Basta!
Version 2.0
User’s Guide
Ó Tolvan Data 2005-2008
2008-05-03
System response / Driver response / Vent response / Electrical impedance
Cone velocity and displacement
Vent velocity and displacement
Electrical impedance, resistance and reactance
Reactance interpreted as an inductance
Cone excursion and velocity at MOL
Vent velocity and excursion at MOL
Wall/floor/ceiling reflections, Room resonances
Basta! is a computer program for simulation of loudspeaker systems. Basta! can simulate open baffles, closed boxes, vented boxes (“bass reflex”) and 1- and 2-ported bandpass systems. For ported enclosures, pipe resonances in the vent can be simulated. Instead of a vent, the ported enclosures can have a passive radiator.
Basta! also includes simulation of baffle step, wall-mounted loudspeakers, lossy voice coil inductance, multiple and isobaric drivers. Basta! can also simulate Active and passive crossover filters, the Linkwitz transform, most passive crossover networks, AC-bass and an approximation of the room gain in an average room.
Basta! shows graphs for the frequency response of the system and the individual driver and ports, cone and vent velocity and excursion, driving voltage box pressure, electrical impedance and its resistive and inductive parts.
Finally, Basta! can also calculate a frequency dependent, maximally allowed output level from the system, based on the maximum power amplifier voltage, Re power dissipation, cone excursion, vent excursion and vent velocity.
The Basta! simulation can be illustrated by the diagram below. Starting from the left, there are
· A voltage source
· An active filter
· A power amplifier with gain=1 and optionally AC-bass
· A passive electric circuit (filters/conjugate link etc)
· The loudspeaker driver
· The box
Block diagram for the Basta!
simulation.
The main window is
the place to configure the systems. In the system list, systems can be selected
to be plotted in the response graph. By selecting a system in the list, the
parameters of this system appear on the tabs below the list. New systems can be
created and existing systems can be copied, deleted and renamed by using the
buttons to the right of the list. On the tabs in the System parameters group
the systems are configured.
In Basta! a “system”
is one branch in the crossover filter. This means that a typical two-way
loudspeaker needs two “systems” in Basta!; one for the woofer and one for the
tweeter.
The main window with three systems,
and the driver tab for “Subwoofer” system selected.
The parameters describing the loudspeaker system are entered on a number of tabs. The Basta! simulation can show several systems simultaneously for comparison. Multiple systems can be shown in the System list and the response graph. Whenever a system is selected in the System list, its parameters are shown on the tabs. These parameters and tabs are described below.
On this tab the input voltage to the model can
be selected and the active filter can be configured. The input voltage is
typically set to 2.83 volts, since this voltage normally used to determine the
sensitivity of a loudspeaker. The response curve level will correspond to the
sensitivity of the loudspeaker at mid frequencies. Normally the baffle should
be disabled for this to work; sensitivity is typically measured in half-space.
The active filter consists of two cascaded
parts, one low-pass filter and one high-pass filter. Each of the filters can be
of order zero to four, where zero corresponds to a disabled filter. Each of the
filters consists of cascaded first or second order sections; the first order
section is described by a cutoff frequency, f0, the second order
sections are described by a cutoff frequency, f0, and a Q value.
A table lookup function is available, which
provides the required values for f0 and Q at a given filter cutoff
frequency. The lookup functions set the response of the filter to Butterworth
for odd order filter and to Linkwitz-Riley for even order filters.
At the bottom of the screen, a circuit diagram
that can be used for the realization of the filter circuit is suggested. For
details on the component values, please consult the Basta! technical
documentation.
u
The Basta! Source /Active filter tab. Here the
voltage source is set to 2.83 volts and connected to a fourth order lowpass
filter is cascaded with a fourth order highpass filter.
On the
Linkwitz transform tab, an active circuit for extending the bass response of a
closed box can be entered. The bass boost is created by a pole pair and a zero
pair. Typically, the zeroes are used to cancel the poles of a closed box
design, and new system poles are defined by the poles in the transform circuit.
In practice, this is the same as applying a bass boost to the system. For more
details on a practical realization of the circuit, see http://www.linkwitzlab.com/. The
response of the Linkwitz transform circuit can be made visible as a separate
curve in the response window.
The Basta! Linkwitz transform tab. Here, is an
example of how to compensate a closed box that has a system resonance of 50 Hz,
Qtc=0.5. The virtual system resonance becomes 20 Hz, and virtual Qtc=0.4.
The signal from the active filter is sent to an imaginary power amplifier which has the gain=1 and the output impedance Rg which can be positive or negative.
The power amplifier can also be set in an
AC-bass configuration, which gives it a special output impedance. In short, AC-bass
seemingly modifies the mechanical parameters of the driver. In effect, the fs,
Vas and Qts parameters of the loudspeaker driver can be
freely selected.
The AC-bass output impedance is described by
four components; Racneg which is usually near Re of the
driver but with opposite sign (i.e. negative), and Lac, Cac
and Rac which together with the driver determines the parameters of
the virtual driver. Basta! can calculate the values of these components from
the virtual driver parameters, or the values can be entered manually.
