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speaker design basics
O.K. So you would like to design some speaker cabinets for yourself. Easy. We don't expect to turn you into an acoustic
engineer, but you may be wondering what all those funny symbols are about. The design applet we have provided allows you
to design cabinets for a single transducer. The issues surrounding multi-speaker designs, crossover design and so forth
are well covered in other references.
Introduction
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A speaker is an electroacoustic system which combines the characteristics of the loudspeaker (or transducer) itself and
the cabinet in which it is mounted. Most of the work involved in building a good sounding speaker cabinet involves
trading off various parameters of a desired speaker's performance within the limits of acceptable box size, low end
frequency response, maximum acoustic output (perceived loudness) and efficiency. |
Types of speaker cabinets
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Closed and Vented Cabinets
There are a number of different types of cabinets. The simplest is the closed-box. This is simply a box with a hole
in it where the transducer is mounted. A lot of hi-fi cabinets are closed box designs. A rough rule of thumb is that
the bigger the box, the lower the frequency response of the system. This is only true up to the point where the
transducer can no longer produce lower frequencies. Many old speaker designs used closed cabinets, as the frequency
response was fairly good, despite almost no design work needed. It is possible to predict the frequency response of a
closed-box, but our applet will not do this.
For a long time it has been known that the bass response from a speaker cabinet may be improved by introducing a port.
A port is just a tube or similar that looks like a hole in the speaker cabinet. By choosing the port dimensions to
match the speaker and cabinet, an extened bass response is possible (for a fixed box size). A well designed ported
(or vented) cabinet will usually outperform a closed box, but more design work is necessary. Choosing port dimensions
was until semi-recent times (1970s or so) a trial-and-error affair. Two engineers by the names of Neville Thiele and
Richard Small devised an analysis method that may easily be used to design vented cabinets well. These days most
speaker manufacturers will provide a set of parameters for their speakers known as Thiele-Small parameters from which
cabinets may be designed. All those funny symbols in the applet (and on your speaker brochures) such as Qes, Xmax,
Vas and so forth are Thiele-Small parameters.
You can find out the Thiele-Small parameters for a transducer you have no information for if you have the appropriate
test equipment. This should not usually be necessary.
Our design applet allows you to use the Thiele-Small parameters for a speaker to design a vented cabinet that is tuned
correctly. There are a number of different tunings possible for a vented cabinet. We have chosen the so-called
Butterworth B4 maximally-flat amplitude alignment (tuning). This just means that smooth frequency response is our main
design criteria. If you buy a woofer with known Thiele-Small parameters then you can plug the parameters into the
applet, then choose box dimensions and the applet will calculate the vent dimensions. Just add a tweeter and crossover
and voila, your very own speaker design.
If you are using a tube or some such other thing for the port, then you can enter its diameter into the duct
diameter text field (in place of the floating word), and the designs will all use that diameter for the port. Note,
that the minimum recommended diameter is that shown when the text field is left as floating.
If you want to design speakersfor hi-fi use, then a vented box is probably your best bet.
Horn-Loaded Cabinets
When you are building speakers for public address (P.A.) use, a closed box or vented box is probably not very good.
There are a number of reasons for this. Firstly, they are not very efficient. Typical closed and vented cabinets are
less than 5% efficient, so you generate a lot more heat than sound volume. Also, the maximum acoustic power that may
be produced is limited. What that means is that although your speaker may be rated at 100 watts continuous (RMS), it
may be unable to produce any noticeable increase in sound output above a much lower power level. i.e. your speaker
may be producing its maximum sound output at say 5 watts, and any increase in power really just ends up as distortion,
not more noise! So, a 100 watt continuous rating means nothing other than the speaker won't blow up until you start
putting more than 100 watts into it.
How can this be? Well, one of the Thiele-Small parameters is known as Xmax. This is a measure of the maximum
displacement (front-back movement) that the transducer can exert before ten percent (10%) distortion sets in. This
is because the voice-coil in the transducer is beginning to leave the strongest part of the magnetic field in the
transducer's magnet (that big heavy lump of metal on the back of the speaker).
Yet another problem with closed and vented cabinets for P.A. use is that the size of the room plays an important part
in the frequency response of the speaker. Why? Imagine that the entire room is a cabinet mounted to the front of the
speaker - which acoustically it is. It is usually said that you need a big room for low frequency sound reproduction,
and that is the reason why.
So what's a budding rock star/disc-jockey to do? Build a horn-loaded cabinet of course.
A horn-loaded cabinet is a lot like sticking a trumpet on the front of your transducer. The effect is similar to
cupping your hands around your mouth when yelling to someone at a distance. It makes it louder. Why? Well, a horn is
like an acoustic tranformer. What happens is that a big horn (or funnel if you like) effectively makes the transducer
drive the entire area of air at the end of the horn. So, say the horn opening is ten times the size of the transducer,
then the driven area is ten times greater. The transducer is said to be better coupled to the air. You know those big
black boxes at the bottom of a rock band's P.A. system? They are horns. The transducers inside the cabinets
themselves are not very big compared with the box.
Why bother, when you can just use more power? A horn-loaded cabinet designed for maximum efficiency can be as much
as seventy-five percent (75%) efficient - so you'd need about 15 times as many speakers and amplifiers in a vented
system to match such a horn. But that's not all - remember Xmax? Well, one of the really nice things about a
horn-loaded cabinet is that since the driven air is 'leveraged' by the horn, the cone of the transducer doesn't move
as far to produce the same power output. In fact, it is easy to design a horn so that the maximum electrical power
to the speaker (i.e. the continuous power rating) can be fed to the speaker before it reaches the limit given by Xmax.
