Experimental Physics II
Experimental Physics II PHY 462
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Date Created: 10/21/15
January 2009 Phy 462 Electrical Waves and Impedance Matching Introduction In a given system7 the propagation of waves is characterized by the impedance of the particular medium An interface between two media with different wave impedlances7 Z1 and Z2 will cause a traveling wave propagating along medium 1 to be partially re ected from the interface with medium 2 This re ection process is described by the following expression Z27Z1 1 ZHZI where P is a complex quantity relating the amplitude and phase of the re ected wave When Z2 Z17 P 0 and there is no re ection In this case7 the system is said to be impedance matched Thus7 to deliver the maximum power to a particular load7 the characteristic impedance of the transmission line must be matched to that of the load Objectives 0 Use a pulse propagation technique to measure the velocity of wave propagation along a coaxial cable Learn about the characteristic impedance for a transmission line Characterize impedance mismatches by measuring pulses re ected from the mis match interface Learn about the behavior of a microstrip transmission line Fabricate a microstrip line to achieve a particular impedance Suggested Reading Read a treatment of coaxial cables in an electromagnetism textbook7 such as Grif ths7 Introduction to Electrodynamics Read about impedance matching in a microwave engineering text7 such as Planar Microwave Engineering Cambridge7 by TH Lee Suggested Apparatus H 3 9 7 Cf Agilent arbitrary waveform generator 33250A Digital oscilloscope 7 the 2 channel lnstek scopes are suf cient Mini circuits power splitter ZFRSC 42 BNC SMA adapters BNC cables several lengths 509 terminators Circuit board pieces and SMA connectors for rnicrostrip fabrication Instructions Investigating arbitrary waveform generator This instrument can output various waveforms including narrow pulses or arbitrary shape 0 Connect to oscilloscope with 50 Q terminator and BNC tee Try outputting continuous waveforms 7 vary frequency amplitude Next try generating pulses 7 set amplitude pulse height width edge time Explore the behavior of the sync signal and its possible use for triggering the scope Instructions Power splitter Connect one side of power splitter to output of arbitrary waveform generator Connect each of the other two ends to separate channels on the oscilloscope each with terminators Observe the two signals on the scope and compare with the output of the generator Switch the order of the connections on the splitter and observe the results Disconnect one of the cables from the splitter to the scope and observe the result on the remaining scope channel Attach a terminator directly to the connector on the splitter which is now free and observe the result Discuss the power splitter with the instructor and sketch out a possible con g uration for the routing of the signals inside the splitter Instructions Re ections measuring velocity Before starting these measure merits7 compute the impedance and propagation velocity on a BNC coaxial cable Next7 you will measure the propagation velocity directly 0 With the output of the arbitrary waveform generator attached to one port of the splitter and another port connected to the scope with a terminator7 attach a long BNC cable to the remaining terminal Attach a terminator to the free end of the long BNC cable 0 Send narrow pulses from the generator and observe the signal on the oscillo scope 0 Remove the terminator from the end of the long BNC cable and record the resulting waveform from the oscilloscope Try varying the pulse width from the generator and record the result Try at least ve different lengths for the BNC cable and for each one7 record the shape of the resulting waveform from the oscilloscope Compute the delay of the pulse that travels along the long BNC cable Be sure to account for the complete path taken by the7 including the number of times it passes through the splitter Plot the time delay of the pulse against the relevant length based on the free BNC cable7 and use this to determine the propagation velocity on the coaxial cable Compare with your expected value and describe any anomalies Instructions Characterizing impedances In this section7 you will explore the in uence of the particular termination at the end of the free BNC cable on the nature of the re ected pulse Send pulses through the splitter arrangement from the previous section using a long enough BNC cable to allow the outgoing and re ected pulses to be resolved Try attaching the following impedances onto the end of the free BNC cable 0 50 Q terminator 0 Open circuit as in previous section 0 Shorting cap 0 Resistors soldered from the signal to ground of a BNC bulkhead connector Try at least one resistor somewhat above 50 Q and one somewhat below o Inductor soldered from the signal to ground of a BNC bulkhead connector 0 Capacitor soldered from the signal to ground of a BNC bulkhead connector 0 Microstrip lines see below 0 In each case7 use the measurement of the re ected pulse waveform and the previously calibrated outgoing pulse waveform to compute the impedance at the end of the long BNC cable using Eq 1 The discussion in the Lee microwave textbook is particularly relevant here Instructions Microstrip lines 0 Compute Z for different microstrip geometries 0 Using a razor blade7 cut out the copper on the circuit board pieces to produce a microstrip line Solder SMA launchers onto either end of the board 0 Observe the re ected waveform and interpret this in terms of the computed Z and your previous measurements of various terminating impedances