Loudspeaker enclosure design formulas for triangles
One of the most popular pastimes in the DIY audio world is building loudspeaker systems. A web search will reveal literally thousands of different designs, a great many of which are at least superficially quite similar. We can be fairly certain that some of the published designs will sound very good, and others awful. This is reflected in commercial offerings as well. There aren't many 'real' audio brands that will be truly awful, but there will be differences. This is often despite the fact that many will show frequency response both on and off axis to be very similar, with many sharing one or more of the same speaker drivers as used by other manufacturers.
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Home Theater Speaker Placement
It is a bit technical, and unavoidably requires some familiarity with electrical circuit theory. The first section presents a derivation of the equivalent circuit of a speaker in sealed, and vented bass-reflex , enclosures. Then the relationship between the equivalent circuit response and sound level is presented. The effect enclosure volume has on efficiency , frequently misunderstood, is discussed.
Then infinite baffle, acoustic suspension, and bass-reflex enclosure designs are compared. Additional issues regarding bass-reflex designs are briefly reviewed. Sensitivity of results to misalignment is discussed, and finally the interaction between enclosures, crossovers, and cables is investigated , as well as the effect of the amplifier damping factor. The Thiele-Small approach is to first analyze the electro-mechanical behavior of a speaker voice coil, magnet, and cone, interacting with the cone suspension and the air in and outside the enclosure.
The resulting equation is mathematically identical to the equation describing a purely electrical "equivalent circuit" consisting solely of resistors, capacitors and inductors. The sound produced by the loudspeaker can then be obtained via a relatively simple circuit analysis. The highly evolved theory of filter synthesis can be used to adjust circuit parameters to obtain a desired frequency response. The parameters can then be translated back into physical quantities, such as enclosure size, to build the loudspeaker.
This procedure provides a scientific framework veneer? A very useful result is that after the speaker has been assembled, the electrical impedance at the speaker terminals can be measured and compared to the theory.
If it differs, the design can be tuned based on this measurement, which is both simple and accurate. The location and height of the impedance spike at resonance are sensitive to any errors in the design, as will be shown. However, as noted below, for a bass-reflex design some shift in the location of the peaks can be caused by mutual coupling, rather than by a design error per se.
This analysis is particularly valuable for designing bass-reflex enclosures where a ducted port also called a vent allows air inside the enclosure to radiate in conjunction with the speaker cone.
The driver parameters, which determine several of the equivalent circuit elements, are known as "Thiele parameters," and are fairly standardized; a table given here [ A method for measuring the parameters is given on the Subwoofer DIY page. The notation in this section generally follows Small's June paper he alters his notation between analyzing drivers, sealed enclosures, and vented enclosures, but all three situations are covered by the circuit derived here.
Small's papers and Dickason's book skip the derivation of the equivalent circuit. You don't need this to build a loudspeaker, but I like to feel as though I understand what is going on physically, so I'm going to go through it in detail. Besides, I enjoy starting from bedrock physics. There are three basic equations:. The cone is assumed to be rigidly connected to the voice coil.
All equations are in MKS units. The goal of the equivalent circuit analysis is to solve for the velocity of the cone, and velocity of the air in the vent. The far-field sound pressure produced by a known velocity is then obtained from equation P6 in the physics section on piston radiation.
This equation is an exact solution for a flat piston mounted in an infinite baffle, and is generally a good approximation for real speakers.
The voice coil of a real driver is ring-shaped, and rests within a concentric magnet structure see illustration [8kb]. However the equations can be derived from a simplified rectangular structure shown here [3. The voice coil is represented by the yellow wire loop in the simplified figure.
The driver permanent magnet produces a field B, shown in red, pointing in the positive y direction. When the wire loop in the figure moves sinusoidally with a peak displacement x c , applying Maxwell's equations Stratton's equation 1, page 2 shows that the motion induces a voltage across the loop terminals given by. The cone motion produces a change in the pressure inside the enclosure. A vent in a bass-reflex design also affects the pressure. The enclosure walls vibrate as well, but this contribution to the pressure is assumed to be negligible.
A side view cutaway shows the geometry [2. A speaker cone with effective area S D moves sinusoidally with a peak excursion x c.
