Basic Operation of the Series Vented Band-Pass Sub-Woofer Enclosure with Pressure Driver Environmental Radiator

Transcription

1 Basic Operation of the Series Vented Band-Pass Sub-Woofer Enclosure with Pressure Driver Environmental Radiator By Jeff Anderson & Jason Linse Abstract: This paper will describe the basic woofer-in-box loudspeaker alignment. Then the basic principals of the standard vented loudspeaker enclosure system are presented with explanation of the different regions of operation. Furthermore, a standard 4 th order band-pass box will be described. Then, the Series Vented Band-pass Sub-woofer Enclosure will be introduced and explained with further improvement with the use of a passive Pressure Driver will be presented with explanation of the advantages for its use. The focus of this paper is NOT to thoroughly describe in ad nauseam the mathematical details of the band pass alignments however an intuitive narrative will be presented such that the layperson can understand the basic principals. A woofer driver operated in free-space (i.e. no enclosure) has two significant performance limiting problems. First, there is no isolation of the pressure waves being emitted from the front side of the cone and the rear side of the cone: thus, at low frequencies, the back pressure wave will cancel out the front and produce no bass frequencies at a distant listening position. The second problem is that most woofer drivers do not have a stiff enough suspension to prevent the woofer from over excursion. Over excursion will cause massively distorted output, or even self-destruction. Figure 1: Driver in sealed box

2 It was not long after the invention of the loudspeaker driver that the enhancement in performance was found when the speaker driver was placed in a sealed box (see figure 1). The sealed box prevented the back wave from destructively interfering with the front wave while also providing the additional compliance, by means of the trapped air, to prevent the driver from over excursion. The result from a properly designed box (i.e. a box which has an air compliance well matched to the compliance of the drivers own suspension 1,2 ) is clear bass and good control of cone excursion at moderate power levels. The standard vented woofer enclosure, herein referred to as the vented alignment, operates on principals that are well known and well defined in the industry 2,3,4. The basic operation relies on the Helmholtz 4 resonator set up by the port tube and the volume of air enclosed by the box. The Helmholtz resonator effect is best illustrated by the tone produced when a person blows across the top of a beer bottle. The air trapped in the bottle, and the tube made up by the neck form a simple acoustic mass- Figure 2: Standard vented sub-woofer alignment and-spring relationship. The air lump in the tube behaves like an acoustic mass, and the air inside the bottle creates an acoustic spring or compliance. When the mass-and-spring are excited, they will oscillate at a resonant frequency predetermined by a simple mathematical relationship: Frequency := 1 2 π 1 Compliance Mass It was discovered that forming a resonant chamber with the box by adding a vent tube could enhance the performance of the sealed woofer alignment described earlier. This provided improved bass response and efficiency by constructively utilizing the back pressure normally trapped in the box to create more sound output. The box and vent tube form a Helmholtz resonator that will produce additive sound output at the resonant frequency. Additionally, at the resonant frequency, the driver excursion is

3 controlled because all the energy is used to excite the resonance. Thus, unwanted excursion related distortions are prevented. A properly designed vented alignment will have more efficiency in the bass response than a sealed alignment, and can do so in a smaller enclosure than required for a sealed alignment. The vented alignment will also have increased power handling due to the better excursion limiting around the enclosure resonance. The following paragraphs describe the three general modes of operation for the standard vented alignment: Figure 3: Standard vented loudspeaker operation at the resonant frequency Properties of the vented alignment at resonant frequency: At the frequency of box-vent resonance, the bulk of the sound pressure output comes from the vent tube. The woofer driver is providing some output, but the excursion is limited because the energy is being used to excite the resonator (Figure 3). The phase relationships are such that the vent tube output is constructively adding to the driver output, thus the increased total sound output.