The amplifier has a maximum
output voltage, which can set. The voltage appears after either of Rg
or the AC-bass network, since these are typically achieved by means of current
feedback within the amplifier. This maximum output voltage is one of several
limits, which together determine the maximum output level of the loudspeaker
system.
At the bottom of the screen a circuit diagram
is shown indicating the power amplifier and its output impedance. The diagram
does not show how the actual amplifier is implemented, but rather a conceptual
model of how the technique works and also how it is implemented in the Basta!
simulation.
For an explanation of AC-bass, see the tutorial
below.
The power amplifier / AC-bass tab. Here, the
voltage limit is set to 100 volts, and in the left panel the amplifier is set
in AC-bass mode; the AC-bass amplifier is set to give the virtual driver fs=20
Hz, Vas=20 liters and Qts=0.383. Racneg is automatically selected to
–6.1 W. The other values of the output
impedance that needs to be implemented by the AC-bass amplifier can be seen
under AC-bass amplifier properties. The right panel shows a configuration where
the amplifier has been give a negative output resistance of –2 ohms.
The signal from the power amplifier is fed to a freely configurable passive network. This is typically the place to enter more advanced crossover and baffle step compensation networks. This network alone can implement the complete crossover, or it can be used combined with the passive filter described below. The network is described by the component list, in which each component is given either of the types “R”, “L” or “C” for a resistor, inductor or a capacitor, it is also given a value, two nodes and an optional comment. The value is in W for resistors, in mH for coils, and µF for capacitors.
The node names can be freely selected, except for the input node, which is named “in”, the output node, “out”, and ground, “gnd”. The input node is connected to the power amplifier, and the output node is connected to the passive filter described below.
In some cases, such as for a conjugate link, the passive network does not have a separated input and output, but only components connected in parallel with the driver. In this case the in and out nodes can be shorted by checking the “short in and out” checkbox, and the node name “in” is treated as a synonym to “out”.
Components can be added/deleted/copied/moved with the buttons below the list.
The
Advanced network tab. The network described here consists of one 15 µF
capacitor, one 3 mH coil with an internal resistance of 0.2 W, and two resistors of 6.1 and 8 W. Internal node names are “1” and “2”.
The passive filter tab offers a few commonly
occurring pre-defined filter configurations. The passive filter consists of
four optional sections; a lowpass filter, a highpass filter, a voltage divider
(L-pad), and a conjugate link. The filters can be of order zero to four, where
zero means that the section is bypassed. As with the active filter there is a
lookup table that supplies the values for the filter, based on the voice coil
resistance Re. The table lookup values are not likely to produce the
optimal response curve, however, since the driver impedance deviates from Re.
The values should normally be altered manually to achieve the optimal solution.
The L-pad attenuates the signal to the driver.
Doing so, the driver also sees a driving impedance that is higher than zero
ohms. One effect of this is that the apparent driver Qts increases,
and the new Qts value can be seen next in the L-pad box. Note,
however, that this new Qts value does not include the effects of any of the
other resistances in the rest of the AC-bass, passive or advanced networks.
The conjugate link compensates the increased impedance that occurs due to the voice coil impedance. Basta! can calculate the values of this compensation network, but again these values should probably be changed a bit to fit the actual driver due to the lossiness of the typical voice coil inductance.
At the bottom of the screen a circuit diagram
for the selected passive filter configuration.
The
passive filter tab. Here, the full configuration of a fourth order low-pass
filter, a fourth order high-pass filter, an L-pad and a conjugate link is used.
On the Driver tab the parameters on the
loudspeaker driver are entered. The parameters are entered in groups; the first
group consists of fs, Mms, Cms, Vas
and Sd. Of these five only three should be given, Basta! calculates
the other two. You select which parameters you want to enter by selecting their
corresponding checkboxes. The same principle is used for the other group, Bl, Re,
Qes, Rms and Qts.
On the driver tab also the number of drivers,
their mounting (normal or isobaric), the voice coil temperature and an added
acoustic pathway can be entered. The single driver data can be loaded from a
file or entered manually. Most parameters can usually be found in the data
sheets from the manufacturer, but the Le and Le loss
values are rarely specified as in Basta!. Instead, the Le and Le
loss values should be determined by comparing a measured impedance curve with
the Basta! model. See Determining Le and Le loss below.
The driver also has two level limiting factors
that are used to determine the maximum output level (MOL) of the system; the
maximum peak one-way cone amplitude, Xmax, and the maximum power
dissipated in Re, Pmax.
If the number of drivers is even, the drivers can be mounted in isobaric configuration. The voice coil temperature can also be changed; it is normal that the voice coil gets heated during heavy load, and the effects of this can be seen by changing value in the temperature box. The data for the single driver are assumed valid at 20 °C.
An added pathway can also be added; the effect of this is a delay that is added to the signal. This feature is useful to simulate the effects of multiple drivers mounted at different distances from the microphone. Note that the vents have a similar setting that can be used for vents mounted far away from the driver, for example if it is mounted on the back of the box.
Basta! calculates some data on a driver equivalent to the configuration selected; the total compliance, moving mass, an equivalent effective drive diameter, Qes, Qms and Qts, and a maximum volume displacement. Some erroneous driver data can yield negative values for Qms, this is indicated by red color on the Qms value. The maximum volume displacement, Vmax, is the product if Sd and Xmax. This value is an important factor for the maximum output level at low frequencies, and can be used to compare drivers and driver configurations in that aspect.
