主题：寻求Hoffman's iron law中文版

Hoffman's iron law,我不知道中文叫什么可能是赫夫曼定理吧.说的是在长冲程,高效率和小容积之间只能三者取其二.指的是F0,VAS和SPL之间的相互转化关系. 想听一下各位大侠的看法,套讨论一下.

Back in the early 1960s, Anthony Hoffman (the H in KLH) developed a mathematical formula that became known as Hoffman's Iron Law. Thiele and Small later refined the law's mathematics. The 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). To reduce the cutoff frequency from 40Hz to 20Hz you need to increase the enclosure volume by eight times. In other words, to produce half the frequency at the same output level you need a very big box. You can get around this by accepting a much lower efficiency, but this requires both a very large amplifier and a driver that can handle a lot of power, move a lot of air (requiring a long excursion), and do both while generating very little distortion.

A so-called reflex design provides a way around the Iron Law. A hole, or port, in the speaker enclosure loads the driver, reducing its excursion at the low end of its operating range. Below this range, the port itself contributes much of the system's output. One variation on this design uses a passive radiator in place of an open port or vent. A passive radiator is essentially a speaker without a drive mechanism (no magnet or voice-coil) that moves in sympathy with the vibrations and pressure created by the active speaker. By changing the size of the port—or the size and mass of the passive radiator—you can control the frequencies augmented by a reflex system.

Unfortunately, a reflex enclosure has its own set of compromises, including phase and group-delay anomalies and (in the case of a port) vent noise, which add to the woofer's total distortion. Ever since the introduction of the first ported enclosure in 1934, speaker designers have tried to come up with solutions to reduce these problems.

In the early days, people who sought full-range sound typically needed very large speakers. However, because of placement issues, cost, and the vast living-room real estate these speakers required, not to mention the subsequent aesthetic disapproval they inspired, the majority of hi-fi lovers were forced to accept smaller and sonically inferior speakers. With the advent of home theater, the need for low-frequency sound became apparent. In the process, the benefits a subwoofer offered for music reproduction became more widely appreciated. In this month's Boot Camp, we'll cover how subwoofers work, the benefits they offer, and what to look for when purchasing one for your system.

First of all, true subwoofers function in the lowest octaves of the audible frequency range, the most physically difficult region to reproduce. Due to the long wavelengths of these low frequencies, a subwoofer requires a large woofer, big cabinet, or massive amplifier. Hoffman's Iron Law, described by Henry Kloss in the mid-1950s and later turned into an exact mathematical formula by engineers Thiele and Small, governs the behavior of woofers. Essentially, it says that a woofer's efficiency is proportional to the volume of its cabinet and the cube of the lowest frequency it can produce before losing relative level (aka the cutoff frequency). Take, for example, a woofer whose response is flat down to 40 hertz in a 2-cubic-foot enclosure. To make its response flat down to 20 Hz, you must either increase the cabinet volume by eight times (to 16 cubic feet) or use eight times the amount of amplifier power to achieve the same listening volume. Given these requirements, you can see how difficult it can be to get respectable low-frequency response from small "full-range" speakers.

Designers eventually realized that the lowest frequencies could be relegated to a separate bass cabinet and "hidden" in a corner. Since low-frequency sounds have such long wavelengths, the subwoofer emits energy in all directions, making it relatively nondirectional. Consequently, smaller satellite speakers could handle the midrange and high-frequency sounds (everything from about 80 or 100 Hz up to 20 kilohertz), including all of the spatial and directional cues for the music or soundtrack that need to be more specifically placed. By dividing these sound responsibilities, full-range sound could now be enjoyed without sacrificing space or aesthetics. The idea is really quite simple: High frequencies are directed through the main satellite speakers and placed in specific locations, while the nondirectional subwoofer can be placed virtually anywhere in the listening room.

Beyond aesthetics, placing your subwoofer in a different location than your main satellite speakers provides sonic advantages, as well. For instance, placing your speakers closer to any room boundary (like the floor) augments the low-frequency output by 3 decibels, which is like doubling your amplifier power. Placing the speaker next to two surfaces (like the wall and the floor) will increase output by 6 dB. Add in a corner, and the three surfaces maximize output of bass with a 9-dB boost in level. Middle and upper frequencies, on the other hand, generally sound better when placed away from room surfaces. By separating the upper and lower frequencies, we can put the subwoofer and satellite speakers in locations that achieve the best sound for each type of speaker.

