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  • Vas vs. Qtc?

    I just learned what Vas meant. At least the explanation in the article I just read made sense to me. In this article it says in a sealed enclosure that the Qtc, which if I understand right is box volume, should be around 1/3rd the Vas of the driver to be optimal or a Qtc of .7. I am assuming this is correct?
    I looked for a formula for a vented alignment but could not find one.
    I thought I read in another thread that in a vented box the Qtc should be higher then the Vas?

    Here is a link to what I was reading.
    Thanks Dave
    http://www.pellegreneacoustics.com/

    Trench Seam Method for MDF
    https://picasaweb.google.com/101632266659473725850

  • #2
    Re: Vas vs. Qtc?

    For a sealed box,

    Qtc = Qts x sqrt[ (Vas/Vab) + 1]
    and
    Fc = Fs x sqrt[ (Vas/Vab) + 1]

    For example, say you have a woofer with Vas = 51.8 liters, Fs = 35.8 Hz, and Qts = 0.39. Then you put it in a sealed box with Vb = 37.5 liters.

    Qtc = (0.39) x sqrt[ (51.8/37.5) + 1] = 0.60
    and
    Fc = (35.8) x sqrt[ (51.8/37.5) + 1] = 55.2 Hz

    That's for a sealed box. A vented box is more complicated, and there are no simple formulas for them. Usually software or tables are needed for calculating vented response.
    - Dave R
    the 200% Norske

    Comment


    • #3
      Re: Vas vs. Qtc?

      The Q values (Qts, Qtc, Qes, Qms) describe the "quality factor" of the resonance for that particular system, or part of it, at its resonant frequency.

      In a driver, the physical and mechanical parts (e.g. the cone, the surround and the spider) make up a resonant system, and this is described by Qms. Likewise, the motor (the voice coil, magnet, pole piece, etc.) makes up an electrical resonant system, and this is described by Qes. These act together, in parallel, to generate the free-air resonance of the driver, and that is known as Qts. When you put this in a closed (or other type) box, the air volume in the box adds another component to the mechanical resonant system and, to distinguish this from the free air resonance, we use the term Qtc.

      Keep in mind that "resonant system" does not imply that there is high Q. Resonant systems can be highly damped just as easily as they can be resonant. It all depends on what you want the system to do: If you are designing a car suspension, you want a damped (mechanical) system. If you are designing a tuner circuit to pick out a station at a particular frequency, you want a highly resonant (electrical) system/circuit.

      For more info on Q and resonance, check out:
      http://en.wikipedia.org/wiki/Q_factor

      So, lastly, getting back to your post about Qtc... Qtc is not the box volume, and should not obey and rules such as "should be higher than" with respect to Vas or box volume. It is a separate parameter that describes the frequency response around resonance, however Qtc can be manipulated by the box volume because the volume of air in the box determines the "additional component" of the mechanical resonant system of the driver-in-box. The second poster listed the formulas describing this for a closed box.

      -Charlie
      Charlie's Audio Pages: http://audio.claub.net

      Comment


      • #4
        Re: Vas vs. Qtc?

        The Wikipedia article on T/S is pretty explanative, Dave:
        http://en.wikipedia.org/wiki/Thiele/Small

        Vas is just Cms expressed with respect to the fluid medium that the speaker is performing in. For instance, if you designing a speaker to work on top of mount Everest, the value of Vas would decrease, but the Cms would not.

        The article's example worked out for the ratio of Vas to box volume to be 3:1 solely because of the Qts of the driver in the example. As the driver Qts increases, so does the enclosure size.

        There is no Qtc in vented alignments (The 'c' stands for closed.) There the situation is more complicated as there is the 'air sping' provided by the volume of air in the enclosure and the 'air spring' provide by the air mass of the vent. If you picture the compliance of a sealed box to be represented by a spring with a weight on it, the vented box would have an additional spring and weight suspended from the first spring and weight, and bouncing up and down (or not) at differing frequencies.

        C
        Curt's Speaker Design Works

        "It is the mark of an educated mind to be able to entertain a thought without accepting it."
        - Aristotle

        Comment


        • #5
          Re: Vas vs. Qtc?

