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  • Semi Inductance

    "Semi Inductance".

    It's a term that most of you might not be familiar with, but you're likely going to find it being used more and more often, particularly with subwoofer design :-).

    Traditionally, designing an "alignment" (combination of box size, tuning, etc) for a particular subwoofer driver involved using parameters that basically described the driver's characteristics, these being the ones that most of us are familiar with - Vas (equivalent air compliance), Fs (resonance frequency) Qts (basically a measure of the driver's tendency to resonate at Fs), Re (DC impedance), and Le (inductance at a specified frequency, usually 1kHz for subwoofers).

    It's that last one, Le, that's of interest here. The fact that it's specified at a particular frequency suggests that perhaps it does not actually remain constant, and that's usually the case. In fact, with today's high performance subwoofer drivers, Le can vary quite significantly. So here's the thing - if the modeling program that you're using assumes that Le remains constant (and most of them do), then there's likely to be a noticeable difference between the simulated results and the actual measured results when you build what you simulated, and if Le changes significantly, that difference is going to be more significant, to the point of where the measured response does not look anything like what the simulation said it should be.

    Enter "semi inductance". Without getting into the nitty-gritty details, the "semi-inductance" model is an extension of the basic t/s param model, and it uses several additional parameters that "describe" how the driver's inductance changes with frequency, the end result being a simulation that predicts performance significantly more accurately. To put it in simple terms, using a simple t/s parameter based box modeling program will put you in the ballpark; using a modeling program that uses the semi-inductance model can put you on first base, or at least very near it.

    Those extra parameters? Well, they are not typically quoted by speaker manufacturers (yet!), but they can be derived from the driver's impedance curve. Thankfully Parts Express does publish the ZMA files for many of the drivers it sells, so that makes getting hold of the "semi-inductance" parameters for those drivers at lot easier. Otherwise you'll need to use a tool like DATS, measure the driver's impedance curve, and then use that to determine those additional parameters.

    Anyway, a few links that might be of interest:

    Thread on DIYAudio where the semi-inductance parameters for many drivers are being published:
    http://www.diyaudio.com/forums/multi...nductance.html


    A worked example, using Hornresp
    https://www.diysubwoofers.org/misc/semi-inductance.html
    Brian Steele
    www.diysubwoofers.org

  • #2
    Thanks!

    Here's a link to an article by Thorborg about the semi-inductance model that doesn't require an AES account to download.

    Comment


    • #3
      Originally posted by Brian Steele View Post
      "Semi Inductance".

      Without getting into the nitty-gritty details, the "semi-inductance" model is an extension of the basic t/s param model, and it uses several additional parameters that "describe" how the driver's inductance changes with frequency ...
      Would the ideal be: An driver Le graph (akin to .frd, .zma files) and modeling software that could incorporate the data in the simulation?

      Comment


      • #4
        Stephen Bolser has produced a spreadsheet that not only calculates the extra parameters when given the ZMA data of the driver to work with, it also produces a graphical display of how the inductance of the driver varies with frequency. He should be posting up a thread about his spreadsheet shortly on the DIYAudio Subwoofers forum.

        Some modeling programs like Hornresp can take these extra parameters into consideration when simulating a design. These extra parameters allow the program to take into consideration how inductance changes with frequency for that particular driver. For those programs that can't do this, a close approximation could be achieved by using the average inductance over the design passband as "Le". In the attached example, the driver's Le is 3mH @ 1kHz, but as this driver is designed for subwoofer duty, a much closer alignment with measured results would be obtained if the value for "Le" used in one of those basic box-modeling programs was set to around 7.5mH.

        Brian Steele
        www.diysubwoofers.org

        Comment


        • #5
          Originally posted by Brian Steele View Post
          Stephen Bolser has produced a spreadsheet that not only calculates the extra parameters when given the ZMA data of the driver to work with, it also produces a graphical display of how the inductance of the driver varies with frequency. He should be posting up a thread about his spreadsheet shortly on the DIYAudio Subwoofers forum.

