Homepage of atlc - Arbitrary Transmission Line Calculator
Author: Dr. David Kirkby, drkirkby@ntlworld.com
Description: Transmission line calculator, of *any* cross section
Keywords: Transmission line calculator arbitrary any shape cross section finite difference

# `atlc` - Arbitrary Transmission Line Calculator.

The programme `atlc` calculates the impedance of two or three wire electrical transmission lines of totally arbitrary cross section, using a numerical technique called finite difference. The conductors can be coaxial, run side by side, or in just about any configuration you can think of. The diagrammes below shows 3 types of 2-wire transmission lines and a directional copuler, all of which may be analysed. In each diagramme, one conductor is shown red, the other conductor shown green and in the case of a coupler, the third conductor is shown blue. The dielectrics are shown in a few other colours, with white being a vacuum and turquoise being a dielectric with an effective permittivity of 4.8 (about the same as fibreglass PCB).

Zo=69.690 Ohms C=47.865 pF/m L=232.454 nH/m | Zo= 49.335 Ohms C= 67.611 pF/m L= 164.565 nH/m | Zo= 56.020 Ohms C= 59.544 pF/m L= 186.862 nH/m | Zo= 66.3699 Ohms Zeven=138.9950 Ohms Zodd= 31.6915 Ohms

The programme `atlc` needs to know shape of the transmission line's cross section. This cross section is stored in a data file, which happens to be a Windows bitmap file. The bitmap file is read by `atlc`, following which the programme performs the analysis.
There are two ways to generate the bitmap for `atlc`.

1. As you might expect, you can draw the transmission line's cross-section in a graphics programme such as Gimp, Photoshop, Windows Paint Corel Photopaint etc. The programme must be able to save images as bitmap (.BMP or .bmp) files, in 24-bit (true colour) mode The graphics programme can run under whatever operating system you like. If for example you have some U-section brass and some hollow rectangular tube, and wanted to know the properties of a transmission line formed from these, you might draw something like this, and save it as a file, which we might call `ushape.bmp`
2. In the case of simple cross-sections, the bitmaps can be generated automatically. Currently 6 such programms have been written, to quickly generate bitmaps for rectangular and circular conductors, striplines and a directional copuler. An example of such as programme is `rect_in_rect`, which is able to automatically generate a bitmap for any rectangular conductor, inside any other rectangular conductor, with no more than 2 dielectrics. One dielectric must lie under the centre conductor. Other programs include `circ_in_circ`
   Using rect_in_rect,.is very fast - much faster than generating the bitmaps with a graphics programme.

A unix computer, with a gcc or other C compiler, is needed to compile and run `atlc`. The programme should compile very easily and quickly. Being rather CPU intensive, `atlc` has been written to support multiple processors if available. Here is an example of using atlc, with the file `ushape.bmp` being drawn by a graphics programme.

    % atlc -v ushape.bmp
    ushape.bmp Er= 1.000000 C= 77.2797 pF/m L= 143.977094 nH/m Zo= 43.163247 Ohms v= 299792458.010503 m/s v_f= 1.000000    VERSION= 3.0.0
    ushape.bmp Er= 1.000000 C= 77.1386 pF/m L= 144.240432 nH/m Zo= 43.242194 Ohms v= 299792458.010503 m/s v_f= 1.000000    VERSION= 3.0.0
    ushape.bmp Er= 1.000000 C= 77.1385 pF/m L= 144.240554 nH/m Zo= 43.242230 Ohms v= 299792458.010503 m/s v_f= 1.000000    VERSION= 3.0.0
    ushape.bmp Er= 1.000000 C= 77.1385 pF/m L= 144.240554 nH/m Zo= 43.242230 Ohms v= 299792458.010503 m/s v_f= 1.000000    VERSION= 3.0.0

It will be seen that `atlc` makes several estimates of the transmission line's properties, each subsequent one being closer to the true values (normally only the final result is shown, but the -v option added above causes `atlc` to print intermediate results).
Here's an example of using `rect_in_rect` to generate a bitmap The programme needs 11 parameters on its command line, which are described fully elsewhere. For now, just accept that these 11 parameters describe a transmission line. The output of `rect_in_rect` is redirected to the file `ex2.bmp`, which is then read by `atlc`>

    % rect_in_rect 250 175 10 32 4 200 56 25 1.0 2.5  >  ex2.bmp
    % atlc  ex2.bmp
    ex2.bmp Er= MIXED C= 87.8016 pF/m L= 240.9628 nH/m Zo= 52.387023 Ohms v= 217407041.146 m/s     v_f= 0.725192 VERSION=3.0.0

The programme `atlc` was written by, and is supported by, Dr. David Kirkby (G8WRB).

atlc is written and supported by Dr. David Kirkby (G8WRB)It is issued under the GNU public license.

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