.TH "BOXDESIGN" 1 "April 19, 1987"
.SH NAME
boxdesign\ \-\ enclosure design spreadsheet
.SH SYNOPSIS
.B "sc boxdesign.sc"
.SH DESCRIPTION
.PP
The
.B boxdesign
database for the
.B sc
spreadsheet calculator provides a simplified method of designing and
simulating both sealed and vented box enclosures, given a minimal set of
low frequency driver parameters (either the basic electro-mechanical
or the 
.I "Thiele-Small" 
parameters). The calculator attempts to optimize the design of each for
maximally flat frequency response, and provides a comparison of frequency
response, bandwidth and power handling and ultimate SPL between the 
two different enclosure types. Details of vent parameters are provided for
vented-box designs. Provision are incorporated for different box volumes.
.PP
This particular system is based on algorithms outlined by Margolis
and Small [1] for personal programmable calculators, here implemented on a
public domain spreadsheet calculator for
.I Unix
systems called 
.BR sc ,
which is available from a variety of Usenet sources. It has also been
implemented on a variety of other spreadsheet calculators as well [2]. If you
are, in fact, using
.BR sc ,
it is recommended that this application be run with version 3.1 or later,
as it has not been tested on any earlier versions. The database from the
distribution kit, 
.IR boxdesign.sc ,
contains a sample driver illustrating the basic principles.
.PP
The spreadsheet is divided into 5 major sections, and each of these will be
treated in turn below. In each section there may be one or more parameters
that you can change, and many others that display resulting values. In most
cases, data is entered and displayed in units that are convenient to the
item being described, and conversion to standard units is handled within the
spreadsheet database. This means that data such as diameter and excursion
are entered in centimeters, and volume in liters, but internal calculations
are based on standard MKS units. Some of the values are displayed in English
units as well.
.bp
.PP
.B "ELECTRO-MECHANICAL\ PARAMETERS"
.br
In this section, you can enter the basic electro-mechanical parameters of the
driver as follows:
.IP "\fIEffective cone diameter\fR"
The effective projected diameter of the driver in centimeters.
If not available from the manufacturer, it can be approximated by taking the
diameter of the diaphragm plus two-thirds of the width of the surround.
.IP "\fIMaximum excursion\fR"
This is the maximum linear displacement of the driver to ensure less than
10% harmonic distortion, measured in centimeters. If unknown, can be set 
to .6 cm for high-compliance woofers.
.IP "\fIBl product\fR"
This is a measure of the electro-magnetic coupling in the driver, stated
in either tesla-meters or (more appropriately to the problem at hand) newtons
per amp. It is equal to the product length of wire in the magnetic field
(in meters) and the density of the magnetic field in the gap (in teslas).
.IP "\fIVoice coil dc resistance\fR"
This is the total DC resistance, measured in ohms, that the system has to
contend with. You might want to include the effective series DC resistances
in the crossover, lead-in wires and so forth for maximum accuracy.
.IP "\fIMechanical mass\fR"
The effective mass of the driver, including air loads, in grams.
This is not the same as the simple static mass of the driver
(although it is related).
.IP "\fIMechanical compliance\fR"
The effective stiffness of the suspension, including the effects of the air
load, in millimeters per newton.
.IP "\fIMechanical losses\fR"
The total resistive losses in the system, in MKS mechanical ohms
(kilograms per second).
.PP
Many of these parameters will not be available from the manufacturer. In
that case, simple move on to the next section, "Thiele-Small parameters".
.bp
.PP
.B "THIELE-SMALL\ PARAMETERS"
.br
This section displays the resulting Thiele-Small parameters derived from the
electro-mechanical parameters entered above. If you have the Thiele-Small
parameters already, you may enter those in the appropriate cells directly.
(Note that this overwrites the equations needed to derive these parameters from
the electro-mechanical parameters, so make sure you don't try to save the
new template in place of the old one).

To enter the Thiele-Small parameters directly, you must supply the following:
.IP "\fIEffective cone diameter and Maximum linear excursion\fR"
Both of these parameters are the same as those in the previous section, and
can be entered in either section.
.IP "\fIResonant Frequency\fR"
This is the fundamental free-air resonance of the driver, measured in hertz.
.IP "\fIEquivalent volume\fR"
This is a volume of air(in liters) whose compliance is equal to that of the
driver. If this parameter is stated in cubic feet, multiply by 28.3 to get
liters.
.IP "\fIMechanical Q\fR"
This is the Q of the driver due to purely mechanical losses.
.IP "\fIElectrical Q\fR"
This is the Q of the driver due to purely electrical losses.
.PP
All of the rest of the Thiele-Small parameters can be derived directly from
these few, and there is no need to enter any more data in this section.
Several other values are displayed here:
.IP "\fITotal Q\fR"
The Q of the driver due to all losses (mechanical and electrical).
