rect_cen_in_rect ‐ bitmap generator for rectangular
conductor inside rectangular conductor (part of atlc)

rect_cen_in_rect [options... ] W H w h Er

This man page is not a complete set of documentation. See
the html files for more complete information. So far, I’ve
not managed to install the html files into /usr/local, so
you will have to look into the atlc‐2.X.Y.Z/docs/html‐docs
directory for them.

rect_cen_in_rect is a pre‐processor for atlc, the finite
difference programme that is used to calculate the
properties of a two‐conductor electrical transmission line
of arbitrary cross section. The programme rect_cen_in_rect
is used as a fast way of generating bitmaps (there is no
need to use a graphics programme), for a rectangular
conductor placed centrally inside another rectangular
conductor, like this:
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  ^
|                                                   |  |
|            Dielectric, permittivity=Er            |  |
|                                                   |  |
|                                                   |  |
|                                                   |  |
|             <‐‐‐‐‐‐‐‐‐‐w‐‐‐‐‐‐‐‐‐‐‐>              |  |
|             ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐   ^          |  |
|             |                      |   |          |  |
|             |  Metallic conductor  |   |          |  H
|             |  conductor (must be  |   h          |  |
|             |  in  the centre)     |   |          |  |
|             |                      |   |          |  |
|             ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐   ^          |  |
|                                                   |  |
|                                                   |  |
|                                                   |  |
|                                                   |  |
|                                                   |  |
|                                                   |  |
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  |

The parameters ’W’ and ’H’ and the inner dimensions of the
outer conductor.  The outer dimensions of the inner
conductor are ’w’ and ’h’. The inner conductor is assumed be
be placed centrally inside the outer conductor. The spaced
between the two conductors is filled with a dielectric of
relative permittivity Er

     The bitmap is printed to standard output, which MUST be
re‐directed to either a file, or piped into the standard
input of atlc, in one of the following two ways.
rect_cen_in_rect W H w h Er > filename.bmp OR
rect_cen_in_rect ‐f filename.bmp W H w h Er


The bitmaps produced by rect_cen_in_rect are 24‐bit bit
colour bitmaps, as required by atlc.

The permittivity of the bitmap, set by ’Er’, determine the
colours in the bitmap. If Er is 1.0, 2.1, 2.2, 2.33, 2.5,
3.3, 3.335, 4.8 or 10.2, then the colour corresponding to
that permittivity will be set according to the colours
defined in COLOURS below. If Er is not one of those
permittivities, the region of permittivity Er will be set to
the colour 0xCAFF00.  The programme atlc does not know what
these permittivites are, so they atlc, must be told with the
comand line option ‐d, as in example 4 below.

‐b bitmapsize
is used to set the size of the bitmap, and so the accuracy
to which atlc is able to calculate the transmission line’s
properties. The default value for ’bitmapsize’ is normally
4, although this is set at compile time. The value can be
set anywhere from 1 to 15, but more than 8 is probably not

     ‐f outfile
Set the output filename. By default, the bitmap is sent to
stdout, but it *must* be sent to a file, with this option,
or as described above.  ‐v
Causes rect_cen_in_rect to print some data to stderr. Note,
nothing extra goes to standard output, as that is expected
to be redirected to a bitmap file.

The 24‐bit bitmaps that atlc expects, have 8 bits assigned
to represent the amount of red, 8 for blue and 8 for green.
Hence there are 256 levels of red, green and blue, making a
total of 256*256*256=16777216 colours.  Every one of the
possible 16777216 colours can be defined precisely by the
stating the exact amount of red, green and blue, as in:

     red         = 255,000,000 or 0xff0000
green       = 000,255,000 or 0x00ff00
blue        = 000,000,255 or 0x0000ff
black       = 000,000,000 or 0x000000
white       = 255,255,255 or 0xffffff
Brown       = 255,000,255 or 0xff00ff
gray        = 142,142,142 or 0x8e8e8e

     Some colours, such as pink, turquiose, sandy, brown,
gray etc may mean slightly different things to different
people. This is not so with atlc, as the programme expects
the colours below to be EXACTLY defined as given. Whether
you feel the colour is sandy or yellow is up to you, but if
you use it in your bitmap, then it either needs to be a
colour recognised by atlc, or you must define it with a
command line option (see OPTIONS and example 5 below).
The following conductors are recognised by atlc:


red    = 255,000,000 or 0xff0000 is the live conductor.
green  = 000,255,000 or 0x00ff00 is the grounded conductor.
blue   = 000,000,000 or 0x000000 is the negative conductor

     All bitmaps must have the live (red) and grounded
(green) conductor. The blue conductor is not currently
supported, but it will be used to indicate a negative
conductor, which will be needed if/when the programme gets
extended to analyse directional couplers.

     The following dielectrics are recognised by atlc and so
are produced by rect_cen_in_rect.

     white      255,255,255 or 0xFFFFFF as Er=1.0   (vacuum)
pink       255,202,202 or 0xFFCACA as Er=1.0006 (air)
light blue 130,052,255 or 0x8235Ef as Er=2.1   (PTFE)
Mid gray   142,242,142 or 0x8E8E8E as Er=2.2   (duroid 5880)
mauve      255.000,255 or 0xFF00FF as Er=2.33
(polyethylene) yellow     255,255,000 or 0xFFFF00 as Er=2.5
sandy      239,203,027 or 0xEFCC1A as Er=3.3   (PVC)
brown      188,127,096 or 0xBC7F60 as Er=3.335 (epoxy resin)
Terquoise  026,239,179 or 0x1AEFB3 as Er=4.8   (glass PCB)
Dark gray  142,142,142 or ox696969 as Er=6.15  (duroid 6006)
L. gray    240,240,240 or 0xDCDCDC as Er=10.2  (duroid 6010)
D. orange  213,130,067 or 0xD5A04D as Er=100.0 (mainly for
test purposes)
If the permittivity is one not in the above list, then those
parts of the image with Er will be set to 0xCAFF00.

Here are a few examples of the use of rect_cen_in_rect.
Again, see the html documentation in atlc‐X.Y.Z/docs/html‐
doc/index.html for more examples.  1) In the first example,
there is just a vacuum dielectric, so Er=1.0.  The inner of
1x1 inches (or mm, miles etc) is placed centrally in an
outer with dimensions 3.3 x 3.9 inches.

% rect_cen_in_rect 3.3 3.9 1 1 1 > 1.bmp
% atlc 1.bmp

2) In this second example, an inner of 15.0 mm x 5.0 mm is
surrounded by an outer with internal dimensions of 71.5 x
60.0 mm. There is a material with permittivity 2.1 (Er of
PTFE) around the inner conductor. The output from
rect_cen_in_rect is sent to a file 2.bmp, which is then
processed by atlc

% rect_cen_in_rect 71.5 60.0 15.0 5.0 2.1 > 2.bmp
% atlc 2.bmp

3) In example 3, the bitmap is made larger, to increase
accuracy, but otherwise this is identical to the second
example.  % rect_cen_in_rect ‐b7 71.5 60 15 5 2.1 > 3.bmp
% atlc 3.bmp


In the fourth example, instead of re‐directing
rect_cen_in_rect’s output to a file with the > sign, it is
done using the ‐f option.
% rect_cen_in_rect ‐f 4.bmp 61.5 28.1 5 22 2.1
% atlc 4.bmp

atlc(1), circ_in_circ(1). rect_in_rect(1), circ_in_rect(1).
rect_in_circ(1), readbin(1) and sym_strip(1).                ‐ Home page       ‐ Download area
atlc‐X.Y.Z/docs/html‐docs/index.html       ‐ HTML docs
atlc‐X.Y.Z/docs/qex‐december‐1996/atlc.pdf ‐ theory paper
atlc‐X.Y.Z/examples                        ‐ examples
http://www.david‐              ‐ my home page
http://www.david‐          ‐ ham radio pages