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Was using 1200 watts, but I'm moving to a smaller car and I'm going to put this in a box that's just below the min requirements. How many watts would this sub need? 300? 500? And I'm talking RMS watts. Thanks

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Typically you use more power when you have a smaller box and a bigger box when you have a less power. Why can't you use 1200?

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minimum watts for what exactly? What are you trying to achieve? If you're just trying to make noise then hell, 50 watts would do. But I don't think that's the answer you're looking for. I would use a 2000 watt amp if it was me. But I don't think that's what you're looking for either. So just pick a number between 50 and 2000.

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Just use whatever your electrical system can handle...

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1w to get it moving

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There is a way to calculate it but I don't have it with me.

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They can be found towards the end of this

SPEAKER DESIGN EQUATIONS 3.6

[billmc@agora.rdrop.com]

The most current version of this file can be found at:

http://www.rdrop.com/users/billmc

1. Introduction

This is a library of equations for designing ported and closed-box

speaker enclosures. The equations were taken from speaker design books

and technical papers by Richard Small and Neville Thiele (see references

in tutorial section). They are designed for un-stuffed enclosures.

The equations are intended to be used with the HP48GX/SX multiple

equation solver but can also be run with the solver built into the

HP48SX. The binaries are provided in uu-encoded and ->ASC form. An RPL

version is also provided, but does not include the binary variable Mpar

needed by the multiple equation solver.

The initial default speaker parameters are for the Eminence 18029 18"

driver.

I welcome any comments or refinements.

2. Variables

The main directory is called SPKR and consists of two subdirectories:

CB Closed Box Design

PORTED Ported Box Design

Running the multiple equation solver from either subdirectory will

Vas Volume of air having same acoustic compliance as driver

suspension

Qts Total driver Q at Fs

Fs Resonant frequency of driver

PEmax Thermally-limited maximum RMS input power

SPL Efficiency of driver in dB SPL at 1W/1m

Dia Diameter of driver

xmax Peak displacement limit of driver diaphragm (1/2 of "throw")

Vb Inside volume of enclosure

Fb Resonance frequency of enclosure

F3dB Half-power (-3 dB) frequency of loudspeaker system response

Fmax Upper frequency limit of driver's piston range

dBpeak Maximum peak or dip of loudspeaker system response

Par Estimated displacement-limited acoustic power rating

Per Estimated displacement-limited electrical power rating

\Gno Driver efficiency (\Gn is Greek character eta)

PeakSPL Thermally-limited RMS sound pressure level in passband

Sd Estimated effective projected surface area of driver diaphragm

Vd Peak displacement volume of driver diaphragm

K1 Power rating constant

K2 SPL rating constant

The following additional variables are defined for the closed box case:

Qb Total Q of system at Fb

Amax Maximum amplitude of loudspeaker frequency response

Vr Ratio of Vas to Vb

Qr Ratio of Qb to Qts and Fb to Fs

The following additional variables are defined for the ported box case:

Dmin Minimum diameter of tubular vent to prevent excessive vent

noise

Dv Diameter of tubular vent

Lv Length of tubular vent

For the ported box case, the following apply:

1. Fb is the tuning frequency for the vent.

2. To use a square vent, enter the vent width times 1.13 or [2/SQRT(pi)]

for Dv.

3. Design

When designing a loudspeaker, two approaches may be followed. The

easiest is to select a driver and design an enclosure for it. The other

is to design the enclosure first, then select or build a driver that

matches it.

The choice between a closed box and ported box depends on several

factors. Closed-box systems are the easiest to design and build and

have the advantages of smaller box size, good low-frequency power

handling, and superior transient response. Ported-box systems are more

difficult to design because they require precise duct tuning. However,

ported boxes have the advantages of superior bass response, good

efficiency, and superior peak power handling in the passband.

3.1 Closed-Box Systems

Closed-box systems are designed around one variable, box volume. Box

volume is a function of the driver parameters and the system Q, Qb.

To design a system with minimum peak or droop in the passband, Qb

must be 0.707.

The designer has the choice of setting Qb and solving for the box

volume, or setting the box volume and solving for Qb. There is also

the choice of assigning values to both of these variables and solving

for one of the driver parameters.

