App Note
Application Note 1
EnclosureShop Application Manual
Transmission Line Enclosures
Application Note
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Transmission Line Enclosures
n Highlights
Ported Highpass Model Port Area & Length Effects Port Standing Waves Port Loss & Damping Media Characteristics Model Comparisons
n Design Objectives
Design a transmission line enclosure. Woofer to be used, 8 Inch (200 mm). Maximize the low frequency response. Minimize the port reflection ripples. Compare response to other model types.
Triple Folded
Double Folded
The phrase transmission line enclosure is common terminology used to describe a special variation of the ported highpass enclosure family. In reality this name is not very descriptive or unique, since any port in any enclosure behaves and can be viewed as a short transmission line. However, in this class of enclosure the port is so long that the transmission line effects become a dominant characteristic that cannot be ignored or modeled with lumped parameter methodology. Some may view these characteristics as desirable or undesirable. This class of enclosure can probably best be defined by two fundamental characteristics: a small chamber volume and a very long port. Due to the longer port the standing waves within the port begin at much lower frequencies. These standing waves (reflections or pipe modes) are very strong and produce aberrations in the response of the enclosure. To minimize this the port is typically filled with a batting media such as fiberglass, polyester, etc. which dampens the reflections. However, the losses produced from the batting also reduce the effectiveness of the port at very low frequencies. Therefore TL designs often come down to a tricky balancing act between adding loss to reduce the reflections, while still achieving a suitable low frequency response. The different types of media and how they are applied all play a critical role in the final response.
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n TL Parameters & Construction
Ideally the TL type enclosure has the rear port coupled directly to the back of the transducer, in much the same fashion as would be a plane wave tube. In this case there is no effective chamber volume Vab. As we shall see this parameter is assigned only a residual value which has negligible effect on the response. Therefore the Vab parameter is not critical or of interest in TL designs. The associated chamber/port resonance frequency Fp of classical tuning is also irrelevant and unimportant. The port itself is the primary focus of the design. The port may be configured with constant area or tapered. In the later case it becomes a horn/waveguide. TL designs have been made with either expanding or contracting area from the transducer to the mouth. However, in this example we will only consider the constant area type. Therefore the two fundamental parameters for the port are its area Sp and its length Lp. Due to the vital role played by the filling material; the type of media, fill volume, and media density also become important parameters. Quantitatively prescribing the fill of fibrous material is difficult. Stuffing a tube with the exact same quantity of material two different times will produce two different results. Fibrous material is not a homogeneous media that can be accurately parameterized with any high degree of precision. Nevertheless the specification of the batting media must be included in the analysis to accurately simulate TL designs. In this respect EnclosureShop has very good models for various batting media which greatly improve the accuracy of TL simulations. The use of hyperbolic trigonometric functions is also crucial to the accurate simulation of transmission line behavior, and the standing wave patterns. EnclosureShop actually uses a multitude of transmission line elements to model all of the acoustic elements in an enclosure. These are complete four parameter lossy transmission line elements and are vital for media representation. In some cases TL designs are constructed with batting material in only certain locations. These highly specialized nonuniform configurations are difficult to model in any convenient fashion. For this example we will only consider the specification of batting by media type, density, and fill percentage.