The Show kr=1 checkbox enables a vertical dashed line in the response graph at the frequency where the circumference of the equivalent driver equals the wavelength. Below this frequency the driver is approximately omni-directional, above this frequency the driver has a more pronounced directivity, all under the assumption that the cone behaves like a rigid piston. Even though the transition from omni-directional to directional is gradual, the line can help to get an estimate on the directivity of the driver, in particular to indicate if the frequency range of interest is well below kr=1, i.e. in the omni-directional region.
The Vent / passive radiator tabs also have a Show kr=1 checkbox.
The
Driver tab. Here, the user has selected to input fs, Vas
and Sd, Mms, and Cms are calculated by Basta!.
The user has also selected too input Bl, Re and Qts, and
Qes and Rms are calculated by Basta!.
On the box tab the type of box and the box size is selected. The data for baffle edge diffraction, ie the baffle step is entered in the baffle designer, which can be started by the baffle designer button or from the tools menu.
Box types:
For the box there are three parameters, the box volume, degree of isothermalization and the Q value of the box. The two latter are closely associated with the amount and type of damping material in the box.
The Q value models the other effect of damping material. A lower Q value corresponds to a more damped box with more damping material. For the bandpass boxes that has two cavities, each of those boxes have volume and Q settings.
Damping material also has the effect that the compression and de-compression of air becomes isothermal, rather than adiabatic due to heat exchange between the air and the damping material. The result of this is that the box can appear up to 40% larger for a heavily damped box than for an empty box. Basta! does model such isothermal behavior, by treating a percentage, Viso, of the box volume as having isothermal decompression/compression of the air. Depending on the damping material, this volume should be set slightly smaller than the actual volume of the damping material. Basta! calculates an effective Vb from Vb and Viso that is used in the simulations.
Viso is a number between 0% and 100%. If Viso is 0% the box is empty and the compression of air is considered adiabatic. If Viso is 100%, the box is full with an ideal material that makes compression completely isothermal.
When a driver is placed in a lossless closed
box, the system will have a higher resonance frequency and Q value than the
driver had in free air (fs and Qts). These values are
calculated automatically for the closed box, but also for the vented box and
the 1-ported bandpass box. For the 1-ported bandpass box, Vb2 only
is used for this calculation. It might seem odd to display these numbers for
all boxes, since they strictly are only valid for the closed box, but it turns
out that they can be useful for the dimensioning also of the other box types.
The Box tab. The first panel illustrates a
vented box with a volume of 23 liters. The other panel illustrates a 2-ported
bandpass system with two cavities of 23 and 10 liters, respectively. Boxes have
some amount of damping material, giving a box Qb of 5 and a partly
isothermal compression/decompression of the air (Viso=40%).
The baffle geometry is entered in the Baffle designer. A baffle adds edge diffraction, which affects the frequency response of the system. This change in the response is called the baffle step. The baffle edge diffraction, and thus the baffle step, can be included in the Basta! simulation of response curves. The number of edge sources per driver and vent source can be set under Edge sources. A higher number of edge and driver sources results in a higher precision of the simulation, but takes longer to compute. The appropriate source density can be set by changing the value while looking at the changes in the response. Once the changes are small, the source density does not need to be increased further.
A high source density is most important for simulation at high frequencies, and simulations with the microphone extremely close to the driver/vent.
The wall behind the loudspeakers
reflects the sound, and just as the reflections at the baffle edges, the back
wall reflection alters the response of the system. The back wall reflection can
be included for any speaker, but it is particularly relevant for wall mounted
speakers, since the baffle-to-wall distance is well known.
The arrow buttons can be used to
restrict the movement of the items horizontally or vertically. There are also
2-4 buttons to lock or free the movement of corners, drivers, microphone and
back wall fixpoints.
Note: Basta! uses the same model for edge
diffraction as The Edge free software from Tolvan Data, available at http://www.tolvan.com/edge
The geometry seen in a 3D perspective. Here, the virtual
microphone position is 1 meter in front of the baffle, and 0.3 meters to the
side.
The Baffle
designer. This system has two drivers (blue circles) and one vent (green
circle).
If the Far field check box on the Box tab is checked, the distances to all driver and edge sources are the same. If the far field check box on the box tab is not checked, a microphone symbol appears in the baffle designer. In this case the z-coordinate of the microphone is specified under Mic-baffle distance and the x- and y-coordinates are specified by the placement of the “mic” symbol in the Baffle designer.
n
Here the
Far field checkbox is unchecked which reveals the mic symbol. In these cases
the microphone is placed 1 meter in front of the baffle and at 0.6 m above the
lower edge of the baffle. In the first case the microphone is placed straight
in front of the baffle, in the other the microphone is offset 0.5 meters to the
right, or 30° off axis.
The
response of the three microphone positions above. The black curve corresponds to
the far field response, the blue curve to the 1 m response in front of the
drivers, the red curve corresponds to the system with the microphone to the
side. Note the response drop at high frequencies.
For additional details on the Baffle step, see the Baffle step tutorial below.