4 Figure 4: Standard vented loudspeaker operation above alignment resonance Properties of operation above the vented alignment resonant frequency: At frequencies higher than the box-vent resonance, the air mass in the vent tube and the air compliance in the box no longer have a productive relationship. Because the air in the tube is a mass, and because any mass becomes harder to move as the required speed of oscillation increases, the air in the tube acts like a plug (Figure 4). The air in the box compresses rather than forcing the air in the port to move in and out, i.e. The air in the port behaves like a plug. Therefore, at frequencies above the alignment tuning of the enclosure, the box acts like a sealed alignment. Figure 5: Operation of the standard vented loudspeaker below alignment tuning

5 Properties of operation below the vented alignment resonant frequency: At frequencies below the box-vent resonant frequency, the vent tube air mass becomes very easy to move. The air inside the box does not compress like a spring at all, thus causing the driver and vent mass to operate out of phase; that is to say, as the driver pushes out, the vent sucks air in, and transversely, as the driver sucks in, the vent pushes air out (Figure 5). Therefore, at this low frequency operation, the cone excursion is no longer being controlled by the air compliance in the box. Additionally, the vent sound pressure output is destructively interfering with the sound pressure output of the driver. Generally speaking, the bulk of the sound heard at these low frequencies are the distortions generated by the driver over-excursions and noise generated by air turbulence in and emitted by the vent tube. Due to the vented alignment having poor operating performance at frequencies below port tuning, a properly designed speaker enclosure will have a port resonance near the lowest frequency of expected operation. In addition, the woofer driver must be selected to have electro-mechanical parameters which complement the enclosure and tuning 2,3,4. Figure 6: Standard Band Pass Alignment: The standard band-pass alignment is a clever use of the Helmholtz resonator to limit distortion and high frequency output from a sealed alignment to create a true subwoofer; a speaker that is meant to reproduce only strong bass energy. As you can see from figure 6, the standard band-pass is a sealed box with a second vented chamber attached to the front. The vented chamber will operate at the peak efficiency around the region of Helmholtz resonance, and as described above, will impede output of sound pressure at frequencies above resonance. Additionally, as described above, at frequencies below resonance, the second box and vent offer little resistance to the output of the driver. Since the driver in the sealed box sits inside of the resonant

6 chamber, the net result is a sub-woofer alignment having the high frequencies attenuated at a constant rate with increasing frequency. More about this acoustical property later. Figure 7: Series Vented Band-Pass Alignment: It is obvious to conclude that if the standard band-pass can offer improvements to the sealed enclosure alignment, then the second vented chamber of the band-pass should also be able to improve the standard vented alignment. This is true. In figure 7, the diagram for a series vented band-pass alignment is given. Essentially, we have a standard vented box being fed into a 2 nd resonant chamber so that the total output can be band-passed or more accurately low-passed. The first vented chamber is tuned for the lowest desired frequency of operation, while the 2 nd chamber is tuned for the highest desired frequency of operation. The net result of this alignment is that you maintain all the low frequency advantages that the vented system has over the sealed system, and you GAIN the high-frequency roll-off for true sub-woofer operation and distortion suppression. Again, we ll discuss more about the distortion suppression properties in a moment. Here is the catch - the tunings of the chambers are NOT independent. The two chambers operate dependently. That is to say there are extraordinarily complex mathematical relationships governing the two tunings and the design of such a subwoofer system is only for the well-skilled in the art. What are the advantages of acoustic band-pass filtering vs. electrical band-pass filtering? First, before discussion continues on this topic, let us name the function more accurately; the acoustic function occurring here is not band-passing, but low-passing that is, the output sound pressure is being acted upon such that the high frequency content is being attenuated at a constant rate with increasing frequency.

7 Electrical filtering of the signal prior to reaching the loudspeaker enclosure is a cheap and simple way tailoring the sound of the woofer alignment. However, the electronics will do nothing to suppress the distortions that are generated by woofer driver excursion limitations, woofer driver motor limitations, and vent tube turbulence. No matter how elaborate the electronics, the listener will still hear the effects of these acoustic nonidealities because there is nothing to limit their contribution to the sound. With acoustic frequency contouring, especially in subwoofer design, the reduction of high frequency output can significantly reduce the audible effects of driver and port distortions. Figure 8: Time domain graph of a distorted tone One of the biggest advantages to the acoustic roll-off of high frequency content in the band-pass alignment is that the apparent efficiency of the system at low frequencies appears to increase dramatically! One of the reasons for this can be explained with some simple understanding of signal analysis. Figure 8 shows a time domain graph of a distorted tone. Figure 9: Frequency domain transform of the distorted tone

