In order to manipulate and plot data, it needed to be transported from what we observed on the scope onto another computer program.
The data was exported by means of the GPIB slot on the oscilloscope. It was fed to a PC computer running a DOS program (called TEKDIG) which acquired the data and converted the coordinates of data into two arrays: one for the x-coordinates (time) and one for the y-coordinates (voltage). These arrays were then transposed into coordinate pairs and plotted on Mathematica. (get me back!)
The following is sample Mathematica code and its resultant output:
This is what that code does:
Notice that the input pulse is not as large as it should be (how can the first reflected pulse be larger than the input?). This is a result of the oscilloscope averaging the data as it receives it. Averaging clears up a lot of "noise" that appears on a sample plot, but resulted in the initial pulse seeming small. The pulse appeared fairly unstable on the scope which resulted in its current apparent magnitude
Here is some code used for data manipulation:
Here is its output:
A note on the above plots:
It is obvious that as time progresses and the initial pulse has time to reflect one or more times, that the half-width of each peak is increasing (well, maybe not so obvious as the time-scale on the x-axis is distorted, but trust me). This can be explained by the quantum mechanical knowledge that a wave packet composed of different frequency waves spreads with time. Different frequencies travel at different speeds, so if sufficient time elapses, the spreading becomes noticeable.
If the area under each peak were to remain constant, the input pulse could travel through the cable with no attenuation. The loss in amplitude of each peak is due to the spreading of the pulse. In order to conserve energy, the area under each peak should be the same (in an ideal cable with no attenuation). Therefore, if the pulse spreads through time, then the width must become wider to compensate.