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Transmission Line Enclosures
n Transducer Parameters
A simple 8 Inch woofer model was created for this example. A TSL model was use for simplicity. The driver is located in the Tutorial.LTD file of the Transducers folder. The driver TSL parameters are shown below. * Loudspeaker Enclosure Analysis Program * LEAP® EnclosureShop 5.0.0.316 Mar/04/2003 * ©1993-2003 LinearX Systems Inc * Date: Mar 5, 2003 Wed 3:30 am * LTD File=D:\Program Files\LEAP\Transducers\Tutorial.LTD * Electro Mechanical Parameters Name= TL 8 Inch Note= Model= TSL Domain= FreeAir Shape= Round Profile= Cone Fmd= 1.0000 KA Qmd= 0.7070 Flp= 4.0000 KA Qlp= 2.0000 Znom= 8.0000 Ohm Revc= 7.7000 Ohm Sd= 22.1700E-3 M² Mmd= 22.8000 g Pmax= 100.0000 W Rtvc= 2.5000 °C/W Xgap= 8.0000 mm Xcoil= 22.0000 mm Xmax= 7.0000E-3 M Krm= 10.0000E-3 Ohm Erm= 700.0000E-3 Kxm= 20.0000E-3 H Exm= 700.0000E-3 Rms= 1.9124 N·S/M Mms= 24.6970E-3 Kg Cms= 999.9972 uM/N Vas= 70.2020 Ltr Fo= 32.0257 Hz Qms= 2.5986 Qes= 0.4521 Qts= 0.3851 BL= 9.2001 T·M Levc= 1.4510 mH SPLo= 88.9110 dB No= 0.489 %
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0o On-Axis
Infinite Baffle
n
Infinite Baffle Reference Model Before we dive into the TL simulations it is probably a good idea to create some other models for reference and comparison. The first reference model will be a simple infinite baffle. This consists of merely simulating the transducer on an infinite plane. - 3D Layout Views The 3D layout for this setup is shown on the following page. The scene was rotated to show both the frontal and rear views of the infinite plane. The primary simulation position is shown by the target object, and the polar paths are shown by the arrow arcs. - SPL & Impedance Response The graphs on the next following page show the acoustic response for both the 1 Meter field location and near field diaphragm, as well as the impedance response. Both magnitude and phase is given. We see that the speaker is about 88dBspl @1W/1M in the mid range. - Excursion & Velocity Response The graphs on the next following page show the diaphragm excursion and velocity response. Even at a low level of 1W the excursion is 2.6 mm at 10Hz. - Acceleration & Volume Response The graphs on the next following page show the diaphragm acceleration and volume response. Volume velocity is merely acoustic current. - Polar Response The graphs on the next following page show the polar pattern. Two versions are given: absolute and normalized (to zero degree on-axis values).
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Infinite Baffle Front View
Infinite Baffle Rear View
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Infinite Baffle
Spkr Near Field
Spkr @ 1M OnAxis
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Infinite Baffle
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Infinite Baffle
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Transmission Line Enclosures
Infinite Baffle
Horizontal Polar Response Absolute
Horizontal Polar Response Normalized
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0o On-Axis
Infinite Baffle
Vented Highpass Enclosure Model
n
Vented Highpass Reference Model It would also be useful to have a conventional vented highpass enclosure model for comparison. Since diffraction around the enclosure is a separate issue and unrelated to the transmission line behavior we wish to explore, all of our enclosures will be simulated on a simple infinite baffle domain. As a quick & dirty approach the parameters for this vented enclosure were chosen as follows: Vab equal to Vas, and Fp equal to Fs. A 50% fill of 1 lb/Ft³ density fiberglass was assumed for the chamber. A rectangular shell/chamber and port were used with area Sp of about 1/3 the Sd value of the transducer. - 3D Layout Views The 3D layout for this model setup is shown on the following page. The scene was rotated to show both the frontal and rear views of the box. The primary simulation position is shown by the target object, and the polar paths are shown by the arrow arcs. - SPL Response The graphs on the next following page show the acoustic response for the 1 Meter field location, and the localized regions of the enclosure. This includes the internal chamber, near field speaker, and near field port response. The response has quite good bass response and is 3dB down at 35Hz. The primary port reflection occurs at about 500Hz due to the 10.4 In duct length.
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Transmission Line Enclosures
Vented Highpass Enclosure on Infinite Baffle Front View
Vented Highpass Enclosure on Infinite Baffle Rear View
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Vented Box
Spkr @ 1M OnAxis
Internal Chamber
Spkr Near Field
Port Near Field
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The port reflection just shown at 500Hz is a transmission line effect, and underscores the previous point that all ports are transmission lines. In this case the port had a length of only 10.4 In. Longer ports will cause the reflection frequencies to move down accordingly. - Impedance Response The graph below shows the impedance response, and displays the classic double hump behavior as one would expect for a vented enclosure. - Excursion, Velocity, Acceleration & Volume Response The graphs on the following pages give the excursion, velocity, acceleration, and volume current for the vented enclosure. Note that the air in the port is traveling about 3 times as far as that of the transducer. This is due to the area ratio between the port and the speaker. The area of the port is only 1/3 that of the speaker, so it must move faster and farther to yield the same total volume current. Both sides of the diaphragm deliver the same quantity of acoustic volume current, and ultimately at very low frequencies, the volume velocities of the port and transducer become equal as shown in the volume velocity graph. Vented Box
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Vented Box
Port
Spkr
Port
Spkr
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Vented Box
Port Spkr
Spkr
Port
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n TL Design #1
0o On-Axis
Infinite Baffle
TL Enclosure Model
Much has been written about the design criteria for transmission line enclosures. While it would be highly desirable to utilize a simple set of formulas or tables to arrive at values for port length and area, this is often not practical or even possible.
