters when using a standard sensitivity test.

                    For example, most woofers (at least in systems that do not have them also behaving as midrange drivers) will radiate omnidirectionally, or at least close to that, over their operating ranges. Midranges and tweeters, however, generally do not follow that rule. Different tweeter and midrange designs obviously will have radiation-pattern characterisitcs that vary considerably from brand to brand and design to design.

                    Let's just deal with midranges in this case, since the same rules apply to tweeters. For example, you might measure a 5-inch cone midrange on axis with a 2.83 volt input and get a certain spl readout. This midrange may be fairly omnidirectional in the lower-midrange frequencies, but it will begin to beam if it has to reach up fairly high to dovetail with a tweeter. It may be flat as can be on axis and have the same on-axis sensitivity over its crossover-controlled operating range, but at wider off-axis angles its sensitivity falls off as the frequency climbs. Now, take, say a 2-inch dome midrange with the same on-axis sensivity over the same frequency range. At wider off-axis angles, especially as the frequencies covered go higher and higher, its "sensitivity" will be higher than that of the 5-inch cone, because its dispersion characteristic is more uniform over a broad bandwidty.

                    In a fairly well-damped listening room, especially if it is fairly large, the five-inch cone mid might have the same sensitivity at the listner's ears as the 2-inch dome, and they might sound similar. (I am discounting distortion issues, of course, to keep things simple.) However, in a more reflective and smaller room (a typical home living room, for example) the 2 incher would be brighter sounding (more sensitive, subjectively) than the 5-inch cone, at least at the higher end of its crossover-controlled operating range, simply because of the larger amount of energy being reflected from room walls. With tweeters, because their frequencies are absorbed better than midrange frequencies, the discrepancy might be even greater. In other words, with wide-dispersion drivers you will get a more uniform power response at the listening position, assuming the on-axis responses of the two types of drivers are similar both in terms of sensitivity and uniformity.

                    Ultimately, the "sensitivity" ratings of drivers, especially midrange and tweeter drivers, have to be taken with a grain of salt, because dispersion characteristics and room absorption are additional factors that will determine just how bright or dull a given driver will sound with a given voltage input. On-axis sensitivity is one factor in determining driver efficiency, but not the only factor by a long shot.

                    Howard Ferstler

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                    • #11
                      Re: Stupid question: Parallel driver gets +6dB?

                      My response intentionally ignored things like dispersion patterns, power response, baffle diffraction, room gain, room absorption, frequency response, distortion, etc., due to the nature of the question. While it is true that all of these play a role in how a driver will be crossed-over and implemented, and so must be taken into consideration in the design process, they are really not a party to the question of how two woofers increase 6dB when wired in parallel (as long as they are acoustically close, anyway).

                      Your points are all valid when it comes to speaker system design, but I was just pointing out that voltage sensitivity is the parameter we need to use for the comparison and not power, efficiency, or current draw, due to the way amplifiers drive speakers.

                      Jeff



                      Originally posted by Howard Ferstler View Post
                      Good points. However, regarding your comments when matching woofers and tweeters in terms of sensitivity (and this obviously will apply to midrange drivers, too), I would like to interject a comment. I believe that things can get complicated when trying to get a good level match between woofers, mids, and tweeters when using a standard sensitivity test.

                      For example, most woofers (at least in systems that do not have them also behaving as midrange drivers) will radiate omnidirectionally, or at least close to that, over their operating ranges. Midranges and tweeters, however, generally do not follow that rule. Different tweeter and midrange designs obviously will have radiation-pattern characterisitcs that vary considerably from brand to brand and design to design.

                      Let's just deal with midranges in this case, since the same rules apply to tweeters. For example, you might measure a 5-inch cone midrange on axis with a 2.83 volt input and get a certain spl readout. This midrange may be fairly omnidirectional in the lower-midrange frequencies, but it will begin to beam if it has to reach up fairly high to dovetail with a tweeter. It may be flat as can be on axis and have the same on-axis sensitivity over its crossover-controlled operating range, but at wider off-axis angles its sensitivity falls off as the frequency climbs. Now, take, say a 2-inch dome midrange with the same on-axis sensivity over the same frequency range. At wider off-axis angles, especially as the frequencies covered go higher and higher, its "sensitivity" will be higher than that of the 5-inch cone, because its dispersion characteristic is more uniform over a broad bandwidty.

                      In a fairly well-damped listening room, especially if it is fairly large, the five-inch cone mid might have the same sensitivity at the listner's ears as the 2-inch dome, and they might sound similar. (I am discounting distortion issues, of course, to keep things simple.) However, in a more reflective and smaller room (a typical home living room, for example) the 2 incher would be brighter sounding (more sensitive, subjectively) than the 5-inch cone, at least at the higher end of its crossover-controlled operating range, simply because of the larger amount of energy being reflected from room walls. With tweeters, because their frequencies are absorbed better than midrange frequencies, the discrepancy might be even greater. In other words, with wide-dispersion drivers you will get a more uniform power response at the listening position, assuming the on-axis responses of the two types of drivers are similar both in terms of sensitivity and uniformity.

                      Ultimately, the "sensitivity" ratings of drivers, especially midrange and tweeter drivers, have to be taken with a grain of salt, because dispersion characteristics and room absorption are additional factors that will determine just how bright or dull a given driver will sound with a given voltage input. On-axis sensitivity is one factor in determining driver efficiency, but not the only factor by a long shot.

                      Howard Ferstler
                      Click here for Jeff Bagby's Loudspeaker Design Software

                      Comment


                      • #12
                        Re: Stupid question: Parallel driver gets +6dB?

                        I appreciate the additional points and they make sense now that someone points them out to me. But u do also appreciate Jeffs simplistic explanation to not cloud my already smoggy brain from understanding the 6dB thing.
                        Nichikuros - Peerless 831735 Nomex + Vifa NE25VTA
                        Digger8 - Small compact 8" sub with F3 = 20Hz
                        Madison-D and Madison-R - Tang Band W4-1720 + Vifa BC25SC06 or Beston RT003C (TM and MTM)
                        Jeffrey - Tang Band W5-704D + Beston RT003C
                        Jasmine - Fountek FW146 + Fountek NeoCD3.0 Ribbon in Pioneer BS21 Cabinet

                        Comment


                        • #13
                          Re: Stupid question: Parallel driver gets +6dB?

                          Originally posted by jsr View Post
                          Thank you Jeff and John. I think I finally see it now. I couldn't stop looking at it as power. Thanks again!
                          It is completely valid to look at it from a power standpoint and the behavior is rather
                          unintuitive. The reason is that the output from the drivers sum as volume velocity,
                          both cones move the same and the volume velocity doubles. Volume velocity is
                          analagous to voltage and if you double the voltage in a circuit the power delivered
                          goes up by a factor of 4 and in the parallel case the power input goes up by 2. So the system
                          is more efficient by a factor of 2 (+3dB). Keep in mind that most direct radiator drivers
                          are less than 1% efficient often less than .5% with the rest of the power going into
                          heating the voice coil. This can be a factor in understanding exactly what is going on.
                          Sensitivity, as others have mentioned is generally quoted as voltage sensitivity and if
                          you wire them in parallel you draw twice the power for a given voltage (+3dB) combined
                          with efficiency increase provides a total sensitivity increase of +6dB. The power is 1/2
                          (-3dB) for the series connection combined with the +3dB efficiency increase nets a 0dB
                          change in voltage sensitivity.
                          The change in electro-acoustic conversion efficiency is +3dB in both cases.

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