Appendix A - Loudspeaker Design
Tuesday, 09-Feb-2010, 05:35:29 GMT
Last modified: 25-Mar-2007, 19:49:46 GMT






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Selecting a project
Selecting a system and drivers
"Hoffman's Iron Law"
Enclosure types, aesthetics, & gallery



Selecting a DIY project:

There's a temptation common to beginning DIY'ers to try to go from novice to dream system designer in one big step. Resist this temptation! Select a project that is a little more challenging (both technically and financially) than your current level of experience. Not all DIY projects turn out well. If your reach exceeds your grasp, you may find yourself with a pile of expensive components that sound terrible. Not only is this a bad investment of your time and money, it will also discourage you from trying again. As with any investment, the secret is to optimize the ratio of risk to potential gain.

A corollary of this principle is that, if you're a complete beginner, it might be a good idea to begin by building a kit or other predesigned system, then work your way up to a "from scratch" DIY design. In Section 15 of the LDSG, I list a number of available kits, what drivers they use, and their prices.


Selecting a system and drivers for DIY projects:

An integral part of any DIY project is selection of the drivers. If you're building a kit or working from a set of plans, in most cases this has already been done for you. Still, even in the case of a kit, many different drivers can fit into the same panel cutout and you may wish to select alternatives. If you're building from scratch, driver selection is a required part of the design process. Despite lots of agonizing by many DIY'ers, driver selection isn't rocket science.

  1. First, consider the primary purpose of your speakers. Is your application for a home theater (HT) system, or for music? Must people will use theirs for both, so here are the basic guidelines you need to observe:
    1. Home theater requires at least 6 speakers - two main (left and right front) speakers, a center (front) channel speakers, two rear channel speakers, and a subwoofer. Digital Dolby can require still more speakers. For HT systems, the recording engineers are in control of the sound field, so all 5 of the main and rear speakers should sound pretty much alike. Also, since there are so many of them, they should be as small and cost effective as possible. If you don't want to make all 5 alike, you should at least try to make the front 3 alike and the back 2 alike, both sets with a common "sound". The front 3 should also be magnetically shielded to avoid interference with the TV screen. All should have response down to around 80 Hz, where the subwoofer takes over. Since one of the things that contributes to the realism of HT is the bass, don't scrimp on the subwoofer!
    2. Music systems are still mostly stereo. Although some movie sound tracks and audio discs offer multiple channels similar to HT, most of your attention should be paid to your front two speakers, since other channels are definitely optional. Whether to use full- range systems or a subwoofer is your choice. If you wish to use a subwoofer, you will either need an electronic crossover in the signal path, or one of the many available purpose built basic amplifiers designed to be mounted within the subwoofer enclosure. Some sources of such amplifiers include major distributors (e.g. Madisound, Parts Express, Meniscus) as well as specialty distributors (e.g. ACI, Burnett & Associates).
    3. Combination systems have to balance the above requirements. To design such a system, you have to assess what percentage of the time your system will be used for HT, and what percentage of the time for music. As the numbers become very large on either side of 50%, you will need to make fewer and fewer compromises. Systems which will be used about 50% of the time for each application will require the greatest compromises. Such hybrid systems usually use two extremely high quality front speakers with a center channel speaker of the same "sound". The two front main speakers may be located far enough away from the TV screen to not necessarily require shielding, but the center channel speaker will still require shielding. Rear channel speakers in such a system, should share the same sound as the front channel speakers, but are otherwise less important. A subwoofer is recommended for such combination systems, although most HT receivers and amplifiers are configurable to allow you to eschew a separate subwoofer.

    Note that in all of the preceding discussion, the term "sound" really refers to timbre matching. No matter how neutral, all speakers will still slightly add their own unique aural stamp to the sound they present. The easiest way to achieve timbre matching is to use either identical drivers, or similar drivers, preferably from the same manufacturers.

