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


     circ_in_circ [options... ] D d O 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-X.Y.Z/docs/html-docs
     directory for them.


     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        ***********                  **
       ***         |            ***                      ***
       **          |                                      **
       **                                                 **
       **                                                 **
       **                                                 **
       ***                                               ***
        **                                               **
        ***                                             ***
         **                                             **
          **                                           **
           **                                         **
            ***                                     ***
             ****                                 ****
               ****                             ****
                 *****                       *****
                    ******               ******

     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.


     -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.

     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.


     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)


     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.


     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


     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).                - 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              - my home page          - ham radio pages

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