happy birthday, at the same time that you try to blow out the candles. You are still outputting an air stream from your mouth, in that process we call talking. But, in order to make you speech intelligible, you have to accurately modulate and control the air output stream coming from your mouth, creating a specifically and accurately modulated signal that we call talking. Suddenly, because you have assigned one engine (your mouth) to do two distinct tasks, you will become far less effective at outputting enough energy in your pushed out airstream to blow out the candles. Moreover, since it is imperative that your modulated speech signal be understood, the task of accurately modulating your mouth's output airstream (in the process we call talking) becomes the dominant task, taking precedence over how much energy you can output for the other, now secondary, task of blowing out the candles. Thus, your effectiveness at the task of blowing out the candles takes a huge nosedive, merely because you are trying to multitask with your single mouth engine.
       Conventional subwoofers also multitask, assigning two distinct tasks to one engine. The one engine, comprising voice coil and cone diaphragm, is assigned the task of moving as much air as it can, in order to generate adequate sound intensity at low frequencies (that's like using your mouth to blow out the candles). But, in conventional subwoofers, this same engine is also assigned the second and very distinct task of modulating the airflow, so that the bass signal is reproduced (that's like talking by using your mouth to modulate the airflow). Moreover, since the bass signal must be accurately reproduced, it is the modulation task that becomes dominant, and takes precedence over the blowing task. This makes the conventional subwoofer cone driver much less effective at its other task, blowing enough airflow energy to adequately create the large energy that bass reproduction requires (like blowing out the candles).
       To understand this better, simply visualize a conventional cone subwoofer driver playing a 40 Hz bass sine wave. The cone cannot simply fly back and forth willy-nilly, trying to be as energetic as possible at the one task of blowing as much air as possible, in order to be as effective as possible in creating acoustic bass energy. Instead, because this driver's single engine also has the second task of correctly modulating the airflow to reproduce as signal, the cone is constrained to go back and forth in its excursion at a cycling rate of 40 Hz, no more nor less, in order that it may accurately modulate the airflow at a 40 Hz rate, and thereby reproduce the 40 Hz signal.
       Next, visualize that same driver reproducing a 20 Hz sine wave, half the frequency. Because the driver's single engine has been assigned a multitasking role, it must correctly modulate the signal, even while it does the best it can at the second task, generating whatever acoustic energy it can. This means the cone is constrained to go back and forth at half the cycling rate, 20 Hz, thereby taking twice as long to complete its excursion.

F.2. The Excursion Curse

       Now, a dynamic driver's motor, like many other motors, operates in a natural acceleration mode. It produces a constant acceleration of the cone diaphragm, for a given input signal level, since (as you'll recall from high school physics) a constant force (which comes from the given input signal level through the voice coil sitting in the magnet's field), applied to a constant mass, produces a constant acceleration.
       But this natural acceleration mode means that the multitasking, assigned to conventional subwoofer drivers, creates a curse for conventional subwoofer drivers, a curse that so severely limits the capabilities of conventional subwoofers to function as true subwoofers that they scarcely deserve the name subwoofer. As just discussed above, the multitasking assigned to conventional cone drivers means that they must track the signal (in order to accurately modulate the bass energy flow they are generating). And this in turn means that, when reproducing bass at half the frequency (one octave lower), conventional cone drivers are constrained to take twice as long a period of time to make an excursion.
       Why does this create a curse for conventional subwoofer drivers? Because a constant acceleration applied for twice as long a period of time results in the cone traveling at a way higher velocity. Now, higher velocity per se is not that problematic (and indeed is beneficial in one technical sense, helping to maintain flat frequency response to lower frequencies, even in the face of severely declining radiation resistance). But the real kicker is the next, inevitable step imposed by the laws of physics. A way higher velocity, imposed for twice as long a period of time, results in a way, way higher cone excursion distance.
       You'll recall from high school physics that excursion distance traveled is proportional to the period of time squared. Thus, as the bass frequency to be reproduced goes lower, here by half, the time for each excursion doubles, and the distance of each excursion thereby quadruples (other technical factors can make woofer excursion increase by even more than four times, or less, but the basic point here stays valid). In other words, this simple lengthening of the time period for each excursion (caused by the assignment of multitasking to the driver, and the driver's consequent obligation to track the signal it is modulating) in turn causes a huge increase in the distance of each excursion, as the bass frequency to be reproduced goes lower.
       The simple conceptual fact that, in conventional subwoofers, the driver is assigned multitasking, and is thereby constrained to take twice as long a period of time per excursion when the bass frequency to be reproduced goes down by half, means that its excursion will quadruple (more or less) when this subwoofer driver is asked to merely reproduce bass energy one octave lower.
       As discussed above, all cone drivers are really very limited in their maximum achievable excursion. Thus, this quadrupling of excursion, brought on by the assignment of multitasking and consequent doubling of excursion time for each octave, becomes a true curse, the nemesis of conventional subwoofers. It takes a lot of effort for the driver to make this hugely bigger excursion, it stresses the driver, and all this effort and stress soon result in severe limits on how big an excursion the driver can make, as it first distorts and then hits a stone wall (this in turn severely limits how low in frequency the subwoofer can go, and how loud it can play bass).
       Thanks to the assigned multitasking, conventional subwoofer drivers run out of excursion capability very quickly when trying to reproduce frequencies that are in true subwoofer territory. So subwoofers using conventional drivers have dubious claim to the pretense of even being true subwoofers at all.