To design a closed-box system, enter the CB subdirectory and run the

multiple equation solver. Alternatively, run the built-in HP48SX

solver and select DESIGN.EQ as the current equation. Choose one of

the following variables to solve for and assign values to the rest:

Vas, Qts, Fs, SPL, Dia, xmax, Qb, and Vb.

If you don't have all of the parameters available, purge the ones you

don't know, so they'll be undefined and the solver won't attempt to

use them. At a minimum, you will need to supply all but one of Vas,

Qts, Fs, Qb, and Vb.

Next, press <- ALL in the multiple equation solver to solve for all

the unknowns. If using the built-in HP48SX solver, you will need to

solve for each unknown individually, using NXEQ to sequence through

the equations.

3.2 Ported-Box Systems

Ported-box systems are a little more difficult than closed box

systems because there is an additional variable, tuning frequency.

The optimum tuning frequency depends on the driver parameters and box

volume.

To design a ported-box system, enter the PORTED subdirectory. Run

the equation solver of your choice as described above and enter the

driver parameters. Notice there is no Qb variable.

At this point solving for the unknowns will automatically create a

system with optimum passband response. Alternatively, you can

specify values for Vb and/or Fb to see what effect they have on the

system response.

To find the minimum recommended diameter of a tubular vent for the

enclosure, solve for Dmin. This is smallest diameter permissible to

keep the air velocity below 5% of the speed of sound. Higher

velocities can produce audible noise. To calculate the vent

dimensions, enter either of Dv and Lv and solve for the other,

keeping in mind the minimum recommended value of Dv.

3.3 Cabinet Design

In the CST menu of the CB and PORTED subdirectories is a key labeled

BCALC. Pressing this key runs the box calculator program. Don't run

it directly from the SPKR subdirectory, or it will not work

properly. The program is rather crude, and does not handle dual

woofers, but is adequate for most designs. It works as illustrated

by modeling the driver as a segment of a solid cone:

_____

/| ^

/ | |

/ | |

/ | |

_____ / | |

^ | | |

| | | |

Rdia | | Dia

| | | |

__v__ | | |

\ | |

| \ | |

| \ | |

| \ | |

| \| __v__

|

| |

|<-Depth->|

| |

To use, enter the driver's depth (distance from front of driver to

back of magnet) and press DEPTH. Enter the rear (magnet) diameter of

the driver and press RDIA. If you want the program to account for

any extra volume taken up by bracing and other drivers, enter this

volume and press XVOL. The program uses the driver's diameter as

entered previously in the equation solver.

The dimensions default to English units. The program will only

accept real numbers as input; unit objects will cause an error. (I

said it was crude.) To change units, store a value containing the

new unit by typing 'name' STO, where name is one of Depth, Rdia, or

Xvol. The units of the results should make sense based on the units

of the data, but I won't guarantee it.

You can also change the ratio of Height:Width:Depth used in the box

calculation by pressing GOLD, 1.25:1, or CUST. GOLD selects the

golden mean, 1.62:1:0.62 ((sqrt(5)+1)/2), which is the most common

ratio. 1.25:1 selects another common ratio, 1.25:1:0.8. If you wish

to use a custom ratio, enter it and press CUST.

Each time you change a parameter using a menu key, the results will

be recalculated and redisplayed. The display shows, from top to

bottom, the driver's front diameter, the driver's rear diameter, the

driver's depth, the extra volume taken up by other objects inside the

cabinet, the total internal volume of the cabinet (including driver

and extra volume), the ratio used to calculate the box dimensions,

and the inside height, width, and depth of the cabinet. FIX 2 is the

best display format to use with the default units.

3.4 Equalization of Closed-Box Systems

There is a subdirectory in CB called EQUALIZER that will find the

component values for an active equalizer that can extend F3dB of any

closed box system to any desired lower limit (at the expense of

efficiency and power handling--watch out!) See  for theory and

circuit details.

First, use the equation solver in the CB subdirectory to solve for

the system as shown above. Next, enter the EQUALIZER subdirectory.

Store the new desired cutoff frequency into F3dB, and press CIRCUIT.