Unfortunately the response of a TL type design is strongly dependent on the characteristics of the filling material itself. Different types of materials, densities, and fill factors can and will change the response quite dramatically. In most cases the reflection ripples cannot be eliminated but merely pushed around and damped to acceptable levels. This then becomes a subjective process not well suited to quick and easy design tables. A trial & error methodology is probably more effective. The response can be simulated with much higher detail and accuracy to better optimize a particular set of design objectives. In this respect EnclosureShop provides an ideal means of simulating many different TL designs quickly and accurately. It is possible to simulate very complex arbitrary structures with EnclosureShop, but for this example we will simply use the standard Ported Highpass model. The structure is the same, and we merely need to edit the parameters where needed to produce the TL configuration. The previous vented design used a 2.7 Ft³ box. For the case of the TL, we will change the occupied volume to use up nearly all of the available chamber volume. This is actually what takes place in reality, since the port is often folded up inside the box which consumes the internal volume. In this case we leave a residual value of 0.06Ft³. The value is not at all critical, but cannot be zero. Depending on how the TL is actually constructed, there may indeed be a finite effective value for Vab.
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Transmission Line Enclosures
As a starting guess for the area of the port, we will simply choose a value equal to that of the transducer. Since the width of the enclosure was 16 Inches, a rectangular port is used with the same width and a height of 4 Inches. Given the wall thickness this yields an area of about 0.022 M².
We really have no idea what to choose for the port length. However, one general rule does apply here. The low frequency cutoff will be somewhat related to the length of the port. The longer the port, the lower the cutoff frequency. To begin we choose a port length of 6 Ft (72 In). In some cases the port length is simply the longest length possible to fit in the desired enclosure size. As mentioned previously the port resonance frequency is meaningless and unimportant. For this initial design we will only use Air as the media within the port. The 3D layout is shown on the following page. The port is very long and protrudes through the back of the enclosure. This is of course only an visual representation. The 3D editor has no means of folding the port. However, the rear of the port is always treated as though it is within the chamber.
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TL Design
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The resulting acoustic response for this first TL design is shown below. There are an abundance of reflections throughout the mid band region. These are the standing wave reflections within the port, and they are substantial. Note that the level drops over 20dB in the first primary hole. Such is the need for damping. The acoustic response at both ends of the port and near the speaker is shown on the following page. Likewise the impedance graph is also shown. These are the classic impedance reflections which occur from finite length tubes. The excursion and velocity graphs are shown on the next following page. The port reflections are extremely pervasive throughout the system. They affect every response parameter. Note also that unlike the previous vented design, the excursion and velocity amplitudes for both the transducer and port are now equal. For the TL case the port area was chosen to be equal to the transducer area. It is probably fair to say that very few people would desire a listening experience with this design. TL #1 (port media 100% air)
On-Axis Response
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TL #1 (port media 100% air)
Internal Chamber (port throat)
Port Near (port mouth)
Spkr Near
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TL #1 (port media 100% air)
Port
Spkr
Port
Spkr
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n TL Design #2
The obvious improvement needed from the first design is to add acoustic losses through the port to dampen the nasty reflections. To give this a try we shall now fill all of the port (100%) with 0.5lb/Ft³ Polyester (PE). This is a common batting material. The resulting acoustic response for this PE damped TL design is shown on the following page. This is a tremendous improvement over the previous case. The large 20dB hole is now 6dB, and the numerous other ripples have also been greatly reduced. The impedance graph now shows a very damped response, with the resonance and reflection humps largely removed. Only a broad hump rise remains. However, the excursion curves and their new values at 10Hz should be noted. The amplitudes have now dropped from their previous values of about 2.6 mm to less than 2.0 mm. The Polyester within the port adds considerable resistance, and this restriction results in less overall output at all frequencies. In order to reduce the port reflections, port resistance must be added. At the same time this also reduces the low frequency response. Such is the compromise associated with a TL design. Of course we may take the position take we desire a very soft knee for the response, and are not bothered by the loss of low frequency output. In that case we should increase the port losses further.
