em_waves - Introductory Lab Electromagnetic Pulses...

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Unformatted text preview: Introductory Lab: Electromagnetic Pulses Experiments in Modern Physics (P451) Coaxial cables are ubiquitous in the modern laboratory. In this lab we will focus on the signal propagation properties of the cable. You will learn how to properly terminate signal cables to avoid erroneous results when working with electronic circuits. We will also explore fitting data to a user-defined function and judging quality of the fit based on χ 2 . Introduction Coaxial cables operate as wave guides in the TEM mode and effectively have inductive, capacitive, and resistive elements. The EM waves propagate through the dielectric that fills the space between the center conductor and the outer shield. The physical properties of the cable give it a characteristic impedance. Most cables we will encounter in the lab have a 50 Ω impedance. Note that this impedance is independent of length and cannot be interpreted as a simple resistance between the center conductor and ground. In fact, in the DC limit there is virtually infinite impedance between the center conductor and ground. It is important that loads connected to the end of the cable have an input impedance that matches that of the cable. Otherwise, a reflection will be generated at the boundary between the cable and the load. The coefficient of reflection Γ is given by Γ = Z L- Z c Z L + Z c , (1) where Z L and Z c are the load input impedance and cable impedance, respectively. The impedances are said to be “matched” when Z L = Z c . Impedance mismatches can generate spurious pules from reflections that are problematic in electronic circuits. Read the detailed discussion of coaxial cables outlined in Experiment 1 of Ref. [1] before beginning this lab. Setup and Equipment • pulse generator • oscilloscope • assorted coaxial cables of various lengths and connectors • resistors of various values Connect the output of the pulse generator to the scope using a T connector. The remaining open end of the T should be connected to the cable under test. Pulses will then propagate from the pulse generator across the scope input down to the end of the cable and back across the scope input. The scope will be used to examine both the initial pulse and the reflected pulse. The duration of the pulse should be much shorter than the propagation time through the test cable, and the time between pulses should be much longer than the propagation time through the test cable. Exercises Conduct the following experiments. Prepare a PDF file using L A T E X that describes your results. For this lab, you do not need to write a formal report – only address the discussion points itemized below. • Measure the signal propagation velocity for the two cables labeled A and B . This can be done by reflecting a pulse off of the open end of the cable and measuring the time delay. What are the velocities and the estimated uncertainties on these velocities?...
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em_waves - Introductory Lab Electromagnetic Pulses...

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