8 The distortion in this example is assumed to be caused by woofer driver excursion limitations, or possibly amplifier clipping. The wave shape has similar properties to a square wave (Figure 8). It is well known that signals with square wave type properties are made up of many pure tones spaced at odd harmonic distances in the frequency domain. The fundamental tone in this example is 50Hz. If an FFT analysis were performed on the wave, it would be found that that the power of the fundamental is far stronger in amplitude than the absolute value of the peak amplitude of the distorted wave-shape (see figure 9). Figure 10: Low-passing the higher harmonics leaves only pure tones From this, the extra odd harmonic content of the wave-form destructively interferes with the fundamental thus reducing it s apparent output amplitude, it s also well known that odd harmonics are subjectively viewed as non-musical and unpleasant. The acoustic rolloff provided by the box alignment reduces quite significantly the amplitude of the destructive harmonics because they are beyond the pole frequency of the low-pass, leaving a much stronger pure tone at the fundamental (Figure 9 &10). Designing the acoustical system to be slightly under-damped (a Q greater than 0.707) can enhance this feature at the expense of transient response. Another way to look at this is a mechanical analogy. As described before, the mass of air in the port is exactly that; a mass. It is easy to move it back-and-fourth at a low rate of speed (a low frequency). But ask the mass to move very quickly and it won t. A more poignant way to look at this is an analogy of driving your car.

9 Figure 11: Viva Las Vegas! Figure 11 shows a race track with two strait-aways going in opposite directions with a sweeping turn connecting the two. There is also a short cut connecting the two straitaways with two sharp corners and another short stretch. If you re traveling down the first strait-away at 60mph, is it going to be easier to use the sweeping turn or the short cut? The same principal applies to the lump of mass in the vent. Rather than attempt to follow the exact position of the distorted waveform from the driver, the mass lump is going to maintain momentum by making the sweeping turn-around. So, in summary, the series vented band-pass alignment offers many advantages over the sealed, vented alignment, and sealed band-pass alignments. The vented alignment offers deeper and more efficient bass response over a sealed alignment, the sealed band-pass offers distortion and harmonic suppression for improved bass reproduction, and finally the series vented band-pass offers the most having extended efficiency of the vented alignment with the improved bass response of the band-pass for an extraordinarily high performing sub-woofer system. What further improvements could possibly be made? There is one drawback to the band-pass alignments utilizing simple vent ports for the exterior radiator. Because the vent port is a simple tube, it cannot prevent direct radiation of high frequency energy from being beamed out of the port. The acoustic mass-and-spring properties do not affect beaming high frequency energy.

10 Figure 12: Beaming high frequency noises escape out the vent tube Figure 12 shows a diagram of beaming high frequency sound that is present in a system due to amplifier clipping, driver excursion limitations, and port turbulence. These sound waves can, and will bounce around the interior of the box until they find there way out through the vent port. Understand that these distortions are very much so present in every alignment described so far, and the band-pass does a good job of suppressing them and better than a simple direct radiating alignment such as the sealed alignment or standard vented alignment systems. But, fortunately, there still a further improvement to the series vented band-pass that can be made to suppress even the beaming high frequency energy.

11 Figure 13: Pressure driver reduces radiation of beaming noises Figure 13 shows the final performance enhancing addition, the Pressure Driver. The Pressure Driver is a rigid disk shaped diaphragm supported by a suspension mounted to a fixed frame. The Pressure Driver looks and acts very similar to a speaker driver cone by moving back and fourth, but it has no motor mechanism driving it (such as the coil and magnets of a traditional driver). It is, again, analogous to a mechanical mass and spring. It also has a restoring force. So, after removing external forces, it will return to its natural center position after oscillating at the resonant frequency for a few cycles (Figure 13). The Pressure Driver can be used as the environmental radiating element in the bandpass boxes instead of the vent port. The box and the Pressure Driver can be tuned to operate exactly as the lump of air mass in the vent port did. And since the diaphragm is made of a rigid material, it will no longer pass the high frequency noises through it. Most of the noises (i.e. distortions) remain trapped in the box while only letting out the fundamental frequency s or tones giving a purer tonal reproduction. In conclusion, the Series Vented Band-pass alignment with Pressure Driver environmental transducer offers unprecedented efficiency, superior low frequency response, and greater tonal purity than any of the popular sub-woofer alignments. References: 1.) R. Small, Direct Radiator Loudspeaker System Analysis, JAES, June ) R. Small, Closed-Box Loudspeaker Systems, Part 1,2, JAES Jan, Feb ) A.N Thiele, Loudspeakers in Vented Boxes, JAES, May ) L. Beranek, Acoustics, McGraw-Hill, 1996 edition.