Basta models back wall reflections in a way intimately connected to the modelling of the baffle step. When back wall reflection is on, each edge source result in another source of opposite sign and delayed corresponding to twice the distance between that particular source and the wall. Three fixpoints in the baffle designer define the baffle-to-wall distance. If all distances are set equal or if the Baffle and wall are parallel checkbox is checked, the baffle and wall are parallel.
If the Box is mounted on a wall checkbox is checked, three back wall fixpoints become
visible in the baffle designer. The fixpoint locations in the baffle designer
and their distances defined on the box tab define the orientation of the wall
behind the baffle.
The back wall reflection feature is primarily intended for
speakers mounted on-wall, such as surround speakers. The simulation is most
accurate for small angles between the back wall and baffle.
The three
fixpoints are shown in the baffle designer by yellow markers. The distance
between the baffle and back wall in these three points are set under
Baffle-wall distance. In this case fixpoints 1 and 2 define the distance to 150
mm across the left edge of the baffle, and the placement and distance of the
third fixpoint sets the distance at the right edge to 30 mm, since fixpoints 1
and 2 are equal and aligned vertically. The vertical dashed line indicates
where the baffle plane and the back wall would intersect if the baffle was
infinitely large.
If Basta!
has several systems loaded, such as a woofer and a tweeter, the baffle designer
can show them all simultaneously, for example to avoid placement of the drivers
on top of each other. Basta can also use a common microphone position, and this
is very useful for studying the directivity near the crossover frequency of
multi-way loudspeaker systems.
A system
with a dual driver bass reflex woofer system (gray circles) and a tweeter
system (black squares). A common microphone position is used (yellow)
positioned to the right.
Basta! can
import response curves from Tolvan’s loudspeaker analyzer Sirp. Basta! needs at
least one response curve and the electrical impedance of the driver mounted in
the box in order to simulate the behaviour of crossover filters etc. Several
response curves can be imported, for example for different directions.
If there is
no impedance curve, Basta! cab use a purely resistive load of 4 ohms. This is not
recommended if passive circuits are to be used, but if only active circuits are
used it is ok. A delay corresponding to an added pathway can be added to
compensate for different loudspeaker-to-microphone distances. Note, however,
that this compensation does not take the varying directivity and baffle
diffraction effects into account.
The Measured response tab. Here impedance and frequency response data can be imported to Basta! from Sirp.
Text files
from various other softwares can be imported to Basta!. The settings for the
import may have to be altered. The column separator is the character between
the columns. The decimal separator is typically the period in decimal numbers,
but for some international settings some softwares use a comma as a decimal
separator. This is particularly true for Microsoft Excel. The amplitude data
can either be expressed on a linear or logarithmic scale. Sound level data is
mostly expressed in dB re 20 µPa i.e. on a logarithmic scale, and electrical impedance
data is expressed in ohms, i.e. on linear scale. Basta! assumes that frequency
in Hz appears in the first (leftmost) column, amplitude data in the second
column and phase information in degrees in the third column. Any additional
columns are ignored.
The Text
file import dialog. Be careful to select the settings so they match the file.
For the vented and bandpass boxes, one or more
vents are needed. This vent is considered as one or more cylindrical tubes with
a diameter and a length. This air mass in this vent will form a Helmholtz
resonator together with the cavity of the box. The diameter or cross-sectional
area Sp, and the resonance frequency fp is entered and
Basta! calculates the length of the tube.
Some of the free air on both sides of the port
adds to the oscillating mass, the actual port length needed is somewhat shorter
than the effective length. Both these lengths are calculated by Basta!, but
usually only the actual length is interesting for the box design.
If multiple vents are used, the diameter, Sp
and lengths numbers represent each one of the vents.
The vent can also have some resistive losses,
and these are entered by the Qp value. A higher Qp value
corresponds to smaller losses.
Like organ pipes, vent tubes have pipe
resonances in addition to the Helmholtz resonance. This resonance originates in
that the air in the tube is compressible, and that the tube behaves like a wave
guide. The resonances occur at frequencies where the tube length is an integral
number times the wavelength. Basta! can model these resonances by dividing the
tube in sections, and considering each of these parts having a mass and a
compliance. By entering a number of tube sections greater than zero, this model
is invoked. Typically 5-10 sections are sufficient to predict the behavior of
the first resonances. Note: Compared to measured data on real systems, Basta!
seems to overestimate the amplitude of the resonances, probably due to that
some losses that occur at high frequencies in the real world are not included
in the Basta! model. Nevertheless, the frequencies of the resonances that
Basta! predicts are accurate if the number of sections is high enough.
Ideally, the vent tube behaves like an acoustic
mass in the frequency range of interest. However, the behavior of a real vent
changes when the amplitude becomes too high. The mechanisms behind vent
overloading are very complex and in critical designs the tube should not be
made a cylindrical tube with sharp edges but rather have smooth, rounded edges
at both openings. Anyway, there is a level at which the tube stops behaving
like a mass, and critical factors determining this level is the excursion and
velocity of the air mass.
The excursion and velocity can be given limits
for the calculated maximum output level (MOL) of the system. The max peak
excursion can be entered either in millimeters, or relative to the actual port
length. The latter ensures that a certain percentage of the port air mass stays
inside the tube during the oscillatory cycle.