There is a vent of cross-sectional area S V and length L V. It is assumed that the air within the vent moves sinusoidally as a rigid mass with peak excursion x v discussion regarding this assumption later. Finally, it is assumed that the wavelength is large compared to the dimensions of the enclosure, so the pressure can be approximated as uniform throughout the interior.
Then using equation 25 , and equation 30 in the Physics section, applying the divergence theorem , and temporarily neglecting losses, it is found that the change from atmospheric pressure is. Including the vent loss term in T2, and substituting T3 yields the final equation for pressure inside the enclosure in terms of the cone excursion.
The pressure in the enclosure produces a force on the cone given by S D times equation T4. The force driving the speaker is produced by the current I c flowing through the voice coil. For the simplified figure [3. The next forces are due to the cone suspension via the surround and spider.
As noted above, for a sealed enclosure R MS is modified to include absorptive enclosure losses as well. Then the equation is. The resultant of the above forces acts to accelerate the cone assembly and air in front of the cone, defined as the moving mass M MS. The final force equation is. Now the procedure is to convert the physical parameters in equation T7 into equivalent inductors, resistors, and capacitors. Equation T1 is used to substitute for x c. Then the following definitions are made.
The full circuit also includes the amplifier, with its output impedance R A , speaker interconnect cable with resistance R C , and the crossover with resistance R XO. Therefore the full equivalent circuit of the system is as shown here [6. For a bi-amped design minor modifications are made to the circuit, and for higher-order crossovers additional components are added. The components of equation T9 do not physically exist, but I c is the real current through the voice coil, and v c is the real voltage across the driver terminals.
As stated in the beginning, the goal is to obtain the velocities of the cone and vent air. The amplifier is assumed to output a voltage with equal amplitude and phase at all frequencies. The equivalent circuit response is then analyzed, and the voltages v x and v v , as defined in the equivalent circuit schematic, are obtained.
The physical peak cone velocity is then given by. At this point, all references I have seen use the real part of the radiation impedance of a flat piston to compute the total output sound power. An exact solution of the radiation impedance of a piston, and a numerical solution for a cone, are given in the physics section.
For a peak velocity that is constant with frequency, the real part of the impedance causes a power increase of 6 dB per octave in the "piston range," roughly where the speaker diameter is less than a wavelength.
The power then levels out for higher frequencies. However the sound level on axis continues to rise at the 6 dB per octave rate because the sound becomes focused in a beam that gets narrower as frequency increases.
In fact, for an ideal flat piston moving with a constant peak velocity, the sound level on axis grows 6 dB per octave for all frequencies, "DC to light" as engineers say. This is shown by equation P6 in the Physics section , the exact solution for sound produced by a piston in an infinite baffle, which is valid for any frequency.
It is surprising to me that this on-axis behavior is not mentioned in the references I have seen, or if it is I missed it. Although total output power is important, in my opinion on-axis sound level is more important.
At a distance on 1 meter from the speaker, the sound pressure on axis for the driver cone and vent are. Consider a simple case of a sealed enclosure, no crossover, and neglect the voice coil inductance. For an input voltage that is constant in amplitude and phase, the cone velocity peaks at the resonant frequency, and drops by 6 dB per octave on either side of resonance. If the cone velocity were constant with respect to frequency, the sound pressure would increase 6 dB per octave.
For the cone velocity as described, the sound pressure is constant above resonance, and drops 12 dB per octave below resonance.
The sound pressure phase varies linearly with respect to frequency and distance from the speaker, which simply represents a time delay.
Neglecting this, there is an additional degree phase shift between cone velocity and pressure. Therefore the sound phase is shifted degrees with respect to the input voltage.
But assigning a label of "positive" and "negative" is arbitrary in the analysis, and reversing the labels yields the result that the sound pressure has zero phase shift with respect to the input voltage, above resonance. The bottom line is that the wave shape of the input voltage is replicated by the sound pressure, for frequencies within the operating range of a single driver.
In general, the wave shape is changed dramatically by the crossover, and by multiple drivers. Efficiency is defined as the ratio of radiated sound power to electrical input power. The sound power is equal to the square of the sum of the velocities equations T10 and T11 times the real part of the radiation impedance, which is given by equation P11 in the physics section. The input electrical power can be defined as the real part of the product of the voice coil current and voltage, or it can be defined as the real part of the product of the amplifier output current and voltage, which will give a slightly lower value.
