The Edge

Technical
documentation

2006-02-19

© Tolvan Data
2004-2006

The Edge program is a baffle diffraction simulator.
Typically it is intended to use for estimation of the "baffle step" that occurs
when a loudspeaker is mounted in a baffle of finite size. It is common that the
baffle step is approximated with a pole-zero pair to approximate the 6 dB raise
towards higher frequencies. The Edge uses the geometrical theory of diffraction
(GTD) to estimate this transition better.

The Edge is and will probably
remain a pure baffle diffraction simulator. The results from the Edge should of
course be added to other properties of a loudspeaker system, such as those
described by Thiele-Small and others and also the effects of crossover filters
etc, such as can be done in the Basta! loudspeaker simulator (http://www.tolvan.com/basta).
The Edge can simulate a simple baffle step compensation, or an open
baffle bass drop compensation, but that is probably as far as the development
will go. The edge can also export the response data in text format, for further
use in other programs.

The Edge has a home page at http://www.tolvan.com/edge

Suggestions and opinions both
on the program and this documentation are happily accepted by [email-masked]

Baffle
designer

With the baffle designer, the
dimensions of the baffle are entered into the Edge, the loudspeakers are placed
on the baffle and the microphone is placed in front of the speaker system. The
baffle shape is determined by a number of corners, and they can either be
dragged with the mouse to for the shape of the baffle, or they can be moved to
form a baffle with a width and height as defined in the "size" group box.

Figure 1. A baffle of size
300 x 500 mm, with the loudspeaker placed slightly to the right. The Edge models
this particular system by means of one point source at the speaker centre
(blue), and 36 sources (green) of opposite sign at the baffle edge (red). The
microphone is in the far field (100 m away), so the positioning of the "mic"
symbol has little effect in this case.

Up
to 50 drivers can be placed on the baffle, and each of these is modelled by a
set of point sources and their mirrors. The "speaker source density" spin box
determines the number of point sources used per driver. Increasing this number
is essentially a way of modelling the speaker directivity. It does not, however
include cone break-ups, since all of the sources are of equal magnitude and
phase. Each of these point sources has an amplitude of 2, corresponding to the
sources and their mirrors. For each of these sources, a number of edge sources
are placed along the edge of the baffle. The sum of these sources has an
amplitude of -1. The edge sources are distributed along the edge of the baffle
such that each edge source represents the same angle, as seen from the driver
source(s). As can be seen in Figure 1, this method automatically results in a
higher edge source density when the driver is placed near the baffle edge and
that each source can have the same amplitude. In the case of the open baffle the
amplitude of the edge sources is doubled, to model the diffracted radiation from
the back of the driver. The number of sources used in the simulation can be
large, and this may slow down the calculation of the response. Some
experimenting with the number of edge sources and speaker source density is
recommended. In general, a higher number of sources are needed for a more
accurate simulation of higher frequencies. The response is normalized so that
the sum of all driver sources corresponds to 0dB if they had been located at the
same distance to the mic.

Driver shape

The
driver shape option can be used to simulate drivers of circular, elliptical,
square and rectangular shaped membranes. In order for the shape option to have
any effect the "Speaker source density" has to be 2 or larger. The Edge spreads
out a number of point sources over the area covered by the membrane. The
rectangular shape can also be used to approximate an array of equally spaced
loudspeakers. This might be convenient during the design process, since the
whole array easily can be moved on the baffle as if it was one
speaker.

Response

To
simulate the frequency response of the system, all of the point sources are
added taking the distance to the microphone into consideration. The distance
will affect both the phase and magnitude of each contribution to the summed
signal. The resulting frequency response is shown in the response
window.

Figure 2. The response of
the system in figure 1 (red). This graph shows the response as a function of the
frequency. Above the graph, the wavelength is also shown. The blue curve shows
the effect of compensation, which is not used in this case.