The divorce of low and mid/ upper frequencies results in other very important benefits. First of all, by separating the low frequencies from the main ensemble, you free your midrange driver to concentrate only on midrange frequencies, thus eliminating the distortion that occurs when small drivers try to reproduce extremely low frequencies. Second, in a full-range system, most amplifier power is eaten up by the power demands of low frequencies and large woofers. Adding a separate, dedicated amplifier for the low frequencies not only allows for more bass but leaves more power for your midrange and upper frequencies. More importantly, manufacturers can design amplifiers specifically for a subwoofer's size and application. Early on, there weren't very many active (or self-amplified) subwoofers; fortunately, they've become more common.

Before you venture to your nearest home theater dealer, though, you should qualify your needs. To begin with, the size of your room and the volume you listen at are extremely important. If you have a large room or listen at high levels, you'll want a bigger, more-powerful bass box. If you have a small room and don't play the music too loud, you can get by with a smaller subwoofer. In general, 2,000 cubic feet is considered an average-size room. When you're figuring out the size of the theater, it's very important to calculate the total room volume (length by width by height). Of course, vaulted or raised ceilings are going to dramatically affect this sum. Also, if the room opens up to or adjoins another room that cannot be sealed off from the theater, this must be factored in to the total volume.

Subwoofer Designs
Common Subwoofer Designs

Bass-Reflex Enclosure: Utilizing a ported design, this is one of the two most common sub enclosure types today. Pressure waves from the back of the woofer cone excite an air mass in a port (or ports), producing low-bass output that augments the waves generated by the front of the cone. The result is an additional 3 dB of output in the octave of the system's cutoff frequency. Although 3 dB may not seem like much, to gain it through amplification would take twice the amount of power. This design will also boost previously inaudible fundamentals up to an enjoyable level. The drawback of a bass-reflex design is that the response rolls off rapidly below the cutoff frequency. Phase shift may also alter the character of bass transients. Another drawback is the potential for port noise. Misalignment of box and port parameters relative to the driver may alter the character of the bass by introducing transient ringing.

Closed Box: Often referred to as acoustic suspension, this design also has positive and negative characteristics. Typically, the enclosure is much smaller than a ported application using the same size woofer, but more amplifier power is required to achieve the same level of output. Low frequencies roll off much more gradually below the cutoff frequency than with a ported design, so there can be more usable low-frequency energy, albeit at a reduced level. An argument can be made that "room gain" from placement near room boundaries somewhat compensates for this rolloff.

Bandpass: In a bandpass sub, the woofer or woofers are entirely concealed within a dual-chambered enclosure. The chamber behind the woofer(s) is the normal "enclosure" and can be either sealed or ported. A second chamber in front of the woofer(s), also contained within the enclosure, functions as an acoustic filter, allowing only low frequencies to emerge through a tuned port. This effectively eliminates the need for a crossover but doesn't allow for variable frequency attenuation. It does allow the woofer(s) to be connected directly to the amplifier for increased damping (cone control), and there's less harmonic distortion than with more-conventional designs. The major drawback is that you often can't hear the internal woofer(s) distorting (due to a poor signal or overamplification) until it's too late—the woofer has blown.

这套英文版也不错,谢谢水仙老师.

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好问题.好文章.

Subwoofers use speaker drivers (woofers) typically between 8" and 21" in diameter. Some uncommon subwoofers use larger drivers, and single prototype subwoofers as large as 60" have been fabricated.^[12] On the smaller end of the spectrum, subwoofer drivers as small as 4" may be used, depending on the design of the loudspeaker enclosure, the desired sound pressure level, the lowest frequency targeted and the level of permitted distortion. The most common subwoofer driver sizes used for sound reinforcement are 10", 12", 15" and 18" models. The largest available sound reinforcement subwoofers, 21" drivers, are less commonly seen.

The efficiency of a speaker driver is given by:

此主题相关图片如下：001.jpg

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Where the variables are Thiele/Small parameters. Deep low frequency extension is a common goal for a subwoofer and small box volumes are also considered desirable. Hoffman's Iron Laws therefore mandate low efficiency under those constraints, and indeed most subwoofers require considerable power, much more than other individual drivers.