          I was researching this trying to understand what is going on in my latest speaker build the Metallica's here. I am mainly wanting to translate what I am seeing in graphs, make changes, and see how it translates to what I am hearing. The boxes I am using are to small for the drivers and I was messing with the damping material. I understand, in a sealed box, stuffing makes the box up to 40% larger. So I was experimenting to see how it would change my under sized vented boxes. I have 1" rigid fiberglass lining the box. I was adding poly fill and could here a difference in vocals. It seemed to sound better in the vocals the more fill I put in, but the trade off was lose of the lower base. I remember Curt C. saying on one of his speakers to add enough fill until you start to hear the lose of base. These boxes are my MDF seam test boxes that I am going to give to my wife for her office, so small is a good thing plus they will be played at low volumes. I figured I am starting to know enough over all to try to understand what the t/s parameters really mean.
          Thanks for the info so far and I will read the links that you gave me.
          Dave
          http://www.pellegreneacoustics.com/

          Trench Seam Method for MDF
          https://picasaweb.google.com/101632266659473725850

          Comment


          • #6
            Re: Vas vs. Qtc?

            Originally posted by davepellegrene View Post
            I just learned what Vas meant. At least the explanation in the article I just read made sense to me. In this article it says in a sealed enclosure that the Qtc, which if I understand right is box volume, should be around 1/3rd the Vas of the driver to be optimal or a Qtc of .7. I am assuming this is correct?
            I looked for a formula for a vented alignment but could not find one.
            I thought I read in another thread that in a vented box the Qtc should be higher then the Vas?

            Here is a link to what I was reading.
            Thanks Dave
            What Vas means, is what volume of air has the same "stiffness" (or compliance) as the driver's suspension (surround and spider). Imagine 2 totally sealed boxes, one is a 6" cube and the other is a 36" cube. They each have a 4" dia. tube with a piston with a handle on it. It's intuitive (I think) that to push that piston in, say 4" (a displacement of approx. 50 cu. in.), would require a LOT more effort on the small box (which is only 1/8 cu. ft., if it's 6" dims. are internal dims.) than on the large box (which is 27 cu. ft.).

            That's because you'd be having to compress the air in the small box down to about 77% of its volume (the 4" stroke on the 4"d piston is about 23% of the internal volume of the small box). The same piston displacement on the large box would only be compressing the air in the box by 0.1%. I think if the piston had any weight at all, and it was on the top side of the box, gravity alone would probably pull the piston right down.

            The relationship between Vas and Qt"S", is well known for both sealed and vented boxes. Qts is a T/S parameter. Putting a driver in a sealed box generates Qt"C" (which is the tendency of the driver+box COMBINATION to resonate), which is always higher than a driver's Qts. If you want the "nominal" Qtc of .707 (which is half the sq. root of 2, btw) for a closed box rolloff, you can't get there by using a driver with a Qts that's higher than that. In general, Qtc is only used with closed box alignments, not vented boxes. Vented box alignments are described by their box size, tuning freq. (Fb), and F3, or F6, etc.

            "In this article it says in a sealed enclosure that the Qtc, which if I understand right is box volume, should be around 1/3rd the Vas of the driver to be optimal or a Qtc of .7. I am assuming this is correct?"

            I'd say that your quoted statement is not correct. Qtc is NOT box volume, but it relates box volume (Vb) to Qts and Vas. It's a "unitless" number, whereas volume is measured in cu. in., cu. ft., or liters. If your aim Qtc is 0.71, then the 2nd part of the statement would only be correct if the driver had a Vas of about 2.1 cu. ft. Maybe 1 out of 100 woofers will have a Vas of 2.1 cf.

            When I'm not by a computer, and I get a new PE flyer, and I want to model a woofer in a vented box "in my head", something that works very well (provided that the woofer's Qts is in the range of 0.30 to about 0.43) is to look at Qts, Vas, Fs, Vb, and F3 in this way:

            A driver with a Qts of 0.40 will be able to have an F3 equal to its Fs in a properly tuned box that's the same size as the driver's Vas. For every 0.01 that Qts is HIgher than .40, the F3 will drop by 1 Hz, and the box will have to get 6% larger. For every 0.01 that Qts is LOwer than .40, the F3 will increase by 1 Hz, and the box will be 6% smaller.