  2. Choose a basic design. This will determine the number of drivers and their specific parameters. But just remember, the more drivers you use, the easier it is to mess things up. Two-way designs are the simplest and can sound amazingly good, given the use of appropriate drivers. Three-way designs require more care to properly match all the pieces. Four-way or higher-order designs get really complicated. Often, these will have crossovers in the middle of the critical musical range of 300-3,000 Hz, which makes driver matching much more critical.


"Hoffman's Iron Law":

One of the most fundamental design principles that the new DIY speaker builder must learn is generally known as "Hoffman's Iron Law". First formulated back in the early 1960's by Anthony Hoffman (the H in KLH), Hoffman's Iron Law is a mathematical formula that was later refined by Thiele and Small, whose work now forms the basis of all modern loudspeaker design.

Hoffman's Iron Law states that the efficiency of a woofer system is directly proportional to its cabinet volume and the cube of its cutoff frequency (the lowest frequency it can usefully reproduce). The obvious implication is that to reduce the cutoff frequency by a factor of two, e.g. from 40 Hz to 20 Hz, while still retaining the same system efficiency, you need to increase the enclosure volume by 23=8 times! In other words, to reproduce ever lower frequencies at the same output level you need an extremely large box!

However, box size isn't the only variable… You can continue to use a small box by accepting a much lower efficiency. In order to retain the same sound pressure level (SPL, meaured in dB's), though, this requires both a very large amplifier and a driver that can handle a lot of power and move a lot of air (requiring high excursions). Furthermore, it must be able to do so with minimal distortion. This is exacerbated by power compression, a phenomenon where the power heating of the driver's voice coil results in a non-linear relationship (read "distortion") between the electrical power in and the acoustical power out. Another variable not often mentioned is bandwidth… You can provide the perception of violating Hoffman's Iron Law by using a bandpass design, which can provide a lot of bass primarily across a very limited bandwidth. In all too many bandpass designs, the impressive bass is produced around a single frequency. This is often referred to as "one-note bass". It can rattle the furniture and impress your friends, and may even be OK for sound effects in action movies, but don't expect too much accuracy when listening to music with a lot of low bass content.

Summarizing, Low-frequency capability, box size, and efficiency form the three key aspects of system design. To increase any of the three, you have to give up something from the other two, with box size being the most sensitive. The often unpopular bottom line is therefore to plan on using the largest box you can comfortably live with. This partially explains the popularity of subwoofers, which can be both large and hidden from view, and often include their own built-in high power amplifier.


Enclosure types, aesthetics, & gallery:

OK, now you're ready to begin making implementation decisions…

  1. The first thing you need to decide is a target sensitivity for your system. Knowing the wattage rating of your amp, the size of your room, how loud you like to listen, you can make an estimate of the sensitivity rating you'd like to achieve. The obvious caveat is to not go overboard! If you want something louder, it's best to divide the cost between more amplification and higher sensitivity drivers.
  2. Choose the type of enclosure for your low frequency (LF) driver. Note that the LF driver may be either a mid/bass, woofer, or subwoofer (these are discussed in detail in Section 1 below). In all this, you must remember "Hoffman's Iron Law". Bass extension, efficiency, and box size are all mutually exclusive - you can only increase one at the expense of the other two. If you want efficiency in a small box, you have to give up bass extension. Similarly, if you want bass extension and efficiency, you must live with a large box, etc.

    The purpose of the enclosure is to prevent the back wave which emanates from the rear of the driver from canceling out the front wave, since they're 180 degrees out of phase with one another. To that end, a number of types of enclosures have been devised. The most popular types discussed here are:

    Sealed
    ELFTM
    Aperiodic
    Ported/EBS
    Passive radiator
    Bandpass
    Array
    Isobaric
    Transmission line
    Horn
    Terminated line
    Tapered quarter wave tube
    Dipole

    Enclosure aesthetics Gallery of interesting designs

  3. Select the best drivers you can afford which meet the parameters determined in step one above.
  4. Verify that whatever anomalies are left over can be corrected in the design of the crossover - either active or passive, it makes no difference.

    This is the hardest step for DIY'ers. Before you can fix the anomalies, you first have to recognize and understand them. After that, you're still faced with having the tools (and the skill to use them) to realize the required fixes.




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