The second design project involves some of the steps in configuring a transmission line with minimal distortion. Ideal conditions under which a transmission line is considered distortionless are discussed on pages 442 and 443 of Cheng.
a) 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), and determine how close it comes to meeting the requirements of a distortionless line. Be sure that you fully document the properties of the line you have selected. Assume that the line is 100 km long and that it is used to transmit audio signals. Please note that the characteristic impedance of the line may no longer be real at these low frequencies! To complete this 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 below in CABLINFO.
b) You should find that the line you have selected is not distortionless. To make it as distortionless as possible, we want to add some lumped elements to the line at regular intervals. We might, for example, add an inductor every few thousand meters. This, in effect, builds a combination of a lumped and continuous transmission line out of what was just a continuous line. You can look at a write up on lumped transmission lines to understand them a bit before proceeding. Once you have an understanding of this type of artificial line, design such a line that looks as much as possible like the line in part (a).. There has been some confusion about my wording here. You are to design a lumped parameter trasnsmission line, not a combination line. The line should be configured from several sections, each consisting of an R, L, C, and G, such that it performs like the continuous line of part (a) 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 the cable you analyzed in part (a). 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).
It is no longer necessary to do part(c). The project now only involves the continuous cable you found for part (a) and the lumped parameter line you configured in part (b) to look as much as possible like the line of part (a) throughout the audio range.
c) Finally, design a combination transmission line with regularly spaced lumped elements placed between sections of continuous line (of the type you used in part (a)). Do not place the lumped elements any closer together than 1 km. Hint: This problem was addressed by the telecommunication industry at about the turn of the last century. The solution they found involved adding inductors (coils) to their lines. You might find it useful to look at the historical literature to see what they did.
d) Evaluate the frequency response of all three(Now only two) transmission lines. Assume that they are terminated in a matched load. Discuss the advantages and disadvantages of each as sound transmission lines.
Information on cables can be found by looking at CABLINFO
Please be sure that you send me questions about this project rather than trying to go forward based on possibly erroneous information. During the first project not enough people made use of the course staff. I hope that the changes I have made will clarify what this project is about. Since time remaining in the semester is limited, please send any questions you have about this to me ASAP and I will add any other information that is necessary.
The first design project involves finding your capacitance relative to something. That is, you are one electrode and something else is another electrode (like when you get charged up in the winter time and give someone a shock). The capacitance you are to find is the capacitance of this combination of electrodes. Specifically, your tasks in this project are the following:
Please post any questions you might have regarding this project to the course newsgroup. We will also post suggestions and hints there and here in the course homepage.
Commentary on Design Project #1: The class as a whole did quite a respectable job on this project. Paper copies of commentary are available outside my office. For posterity and for those of you who want only an electronic copy, I have included a postscript copy of my commentary and a postscript copy of the histogram showing all the answers for human capacitance.