            Examples:
            Qts = .42, Vas = 2.0 cf, Fs = 30
            This driver will be able to have an F3 of 28Hz in a properly tuned 2.24 cf box.

            Qts = .35 (.05 lower than .40), Vas = 2.0, Fs = 30
            This driver will only be able to get down to 35Hz in about a 1.4 cf box.

            Of course, there will be other alignments that will work also, but this gives me a feel for how low the woofer will go and what its box size will be.

            Chris

            Comment


            • #7
              Re: Vas vs. Qtc?

              Originally posted by davepellegrene View Post
              I just learned what Vas meant. At least the explanation in the article I just read made sense to me. In this article it says in a sealed enclosure that the Qtc, which if I understand right is box volume, should be around 1/3rd the Vas of the driver to be optimal or a Qtc of .7. I am assuming this is correct?
              I looked for a formula for a vented alignment but could not find one.
              I thought I read in another thread that in a vented box the Qtc should be higher then the Vas?

              Here is a link to what I was reading.
              Thanks Dave
              The prior explanations are far more in depth but to answer your question directly again, you are assuming correctly FOR THOSE PARTICULAR VALUES OF Qts and Qtc. If your drivers do not have the same Qts as in the example, then the ratio is going to be different. Say your drivers have a Qts of .4, then the ratio is 2/1.

              I can see why you want to make those enclosures work. They are beautiful. I have some closed boxes about the same size using the same drivers but added a subwoofer for the low end using the 50 watt PE plate amp but that requires another driver, amp and enclosure.

              I also made a pair using the same drivers but with a 6 liter vented enclosure. I believe you could enlarge and port those enclosures. Others correct me if I am wrong but it seems you could cut a large cutout in the bottom and glue a ported box that has the added volume and port size you need. You could make it to look like a speaker stand or just a part of the current enclosure.

              BTW, Dirk was right when he said that the little Dayton T-amp would put out enough volume for those speakers.

              I decided to look up my BassBox Pro closed box deisgn to see if the formula works. WT3 Driver Qts=.817 & Vas=1.5 liters. BassBox Pro Qtc=.82 for a 2.1 liter heavily stuffed box. Obviously the formula doesn't work with my figures because Qtc/Qts squared is about 1 and 1-1 =0 so the ratio would be 0:1. I don't understand that.

              Looks like I have to use BB Pro so it doesn't include the effects of fill on the inside. In that case Qtc=1 so the ratio would be 1/.817 squared minus 1= about .5:1. So the box volume, according to the formula should be twice the Vas of 1.497 liters or about 3 liters and BB Pro came up with 2 liters???

              Comment


              • #8
                Re: Vas vs. Qtc?

                Originally posted by Chris Roemer View Post
                ...The relationship between Vas and Qt"S", is well known for both sealed and vented boxes. Qts is a T/S parameter. Putting a driver in a sealed box generates Qt"C" (which is the tendency of the driver+box COMBINATION to resonate), which is always higher than a driver's Qts. If you want the "nominal" Qtc of .707 (which is half the sq. root of 2, btw) for a closed box rolloff, you can't get there by using a driver with a Qts that's higher than that. In general, Qtc is only used with closed box alignments, not vented boxes. Vented box alignments are described by their box size, tuning freq. (Fb), and F3, or F6, etc.
                Hmmm. The Dayton specs for the RS100 have Qts as .87. I measured mine with WT3 at .82.

                BTW, great explanation of what Vas is.

                Comment


                • #9
                  Re: Vas vs. Qtc?

                  Some of the statements above might be a little confusing.

                  If you select a driver with a higher Qts - in order to maintain the same overall Q of the driver/sealed box system, you need to increase the box volume. Reducing box volume with the same driver Qts increases damping of the system resulting in a higher overall system Q.