The component values will appear in the display. The values of R, C,

N are chosen by the user to make the remaining component values

realistic (see ).

4. Analysis

4.1 Frequency Response

The equation solver generates three values related to frequency

response, F3dB, Fmax, and dBpeak.

F3dB is the frequency at which the acoustic output power of the

speaker drops by half. Below this frequency, the response will drop

12 dB per octave for the closed box and 24 dB per octave for the

ported box.

Fmax is the upper limit of the driver's piston range. Piston range

is defined as the range of frequencies for which the wavelength of

sound is greater than the circumference of the driver's diaphragm.

In this range, the driver's output is non-directional.

Since this package models the driver as a piston, it is important to

note that the equations are only accurate up to Fmax. In addition,

because it is difficult to predict the driver's high-frequency

behavior, it is a good idea to cross over to a smaller driver at or

below Fmax.

dBpeak is the magnitude of the frequency response peak or dip. For

an optimal design, this value will be zero.

To examine the frequency response in detail, enter the CB or PORTED

subdirectory and run the plotter or built-in HP48SX solver. Select

FREQresp from the equations catalog. F is the frequency variable,

and dBmag is the response at that frequency. Using the solver you

can solve for one in terms of the other.

4.2 Power Handling

The equation solver generates power ratings called Par and Per.

Par is the displacement-limited acoustic power rating. For the

closed box, Par is the worst-case value for wide-band signals (all

the way down to DC). For the ported box, it is an estimate based on

the characteristics of musical signals.

Per is the displacement-limited electrical RMS power rating based on

Par.

Because displacement-limited power handling is actually a function of

frequency, the values of Par and Per only give small part of the

picture. To examine power handling in detail, enter the CB or PORTED

subdirectory and run the plotter or built-in HP48SX solver. Select

POWresp from the equations catalog. F is the frequency variable, and

Pmax is the maximum electrical input power at that frequency.

Pmax is plotted first, followed by PEmax, the manufacturer's thermal

RMS power rating. At some frequencies, Pmax will exceed PEmax. As

frequency increases, Pmax can reach thousands of watts. Exceeding

PEmax is permissible for short durations, but under no circumstances

should you exceed Pmax even briefly or the driver may be physically

damaged.

Because Pmax is calculated with sine waves in mind, the peak power

rating at a given frequency will be 2*Pmax.

Using the ISECT function of the plotter, it is possible to determine

the frequency range(s) over which it is safe to apply the full rated

thermal power, PEmax, without damage from excessive displacement.

Just place the cursor near the intersection of the curves and press

ISECT in the FCN sub-menu. In the same manner, you can also use

ISECT to find frequencies where the curves approach one another but

don't touch.

4.3 Sound Pressure Level

The equation solver generates a value for maximum SPL called

PeakSPL. This is the maximum RMS output level of the system in the

passband when driven by the thermally-limited maximum input power,

PEmax.

Like power handling, displacement-limited SPL is a function of

frequency. To examine displacement-limited SPL in detail, enter the

CB or PORTED subdirectory and run the plotter or built-in HP48SX

solver. Select SPLresp from the equations catalog. F is the

frequency variable and SPLmax is the displacement-limited SPL at that

frequency.

SPLmax is plotted first, followed by the thermally-limited RMS sound

pressure level. As before, for frequencies where SPLmax exceeds the

thermally-limited SPL, the maximum SPL may be limited to a value in

between, depending on the peak-to-average power ratio of the input

signal.

Again, ISECT can be used to find the frequency or frequencies at

which the displacement- and thermally-limited SPL ratings are equal.

4.4 Analysis of Equalized Closed-Box System

Using an equalizer to extend the bass response of a closed-box system

does not come without costs. For each octave of bass extension, a 12

dB boost is necessary (and requires 16 times as much power).

To evaluate these costs, two equations are provided in the EQUALIZER

subdirectory: FREQresp and POWresp. These function like their

counterparts in the CB and PORTED subdirectories, but take into

account the effects of the equalizer.

Because I took the equations right out of the article  without

any optimization for speed, these equations run very slowly.

However, I left out the units wherever possible so the equations

would run faster.