F.3. TRW Single Tasking

       The TRW subwoofer is just the opposite. It is not forced to go to higher velocities as the frequency goes lower. It is not forced to go to higher excursions as the frequency goes lower. It so happens that the TRW does automatically increase its effective excursion as the frequency goes lower, but it experiences no stress or difficulty in making these larger and larger effective excursions. And there is no abrupt excursion limit with the TRW, in fact no limit at all (the TRW's effective excursion automatically approaches infinity, as the frequency approaches DC, without any stress or difficulty). Indeed, the TRW actually benefits from these larger excursions at lower frequencies, rather than being cursed by them as conventional subwoofer drivers are.
       How can all this be so? How can the TRW be so different, so opposite to conventional subwoofer drivers, in handling the increasing velocity and curse of runaway excursion that worsens at lower frequencies? And how can the TRW, rather than being constrained by the severe and abrupt excursion limits that are the nemesis of conventional subwoofer drivers, instead welcome and actually benefit from increased excursion, all the way to a mind-boggling infinite excursion?
       The answers take us back to the fundamental conceptual distinction that started this chapter. Conventional subwoofer drivers multitask, assigning two distinct tasks to one engine, and this is at the conceptual root of the curses that these drivers face with respect to velocity and runaway excursion, which then run smack into the mechanical limitations that severely limit the maximum excursion of these drivers.
       But the TRW is fundamentally just the opposite. It does not multitask a single engine. Instead, the TRW has two separate engines, and it assigns a single task to each engine. Thus, each engine in the TRW can perform its single task optimally, without being constrained or compromised by also having to perform a second distinct task. It's like having two people with two mouths, one to optimally perform the single task of blowing out the birthday candles with maximum force, without having to worry about (or compromise for the sake of) the second distinct task of modulating any signal -- and another to optimally perform the single task of modulating a voice signal to give a thank you speech, without having to worry about the second distinct task of blowing out any candles.
       How, specifically, does the TRW employ two engines to perform these two distinct tasks? The TRW subwoofer looks for all the world like an ordinary electric fan. Like all electric fans, the TRW uses a motor to rotate the fan with its blades. This motor is thus assigned the single task of blowing air, of supplying all the large amount of energy for the airflow needed to generate acoustic bass (like assigning your mouth to the single task of blowing out birthday candles). Then, the blades of the TRW's fan have variable pitch, just like the propeller blades on airplanes. This variation in blade pitch modulates the bass energy, thus tracking the bass signal. And this variation in blade pitch, this modulation of the bass signal, is accomplished in the TRW by a separate motor, dedicated to this single task (like assigning a second separate person with a distinct mouth to perform the distinct task of giving a thank you speech). This separate motor, that is assigned to modulate the airflow, and thereby track and reproduce the input signal, can do its job optimally, without having to work hard to create the airflow that furnishes the large amount of acoustic energy required for bass.
       But the big story here involves the separate TRW motor that drives the fan rotation, which is responsible for generating the airflow and acoustic bass energy. It can continue rotating at full speed, and hence optimally supply bass energy at full effectiveness, regardless of the frequency of the bass signal, and regardless of how the modulation is supposed to occur to reproduce that signal, since it is not constrained by also having to perform this second task of signal modulation.
       Thus, the TRW is just the opposite of conventional subwoofers. With the multitasking assigned to conventional subwoofers, we saw that the cycling periodicity of the cone excursion creating the airflow had to change, lengthening (slowing down) as the bass frequency went lower, since the cone also had to perform the distinct task of tracking and modulating the bass signal as it changed frequency. But here, in the TRW, the fan's rotating velocity creating the airflow does not have to slow down its rotational drive at all, as the bass frequency to be reproduced goes lower, so the fan motor and fan can continue rotating at maximum effectiveness for optimally creating acoustic bass energy.