                  It is helpful to consider Q as a measure of the narrowness of the bandwidth for which a driver "resonates" and also as a measure of how "lossy" the driver is. Highly damped lossy drivers tend to have a higher Qts and a narrow band peaky response around resonance. As a result, they tend to require less damping than more compliant, less lossy drivers in order to achieve the same optimal overall system Q - which for most designers - falls in the region of .5 to .7. If you are after optimal transient response - you tend to move towards the critically damped end of the range Q ~ .5. If you are after a steeper rolloff (for a woofer operating near resonance) you tend to push the Q up towards .7. But it's wise to keep in mind - any time you increase damping - you are also increasing losses which reduces overall efficiency. Striking a balance between maintaining dynamics (reduced signal compression and losses) while controlling over excursion and ringing are inevitably part of the mix when it comes to playing with an oscillating system's overall amplitude response at or near its fundamental resonance.

                  All of the above can be summarized with a few simple sentences - high q drivers are lossy and can be used in smaller cabinets without too much effect on overall system damping. Low q drivers are not as lossy and require larger enclosures for them to "breathe" without being overdamped. Q is a measure of a driver's energy storage versus the energy dissipated.

                  Comment


                  • #10
                    Re: Vas vs. Qtc?

                    Hmmm. Real expert, or just self proclaimed? ;) Almost everything you say below is wrong, or strangely taken out of context.

                    Damping and Q have an inverse relationship. More damping means lower Q and vice versa. More damping means less peaking at resonance and vice versa. Damping = Loss = dissipation, so lossy drivers, by definition, have a lower Q.

                    Reducing box size changes (reduces) damping in a sealed box system by increasing stiffness. Can you think of a reason why this is the case?

                    Originally posted by villastrangiato View Post
                    Some of the statements above might be a little confusing.

                    If you select a driver with a higher Qts - in order to maintain the same overall Q of the driver/sealed box system, you need to increase the box volume. Reducing box volume with the same driver Qts increases damping of the system resulting in a higher overall system Q.

                    It is helpful to consider Q as a measure of the narrowness of the bandwidth for which a driver "resonates" and also as a measure of how "lossy" the driver is. Highly damped lossy drivers tend to have a higher Qts and a narrow band peaky response around resonance. As a result, they tend to require less damping than more compliant, less lossy drivers in order to achieve the same optimal overall system Q - which for most designers - falls in the region of .5 to .7. If you are after optimal transient response - you tend to move towards the critically damped end of the range Q ~ .5. If you are after a steeper rolloff (for a woofer operating near resonance) you tend to push the Q up towards .7. But it's wise to keep in mind - any time you increase damping - you are also increasing losses which reduces overall efficiency. Striking a balance between maintaining dynamics (reduced signal compression and losses) while controlling over excursion and ringing are inevitably part of the mix when it comes to playing with an oscillating system's overall amplitude response at or near its fundamental resonance.

                    All of the above can be summarized with a few simple sentences - high q drivers are lossy and can be used in smaller cabinets without too much effect on overall system damping. Low q drivers are not as lossy and require larger enclosures for them to "breathe" without being overdamped. Q is a measure of a driver's energy storage versus the energy dissipated.

                    Comment


                    • #11
                      Re: Vas vs. Qtc?

                      ROFLMAO, especially about the "Real expert or just self proclaimed" part.:p
                      Paul

                      Originally posted by rone View Post
                      Hmmm. Real expert, or just self proclaimed? ;) Almost everything you say below is wrong, or strangely taken out of context.

                      Damping and Q have an inverse relationship. More damping means lower Q and vice versa. More damping means less peaking at resonance and vice versa. Damping = Loss = dissipation, so lossy drivers, by definition, have a lower Q.

                      Reducing box size changes (reduces) damping in a sealed box system by increasing stiffness. Can you think of a reason why this is the case?

                      Comment


                      • #12
                        Re: Vas vs. Qtc?

                        Chris Roemer is correct as usual - Qtc is not box volume, but rather a ratio that is descriptive of the relationship between box volume and the response characteristics of a specified driver. At least, that's how I view it!

                        Comment


                        • #13
                          Re: Vas vs. Qtc?

                          Originally posted by villastrangiato View Post
                          All of the above can be summarized with a few simple sentences - high q drivers are lossy and can be used in smaller cabinets without too much effect on overall system damping. Low q drivers are not as lossy and require larger enclosures for them to "breathe" without being. Q is a measure of a driver's energy storage versus the energy dissipated.
                          I think that you got this backwards. High Q drivers are NOT lossy, by definition. Q is a measure of the energy "storage", so less Q is less storage, e.g. lossy-er.

