## NAME

         circ_in_circ  -  bitmap  generator  for  circular  conductor
         inside circular conductor (part of atlc)

## SYNOPSIS

         circ_in_circ [options... ] D d O Er

## WARNING

         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.

## DESCRIPTION

         circ_in_circ is a pre-processor for atlc, the finite differ-
         ence programme that is used to calculate the properties of a
         two-conductor  electrical  transmission  line  of  arbitrary
         cross  section. The programme circ_in_circ is used as a fast
         way of generating bitmaps (there is no need to use a  graph-
         ics  programme),  for a circular conductor inside a circular
         conductor (coaxial conductors), like this:

                             *****************
                         ****                 ****
                      ****    <-----d------>     ****
                    ***            *****            ***
                  ***           ***********           ***
                ***            *************            ***
               ***            ***************            ***
              ***      ^      ***************             ***
             ***       |      ***************              ***
            ***        |       *************                ***
            **         O        ***********                  **
           ***         |            ***                      ***
           **          |                                      **
           *<------------------------D------------------------>*
           **                                                 **
           **                                                 **
           **                                                 **
           ***                                               ***
            **                                               **
            ***                                             ***
             **                                             **
              **                                           **
               **                                         **
                ***                                     ***
                 ****                                 ****
                   ****                             ****
                     *****                       *****
                        ******               ******
                            *******************
                                    ***

         The parameter 'D' is the inner dimensions of the outer  con-
         ductor and 'd' is the outer diameter of the inner conductor.
         The inner conductor is offset 'h' from  the  centre  of  the
         outer conductor. The whole region is surrounded by a dielec-
         tric of relative permittivity 'Er'.

         The bitmap is printed to standard output, which MUST be  re-
         directed to either a file in one of the following two ways.

         The bitmaps produced by circ_in_circ are 24-bit  bit  colour
         bitmaps, as are required by atlc.

         The permittivities of the  dielectric  'Er'  determines  the
         colours  in the bitmap. If Er is 1.0, 1.006, 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  permit-
         tivities,  the  region of permittivity Er will be set to the
         colour 0xCAFF00. The programme atlc does not know what  this
         permittivity is, so atlc, must be told with the command line
         option -d, as in example 4 below.

## OPTIONS

         -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
         sensible.

         -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 circ_in_circ to print  some  data  to  stderr.  Note,
         nothing  extra  goes to standard output, as that is expected
         to be redirected to a bitmap file.

## COLOURS

         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 pos-
         sible 16777216 colours can be defined precisely by the stat-
         ing 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 circ_in_circ.

         white     255,255,255 or 0xFFFFFF as Er=1.0   (vacuum)
         pink      255,202,202 or 0xFFCACA as Er=1.0006 (air)
         blue      000,000,255 or 0x0000FF 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)
         Turquoise 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)

## NOTE

         Although circ_in_circ is used for circular inner  and  outer
         conductors, the outside of the outer conductor is drawn as a
         square. This is for convenience and makes no  difference  to
         the  calculations.  The  inside is of the outer conductor is
         drawn as a circle.

## EXAMPLES

         Here are a few examples of the use of  circ_in_circ.  Again,
         see   the   html   documentation   in  atlc-X.Y.Z/docs/html-
         docs/index.html for more examples.

         1) In the first example, the outer conductor has  an  inside
         diameter  of 12 units (inches, mm, feet etc.), the inner has
         an outside diameter of 3.9 units.  The inner is placed  cen-
         trally (h=0) and the dielectric is vacuum (Er=1.0).
         % circ_in_circ 12 3.9 0 1.0 > coaxial_1.bmp
         % atlc coaxial_1.bmp
         atlc will indicate the correct  value  of  impedance  to  be
         67.3667  Ohms,  whereas an exact analysis will show the true
         value to be 67.4358 Ohms, so atlc has an error of 0.102%.

         2) In this second example, the conductor sizes are the sames
         as  in  example  1,  but the inner is located 3.5 units off-
         centre and the dielectric has a relative permittivity of 2.1
         (Er  of PTFE) The output is sent to a file not_in_centre.bmp
         which is then processed by atlc
         % circ_in_circ 12 3.9 3.5 2.1 > not_in_centre.bmp
         % atlc not_in_centre.bmp
         The impedance of this is theoretically  24.315342  Ohms,  as
         circ_in_circ  will  calculate  for  you.  atlc's esitmate is
         24.2493 Ohms, an error of only -0.271 %.

         3) In the third  example  the  bitmap  is  made  larger,  to
         increase  accuracy,  but  otherwise this is identical to the
         previous one.
         % circ_in_circ -b8 12 3.9 3.5 2.1 > bigger_not_in_centre.bmp
         % atlc bigger_not_in_centre.bmp
         This time atlc will take much longer to calculate Zo,  since
         the  bitmap  is  larger  and so it needs to do more calcula-
         tions. However, the final result should be more accurate. In
         this  case,  the  result  reported is 24.2461 Ohms, an error
         that't manginally smaller than before at  0.285  %.   It  is
         possible  there may be something to be gained by decreassing
         the cutoff at larger grids, so this is  being  investigated.
         However,  errors  almost always below 0.25 %, no matter what
         is being analysed.

         In   the   fourth   example,   instead    of    re-directing
         circ_in_circ's  output to a file with the > sign, it is done
         using the -f option.
         % circ_in_circ -f 13inner_22outer_coax.bmp 22 13 0 1.0
         % atlc 13inner_22outer_coax.bmp
         %atlc will calculate an impedance of 32.5063  Ohms,  whereas
         the  correct  value,  calculated  using  the  formula  Zo=60
         log(D/d) is 31.5656 Ohms, so altc has an error of -0.187 %.

         In the fifth example, a material with a  relativity  permit-
         tivity  7.89  of is used. While there is no change in how to
         use circ_in_circ, since this permittivity is not one of  the
         pre-defined  values (see COLOURS), we must tell atlc what it
         is % circ_in_circ 23 9 0 7.89 > an_odd_er.bmp
         % atlc -d CAFF00=7.89 an_odd_er.bmp

         This has a theoretical impedance of 20.041970 Ohms, but atlc
         version  3.0.1  will calculate it to be 20.0300, an error of
         -0.058 % !!! If you look at the file  an_odd_er.bmp  with  a
         graphics  package,  you will see there are 3 colours in it -
         the red inner conductor, the green outer and an  olive-green
         dielectric.

## SEE ALSO

         atlc(1),        rect_cen_in_rect(1),        rect_in_rect(1).
         rect_in_circ(1),  circ_in_rect(1).   rect_in_circ(1),  read-
         bin(1) and sym_strip(1).

         http://atlc.sourceforge.net                - Home page
         http://sourceforge.net/projects/atlc       - 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-kirkby.co.uk              - my home page
         http://www.david-kirkby.co.uk/ham          - ham radio pages