스피커 설계법

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번역을 못하고 원문을 그대로 올리는점 양해 부탁 드립니다.

Loudspeaker Enclosure Alignments

The purpose of this paper is to offer the formulas used to calculate proper loudspeaker enclosure
sizes and tunings ( alignments) to give the best performance for a given loudspeaker driver.
These formulas are only used on the bass loudspeakers, of course, as midrange and tweeter
units are typically sealed, self contained assemblies.
These formulas are based on the studies done in the last century by A.N. Thiele and Richard H.
Small, and use loudspeaker parameters which are now universally referred to as T/S parameters.

The formulas we are concerned with here fall into 3 categories:
1. Maximally flat (4th order)
2. Non-flat
3. 6th order assisted

1. Maximally Flat Alignments
The maximally flat alignment uses 3 different formulas. The first is used to find the ideal box
size for a given low frequency driver, the second formula is used to find its cutoff (-3db) point. The
-3db point is where the output power has fallen to one half, and is generally considered to be the
low frequency limit of the loudspeaker. The third formula calculates the box tuning frequency
(tuned with a port, or hole, in the box).
The formula for calculating a maximally flat 4th order enclosure volume is:
Vb=(15)(Vas)(Qt2.87) Where: Vb = Enclosure volume
15 is a constant
Vas = the equivalent compliance of the driver
Qt = the driver total Q (also referred to as Qts)
Qt and Vas should be supplied by the driver manufacturer, and
can be found on the data sheets.
The formula for calculating the 3db down point is:
F3 = 0.26 (Fs) Where: F3 = bass -3db point
Qt 1.4 0.26 is a constant
Fs = loudspeaker free air resonant frequency (from data
sheet)
The formula for calculating the tuning frequency for the box is:
Fb = 0.42(Fs) Where Fb = the tuning frequency of the box
Qt 0.9
By using those 3 formulas, you can calculate the required enclosure size, -3db down point, and
tuning frequency. If the box size is undesirable, or the -3db point not sufficient, then you can go
to another driver, and start the calculations again until a suitable driver is found.
Let us work through the formulas in case you are not comfortable with them. A simple
inexpensive calculator is all you need, or you can use the one built into Windows
(Start/Programs/Accessories/Calculator). Be sure to set it to scientific mode.
For our example, lets use the Selenium WPU1507QFC 15” woofer. Let us solve the first
equation to find the required box size.
Vb=(15)(Vas)(Qt 2.87)
For Vas, you can use cubic feet or liters. The result will be in the units you use. We will use
cubic feet for our example.
Looking at the data for the WPU1507, we see that Vas = 5.33 cu. Ft., and that Qts = 0.43, so
our formula looks like this:
Vb = (15)(5.33)(.43 2.87)
Lets first solve for .43 raised to the power of 2.87 (the yx button on your calculator). Enter .43
then press the yx button and enter 2.87, then the = button. You should get 0.088726728. With
this number on the display, work the rest of the equation. Multiply by the Vas (5.33), push =,
then multiply by 15. You should have 7.0937 on your display. That is the required box volume for
the WPU1507 driver for a maximally flat alignment, 7.0937 cubic feet.
The second equation will give us the -3db point in that box.
F3 = 0.26 (Fs)
Qt 1.4
First, solve for Qt raised to the power of 1.4, On your calculator, enter the Qt of the driver, .43 yx
1.4 = 0.3068 (save this in your calculators memory).
Now, multiply the free air resonance (Fs) by .26.
36 X .26 = 9.36
Now divide this number by the one in memory:
9.36 / 0.3068 and we get 30.5, which is our -3db down point, 30.5Hz (Which is very
respectable bass response).
The third formula will give us the box tuning frequency required:
Fb = 0.42(Fs)
Qt 0.9
We will again solve Qt raised to the power of 0.9 first. .43 yx .9 = 0.4678 (store this). Next, solve
42 X Fs:
36 X .42 = 15.12.
Now divide this number by the one in memory:
15.12 / 0.4678 = 32.316
This is our tuning frequency (or Fb) for our port calculations, 32 Hz.
Port calculations will be placed at the end of this paper, since all 3 categories we are covering
will need the same port calculations.