So, when you feed in 100 watts into such a design, the sound continually increases up to the maximum power the
speaker can handle. That's why nearly every P.A. you see uses horn-loaded cabinets. Some exceptions to this are
unusual designs like the Bose 802 speakers - but Metallica would need a hell of a lot of them!
O.K. So we've solved the efficiency problem and the useful power handling problem by using a horn. Now what about
the room? Well, yet another advantage of the horn is that it really works from the transducer out, and effectively
decouples the transducer from the room. So, what happens is that the frequency response of the horn is essentially
independent of the room. Not completely, but significantly better than any other type of cabinet design.
If horns are so good - I mean efficient, loud, and almost room-independent, why isn't every speaker a horn? Ahh, the
obvious question. And the answer? Size. A horn-loaded cabinet has to be large to have smooth frequency response.
This is of course dependent on the lowest frequency response the cabinet needs to reproduce. One of the old rules of
thumb said that you need a horn with an opening of 10 metres (30 feet) in diameter to reproduce frequencies down to
about 30 Hz with smooth response - a touch larger than your average vented cabinet. In fact, those humungous boxes
at the rock venue are usually useless below about 50 Hz or so - even though it feels like you're going to shake
apart.
Oh dear, I guess we can't build small horns that go low. Well, yes and no. A common ploy is to build a horn that is
unusually small and use active equalisation to flatten out the frequency response. This works O.K. as a compromise,
and a lot better than you'd expect. Active equalisation is used in many systems, even the Bose 802s mentioned above,
and they aren't even horns! Another approach was developed by Paul Klipsch and is used in some Klipsch speakers. He
uses a trick in the area of the horn near the transducer to produce much flatter frequency response than expected
from the horn dimensions.
Types of Horns
There are a number of different horn-flares that can be used for cabinets. The flare is the cross-sectional shape of
the horn as it goes from the start near the transducer (the throat) to the end (the mouth). A few of the better
known ones are parabolic, conical, exponential and hyperbolic. These, in order, go from least efficient to most
efficient (acoustically). If you draw a parabola (for the cross-section of the horn) and cut a hole in the bottom
for the throat then you know what a parabolic horn looks like. A hyperbolic horn by comparison is pretty much like a
trumpet stretched out - i.e. a tube that flares very little until it gets to the end where it flares suddenly.
The conical and exponential horns are between these two extremes.
So, if a hyperbolic horn is the most efficient, then I guess we use that flare for our loud P.A., right? Wrong. The
problem with such a tight flare is that as sound pressures increase, the restricted passage for the air causes it to
begin to compress. This causes distortion - not good. You don't want to compress the air, cause it gets hot, etc,
etc - and the sound starts to sound really bad. So, what flare type do we choose? Probably the best flare trading
off high-efficiency versus low-distortion is the exponential flare. This is what a very large number of commercially
produced horns are.
Hey, my woodworking skills aren't good enough to build an exponential horn, and I'm not about to build a fibreglass
mold! O.K. Ok! An easy to build flare is of course the conical flare. In fact, it is the easiest - not as efficient,
but a lot easier to build. Just four angled bits of wood will do it. These sort of horns are sometimes seen as the
mid-range part of a P.A. system.
Parabolic horns are so inefficient that they are really of no practical use.
So, there you have it. If you're adventurous, you may want to build an exponential horn, but a conical one may be
good enough - it's up to you. The applet will allow you to design both styles.
Cool, so I'll just replace the vented woofer box with a loud horn - yeah? Well, not exactly. The improved efficiency
of the horn is gained at the loss of bandwidth. So, it may be louder but it will drop off in frequency at the upper
end before the tweeter takes over if you're not careful. How do you work this out? The throat of the horn (the size
of the little hole) can be as big as the transducer cone, or smaller. Maximum efficiency is achieved when they are
the same size, but the bandwidth is also the smallest. To increase the bandwidth, you must shrink the hole. The
ratio of the cone to the throat is known as Sd/St. Of course, as you increase Sd/St (or reduce the throat size) the
efficiency drops. To find out what value of Sd/St to use, you first enter the Theile-Small parameters for the
transducer, then go to the Horn Response page and look at the plot for 'Speaker Limits'. Those graphs show what
your transducer is capable of. You can also use this approach to evaluate the suitability of a transducer for horn-
loading.
Band-Pass Cabinets
Well, no doubt you've heard cars driving by you going thump-thump-techno-techno or similar. Many of these are using
a so-called band-pass cabinet to produce huge amounts of bass from a small cabinet. This is a design where the
entire speaker (or speakers) are inside the box and the only path for sound is out through a port like the one in a
vented cabinet. These designs have very limited bandwidth (hence band-pass), but produce a large low-frequency
acoustic output compared with a normal vented cabinet of the same size. They are fairly inefficient as well. Our
applet does not contain any design abillity for such cabinets, but if you want to build one for your car (or home
hi-fi subwoofer), a good place to get information is to write to Polk Audio in the U.S. and ask for details on their
HVCD subwoofers. Theres is a patented band-pass design that works very well. You can also call them in the U.S. on
800/638-7276 and ask for Dave Lytwynec at extension 208 or Ken Swauger at extension 891. This is second-hand
information, so please treat them nicely.
So there you have it. Lots of information is out there if you want to learn more, try some of the references we've
included on our references page if you like.
Happy designing!
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