F.4. TRW Improvements as Frequency Goes Lower

       We also saw that, with conventional subwoofer drivers, their cone velocity went way up, and their cone excursion went way, way up, as the bass frequency to be reproduced went lower, until very soon the driver excursion limits were reached. This severely curtailed the ability of conventional subwoofer drivers to play low bass and to create the large acoustic energy required by low bass, and since these are the two primary responsibilities for subwoofers, this means that conventional subwoofers cannot even perform their primary responsibilities, so are scarcely worthy of being called real subwoofers in the first place.
       Again, the TRW is just the opposite. Its rotating fan velocity, which drives the airflow, does not go up as the bass frequency to be reproduced goes down. Furthermore, the TRW is also just the opposite in that it does not run into severe excursion limits as the bass frequency goes lower.
       Indeed, the TRW's effective excursion can, in one sense (excursion per cycle of bass signal), continue to increase indefinitely as the bass frequency goes lower, without any of the effort or strain or limits that conventional subwoofer drivers are cursed by. The TRW's effective excursion per cycle can even effortlessly approach infinity (!!), as the bass frequency being reproduced approaches DC. How can the TRW do this? Because the TRW does not multitask, and assigns a separate engine to each task, the fan's rotational velocity can remain constant and unchanged, even as the bass frequency goes lower. Since the TRW fan's rotational velocity per second (per unit time) stays constant, its rotational bite of airflow per signal cycle increases automatically, as the time per signal cycle increases (gets longer), when the bass frequency goes lower. As the bass frequency to be reproduced gets lower and lower, approaching DC, the TRW fan's bite of airflow per signal cycle automatically gets larger and larger, without effort and without limit, finally approaching infinity as the bass frequency approaches DC.
       Thus, the TRW, with its separate motor creating the airflow and bass energy, actually benefits from the bass frequency going lower. This is the complete opposite from conventional subwoofer drivers, which are severely penalized in performance as the bass frequency goes lower.
       We can look at the contrast as follows. With conventional subwoofer drivers, the motor creating the airflow and bass energy is constrained to slow down its cycling as the bass frequency goes lower, since this motor also has been assigned the second distinct task of tracking and modulating the bass signal, and therefore there is only
one excursion cycle per bass signal cycle. With the TRW, the motor creating the airflow and bass energy is not so constrained, since it is not assigned the second distinct task of tracking and modulating the bass signal, so it can make many excursion cycles (fan rotations) per bass signal cycle. Furthermore, since the TRW fan's rotational speed can stay constant per unit time as the bass frequency goes lower, the TRW fan not only can make many excursion cycles per bass signal cycle, but also its number of excursion cycles, per bass signal cycle, automatically keeps increasing as the bass frequency to be reproduced goes lower, thereby automatically increasing the TRW subwoofer's volume of air moved, as the bass frequency goes lower.
       As you know, bass frequencies require a lot of energy, and require a lot of air to be moved. In one corner we have the conventional subwoofer driver, whose physics make its excursion increase hugely as the bass frequency goes lower, but which soon hits a stone wall at say 1 inch excursion. In the other corner we have the TRW subwoofer, whose physics are not adversely affected (indeed are benefited) by the bass frequency going lower, and which then also has infinite effective excursion capability. So, which is the real subwoofer, and which is the pretender? As we said, the TRW is the only subwoofer.

G. Opposites in Factors Limiting Bass Quantity

       Conventional subwoofers face a number of factors, which conspire to severely limit the quantity of bass they can produce (i.e. how loudly they can play), especially at exactly those low frequencies where subwoofers are supposed to be able to do their job.
       First, their steeply declining radiation resistance means that they become much less effective at coupling to the air at progressively lower frequencies, and you can't create loud acoustic levels in the air when you can't couple to the air in the first place.
       Second, their driver's puny and severely limited excursion capability, exacerbated by the fact (discussed above) that their driver's excursion intrinsically gets way, way larger as the bass frequency goes lower (even for the same modest loudness level), means that they cannot play loudly at low frequencies -- and means that their ability to create bass quantity gets severely reduced, merely by the frequency going lower, so that they intrinsically cannot play bass that is both low in frequency and loud. Since bass frequencies inherently require large amounts of energy to reproduce properly, a proper subwoofer needs to be able to play low frequencies loudly. Furthermore, as the Fletcher-Munson curves show, human hearing becomes much less sensitive at low bass frequencies, so a proper subwoofer also needs to play low frequencies loudly in order to even be heard.
       Third, conventional subwoofer drivers also have other inherent physical factors that can prematurely limit their bass loudness capability. For example, there are thermal constraints on a woofer driver being able to play loudly for a reasonable length of time. Most cone drivers are sadly inefficient, which means that most of the dissipated power put into the driver (by your power amplifier) becomes heat within the driver, instead of becoming acoustic loudness radiated by the driver. If voice coils get too hot, they can destroy the driver, melting the glues or plastic parts, setting combustible parts up in smoke, etc.
       Fourth, the fact that all conventional subwoofer drivers are assigned a multitasking role for their single engine (as discussed above) thereby forces your power amplifier, which drives this single engine, to also be assigned the same multitasking role. Your power amplifier has to perform two distinct tasks when driving these conventional subwoofer drivers. Your power amplifier must modulate the motion of the driver, to track and reproduce the bass signal. And, on top of that, your power amplifier must also furnish all the energy needed by the driver to perform its second task, creating the airflow and large acoustic energy required for bass. This latter task is of course what creates the loudness or quantity of bass.
       Most power amplifiers have trouble furnishing enough energy to perform this latter task adequately, so the power amplifier often becomes yet another factor limiting bass quantity. Note that amplifiers with very high power (and high current) ratings are often credited with providing better bass from a given conventional loudspeaker, so this proves that lesser amplifiers fall short of being able to supply the huge amount of energy (usually in the form of current) required for this latter task, and become yet another factor limiting the bass quantity available from conventional subwoofers.

(Continued on page 144)