If you have been following my tutorials in speaker design, you have no doubt read the previous blog on “Geek Speak on Boxes” which dealt with sealed box designs. Please review the variables listed in that blog as I will be referring to them here... Now let’s step a little closer into the design by looking at what a vented box can do for your speaker performance.
We call a speaker “vented” because it is just that. There is a hole in the box to support low frequency output, but not any hole will do. You need a specific length to width ratio to align the box and speaker driver for best performance. The ratio of air flow to length of port gives us a Helmholtz resonance at a particular frequency. In layman’s terms, the speaker box is taking advantage of an “air spring” to reinforce the loading of a speaker cone at certain frequencies.
I always find that analogies are the best way to start thinking about something technical. So let’s deal with some of the terminology.
Imagine that you have a normal 12 oz hammer. Pick this hammer up and act like you are hammering at a nail in the air, back and forth. Now pick up a 20 oz hammer. Act like you are hammering nails with this hammer. Notice how the heavier hammer is more difficult to move at the same speed. This is an effect of Mms or Mechanical Speaker Mass. As the Mms gets larger or heavier, the speaker’s natural resonance, Fs or Fo gets lower.
Have you ever been or at least had your kids play at the local playground where they have the fake animals to sit on? The animals are connected to a large spring. As your weight (or your kids…right) moves forward the animal rocks forward and then springs back the other direction. If the spring was longer or stiffer the oscillation time would change. This is similar to Cms, Mechanical Speaker Compliance. Cms is the opposite of “stiffness.” As the Cms gets lower, the spring gets stiffer and the resonance, Fs or Fo , gets higher. In other words as the speaker gets stiffer, it tends to vibrate at a higher frequency -- or in your case the animal is swinging faster… I mean your “kid” sitting on the animal is faster.
Are you still with me? Let’s try another...
Sd is the area of a driver cone or diaphragm. Atmospheric pressure gives a specific force upon a given area. In an 18” woofer, there is more static air pressure on the cone than a 12” woofer. Think of holding a typical broom in your hands. Now start to move the broom back in forth through the air in a cyclical motion. Keep moving it faster. Notice as it gets faster it becomes more difficult to accelerate the broom to a higher speed.
Now imagine that the broom is twice as wide with a handle the same length. Notice how it is even more difficult to move through the air quickly. Why? This is due primarily to the surface area of the broom and the air that resists the motion due to aerodynamics. This particular variable is Cas, or Air Spring Compliance. You are moving more air in the larger woofer, thus your sound output goes up.
All these terms reflect the resonance of the speaker in a box with a specific air volume or “air spring”. When you put a speaker with a “free air” resonance, (Fs or Fo), of 25 Hz in a sealed box the Fs or Fo goes up. This is because the air spring of the box is now reinforcing the compliance of the speaker. As the cone moves in the box the air spring pushes back making the cone want to travel back the other direction quicker.
How many poles in your box?
We use terms like word “order” or "pole" to describe certain characteristics of response. It is important to note that each order or pole on the design creates a 6 dB per Octave slope to the design. So in other words, a sealed box uses the mechanical stiffness, Cms of the speaker driver as one pole. The second pole comes from the mass of the speaker, Mms. Thus the bass roll off is calculated as:
6 + 6 = 12 dB per Octave
This is noted in the diagram below.
Now if we add a vent to the box, we add two more poles due to the characteristic mass of the port, MAP and the compliance of air in the box, CAB. Notice in the dotted curve that the rate of change with frequency is doubled. Now it is 24 dB per Octave. The bass extend further to a certain frequency then it rolls off quicker and has less output much below the tuning frequency. Nothing is for free in the laws of physics.
The port creates a filter that only lets air out at a certain rate depending on how hard the air inside is pressing. This is like a balloon letting air out at a certain rate. The difference is that the minute the speaker cone changes direction and travels outwards from the box the air changes direction and rushes into the box through the port. So the air in the port is creating a repetitive motion known as a sinusoidal motion.
Now let’s take this particular speaker driver in the example and vary the box volume. (I knew you couldn’t wait for this.) The original pair of curves utilized a ten cubic foot, (10 ft3). In the graph above you can see the effects of decreasing the volume of air, or the size of the box. We are going from 10 ft3 to 1 ft3. See the variation in response as the air volume shifts?
Now things are more complicated. Not only is the cutoff frequency changing, but the shape of the curve is morphing also. That is why we call this box / speaker alignment. The box needs to be optimized to match the particular Thiele Small Parameters of the speaker.
Notice as the box gets smaller the speaker becomes less flat in the response. It is not optimized at 1 ft3 because the response is 5 dB higher than nominal SPL. So our speaker will get louder in this region. If I play a piano scale, when I get to E2, (82.41 Hz), the note will sound much louder than E3, (164.81 Hz). Thus the recording will never sound quite like the engineer or performer wanted. In order for us to use a 1 ft3 box we have to start over with the speaker design. The magnet will need to be larger and the vent will need to be adjusted to give us an optimized speaker design.
So you may be asleep by now with Professor Thumps speaker 101 theory, but there is more to think about, so turn those brains back on!
Let’s think about the motor structure for a moment. If this is a typical well designed woofer the voice coil is “over-hung.” This is different from a hangover and much more pleasant. You could debate this point but I will keep it simple as I can for the sake of understanding the fundamentals.
The voice coil sits in the magnetic gap waiting for signal to pass through its coil, so it can react to the magnetic flux in the gap. As the color of the gap becomes red in our model depicted, the magnetic force of “flux” becomes stronger; therefore the coil and cone will move farther due to the level of flux. If the coil continues up the gap the color turns yellow then green quickly. This is called flux non-linearity. The magnetic force has become inconsistent as the coil travels through the gap. If we have a short coil and it is out of the gap the 3rd harmonic distortion increases. We don’t want this so we make our woofer coils longer. This allows a similar amount of coil to be in the gap at all times no matter where the superposition of the coil is within a reasonable amount of excursion. Thus the THD is lower and we are higher or at least happier. We call this term Xmax. Which is the dimension hanging out of the gap on one side. It is usually 1 -6 mm for most 2 way systems or subwoofers.
Reviewing the response of the 1 and 10 cubic foot boxes we get the results below.
The performance curves above are transposed to show the excursion response curves below, for the vented box.
So I was mentioning that the laws of physics aren’t free. (Neither is your freedom, but I won’t rant about that here). The small box is more controlled in the excursion region down to 30 Hz, but the tradeoff is that the output is much lower. SPL means compressing air. There is only one way to do that. The cone must move to displace the air. This model is using 1 watt power, so we consider this a small signal calculation. The coil is only moving less than 2 mm. Imagine what it is like at 100 watts? It is safe to say that there is lots of excursion. That is why high efficiency speaker are so important.
So now you know a little more about what acoustic engineers do for a living at Klipsch. Careful detail to the box and speaker alignment with a port is crutial to optimizing the performance of a Klipsch loudspeaker system. There is no substitute.
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