Note: To change the axis
scaling, simply drag it with the mouse. There are three zones on each axis,
which enable either stretching or moving of the scale.

The help menu in this window
can open the home page of the Edge. Here you can find this document and also
download the latest version of the Edge.

Compensation

The Edge can apply two types
of compensation to the response curve. The first is used for boxed systems, and
the other is used for open baffle systems. There are other circuit
configurations than the suggested ones that give identical responses.

Figure 3. Compensation of
the diffraction effects. The Edge can simulate the effect of two commonly used
types of diffraction compensations.

Baffle step

For boxed systems, it is
common to compensate for the baffle step by means of a pole-zero pair. In the
Compensation designer such a pole-zero pair can be entered as the "corner"
frequencies f1 and f2 in the response. By entering a resistor value, R1, some
help is provided to design the compensations circuit. Either of circuit 1 or
circuit 2 can be used, circuit 1 is probably best fit for passive filters, and
circuit 2 is best fit for line level filters. The Edge suggests values for L and
R2 for circuit 1 and C and R2 for circuit 2.

The Edge can suggest values
for the f1 and f2 frequencies. It does so by numerically finding the frequency
where the far field baffle response has increased by sqrt(1.25/2) or
approximately 2 dB. The Edge takes this frequency as f1 and twice this
frequency as f2.

Open baffle bass loss

For the open baffle ("dipole
speaker") there is a tilt of the frequency response of 6 dB/octave. This can be
compensated for by an active line-level bass boost. The Edge can simulate the
effect of adding such a network. Like the baffle step compensation, this
compensation is added by entering two "corner" frequencies, f1 and f2. The lower
frequency f1 will be the lower frequency limit of the system (neglecting the
response of the driver), and f2 should be set to the start of the bass drop of
the baffle design. Again, some design help is provided if the resistance R1 is
given, the Edge suggests value for C and R2.

The edge can also suggest a
value for f2. It does so by numerically finding the far field response for 0.1
Hz, and extrapolating by a slope of +6 dB/octave up to the frequency where this
slope reaches +6dB.

Example

I will here describe the
process of using the Edge for simulating a baffle design. We start out with a
single driver is placed on the middle of a 300 x 300 mm baffle. The driver is
modelled by 44 point sources, and 36 x 44 edge sources, a total of 1628 sources.
The response shows a peak at 1 kHz of almost + 9 dB before flattening out at + 6
dB towards higher frequencies.

Attempting to compensate this
baffle design with a pole-zero pair essentially fails, due to the large peak at
1 kHz. The peak remains, but the higher frequencies are successfully brought
down to 0 dB.

The Edge suggests two different compensation circuits,
circuit 1 is suited for passive realization in the crossover, in this case the
driver should be connected in series with L and R2 in parallel. Selecting a
driver impedance of 6 ohms gives that R2 = 6 ohms, L = 2.653 mH. Note that the
impedance of a real driver is not resistive, so there might be some deviances
here. Circuit 2 is more suited for line level connection Selecting R1 to 10000
ohms gives that R2 and C should be 10000 ohms and 44,21nF respectively.

Positioning the driver(s)

Moving the driver to a more
asymmetric position greatly reduces the peak height, now the peak height is only
about 1.5 dB after compensation. Experimenting with the baffle shape and driver
placement can possibly reduce the peak even more. Finally, it should be
remembered that other parts of the loudspeaker system may actually be
compensated by a leftover peak, so the absolutely flat diffraction
response is not always the goal.

Microphone

The microphone position is
given by the "mic distance" and the positioning of the "mic" symbol in the
baffle designer. The mic distance is given in meters, and the default distance
is 100 m, which is about the same as "far field". The mic distance is the
perpendicular distance (z coordinate) between the baffle plane and the
microphone. The x and y coordinates are given by the placement of the mic
symbol.

