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Richard Harrison wrote:
Keith wrote: "Why are you convinced the reflection point had to move?" This is the case when a line is extended to greater length, and the short or open also is moved to the new end of the line. Ever had a short or open somewhere in the middle of a line? Actually, no. I have, and can testify that the signal doesn`t get past a real hard short or open in the line. As energy can`t be destroyed it had to be reflected by the hard short or open. Or just stopped and stored, perhaps. This is certainly what happens when you excite the line with a step function rather than a sinusoid. When excited by a sinusoid, no energy moves at the quarter wave points where the voltage or current is always 0. As you move away from the quarter wave points, more and more energy moves on each cycle until a maximum amount of energy is moved at the point half way between the quarter wave points. And then it decreases back towards the next quarter wave point. All of this is easily visualized by observing the amplitude of the p(t) function at various points along the line. In the case where the line short is moved to a point nearer the source, or where the short or open is moved to a place more distant on the line from the source, we know the energy travels all the way to the actual short or open where it is reflected because nulls occur at several points along a long transmission line. "we know" is rather strong. I would strongly suggest that no energy crosses those points in the line where the voltage and current are always zero since p(t) is always zero at these points. If the energy were turned around before it reached the end of the line, nulls more distant from the source than the turnaround point would not exist. Not so, the line has reached steady-state. Now the nulls exist. They did not exist before the line reached steady-state. There would be no energy at the actual short or open at the end of the line were the energy turned around before it reached the end of the line. Not necessarily. Only once the line has been charged, does the energy move back and forth between the quarter wave points, while not crossing them. Try visualizing how a step function charges the line. How the voltage step propagates down the line. How the voltage step is reflected at the open end and starts travelling back towards the start. How between the start of the line and the returning voltage step, energy is flowing to charge the line, but between the returning voltage step and the open end of the line, the energy previously delivered is statically stored in the capacitance of the line. How once the line is completely charged, no current flows, there is no power, and the energy delivered during charging is stored in the capacitance. Sinusoidal excitation is more difficult to visualize, but the prinicipal is the same. ....Keith |
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