.IP "\fIReference efficiency\fR"
This is the total conversion efficiency of the driver, a measure of the
how much of the electrical input power is converted to acoustical output. It
refers, essentially, to the mid-band efficiency, which would be relatively
unaffected by the low-frequency enclosure effects. This is the maximum
available efficiency of the driver.
.IP "\fIOutput level\fR"
This is the expected output level of the driver into a hemispherical
load, measured 1 meter from the driver, when driven by 1 watt of electrical
input power.
.IP "\fIEffective area\fR"
This is the effective projected area of the driver, measured in square
centimeters.
.IP "\fIMaximum displacement\fR"
This is the maximum volume of air the driver is capable of moving. It is 
a function of the drivers effective area and its maximum linear excursion.
.bp
.PP
.B "PERFORMANCE\ COMPARISONS"
.br
This section provides a side-by-side comparison of the response characteristics
of the closed box and vented box system designs. It compares certain 
performance parameters for the two systems:
.IP "\fIEnclosure volume\fR"
The net volume of the enclosure that was either calculated by the spreadsheet,
or that you supplied.
.IP "-\fI3dB frequency\fR"
The frequency where the output of the driver is 3 dB below that of the
midrange response of the driver. The speaker rolls of below this point.
.IP "\fIPeak response ripple\fR"
The amount of frequency response deviation from flat due to misalignment
(intentional or otherwise). In a closed box system, it indicates the height
of the "bump" in the response when the Q is too high.
.IP "\fIMaximum acoustic output\fR"
The maximum attainable output of the system (in acoustic watts) at the point
where the excursion of the cone is the greatest, measured at 1 meter from the
driver.
.IP "\fIMaximum SPL\fR"
The same measurement as above, stated in sound pressure level, when the 
system is working into a hemispherical load.
.IP "\fIMaximum electrical input\fR"
The amount of input power needed to attain the above acoustical maximums.
.LP
When reviewing the power figures,
it is important to realize what they mean. There are two driver parameters
which limit the ultimate power output and handling capabilities of a
loudspeaker system. First, there is excursion limiting. The woofer, because
of limits in its suspension or motor system, cannot move enough air linearly
to produce the needed acoustic power. Secondly, there is thermal limiting.
Most of the electrical power you put into a loudspeaker is dissipated as heat
in the voice coil and if the voice coil is unable to rid itself of this waste
heat faste enough, it may fail catastrophically.
.LP
The figures quoted here are for excursion limitations only. They are determined
by the worst case excursion found within the passband of the system. These
values do not account in any way for thermal limitations and for excursion
limits caused by signals below the cutoff frequency of the system. In the
case of closed box systems, the worst case excursion usually occurs at the
system resonance, and improves above that point with the square of the 
frequency. This means that above a certain point, the power output is
determined by thermal limits, and the below that, they are determined by
excursion limits. Where that crossover point occurs is very driver and system
dependent.
.LP
In vented box systems, the worst case excursion occurs at the driver-enclosure
resonance point, and drops dramatically as you approach the enclosure-port
resonance frequency (where the excursion of the driver is at a minimum. Below
that point, the driver excursion increases rapidly again. Here we run into the
perennial vented box problem of little cabinet loading below the system
cutoff. This implies that the excursion-limited power capabilities of a vented
box system can be severely reduced when there is a large amount of sub-sonic
noise present, causing large, nonproductive excursions. Limiting the bandwidth
of the system with low frequency high-pass filters will substantially reduce
these problems.
.LP
In any case, it is important to remember that, within the passband of the
system, these excursion limits are the worst case figures. The loudspeaker
systems based on these designs are safe with amplifiers of considerably greater
output capabilities than these figures might indicate.
.PP
.B "FREQUENCY RESPONSE"
.br
In addition to these performance figures, the spreadsheet provides a
point-by-point comparison of the frequency response of each configuration
at a variety of frequencies. You can select the following measurement
parameters:
.IP "\fIIntervals per octave\fR"
Determines the frequency resolution of the measurements. The most useful
parameter here is 3, giving 1/3 octave response.
.IP "\fIStarting frequency\fR"
Determines the lowest frequency that will be displayed.
.LP
By setting these two parameters accordingly, you can display either gross
response characteristics, or center around a specific frequency
for detailed measurements.
.bp
.PP
.B "CLOSED\ BOX\ DESIGN"
.br
This section allows you to design a closed box system based for the driver
parameters you have entered. You can design the system given one of two
targets, either a specified system Q (and, therefore, a particular response
characteristic), or a given size enclosure. There are three parameters you can
set and change in this section:
.IP "\fIDesired system Q\fR"
This is the Q factor for the resultant system. If this value is non-zero
and the desired box volume parameter is 0, then the spreadsheet will attempt
to derive a design to meet this system Q. For maximally flat (Butterworth)
response, a Q of .707 is appropriate. For critically-damped response, a Q
of .5 is needed. This should never be set to less than the driver's total
Q (shown in the Thiele-Small parameter section), otherwise impossible
volumes might result.