FREQresp calculates the response of the equalizer, rather than the

system, to give you an idea of the amount of boost required to

equalize the system. The greatest boost occurs at the new F3dB.

POWresp calculates the equivalent power handling of the system. At

each frequency, Pmax is reduced by the amount of boost the equalizer

provides. This is useful to see what the power handling of an

equivalent, un-equalized system would be.

There is no equation for maximum SPL vs. frequency because it is the

same as the un-equalized system.

5. Design Equations

Here are the equations used by the speaker design library. All values have

SI (mks) units. ^ denotes exponentiation. LOG() is base 10.

5.1 Constants

pi = 3.14159265359

c = speed of sound in air (345 m/s)

Ro = density of air (1.18 kg/m^3)

5.2 Closed-Box Systems

Vb = Vas/Vr

Fb = Qr*Fs

F3dB = Qr*Fs*((1/Qb^2-2+((1/Qb^2-2)^2+4)^0.5)/2)^0.5

Fmax = c/(pi*0.83*Dia)

dBpeak = 20*LOG(Amax)

Par = K1/Amax^2

Per = Par/(\Gno)

\Gno = 10^((SPL-112)/10)

PeakSPL = SPL+10*LOG(PEmax)

Sd = pi*(Dia*0.83)^2/4

Vd = Sd*xmax

Amax = Qb^2/(Qb^2-0.25)^0.5 for Qb >(1/2)^0.5, 1 otherwise

K1 = (4*pi^3*Ro/c)*Fb^4*Vd^2

K2 = 112+10*LOG(K1)

Vr = Qr^2-1

Qr = (1/Qts)/(1/Qb-0.1)

Frequency-dependent equations:

Fr = (F/Fb)^2

dBmag = 10*LOG(Fr^2/((Fr-1)^2+Fr/Qb^2))

Pmax = K1*((Fr-1)^2+(Fr/Qb^2))/(\Gno)

SPLmax = K2+40*LOG(F/Fb)

Thermally-limited RMS SPL = PeakSPL+dBmag

5.3 Ported Box Systems

Vb = 20*Qts^3.3*Vas

Fb = (Vas/Vb)^0.31*Fs

F3dB = (Vas/Vb)^0.44*Fs

Fmax = c/(pi*0.83*Dia)

dBpeak = 20*LOG(Qts*(Vas/Vb)^0.3/0.4)

Par = 3*F3dB^4*Vd^2

Per = Par/(\Gno)

\Gno = 10^((SPL-112)/10)

PeakSPL = SPL+10*LOG(PEmax)

Dmin = (Fb*Vd)^0.5

Lv = 2362*Dv^2/(Fb^2*Vb)-0.73*Dv

Sd = pi*(Dia*0.83)^2/4

Vd = Sd*xmax

K1 = (4*pi^3*Ro/c)*Fs^4*Vd^2

K2 = 112+10*LOG(K1)

Frequency-dependent equations:

Fn2 = (F/Fs)^2

Fn4 = Fn2^2

A = (Fb/Fs)^2

B = A/Qts+Fb/(7*Fs)

C = 1+A+(Vas/Vb)+Fb/(7*Fs*Qts)

D = 1/Qts+Fb/(7*Fs)

E = (97/49)*A

dBmag = 10*LOG(Fn4^2/((Fn4-C*Fn2+A)^2+Fn2*(D*Fn2-B)^2))

Pmax = (K1/\Gno)*((Fn4-C*Fn2+A)^2+Fn2*(D*Fn2-B)^2)/(Fn4-E*Fn2+A^2)

SPLmax = K2+10*LOG(Fn4^2/(Fn4-E*Fn2+A^2))

Thermally-limited RMS SPL = PeakSPL+dBmag

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There isn't a minimum amount of power for the driver.  There will be a minimum amount of power required to reach a certain level of output at a certain frequency, and that will depend on the enclosure as well as your environment.  It's impossible to completely predict unless you know the power compression behavior of the driver and have graphed the response of your environment, but any enclosure modeling software is going to be able to predict output vs power in an idealized scenario, before those two factors are accounted for.

What exactly are you trying to accomplish?  What are your goals?

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