It should be noted that if the
distance is not very much larger than the baffle size, the baffle step will not
be a full 6 dB. For example, a square 250-by-250 mm baffle will only exhibit a
~5 dB step at a microphone distance of 0.25 m. The reason for this is the
longer pathway from the edge to the microphone. The longer distance combined
with the distance law will reduce the sound pressure produced by the edge
sources relatively more at close range. This is true also in real life and is
particularly visible when making extreme close field measurements, where the
baffle step is hardly visible at all.

The bottom line here is that
the microphone distance should be set to a normal listening distance (usually ~4
m) when designing a system, but it should be set to the actual microphone
distance (usually ~1 m) when comparing to measurements if the comparison should
be valid. The default microphone distance is set to 100 m just to make sure that
the microphone is in the far field.

File
format

The baffle designs can be
saved to files. The files are of the windows standard ini type. This means that
the values stored in them can be modified with a text editor, such as notepad.
This may be useful e.g. if you prefer to enter numbers for the dimensions
instead of dragging symbols in the baffle designer.

Command line option

Start the edge from start|run
with the command line switch "/n" (without quotes) to start with a fresh baffle
design. This might be useful if the present design has become irreparably
complex J,
or if any of the windows have ended up outside the screen etc.

History

Version 1.0

-First version based on the experimental program
diffract.exe

Added in version
1.1:

-In addition to circular
drivers, it can now also simulate elliptical, square and rectangular membrane
shapes.

-Multiple response curves can
be shown for comparison. The piece of ice on the toolbar freezes the current
curve.

-Redrawing is done without
recalculation if possible. This speeds things up a bit.

-Redrawing can be shut off.
For systems with many sources, the automatic redrawing was quite annoying.

Added in version
1.2:

-Display of phase.

-Rectangular shape distributes
sources at approximately equal x- and y-wise pitch.

-Notification when a source is
off the baffle.

-A "New" button.

-Placement of edge sources for
strange baffle shapes improved (bug fix)

-Sign of phase at export fixed
(bug fix)

Added in ver 1.3

-Frozen phase curves are now
OK when changing the mic distance (bug fix).

-Mic distance text box is now
updated when opening a system (bug fix).

-Background of frequency
response graph is greyed if sources are placed off the baffle.

Added in ver 1.4

-Suggestions of compensation
frequencies

-Export of compensated,
uncompensated and compensation curve.

Added in ver 1.5

- Hint text changed (+3dB
-> +2dB) for "Suggest f1 & f2" button.

- Correction of the way the
strength of the edge sources was calculated. Previously, the amplitude
reduction of the edge sources by the distance law included the driver-to-edge
distance. This was wrong, since this part has already been taken care of when
dividing the edge in sectors seen from the driver sources. A slight difference
from this change can be seen when the microphone distance is near or shorter
than the dimensions of the baffle. The effect of the change is a lowered level
at low frequencies in the new version.

-The minimum number of
corners, edge sources and speaker source density is now 1. This makes the
editing of these values slightly more well-behaved, even though there still are
issues (which are related to the implementation of the spinedit control in
Delphi).

Added in ver 1.6

-Automatic check for new versions. The Edge now
automatically checks http://www.tolvan.com/edge for a new version if the
computer is connected to the internet. This check is run when The Edge is
launched, but no more than once a day. You can disable this function from the
help menu.

-Fixed a minor bug regarding redrawing after opening a
file.

Added in ver 1.7

-Added information about why The Edge accesses the internet
(to check for new versions as introduced in ver 1.6) on first startup.

-Added a “donate” item in the help menu for users who want
to contribute to the development of The Edge.

-Added a “Basta! loudspeker simulator home page!” item to
the help menu. This change was added 2006-02-09.

Added in ver 1.8

-Added copy of the response image

Known problems

-Strange baffle shapes (like
"L" shape or "T" shape), where several edges can be "seen" by the source for a
given direction, only the first edge is modelled.

-Some computer systems
experience BSOD (blue screens) when The Edge 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.

© Tolvan Data 2004 - 2006