In cases when the tube length becomes
impractically long, i.e. when pipe resonances occur at a too low frequency, a
passive radiator can be considered instead. Typically, this occurs in small
boxes tuned to low frequencies, and when a high maximum output level is
desired. A passive radiator is as an ordinary loudspeaker element, but without
the electromagnetic driver motor. Passive radiators commonly have a longer
maximum linear cone excursion, Xmax, than a driver.
For the passive radiator, Basta! needs an extra
parameter, Vas. Just as with a driver, Vas determines the
suspension compliance of the passive radiator. The compliance, combined with
the moving mass gives the passive radiator a free air resonance frequency,
which typically occurs at least one octave below fp. Basta!
calculates the moving mass needed to get the desired fp. Passive
radiators often have the option of adding an extra mass to the cone, so
adjustment of the mass is possible.
The velocity and excursion limits applied to the
vent tube can also be applied to the passive radiator. The velocity limit is
rarely useful, but the excursion limit should be set to the Xmax of
the passive radiator.
For the Show kr=1 checkbox, see
the Driver tab
For bandpass boxes with two vents, there is a
nearly identical second tab for the second vent.
The Vent / Passive radiator tab. The first
panel illustrates a vent with a cross-sectional diameter of 50 mm tuned to 35
Hz, the other panel a passive radiator with an equivalent piston area of 200 cm2,
tuned to 35 Hz. Note that red text under Max peak excursion, indicating that it
is inappropriate to enter the max excursion relative to the port length, since
a passive radiator does not have a port length. The absolute setting should be
selected instead and the Xmax value for the passive radiator should
be entered under Absolute.
“Room gain”
is a term frequently used term for the boost of low frequencies that occur when
a sound source is placed in a room. Simulating this gain accurately is
difficult (but possible with other software) and it is questionable if it even
is desirable for the loudspeaker designer. Mostly, the room in which the
loudspeaker is to be used is not known and it is even more unlikely that the
exact placement in that room is known. Furthermore, there are psychoacoustical
aspects that might make a complete compensation for the transfer function from
the loudspeakers to the listening position less desirable.
The
approach to consider room gain in Basta! is to approximate an average low
frequency boost by a pole pair and a zero pair. The default values in Basta!
might be considered as a sensible gain to compensate for in an average
listening room.
Acknowledgements
goes to Ingvar Öhman for fruitful discussions on the default values.
The room
gain tab. Here two poles are placed at approximately 80 and 17 Hz, and two
zeroes both at 80 Hz. In this case one pole cancels one zero since the have
(nearly) the same frequency.
On the
Internet, several design formulas can be found that determine the box volume
and tuning. Three of these are implemented in Basta! on the Design suggestion
tab at the request of the users. These equations originate from a time when
computer simulations were rare and loudspeakers were designed with a calculator
at best. They do not consider important factors such as voice coil
inductance, room gain or the baffle
step, which in turn makes their results deviate from an optimal design.
Nevertheless, they can serve as starting points, keeping in mind that it is
usually worth tweaking the design further.
Basta can calculate some 20-40 curves for the systems depending on the box type. Displaying them all at the same time would however be slightly confusing. Therefore, it is possible to show only the curves of interest. Which curves that are displayed are selected on the Curves tab.
The
Curves tab. With this setting, the four selected curves will appear in the
response graph.
Each of the curves in the response graph can be displayed using different style, width and color. An appearance can be saved as a Color scheme, which will contain the style, width and color for each curve. By default the curves of a system are displayed in a preset color scheme suitable for viewing a single system, but when viewing more than one system it is often preferable to assign each system a unique color instead. Such color schemes can be downloaded from Tolvan Data, by the download button.
Note: If
the line width greater than one, the style can only be a solid line on most
graphic drivers.
The
Appearance tab.
Any text can be entered on the comment tab.
The
comment tab.
In the response window,
the results of the Basta! simulations are presented. It can contain 1 to 3
graphs; group/phase delay, phase and amplitude. If all three are visible, the
upper panel contains group and/or phase delay information, the middle panel
contains phase information and the lower panel contains amplitude information.
The two upper panels
can be hidden from the view options dialog on the tools menu. The grid in the
response graph can belong to any of the y-axes, to select a grid, drag the
corresponding axis. The frequency and the amplitude of the currently selected
y-axis at the cursor are displayed on the status bar at the bottom of the
window. Click in the graph move the cursor and show the values. If a curve is
selected on the curves tab, the value of that curve at the cursor frequency is
also shown and the cursor snaps to that curve.
The response is
automatically redrawn as values are changed, but this feature can be switched
off on the Response menu. This is particularly useful when the system
configuration is computationally demanding, for example when the number of
sources in the baffle designer is high. In that case the curves can be redrawn
manually by clicking on Response|Plot now!.
A legend identifying
the systems can be shown in the lower panel, indicating the color and style of
the “System response” curve of each system.
The response window. The impedance axis is
selected, and the impedance grid is therefore active. The mouse cursor is
located at 36.8 Hz / 4.995 W. Since the system response curve
was selected on the curves tab, the system response at 36.8 Hz is also shown as
83.92 dB.
The scales of the axes can be changed by dragging them with the mouse. Each scale has three zones, which will result in different changes when dragging the mouse.