2. Non Flat Alignments
The next type of alignment we will cover is the ‘Non-flat’ alignment. This is used when the box is
larger or smaller then the one required for a maximally flat alignment, and it will result in a
response that is not flat, but will have a hump (smaller box) or a dip (larger box) in the response
curve. This set of formulas will calculate -3db point, tuning frequency, and the amount of ‘ripple’
in the response. The first formula will calculate the -3db point in this ‘non-ideal’ box.
F3 = (Fs)(Vas/Vb)0.5
Using the same driver in our example, the WPU1507, let us say we have a box of 6.1 cubic feet
that we wish to use. Lets now calculate the -3db down point of the WPU1507 in this box:
Lets first solve Vas divided by Vb, raised to the power of 0.5.
(5.33/6.1)0.5 which is 0.87377..0.5 which is 0.9347.. Now multiply that number by Fs(36), and we
get 33.65Hz.
The WPU1507 will have a -3db down point of 33.6 Hz in this 6.1 cubic foot box, which is pretty
good. Now lets calculate the tuning frequency required:
Fb = (Fs)(Vas/Vb)0.32
First, Vas divided by Vb is: 5.33/6.1, which is 0.87377, raised to the power of .32 = 0.9577…
Now multiply that number by Fs (36), and we get 34.478, or a box tuning frequency of 34.5 Hz.
Now we will calculate the ripple to see how much deviation we will have from true ‘flat’ response.
Ripple = 20 log10 ((2.6)(Qt)((Vas/Vb)0.35))
Solve this from the inside out. Vas/Vb = 5.33/6.1 = 0.87377, raised to the power of 0.35 =
0.95386…
Our formula now looks like this: Ripple = 20 log10 ((2.6)(Qt)(0.95386976))
0.95386976 X .43 = 0.410…X 2.6 = 1.06642.., so our formula now looks like this:
Ripple = 20 log10 (1.066426392) With this number displayed (1.066426392) push the LOG
button on you calculator, then multiply by 20:
1.066426392 LOG = 0.02793…, X 20 = 0.5586
So now we know that we will have a hump of about ½ db from true flat response, which isn’t to
bad at all. I would say this box of 6.1 cubic foot is quite usable. We know it will be a ‘hump’
because the box is smaller than the max. flat box. If the box was larger than the ideal max. flat
box, it would be a dip. The graph below shows the predicted response in the 6.1 cubic foot box.

<Graph showing response of the WPU1507 in a non-ideal 6.1 ft3 box>

When deciding whether or not to use a non ideal box size, it is not recommended to exceed
about 1db of ripple if high fidelity results are desired.

