Fields and Waves I Fall 1996 -- Design Project #2

Project Requirements

1. The first part of this project is to find a practical transmission line (look up the properties of standard transmission lines and select a particular line for analysis). You will need values for R, G, L, and C per unit length for your cable. Usually, this information is not given directly. Please check the information noted in CABLINFO
2. Determine how close your line comes to meeting the requirements of a distortionless line. For a discussion of distortionless lines, see Cheng pages 442 and 443. Also, check out some information from a course at WPI: EE 535 - Telecommunications Transmission Technologies. Be sure that you fully document the properties of the line you have selected. Assume that the line is 10 km long and that it is used to transmit audio signals. You are free to define the audio frequency range in any reasonable manner.Please note that the characteristic impedance of the line may no longer be real at these low frequencies! Also, both beta and alpha will depend on R and G as well as L and C. See equations 9-37 and 9-41. Determine the frequency response of this line. The frequency response should be determined by loading the line with a real resistance equal to its listed characteristic impedance. For the usual high frequency applications, this would mean treat the load was matched to the line and the frequency response is flat. You can calculate the input impedance of the line for this condition or assume that the line is driven by a known sinusoidal voltage and find the corresponding output voltage at the load.
3. It is possible to construct an artificial transmission line using lumped circuit elements (see Lumped transmission lines). After reading the background material, design such a line that looks as much as possible like your 10 km transmission line. The line should be configured from several sections, each consisting of an R, L, C, and G, such that it performs like your continuous line over the audio frequency range. You can improve on its properties if you wish, but that is not necessary. Use the minimum number of components for this purpose. Be sure that you describe the criteria you have applied to assure that your design will transmit a quality audio signal. Again, your purpose here is to design a lumped line that looks as much as possible like or slightly better than your cable you analyzed. I have written a simple matlab m-file to analyze lumped parameter lines along with the equivalent continuous line. You can find a copy of this file in my public directory. The file is called lumline.m (a set of sample paramters can be set by also using the file called lumparam.m). I don't think that my lumped parameter analysis is quite correct, but it is simple and gives a reasonable answer.
4. Finally, you can either build the lumped parameter line you have designed and test it using some apparatus I will provide or you can simulate the performace of the line using Spice or some other program. It may work best to write something yourself using Matlab, as I have done.

Due Dates: