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

rect_in_rect [options... ] W H a b c d w h Er1 Er2

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‐X.Y.Z/docs/html‐docs
directory for them.

rect_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_in_rect is
used as a fast way of generating bitmaps (there is no need
to use a graphics programme), for a rectangular conductor
inside a rectangular conductor, like this:
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  ^
|                                                   |  |
|     <‐‐‐‐‐‐‐‐‐‐‐‐‐‐d‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐>          |  |
|                                                   |  |
|         <‐‐‐‐‐‐‐‐‐‐w‐‐‐‐‐‐‐‐‐‐‐>                  |  |
|         ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐   ^              |  |
|         |                      |   |              |  |
|         |  Metallic conductor  |   |              |  H
|<‐‐‐‐b‐‐>|  conductor (can be   |   c   Er1        |  |
|         |  off‐centre)         |   |              |  |
|         |                      |   |              |  |
|     ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ ^        |  |
|     |..................................| |        |  |
|     |...Dielectric, permittivity=Er2...| |        |  |
|<‐a‐>|.....(can be off centre ).........| h        |  |
|     |..................................| |        |  |
|     |..................................| |        |  |
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  |

The parameters ’W’ and ’H’ and the inner dimensions of the
outer conductor.  The outer dimensions of the inner
conductor are ’w’ and ’c’. The inner conductor is assumed to
rest on a dielectric (Er2) which is ’d’ wide and outer
conductor an the inner conductor is offset ’b’ from the left
hand sidewall of the outer conductor. The whole region is
surrounded by a dielectric of relative permittivity ’Er1’.
The dielectrics ’Er1’ and then ’Er1’ and ’Er2’ will both be

     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_in_rect W H a b c d w h Er1 Er2 > filename.bmp OR
rect_in_rect ‐f filename.bmp W H a b c d w h Er1 Er2
The bitmaps produced by rect_in_rect are 24‐bit bit colour


bitmaps, as are required by atlc.

The permittivities of the bitmap, set by ’Er1’ and ’Er2’,
determine the colours in the bitmap. If Er1 or Er2 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 Er1 is
not one of those permittivities, the region of permittivity
Er1 will be set to the colour 0xCAFF00. If Er2 is not one of
those values, then the region of the image will be set to
the colour 0xAC82AC. 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_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).


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 0x0000FF 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)
L. 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    (polystyrene)
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 0x696969 as Er=6.15   (duroid 6006)
L. gray   240,240,240 or 0xDCDCDC as Er=10.2  (duroid 6010)
D. orange 213,160,067 or 0xD5A04D as Er=100.0 (mainly for
test purposes)

Here are a few examples of the use of rect_in_rect. Again,
see the html documentation in atlc‐X.Y.Z/docs/html‐
docs/index.html for more examples.  In the first example,
there is just an air dielectric, so Er1=Er2=1.0.  The inner
of 1x1 inches (or mm, miles etc) is placed centrally in an
outer with dimensions 3 x 3 inches.

The exact place where the dielectric starts (a) and its
width (d) are unimportant, but they must still be entered.

% rect_in_rect 3 3 1 1 1 1 1 1 > ex1.bmp
% atlc ex1.bmp

In this second example, an inner of 15.0 mm x 0.5 mm is
surrounded by an outer with internal dimensions of 61.5 x
20.1 mm. There is a material with permittivity 2.1 (Er of
PTFE) below the inner conductor. The output from
rect_in_rect is sent to a file ex1.bmp, which is then
processed by atlc

% rect_in_rect 61.5 20.1 5 22 0.5 50 15 5 1.0 2.1 > ex2.bmp
% atlc ex2.bmp

In example 3, the bitmap is made larger, to increase
accuracy, but otherwise this is identical to the second
example.  % rect_in_rect ‐b7 61.5 20.1 5 22 0.5 50 15 5 1.0
2.1 > ex3.bmp


% atlc ex3.bmp
In the fourth example, materials with permittivites 2.78 and
7.89 are used. While there is no change in how to use
rect_in_rect, since these permittivities are not known, we
must tell atlc what they are.  % rect_in_rect 61 20 1 4 22
0.5 50 15 5 2.78 7.89 > ex5.bmp % atlc ‐d CAFF00=2.78 ‐d
AC82AC=7.89 ex5.bmp In the sixth and final example, the ‐v
option is used to print some extra data to stderr from

atlc(1), rect_cen_in_rect(1), circ_in_circ(1).
rect_in_circ(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