The three different zones of the level
axis. Each zone is indicated by the change of the cursor. If the mouse button
is pressed on the lower zone, the axis is stretched/shrinked with the topmost
value of the axis fixed. The opposite applies in the topmost zone. The mid zone
is used to drag the entire scale up/down, without stretching/shrinking.
The settings for the response window can be changed by selecting Tools|view options on the menu.
The response window transparency can make the windows transparent, which is very useful for comparing the Basta! simulations with results or measurements from other programs. When the window is transparent, it can be put on top of other windows, and with proper axis adjustment, the curves of Basta! can be compared to those in the other window. To make such comparison possible, all amplitude axes, except for the level axis, can be set to be either linear or logarithmic.
To show the phase phase delay or group delay of the curves in the response window, check the corresponding checkboxes. If group delay is shown, a line can be drawn at the delay d=0.8/f , which is an approximation of the audibility threshold in the range 20-200 Hz.
Finally, a sum of systems can be shown; this is useful for designing loudspeaker systems with different speakers for different frequency ranges (woofer, tweeter etc.). The responses of the selected systems are added, including phase, and if they do not contain active filters, they are included in an impedance curve too.
The View
options dialog.
Below the curves in the response graph are described. They are described for a vented box, but the descriptions are in most cases valid for the other box types as well, when the curves exist.
In the vented box, the system frequency response is the sum of the response from the driver and the vent. The system response is probably the most interesting curve that Basta! generates.
The System response (black) / Driver response
(solid blue) / Vent response (dotted blue) / Electrical impedance (dashed
green). It can be seen that the vent
response has a peak at 35 Hz, which is fp for the vent. Above this frequency,
the contributions are in-phase and the system response becomes greater than the
individual contributions. Below fp, they are out of phase, and the
system response level becomes lower than the individual levels.
The cone velocity and displacement. While the cone velocity is mostly of academic interest, the cone amplitude is a very important property that often determines the maximum output level from a system at low frequencies.
The driver velocity (yellow) and excursion
(red). Both curves have a minimum at the resonance of the vent, fp.
This is one of the benefits of the vented system; the cone excursion does not
have to be as large as for a closed box.
Similarly to the driver, the velocity and displacement of the vent can be shown. Both of these are important for the maximum level that the port can generate.
The vent velocity (yellow) and excursion (red).
The vent velocity has a maximum at fp.
The baffle step is a 6 dB rise towards high frequencies, and the details of the response depend on the size and geometry of the baffle and the placement of the driver. The vent baffle step is mostly of little importance since the vent contribution is small for high frequencies. Here, the vent is only simulated with a single point source, which in turn results in an unimportant ripple towards high frequencies.
The driver (solid gray) and vent baffle step (dotted).
The pressure inside the box is interesting for two reasons. Firstly, a very high box pressure can be a source of distortion, secondly, the box pressure has a very close relation to the radiated sound at low frequencies, and a measurement of the pressure inside the box with a microphone can be used as a verification of the response of the system. Such a measurement is valid below the lowest box resonance, corresponding to the largest dimension of the box. The box pressure can be very high, particularly in small boxes and at low frequencies. Since levels above 140 dB are common, you should either make sure that the microphone can handle these levels, or lower the signal to a sufficiently low level.
The box
pressure (light blue). Note the large level difference between the inside and
outside of the box at low frequencies. At 35 Hz, the box pressure level reaches
140 dB. Still, the level outside the box, at 1 m distance, is only about 83 dB.
The electrical impedance shows the impedance of
the system, including the passive filter and advanced network. This impedance
can be divided in a resistive part and a reactive part. The reactive part
becomes negative if the impedance is capacitive.
The
electrical impedance (green), resistance (red) and reactance (blue).
The reactive part of the impedance can be interpreted as a frequency-dependent inductance. For example, it is common for manufacturers to measure the voice coil inductance as the reactive part of the impedance at a certain frequency, e.g. 1 kHz. While this interpretation of the reactance can be illustrative and useful for determining the value to enter in the Le box, a comparison with a measured impedance curve is far better.
The
reactive part of the impedance interpreted as an inductance (blue). Note that
when the impedance is capacitive, the resulting inductance appears as negative.
The
reactive part of the impedance interpreted as an inductance (blue)(magnified).
An inductance measurement of this driver at 1 kHz would result in about 0.41
mH, but at 10 kHz the result would be about 0.24 mH. This illustrates that the
voice coil inductance varies with frequency and that Basta! can model it.
The room gain
approximation typically results in a bass lift of some 10 dB at the lowest
audible frequencies. This gain can be displayed as a separate curve in the
response window.
Room
gain (thin curve).
The
Linkwitz transform adds a gain at low frequencies by means of an active circuit
before the power amplifier. The effect on the frequency response of the system
is very similar to that on the room gain tab, but in this case also the voltage
from the power amplifier is changed. More information on the Linkwitz transform
and its implementation is available on http://www.linkwitzlab.com/ and on several other sites on the web.
Linkwitz
transfom (thin curve)
Basta! can calculate the maximum output level (MOL) that the system can deliver. This level is based on five limits that can be set individually, and MOL is the maximum level at which neither of the limits is superseded. The MOL curve does not represent actual frequency responses, but simply the highest level of sound that can be produced at different frequencies without exceeding any of the limits.