Efficiency is a function of frequency. Within the primary operating region of the driver the efficiency is close to the "reference efficiency" defined by. T14 is identical with equation 31 in Small's June paper. The efficiency is a function of the driver parameters, but is not a function of the enclosure.
In other words, for a given driver the efficiency will be the same regardless of the enclosure it is put in. Dickason also points this out. Yet there is a frequently reproduced graph from a different paper by Small that appears to show that efficiency decreases as enclosure volume decreases. What's going on here?
Equation T14 can be re-written in a form where efficiency is proportional to the 3rd power of the enclosed driver resonance times the enclosure volume. So what is actually changing as the volume decreases is that the resonant frequency is increasing. It is true that for a fixed low frequency response a larger volume can provide higher efficiency. But you have to buy a different driver to achieve the efficiency increase.
How to Design a Micro Speaker Enclosure
Post Your Comments? Speaker Box Dimensions. Website: Diyaudioandvideo. Category : Use words in a sentence. Speaker , Strong. Build a ported box, sealed box for your low-frequency speaker.
Loudspeaker Enclosure Design Guidelines
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Speaker box volume calculator design
The best possible stereo sound quality still comes from a pair of hi-fi speakers — no matter how good one-box wireless speakers might have become. Our round-up of the best stereo speakers you can buy below will ensure your home audio system is treated to the best possible audio performance for your budget. Whether you're on a tight budget or ready to splash the cash, take your pick from our selection of the best stereo speakers, no matter what genre of music you plan to play. We have both floorstanding speakers and bookshelf speakers to recommend, as well as desktop , active , and a number of all-in-one wireless stereo speakers, as also featured in our best systems guide. So whether you're looking for your first pair of speakers as you build a home music system, upgrading an old pair of budget speakers or going for broke with the best speakers your system, room and finances can accommodate, we're here to help.
US9609405B2 - Slim profile loudspeaker - Google Patents
Enclosures for mini and micro speakers are similar in purpose to those for larger speakers; to protect the speaker and to enhance the audio volume. Enclosures designed with a few simple guidelines will meet the needs of most applications. A speaker consists of a diaphragm suspended in a rigid frame such that the diaphragm can freely move forward and backward. A coil of wire is attached to the diaphragm and suspended between the poles of a permanent magnet. Applying an electrical signal to this coil of wire causes it to move in the magnetic field. The diaphragm moves due to the movement of the coil and thus air pressure waves are created which are detected as sound.
Talk:Loudspeaker/Archive 1
In this article, we are going to discuss how to figure out exactly where to place your speakers. Because this can get complicated quickly, this article addresses only the placement of speakers for 5. These two legacy formats matter a great deal because the placement of these speakers is the same when adding immersive formats such as Dolby Atmos. These layouts are the foundation for all movie audio you enjoy in a commercial theater as well as at home. In a future article, we will discuss adding the overhead speakers. We are also going to leave subwoofer placement for another article as it requires a lot of attention to separate the fact from opinion.
This is an archive of older "talk" from the Loudspeaker article up to and including April, For the most recent discussion, see Talk:Loudspeaker. Would this be the place to have an entry for a line array and point source?
Article by Rod Elliot. The method described here provides a way for the beginner and DIY enthusiast to measure the parameters without any expensive or specialised equipment. While every care is taken to ensure that calculations and formulae are correct, ESP accepts no liability for errors or omissions. Figure 1 shows a typical impedance curve for a loudspeaker see Figure 5 for the equivalent circuit of this speaker, which was simulated for this article. Resonance causes a large increase in impedance, and at some higher frequency, the inductance or semi-inductance of the voice coil causes the impedance to rise again. In the example below, resonance is at 27Hz, and the linear region ranges from about Hz to Hz.
It is a bit technical, and unavoidably requires some familiarity with electrical circuit theory. The first section presents a derivation of the equivalent circuit of a speaker in sealed, and vented bass-reflex , enclosures. Then the relationship between the equivalent circuit response and sound level is presented. The effect enclosure volume has on efficiency , frequently misunderstood, is discussed. Then infinite baffle, acoustic suspension, and bass-reflex enclosure designs are compared. Additional issues regarding bass-reflex designs are briefly reviewed.
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