0:00

Most spec sheets come with the dimensions and the bolt hole parameters.

We saw that earlier in the sketches I provided.

And you should use this in planning your design and also the mounting

configuration. You always want to mount the transducers

from sorry about that, mount all the transducers from the outside of the

enclosure. if you mount them from the inside you end

up with some diffraction and you know, round the opening of the box itself.

And you know, some added dynamics that, that are not desirable.

So you always mount the the transducers from the outside of the box.

So, you know, they'll have a, a flange on them if you, if you imagine the cutaway

of the box looking something like that. the speakers will have a flange and the

flange will sit on the outside. And then of course, they'll fit inside

the whatever opening you that cut in the box.

But mount, mount them on the outside of the box here, so this is the interior of

the box, all right? So with that those basic guidelines those

should apply whether you're designing ported enclosures or you're designing an

enclosed box. But we're going to start today talking a

little bit more about closed box design. And so for the moment we're going to go

back to our old discussion of the Helmholtz resonator.

And if you recall when we put a speaker in a box, the enclosed air in the box

actually adds stiffness. So if we have a speaker with a diaphragm

of a given mass and it'll have its own spider and suspension system.

So this is the tranducer, these two components are fot the transducer on its

own. But once you set that transducer in a

box, you ger an added stiffness that's associated with the enclosure and I've

kind of sketch that over here. you know, where we've, I, I show the box

and the transducer itself, and of course there's a, a stiffness associated with

the speaker. The, the spring doesn't sit up here on

top of the transducer, I just sketched it symbolically.

And then we have some stiffness associated with the enclosure, the box

itself. but it turns out that the the total

stiffness of the box. Or I mean the total stiffness for the

design is going to be the sum of the stiffness of the speaker itself plus that

of the box. And so, if you can calculate a new,

natural resonance frequency associated with the box or you know, the speaker

designed in the box. Based upon the mass of the vibrating

diaphragm of the speaker and then of course the total stiffness in the box.

Now, box stiffness we already covered earlier, but I'll, remind you again with

the equation here that the box stiffness depends upon, you know, some basic

parameters. Such as the density of the air, the speed

of sound in air, the volume of the box and then, of course, the radius of the

driver. so you should remember, for a given box

size/volume, the stiffness really depends upon the area of the transducer, or the

radius of the piston. So a fixed box size doesn't have a fixed

stiffness. A fixed box size has a stiffness that's

dependent upon The radius of the speaker, okay?

And so if you end up with a smaller radius, then you're going to end up with

a higher stiffness. If you end up with I mean, a smaller

stiffness, if you end up with a larger radius, you're going to end up with a a

larger stiffness. So they're proportional but, you know,

it's proportional in terms of the square of the radius and then the square of the

area. it's an important part of the design

consideration. Some basic Thiele-Small parameters

required for design basically are the speaker or transducer, free-air

resonance. This is with no box and then Qt, Q sub

ts. the ts is a subscript just known to

represent the total Q of the driver at resonance.

And again, the Q can be thought of an amplification factor at resonance.

The greater the Q, the sharper the resonant peak.

So I, I shown this here in a diagram that I generated for increasing Q.

And you can see that, you know, basically our our resonant peak is in this domain

here. And as Q increases, and that's what this

arrow is here. The, the peak gets taller, so the

response becomes sharper, if you will, around that frequency.

And you know, we can debate over which curve might be an optimal curve if we

were looking at the response of of of a speaker itself.

5:15

The other thing that we need in the design from the Thiele-Small parameters

is the speaker's compliance. the speaker's compliance is the

reciprocal of the stiffness. But the way they're, it's specified in

the Thiele-Small parameters is the equivalent volume of an enclosed box that

would yield a certain stiffness. So, it's, that's a simple expression

basically it, it, it's just a different way of expressing the spring constant.

Because we can ca, calculate based upon the, the previous equation which relates

to stiffness of a box to a volume in an area.

we can basically assume that we have a box that has this stiffness identical to

to that of the speaker. And then we can solve for that volume.

And that's, that's the volume that specified with the Thiele-Small

parameters. you should also note that when I talk

about compliance, compliance is just the reciprocal.

This is the compliance, that's the reciprocal of the speaker's stiffness,

alright? [COUGH].

So if we're given um, [COUGH], the three previous parameters.

6:32

For any given box volume, you can calculate the following.

you can calculate the closed box resonance, that defines the low frequency

bandwidth of the speaker. you can co, compute the speakers reg,

resonant magnification for a closed box design.

And you can also, this should be magnification, sorry, not magnificent,

but magnification. And then you can compute the 3 dB

frequency. At which the bass response is, reduced by

3 db and that's called the cutoff frequency.

mainly because that's where you start to get diminishing response of the bass.

you're on the downward slope, in so to speak in terms of the bass response,

alright? most closed box designs will aim for a

target of a queue for the closed box to be somewhere between you know 0.7 and

1.1. if queues, if the Q of the closed box is

less than 0.7 the low end response really deteriorates.

Remember the the curve that we looked at earlier where we were looking at the you

know, the peak responses like this. And you know, as, as it gets smaller you,

you're, you end up this was increasing Q if you remember.

And the smaller domain you get this roll off at low frequencies, so you know, you

can see you know. If I were just looking at this frequency

and maybe the response you know, being normalized here.

You got a lot more response here than you do here and you're really way off on the

low side. So, that's for, for small queues.

When the Q of the closed box is much greater than 1.1 then you end up with

this peaky response or the you know, has this real boomy sound to it.

And again that's because, you know the higher queue is going to give you this,

this kind of peak here. And what we're really, what we really

like to have you know is, we really like to have this really flat perfect

frequency response that was cut off really sharply.

And, and gave you a very consistent and flat frequency response over the audible

range. Designs end up being compromises and, you

know, sometimes the curve looks more like that and sometimes it's more like this.

And that's part of the overlaid ensign process, but let's, let's work an example

here. Let's assume we're given a driver, okay,

with a a free air resonance of 30 hertz. And a total queue of 0.5, and a volume,

an equivalent volume for the stiffness that's 283 liters.

And let's choose a Q for the closed box of one, so we'll choose a simple number

[LAUGH] in the range that we were we were given.

And here are your design equations for computing the design of your box.

you first want to get the ratio of, of your desired Q, Q of the clothes box, to

that of the total Q for the speaker. for our choice that, that ends up being

2. we want to be able to compute the volume

of the box. The ratio of the volume of the box to

that of the volume of the equivalent box of the, relating to the speakers

compliance, VAS, is related to the square of the Q of the closed box to the total Q

minus 1. So, if I substitute 2 in here, we get 4

over minus 1 is 3. Then I can solve for the volume of the

box and it's 1 3rd of the volume of the of the equivalent volume associated with

the speaker stiffness. and that is 94.3 liters.

So that's the the size of the box that we would design a closed box design to

achieve that desired cube. for the speaker.