Regarding the temporal (and consequently spatial) resolution of a TDR system, I've read from different sources that the maximum resolution achievable is half of the rising time of the input step response, which is usually in the ns range. How is this relationship (maximum resolution = 0.5 * rising time) calculated or how can it be proved?
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I have made a simulation in one case (end open line). Is this obvious?
The problem is that the wave must go forward and backward (-> 2 times the length of the line).
Antonio51
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The factor of two is common to time-resolved sensing systems (radar, lidar, sonar, etc) and reflects the fact that it takes twice as long for a signal to reach a point and return as it does to go one way.
Rise time has different definitions (10-90%, 80-20%, etc) but is a measure of the one-way time resolution of the system. Combine that with the factor of two for bidirectional travel and you get the overall resolution of the system.
If you want to prove it mathematically you would have to start with a mathematical definition of resolution (of which there are many), and then either work backwards to a definition of rise time that gave that equation, or else fix your definition of rise time and then get a slightly different coefficient than 0.5. In either case your result will depend on exactly how you define rise time and resolution, but will generally be close.
user1850479
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