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Transmission Line Enclosures
TL #2 (port media 100% 0.5lb/Ft³ Polyester)
On-Axis Response
Internal Chamber (port throat)
Spkr Near
Port Near (port mouth)
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TL #2 (port media 100% 0.5lb/Ft³ Polyester)
Spkr Port
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Transmission Line Enclosures
n TL Design #3
We could use several different techniques to increase the port losses. For this attempt we will merely switch to a different media. All batting materials are not created equal. They have very different characteristics. For this example we will use Fiberglass with the same 0.5lb/Ft³ density. The resulting acoustic response for this FG damped TL design is shown in the top graph on the following page. The large ripples are now nearly gone. However some small sharp ripples remain. We must remember that a small chamber volume was included in the TL design. We have not assigned any damping media to this chamber, and it too has reflections - small ones. We can easily assign a fill factor of 50% Fiberglass to the chamber as well. When the design is analyzed again, the response in the lower graph is produced. The small chamber reflections are now damped as well. The impedance and excursion graphs are shown on the next following page. All of the curves are now relatively smooth. Shallow ripples still remain in the acoustic response, but would probably be of smaller amplitude than defects which exist in the response of the transducer itself. It may be of interest to compute the amount of batting material used to achieve this level of damping. The internal volume of the port is about 1.4 Ft³. Using the 1/2 lb Fiberglass media, about 3/4 of a lb would be utilized per enclosure. If Polyester was to be used, a much higher density and quantity would be required.
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TL #3 (port media 100% 0.5lb/Ft³ Fiberglass)
On-Axis Response
On-Axis Response
Note: With 50% fill of FG in Chamber.
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TL #3 (port media 100% 0.5lb/Ft³ Fiberglass)
Spkr
Port
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n
Model Comparisons We can now compare the various response characteristics of the #3 TL design to the different models simulated previously. The acoustic and impedance response graphs are shown on the following page, and the diaphragm excursion on the next following page. Without question, the most efficient bass design is the standard vented highpass enclosure. The response extends very low with substantial output to 35Hz. There is the issue of a 500Hz reflection from the port, but this generally falls outside the frequency range of use in a three-way crossover system. A small amount of damping inside the port would easily reduce this at such a high frequency of 500Hz, where batting materials are highly absorbent. The infinite baffle acoustic response is without question the smoothest, since there is no chamber or port where reflections can occur. The low frequency knee is soft, and the response rolls off at the 12dB/Octave slope. The TL design is essentially a heavily damped 4th order vented design, and approximates a 3rd order response, between that of the infinite baffle and conventional vented. The knee is softer than the vented design. Ripples still remain in the passband, but are much smoother with this level of damping. It should be noted that a conventional sealed or vented enclosure could also be designed to have a soft low Q knee if that was the objective. The impedance curves show the expected characteristics. The TL design has the lowest Q resonance behavior. However, either of the other two curves could be easily squashed down as well by merely paralleling a resistor, with no changes in the acoustic response. The excursion response for the TL design is heavily restricted at low frequencies as compared to the other two. This is of course due to the acoustic resistance damping within the port. Comparing the excursions between the conventional vented design and the TL design near 32Hz highlights the efficiency of the vented design. The excursion for both is essentially the same. Yet the acoustic output from the vented design is 8dB higher. The vented design effectively utilizes the radiation from both sides of the diaphragm.
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Transmission Line Enclosures
Model Comparisons
Vented Infinite Baffle TL #3
Infinite Baffle Vented
TL #3
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Infinite Baffle Vented
TL #3
Speaker Excursion
n
Summary Transmission Line (TL) enclosures can be simulated with relative ease and high accuracy using the capabilities of EnclosureShop. Many different designs are possible and can be explored very quickly to determine the best possible combination of parameters. Their construction is typically far more difficult than most conventional enclosures, and may greatly affect the results. Correlation with simulations are more problematic than conventional designs, since so many non ideal factors all contribute to the behavior of the port. Bracing, filling consistency, and area/corner changes can significantly affect the response. This completes the application note.
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