                          When the air volume enclosed behind the driver is reduced from a very large (e.g. infinite) value, the effect is an increase in both the Q and the resonance frequency (where roll off starts). If you use a high Q driver in a small enclosure, you will end up with an even high Q system, which is undesirable from a transient stand point (e.g. it will ring at the resonant frequency). On the other hand, you can put a low Q driver in a relatively small (measured in units of Vas) box, and still get a reasonable Qtc (e.g. Qtc=0.707), although the Fc will have increased.

                          A further example is this: Peerless sells some XLS and XXLS subwoofer drivers that have very low Q (e.g. 0.19). Also Fs is under 20Hz. On top of that Vas is only about 80L IIRC. You can put this driver in a very small sealed box (e.g. 1 cubic foot) and still get a very low Q. This is pretty unusual compared to the typical subwoofer that has 0.35 < Qts < 0.5. The Peerless subs can be used in a small passive radiator system very effective because of the low Q.

                          -Charlie
                          Charlie's Audio Pages: http://audio.claub.net

                          Comment


                          • #14
                            Re: Vas vs. Qtc?

                            Originally posted by Paul K. View Post
                            ROFLMAO, especially about the "Real expert or just self proclaimed" part.:p
                            Paul
                            Paul your pretty hip! I had to ask my daughter what ROFLMAO meant. THat's funny!
                            http://www.pellegreneacoustics.com/

                            Trench Seam Method for MDF
                            https://picasaweb.google.com/101632266659473725850

                            Comment


                            • #15
                              Re: Vas vs. Qtc?

                              Originally posted by curt_c View Post
                              The Wikipedia article on T/S is pretty explanative, Dave:
                              http://en.wikipedia.org/wiki/Thiele/Small

                              Vas is just Cms expressed with respect to the fluid medium that the speaker is performing in. For instance, if you designing a speaker to work on top of mount Everest, the value of Vas would decrease, but the Cms would not.

                              The article's example worked out for the ratio of Vas to box volume to be 3:1 solely because of the Qts of the driver in the example. As the driver Qts increases, so does the enclosure size.

                              There is no Qtc in vented alignments (The 'c' stands for closed.) There the situation is more complicated as there is the 'air sping' provided by the volume of air in the enclosure and the 'air spring' provide by the air mass of the vent. If you picture the compliance of a sealed box to be represented by a spring with a weight on it, the vented box would have an additional spring and weight suspended from the first spring and weight, and bouncing up and down (or not) at differing frequencies.

                              C
                              Just when I thought I was putting it together I got to the bottom of the wikipedia link and it says;
                              As an example, Fs and Vas may vary considerably with input level, due to nonlinear changes in Cms. A typical 110 mm diameter full-range driver with an Fs of 95 Hz at 0.5 V signal level, might drop to 64 Hz when fed a 5 V input. A driver with a measured Vas of 7 L at 0.5 V, may show a Vas increase to 13 L when tested at 4 V. Qms is typically stable within a few percent, regardless of drive level. Qes and Qts decrease <13% as the drive level rises from 0.5 V to 4 V, due to the changes in Bl. Because Vas can rise significantly and Fs can drop considerably, with a trivial change in measured Mms, the calculated sensitivity value (η0) can appear to drop by >30% as the level changes from 0.5 V to 4 V. Of course, the driver's actual sensitivity has not changed at all, but the calculated sensitivity is correct only under some conditions. From this example, it is seen that the measurements to be preferred whilst designing an enclosure or system are those likely to represent typical operating conditions. Unfortunately, this level must be arbitrary, since the operating conditions are continually changing when reproducing music. The result of level-dependent nonlinearities is typically lower than predicted output, or small variations in frequency response.
                              My brain just froze up.:eek:

                              Really! Now what good does the t/s parameters do when they all change depending on the voltage you put in the driver or when the voice coil gets hot?


                              Dave
                              http://www.pellegreneacoustics.com/

                              Trench Seam Method for MDF
                              https://picasaweb.google.com/101632266659473725850

                              Comment

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