The
maximum output level (gray).
This curve shows the voltage required at the driver in order to reach MOL. If there is no passive filter or advanced network, this curve is identical to the amplifier voltage at MOL (which otherwise can be shown as a separate curve).
The
driver voltage at MOL (green).
Basta! can
show the cone excursion and velocity at the maximum output level of the system.
The cone
excursion (red) and cone velocity (yellow) at MOL. It can be seen that the cone
excursion reaches the maximum allowed excursion (Xmax) below 28 Hz and
between 45 and 120 Hz. From this it is clear that the cone excursion limits the
maximum output of the system at these frequencies.
Basta! can
show the vent excursion and velocity at the maximum output level of the system.
The vent
excursion (red) and velocity (yellow) at MOL. The velocity reaches its maximum
allowed value between 28 and 45 Hz, and from this it can be seen that the port
velocity limits the maximum output level of the system in this range.
Basta! can show the sound pressure level inside the box at the maximum output level of the system. This level can become very high. This is important since the air itself can become non-linear, causing distortion. Also, high SPL inside the box can make the suspension of the cone behave unpredictable due to the high forces from the pressure difference on the in- and outside of the suspension. Thus it is recommended to keep this level reasonably “low”, typically below 160 dB.
Box pressure at MOL. For this system, the box pressure can exceed 150 dB at 45 Hz.
The MOL for the system is based on five limits. One way of viewing the effects of the limits is the MOL. Another way is the margin between the limit and what is used for the simulation. For example, if the power amplifier generates 2.83 volts and has a limit of 283 volts, the margin is 100 times or 40 dB. Such a margin exists for each of the five limits.
Margins. The figure shows the margin for power
amplifier voltage (green), cone excursion (solid red), vent velocity (yellow)
and excursion (dotted red) and Re power (dashed black). The gray
curve shows the lowest value for all the margins and determines the MOL for the
system together with the response curve (solid black).
If there are passive filters or an advanced
network present, the driver voltage will be different from that of the voltage
source. If the filters are active or if AC-bass is invoked, the amplifier
voltage will also be altered. These voltages can be shown by the driver voltage
/ amplifier voltage
Driver
(lower green) and amplifier (upper green) voltage. This system has an active
highpass filter at 300 Hz and a passive lowpass filter at 2000 Hz to
demonstrate the differences between the curves.
The constants dialog box includes the speed of sound and density of air. These values rarely need to be changed. The Significant digits setting changes the number of significant digits that are displayed for values calculated by Basta!. The repaint delay is a delay between entry of numbers and the start of a recalculation of the response curves.
The
constants window.
While Basta! can simulate many of the aspects
that are important in loudspeaker design, there are also a few things that are
not considered in the simulations. In particular, these issues should be kept
in mind:
Above a certain frequency, the cone of the
loudspeaker driver stops acting like a rigid piston. This leads to that different
parts of the cone oscillate at different phase and the response of the driver
becomes irregular. The resulting response is dependent on the design of the
driver, and in particular the propagation speed of waves within the cone, the
cone size and losses in the membrane and suspension.
Basta! does not model this phenomenon, which
leads to a discrepancy at high frequencies between the actual driver response
and the response modeled by Basta!. Using the transparency feature of the
response window and response graphs published by the manufacturers can reveal
these differences, such that they can be considered during the design process.
Basta! does not model the effects of
reflections of a particular room, except for those from the back wall for wall
mounted loudspeakers. However, Basta! can approximate an average room; this
room is represented as a smooth bass lift without the resonant behavior of
typical rooms. After all, this is what the loudspeaker designer typically
wants; loudspeakers should rarely be optimized for a particular room and a
particular placement within that room.
Resonances inside the box can cause changes in the response curve of the loudspeaker system. Such resonances can be avoided, either by adding a sufficient amount of damping material in the box or filtering out frequencies at which resonances occur (e.g. by a lowpass in a subwoofer). Basta! does not model box resonances.
Basta! assumes a cylindrical tube for each vent
of the vented and bandpass boxes. There are, however, good reasons to use other
shapes of the vent, eg flanged ends and/or multiple tubes. Basta! provides no
help to convert between these types of vents. The effects of different cross-sectional
area shapes is however, rather easy to approximate; just enter the total area
of the vent(s) under Sp and use the suggested port length for the
tube(s). After building the system, the tuning can be verified by comparing the
simulated electrical impedance with measurements.
The edge sources used in the Basta! simulation of diffraction does not have any directivity. This is perfectly ok for locations straight in front of the baffle, and actually rather far to the sides too. However, as the microphone position approaches the 90° direction, there will be serious discrepancies between the simulation and reality. This is particularly true for open baffle simulations; the reduced level to the sides due to dipole directivity at low frequencies (the “8”) does not appear in the Basta! simulations.
Basta! only models the small-signal, linear behavior of the system. However, the limits for the amplifier, driver and vents provide a reasonably powerful way to keep the non-linearities under control.
First
release.
Added
features:
·
A
checklistbox for selection of which systems that are to form the system sum.
·
Unit
for coils and capacitors in advanced network are now mH an µF.