3. 6th Order Alignment
The 6th Order alignment is one which utilizes equalization to restore flat response. This is done
with a simple equalization circuit which provides the 6db boost needed to restore flat response,
and also provides a filter to roll of the signal below Fb, which is important in order to reduce
distortion and minimize excessive cone excursion below Fb, where the cone is no longer loaded
by the box. (All vented alignments can benefit from a subsonic filter, not just 6th order alignments).
This alignment is attractive for several reasons. The box alignment itself is critically damped
(down 6db at Fb), and produces extremely tight sounding bass. The 6th order alignment gives a
lower cutoff point than a max. flat alignment, and does this in a smaller box! The only tradeoff is
the 6db boost required at Faux (Fb x 1.07), provided by the EQ circuit. To some loudspeakers,
the 6db boost would be a show stopper, since a 6db boost means that 4 times the amplifier
power is required at Fb compared to a max. flat 4th order alignment. However, when the driver is
a high efficiency one, 6db of boost is no problem at all. For instance, compare the Selenium
WPU1507 we have been using in our examples (96 db/watt) to another driver, lets say one that
has a sensitivity of 87db/watt, which isn’t uncommon for many loudspeakers that are offered as
‘high end’ systems. At a loud continuous listening level, lets say 93 db, the 87db driver would
require 4 watts, where the WPU1507 would need ½ watt. Now lets put them both in a 6th order
alignment. Now the 87db system would need 16 watts (at Fb), where the WPU1507 needs 2
watts. If you have musical peaks that are 10 db above the average level (103db), then the 87db
system now needs 160 watts, where the WPU1507 would need 20 watts. If the dynamic range
were just 13db above average, which is quite common, the WPU1507 would require 40 watts,
and the other driver now needs 320 watts, and likely to be entering its failure mode. Don’t play the
1812 Overture on this system! As you can see, the benefits of a high efficiency driver really come
into play when you consider even modest equalization or realistic listening levels.
Now on to the formulas. Again, we will use the WPU1507 for our examples:
The formula to calculate the box size for a 6th order system is:
Vb = (4.1)(Vas)(Qt2)
Qt squared is: .43 2 = 0.1849, multiplied by Vas (5.33) is 0.985517, multiplied by 4.1 is 4.0406, or
4.04 cubic feet. ( remember the max. flat alignment was 7.094 cubic feet).
Box tuning frequency is:
Fb = 0.3 (Fs/Qt)
Fs divided by Qt is: 36/.43 = 83.72, multiplied by 0.3 = 25.116 Hz
So we can see that the WPU1507 has a -3db point of about 25 Hz in a 4.04 cubic foot box when
used in a 6th order alignment. A nice alternative from the max. flat alignment of a 7 cubic foot box
with a 30 Hz cutoff!.
Port calculations
The last formula we need is to calculate our port size (or duct). A duct is a port (hole), that has
length. All ports are ducts, even if it is only the thickness (length) of the box material (typically ¾
in.).
The formula for determining the duct length is:
Lv = (((1.463)(107)(r2)) / ((Fb2)Vbin))) -1.463 r
Where Lv = duct length
r = radius of vent (inside)
Fb = box tuning freq (32)
Vbin = box volume in cubic inches . 1 cubic foot = 1728 cubic inches.
For our example, lets go back to the first set of calculations we did for the WPU1507 in a 4th
order Maximally flat box of 7.0937 cubic feet.
The vent can be any shape, but the area needs to be converted to the equivalent diameter for
the formula. For instance, we use a 3x12 inch vent on this example system, which is a 36 square
inch vent. The equivalent round vent would be about 6.77 inched in diameter (area of a circle
(round vent) is A = pi x r2, where A = area, pi = 3.14159, and r2 is radius of circle squared).
So, for our 6.77 diameter (equivalent) vent, r is equal to 3.385 inches.
Since this formula uses cubic inches for box volume, we need to calculate this. Our box is 7.0937
cu. ft., so, 7.0937 x 1728 = 12257.9, or 12258 cubic inches.
Using these numbers, our formula looks like this:
Lv = ((1.463)(107)(3.3852)/(Fb2)12258)-1.463(3.385)
3.385 squared = 11.458225
Fb = 32, so 32 squared = 1024
Plugging these numbers in has our formula looking like this:
Lv = ((1.463)( 107)(11.458225)/(1024)(12160))-1.463(3.385)
107= 10000000
1.463 x 10000000 x 11.458225 = 167633831.75
1024 x 12258 = 12552192
This makes our formula look like this:
Lv = (167633831.75/12552192)-1.463(3.385)
167633831.75 divided by 12552192 = 13.3549
1.463 x 3.385 = 4.952255
So now our formula is reduced to:
Lv = 13.3549 - 4.952255
13.4626 - 4.952255 = 8.40 inches.
So, with an enclosure volume of 7.0937 cubic feet tuned to 32 Hz with a port of 36 square inches,
the port duct needs to be 8.4 inches long.
This formula for calculating port length is used for all alignments.
The formulas provided in this paper will allow you to determine which driver best fits your
requirements, and gives you the ability to choose from different alignments in order to meet your
goals.

Good luck from Audio-Kits (www.audio-kits.com)

첨부 : PDF 원본 파일

Loudspeaker_Alignments.pdf

[라이더스 (조용복/경기이천)]

좋은 정보와 자료에 감사드립니다
그런데
하얀건 종이요 꺼먼건 글씨요
했다는 옛말이 제게도 나타나네요
단어만 보여요

[동산(전북 순창 )]

좋은 정보라는걸 아시는 분이 ...

[피터(김준엽/캐나다)]

어렵네요. ㅎㅎㅎㅎ. 근데 스피커 통 짜는건 요즘 웹사이트나 프로그램으로 계산 자동으로 해주는거 같던데요.

[sungho(조성호/서울)]

오잉... 그런 신기한게 있나요? 혹시 가능하시면 공유부탁드립니다. ^^;;;

[피터(김준엽/캐나다)]

https://www.diyaudioandvideo.com/Calculator/SpeakerBoxVolume/ 여기 사이트 돌아다니셔도 되구요. 구글에다가 speaker enclosure calculator 리고 치면 많이들 나와요

[sungho(조성호/서울)]

감사합니다. 신기하네요~^^

[sungho(조성호/서울)]

가입했습니다. 좋은정보 감사합니다. ^^

[손삿갓(손기채/광주)]

음...한 눈에 이해가 쫘~악 되네요.
글이 전부 영어라는 사실이...