atlc's Tutorial

The arbitrary transmission line calculator (atlc) project is used when you wish to know the properties (Zo, capacitance per unit length, velocity factor, electric-field distribution, etc) of a transmission line or directional copuler. Unlike the well known analytical formulas printed in any book on transmission lines, atlc has great flexibility, as any cross section can be analysed, even one like this.
very odd line

All this is required, is that the cross section can be drawn and saved as a bitmap file and the programme atlc used to evaluate the bitmap. The following examples show how this is done.


  1. Very odd transmission line In the first tutorial, that very odd transmissionl line will be analysed. It is shown just how easy it is. By far the most difficult part in using atlc is drawing the cross-section, but luckily this is rarely necessary
  2. Coaxial cable In the second example, a standard piece of coaxial cable will be analysed. This has the advantage for now that we calculate the answer from stardard formula for a sanity check.
  3. Symmetrical rectangular transmission line. In the example, a transmission line with one rectangular conductor centrally located inside another rectangular conductor will be analysed. The programme create_bmp_for_rect_cen_in_rect will be used for this - the name hopefully conveying the conductor shapes and the symmetry.
  4. Directional coupler. Assume we wished to analyse the coupling between two closely spaced square conductors in a rectangular outer conductor, with a vacuum dielectric.
  1. Very odd line Assuming we wanted to analyse that rather strange transmission line above, its cross-section would first be saved as a bitmap. One conductor would be drawn pure red, the other pure green. Assuming for a monent the dielectric is a vacuum (virtually the same permittivity as air), the dielectic would be drawn pure whilte. (The colours are critical and are discussed more in the section marked Colours at the top of the page). Assuming the cross section was in a file very_odd.bmp, we would run atlc like this: 
    wren % atlc very-odd.bmp
    atlc would produce the following output. 
    very-odd.bmp 2 Er=  1.00 Zo=  56.557 Ohms C=   59.0 pF/m L=  188.7 nH/m v= 2.998e+08 m/s v_f= 1.000 VERSION= 4.6.0
    All information is printed on one long line so its easy to process with other software. Note the impedance Zo is 56.557 Ohms.

    The size (number of pixels) in the bitmap should be sufficient that the structure can be drawn accurately, but not so large that it takes too long to process. About 1 MB is reasonable.

  2. Coaxial cable To analyse coaxial cable, we would normally use the formulas published in book. The impedance for instance, is given by Zo=59.95849160*loge(D/d))/sqrt(Er) - (the 59.958 .. is ussually seen in books as 60). atlc can be used too. We are not suggesting that atlc is used instead of the normal formula for coax on a regular basis, but since it's a simple example, it is useful for demonstration. Also, as there is an analytical expression for Zo, we can get some idea of the accuracy of atlc

    Since the cross section consists of a circular conductor inside another circular conductor, the programme create_bmp_for_circ_in_circ can be used to generate the bitmap, rather than the more time consuming procedure of using a graphics package and drawing it manually..

    We will assume that the inner diameter of the outer conductor is 12 mm, the outer diameter of the inner conductor is 3.9 mm, and the dielectric has a permittivity of 1.0. Since the conductors are coaxial, there is zero offset between their centres. The programme create_bmp_for_circ_in_circ will be used to generate the bitmap, with these physical dimensions

    If we run create_bmp_for_circ_in_circ without any arguments, it will print a usage message, showing the first argument should the the outer diamater (D=12 mm), the second the inner conductor (d=3.9 mm), the third the offset 'O' between the conductors (O is zero since they are coaxial and there is therefore no offset between centres). The fourth argument is the relative permittivity (1.0 in this case). Ignoring the options, which are not necessary unless we wish to change the behaviour of create_bmp_for_circ_in_circ, we would type

    % create_bmp_for_circ_in_circ 12 3.9 0 1.0 coaxial_1.bmp
    This will produce a bitmap like the image on the left. The inner conductor is red, the outer green and the dielectric is white in this case, as Er=1.0. Don't worry about the fact that the outer conductor is square, as the inside of it is round, which is all that matters.
    coax 12/3.9 mm
    To calculate the properties of this coaxial cable, we then run atlc, where it will print the important properties to the screen, again on one long line (you will have to scroll the brower to see it all).

    % atlc coaxial_1.bmp
coaxial_1.bmp 2 Er=  1.00 Zo=  67.390 Ohms C=   49.5 pF/m L=  224.8 nH/m v= 2.998e+08 m/s v_f= 1.000 VERSION= 4.6.0

    The correct answer, given by the formula Zo=59.95849160*loge(D/d)/sqrt(Er) is 67.3892 Ohms, so atlc's estimate of Zo= 67.390 Ohms is in error by only 0.001%!! We could probably increase the accuracy further, by generating a larger bitmap with create_bmp_for_circ_in_circ, by adding the -b command line option, but there is no point. Who can argue with an error of just 0.001% ???

    We could if we wanted use an outer conductor which is round on both the inner and outer like this:
    coax 12/3.9 mm
    so it looks more like normal coax. However, there are three good reasons not to do