·
The
automatic replot of the Response window can be disabled. This is useful for
complex systems that take a long time to redraw.
·
User
is informed at first run on a system that Basta! checks for new versions
automatically. Users with a firewall just got a notice that Basta! does
something on the Internet, which may appear suspicious. The autocheck feature
can be permanently switched off on the Help menu.
·
Saving
of .basta files is now allowed also in the demo version.
·
Bug
fix: Bad behavior of the advanced component list when switching between systems
fixed.
·
Bug
fix: Automatic update tended to indicate a new version when there was none.
Fixed.
·
Added
aspect ratio adjustment to 25 dB/decade of the response window to the response
menu. Clicking on this option sets the aspect ratio of the response amplitude
graph to the same as “The” classical paper size. This allows for easy visual
comparison between curves.
·
Back
wall reflection. This feature is necessary for designing wall-mounted speakers,
since the back wall reflection occurs near (in time) to the direct sound from
the loudspeaker.
·
Added
display of group delay.
·
Added
display of phase delay.
·
Bug
fix: Phase response of the sum of systems contained all systems listed in the
“show sum of these systems” listbox, not only the checked ones. Fixed.
·
Removed
the feature back wall for the open baffle. This was available in 1.0.2.0, but
produced inaccurate results.
·
Added
Viso, which represents the isothermal effects that makes the box
appear bigger due to stuffing.
·
Added
groups for data input. The groups are fs-Mms-Cms-Vas-Sd
and Bl-Re-Qes-Rms-Qts and the
parameters within these groups are interdependent. Which parameters that should
be entered is selectable with checkboxes, and the other ones are calculated by
Basta!.
·
Other
minor bugs and quirks fixed.
·
Used a
newer version of the complier; this fixes some minor OS specific errors.
·
Multiple
systems are shown in the baffle designer.
·
Output
impedance Rg of the amplifier (before the voltage margin).
·
Design
suggestions using three different commonly found design formulas.
·
Room
gain approximation.
·
The
response window is now completely non-transparent when the “response window
transparency” slider is in its rightmost position (some screen grabbers had
problems otherwise).
·
A
cursor is now present in the response window.
·
Curve
colors are now saved with the systems.
·
Legend
in the response graph and the systems list box.
·
Axis
ranges are now saved between sessions
·
Slight
adjustment of constants to more accurate values at 20 °C (c=343.6 m/s, r0=1.204 kg/m3).
·
Minor
fixes of hint texts.
·
The
mouse scroll wheel can now be used to zoom in the baffle designer.
·
Fixed
a bug concerning file names during save.
·
Fixed
a bug concerning the microphone position in baffle designer.
·
Fixed
a bug, Qes sometimes became zero when loading a system or driver from file.
·
The
<unknown> design suggestion was replaced by that of Margolis/Small, which
produced nearly identical results.
·
Added
support for multiple vents
·
Added
entry of vent diameter
·
Added
support for Linkwitz transform
·
The
volume of air enclosed by the vent(s) is now shown.
·
Added
support for source density>1 also for vents; this enables simulation of
close-field measurement of vents.
·
Added
individual microphone distance to each system. This enables comparison between
measurement distances
·
Export
of response curves to text files
·
Added
selection of font for the axes in the response window
·
Added a
“Reverse polarity” checkbox on the driver tab
·
The
sensitivity of a driver is shown on the driver tab
·
Qb is
considered for the Q in box value
·
New
color schemes are now available with more colors
·
Added
a delay for updating curves; Basta! now waits approximately 1 s to update
curves in order to avoid frequent redrawing.
·
Moved
baffle designer settings to the baffle designer
·
Fixed
quirk that caused multiple updates, slowing down the redraw procedure
·
Fixed
a flaw in how co-oscillating air was calculated. The difference is small
however, typically within tenths of a dB.
·
Fixed
a bug in opening of .bastaelement files.
·
Changed
clipboard copy shortcut of response data from ctrl-c to ctrl-e, since ctrl-c
prohibited copy between parameter entry fields.
·
Added
a “change all colors” button to the appearance tab.
·
New
file format. Basta! Can still open and save in the old format, but older
versions cannot open the new format.
·
Added
saving/restoring of response window settings.
·
Added
ability to increase/decrease most numerical values with the up/down keys on the
keyboard.
·
Fixed
a bug in recently used file lists for window settings and basta files.
·
Fixed
a bug in file format for window settings.
·
Improved
the increase/decrease functionality.
·
Last
free update for Basta! version 1
·
New
version
·
Added
support for importing measured data from Sirp and text files.
·
Improved
support for text file import
·
Bug
fix: Basta! remembered the .basta file location even if a file was moved to
another computer and saved it in that location on the new computer, rather than
where it was opened from.
·
Fixed colors
of legend for measured systems so that the color of the first measured curve is
shown.
Some older computer systems experience BSOD (blue screens) when Basta! is run. See http://www.tolvan.com/blue_screen_Q_A.htm. I am very interested in having reports from those of you who experience this. I am particularly interested if the test program on the page above (http://www.econos.de/fpu) also causes your system to crash. Note: As time has passed, this appears not to be a problem anymore; nowadays I hardly ever get any reports regarding this.