          Some modeling programs like Hornresp can take these extra parameters into consideration when simulating a design. These extra parameters allow the program to take into consideration how inductance changes with frequency for that particular driver. For those programs that can't do this, a close approximation could be achieved by using the average inductance over the design passband as "Le". In the attached example, the driver's Le is 3mH @ 1kHz, but as this driver is designed for subwoofer duty, a much closer alignment with measured results would be obtained if the value for "Le" used in one of those basic box-modeling programs was set to around 7.5mH.
          I do understand that Le is not constant over a driver's frequency range and to improve the accuracy of a model you need to incorporate that change. Hence my post on an Le graph.

          So, how does this play against the Jeff Bagby's coefficient for driver inductance in response modeler, below? Similar concept?

          If I play back what you've written, you can get a good value for Le at any given frequency with a few parameters and some equations to process those parameters.

          (not trying to be a pain, just trying to internalize the concept).

          Click image for larger version  Name:	LE.png Views:	1 Size:	62.5 KB ID:	1387360

          Comment


          • #6
            Brian Steele Thank you for creating this, the detailed explanations, and everyone else that's posted additional info or extra accompanying data. This will be extremely valuable in the coming months for a fresh build of my beloved 2x Infinity Kappa Perfect 12.1 subs.

            I've used two of them for many years with ported ground pounding joy, but sadly I finally blew one up. Their power handling, earthquake output and sweet tone are something I've never heard matched.

            I'll likely try finding a new set for sale before trying to locate anything on PE that can compete with that description. It's subjective obviously, but they're incredible to me and the best bass tonal quality I've ever heard in my life.

            I don't want to derail the thread. So please, anyone here with personal experience with these specific Infinity Kappa Perfect 12.1, 12" woofers who knows a set from PE you consider equivalent in tonal quality, please shoot me a message. I'll thoroughly research them.
            Last edited by Thump; 09-09-2018, 08:59 AM. Reason: Typo +
            Why you long winded, thick headed, stubborn son of a ... oh, wait, that's me. Carry on!

            Comment


            • #7
              Originally posted by Millstonemike View Post
              So, how does this play against the Jeff Bagby's coefficient for driver inductance in response modeler, below? Similar concept?
              Yes. There have been several models that date back many years that attempt to capture the frequency-dependent change in the voice coil inductance. The most common early model is from Wright, published almost 30 years ago, and which is described in a publication from Wavecor (http://www.wavecor.com/Transducer_eq...nt_circuit.pdf). Leach proposed another model that reduces the number of parameters needed to predict the inductance from 4 to 2: a coefficient and an exponent (https://pdfs.semanticscholar.org/9e3...de8e9c3451.pdf). It appears that Jeff's model used in the Response Modeler is based on the Leach analysis, but that's a guess on my part.

              My understanding of the "semi-inductance" model is that it is a more recent refinement that captures two additional effects: the shorting rings or copper caps used in many new high-performance drivers, and the "visco-elastic" behavior of the suspension. The semi-inductance model appears to have been introduced in a series of papers around 10 years ago (see https://www.researchgate.net/publica...ivalent_Circuit_Model_for_Dynamic_Moving_Coil_Transducers), and it was integrated into LspCAD in version 6.32. Several years ago Scan-Speak started publishing the parameters needed to apply this model to their drivers, and there is a spreadsheet dated 2011 for calculating the effect on their website: http://www.audiocomponents.nl/scansp...dk/toolbox.htm

              These improved models are important if you are trying to predict the behavior of a woofer at higher frequencies. But usually, we use actual measurements for higher frequencies and only splice in modeled behavior below a frequency where measuring becomes more difficult due to room reflections and other measurement issues. So whether or not these newer more refined models are useful will depend on both the driver and the splicing frequency where we switch over from modeled behavior to actual measurements.
              Last edited by neildavis; 09-09-2018, 02:23 PM.
              Free Passive Speaker Designer Lite (PSD-Lite) -- http://www.audiodevelopers.com/Softw...Lite/setup.exe

              Comment


              • #8
                Originally posted by neildavis View Post
                These improved models are important if you are trying to predict the behavior of a woofer at higher frequencies. But usually, we use actual measurements for higher frequencies and only splice in modeled behavior below a frequency where measuring becomes more difficult due to room reflections and other measurement issues. So whether or not these newer more refined models are useful will depend on both the driver and the splicing frequency where we switch over from modeled behavior to actual measurements.
                The example I provided shows a 3dB dip @ 100 Hz and a 5dB dip @ 200 Hz, compared to the "standard" model. These are low enough to consider a different alignment for the driver. For hornloading (really 1/4 wave resonator loading, but everyone uses horn, so...), this could make the difference between a flattish passband response to one that looks like the horn's mouth is undersized for the job.

                Brian Steele
                www.diysubwoofers.org

                Comment


                • #9
                  Originally posted by Millstonemike View Post
                  If I play back what you've written, you can get a good value for Le at any given frequency with a few parameters and some equations to process those parameters.
                  Yep, but the next step is including it in an actual simulation, not just for impedance, but for frequency response, phase response, etc.

                  Hornresp was fairly recently updated to be able to use semi-inductance parameters in its sims.
                  Brian Steele
                  www.diysubwoofers.org

                  Comment


                  • #10
                    Originally posted by Brian Steele View Post
                    "Semi Inductance".

                    It's a term that most of you might not be familiar with, but you're likely going to find it being used more and more often, particularly with subwoofer design :-).

                    Traditionally, designing an "alignment" (combination of box size, tuning, etc) for a particular subwoofer driver involved using parameters that basically described the driver's characteristics, these being the ones that most of us are familiar with - Vas (equivalent air compliance), Fs (resonance frequency) Qts (basically a measure of the driver's tendency to resonate at Fs), Re (DC impedance), and Le (inductance at a specified frequency, usually 1kHz for subwoofers).

                    It's that last one, Le, that's of interest here. The fact that it's specified at a particular frequency suggests that perhaps it does not actually remain constant, and that's usually the case. In fact, with today's high performance subwoofer drivers, Le can vary quite significantly. So here's the thing - if the modeling program that you're using assumes that Le remains constant (and most of them do), then there's likely to be a noticeable difference between the simulated results and the actual measured results when you build what you simulated, and if Le changes significantly, that difference is going to be more significant, to the point of where the measured response does not look anything like what the simulation said it should be.

                    Enter "semi inductance". Without getting into the nitty-gritty details, the "semi-inductance" model is an extension of the basic t/s param model, and it uses several additional parameters that "describe" how the driver's inductance changes with frequency, the end result being a simulation that predicts performance significantly more accurately. To put it in simple terms, using a simple t/s parameter based box modeling program will put you in the ballpark; using a modeling program that uses the semi-inductance model can put you on first base, or at least very near it.

                    Those extra parameters? Well, they are not typically quoted by speaker manufacturers (yet!), but they can be derived from the driver's impedance curve. Thankfully Parts Express does publish the ZMA files for many of the drivers it sells, so that makes getting hold of the "semi-inductance" parameters for those drivers at lot easier. Otherwise you'll need to use a tool like DATS, measure the driver's impedance curve, and then use that to determine those additional parameters.

                    Anyway, a few links that might be of interest:

                    Thread on DIYAudio where the semi-inductance parameters for many drivers are being published:
                    http://www.diyaudio.com/forums/multi...nductance.html


                    A worked example, using Hornresp
                    https://www.diysubwoofers.org/misc/semi-inductance.html


                    Hi Brian,

                    Good points.

                    Just released SoundEasy V23 includes Semi-Inductance parameters extraction from the measured Zin curve and includes SI in all enclosure modelling processes. My tests indicate, that SI is the most accurate representation of driver's impedance curve, when compared to Wright's or Leach's models. All three models are available in SE V23.

                    Best Regards,
                    Bohdan

                    Comment

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