.IP "\fIDesired box volume\fR"
Set this parameter to non-zero if you want to see the effect of a driver
in a given volume. Setting this value causes the desired system Q parameter and
***> the recommended volume to be ignored.
.IP "\fIEnclosure damping\fR"
This is a measure of the effect of stuffing the cabinet with differing
amounts of acoustical damping. A value of 0 indicates no internal damping,
while a value of 5 (the maximum) indicates a cabinet fully stuffed with
100% effective damping. Trying to damp the enclosure any further than this
will result in loss of effective volume and no increase in damping. For typical
selaed box cabinets with a loose filling of fiberglass, a value of 3 is
reasonable.
.LP
Once the appropriate parameters are entered, as described above, the spreadshee
***>t
derives the rest of the system parameters:
.IP "\fIRecommended box volume\fR"
This is the volume needed, given the driver characteristics and enclosure
damping, to achieve the desired system Q, if possible. If this value seems
unimaginably large for your driver (say, 500 liters for a 6 inch woofer), it
is probably because the desired system Q is lower than the driver's total Q.
Short of reverting to techniques such as resistive loading or driving the
system with a negative-impedance amplifier, there is little to be done to
get a reasonable design, given the driver and the target response. This 
value is used in further calculations only if the desired box volume
parameter is 0.
.IP "\fITuning ratio\fR"
This is the ration between the driver compliance and the box compliance.
.IP "\fISystem resonance\fR"
This is the resonant frequency of the total system.
.IP "\fIActual system Q\fR"
This is the resultant Q of the system, regardless whether the system was
derived from the desired Q or the desired volume.
.IP "-\fI3dB frequency\fR"
The frequency at which the response of the systemhas dropped to half of
its mid-band level.
.IP "\fIPeak response ripple\fR"
The height of the peak above the mid-band response tdue to system having Q's
greater than .707.
.LP
The maximum output figure are discussed above.
.bp
.PP
.B "VENTED\ BOX\ DESIGN"
.br
This section designs vented box enclosures, given the characteristics of the
driver. The spreadsheet will, by default, attempt to design an enclosure whose
response approaches the flattest possible. The follwing parameters are
displayed:
.IP "\fIRecommended box volume\fR"
This is the volume calculated by the spreadsheet to achieve the flattest
possible response, given the characteristics of the driver. It will be used
for subsequent design and pereformance calculations if the desired box
volume is 0.
.IP "\fIDesired box volume\fR"
You can set this parameter to some non-zero value to override the recommended
volume in susbsequent calculations.
.IP "\fITuning ratio\fR"
This is the ration of the driver's compliance to the box's compliance.
.IP "\fIEnclosure resonance\fR"
This is the frequency the enclosure is tuned to to achieve the desired
response.
.IP "\fIRecommended vent diameter\fR"
This is the diameter of a circular vent need to ensure that, given the
maximum displacement volume of the driver, no non-linearities will occur
in the air moving through the vent. This figure is extremely conservative,
and somewhat smaller vent diameters can usually be used successfully.
.IP "\fIDesired vent diameter\fR"
You can enter a different figure for the vent diameter here. There are several
reasons for doing this. First, you may not be able to obtain a tube of the
recommended diameter (tubing is usually available in only 1/4 or 1/2 inch
increments).  Secondly, the recommended diameter may result in a vent length
that to far to long to be practical, so reducing the diameter may result in a
vent that can fit in the cabinet. In any case, be sure to add the volume
taken up by the vent to the net volume when building your enclosure.
.IP "\fIVent length\fR"
This is the length of the vent, presuming that it is mounted flush with a
cabinet boundary. It is a good idea when building the cabinet, to make the
vent a bit longer than recommended, then trim the vent to length, measuring
the performance of the system. This will account for slight deviations in
driver parameters, box losses, and so forth.
.LP
The rest of the measurement parameters are analogous to those in the closed
box section.
.bp
.SH BUGS
Many of the bugs are 
.B sc
bugs. For example, when loading the database, many log math error messages
are generated. This is because of the simple-minded re-calculation order
built into 
.B sc.
This in no way compromises the accuracy and the efficacy of the model, it is
only a cosmetic nuisance.
.PP
The algorithm for determining the vented box parameters is somewhat simple 
minded in that its only goal is to search for a maximally flat alignment. This
may be desirable in most cases, but precludes designs optimized for maximum
power handling/bandwidth products, or minimal excursion configurations, and
so forth. Including these capabilities has the potential for severely
complicating the model, destroying the elegance of its simplicity.
.SH AUTHOR
Dick Pierce
.br
17 Sartelle Street
.br
Pepperell, Ma. 01463
.SH REFERENCES
.IP [1]
Margolis, G. and Small, R. H., "Personal Calculator Programs for Approximate 
Vented-Box and Closed-Box Loudspeaker Design,"
.IR "J. Audio Eng. Soc." ,
vol. 29, no. 6, pp. 421-440, 1981 June.
.IP [2]
Pierce, R., "A Novel Approach to Rapid Loudspeaker Design and Prototyping,"
.IR "(unpublished)" ,
1987 March.