1_230 Lab Manual Winter2016.pdf

# 7 disconnect the two 9 cm loops from the coaxial

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7. Disconnect the two 9 cm loops from the coaxial cables and perform the same measurements for the 5 cm loops. Measured Data Copy the following into your lab notebook and fill in the measured data. If you are missing any data, please repeat the necessary parts of this experiment before proceeding. 9 cm loops 5 cm loops Distance (cm) ! !" ! (mU) ! !" (dB) ! !" ! (mU) ! !" (dB) 2 4 6 8 10 12 14 16 ! !" ! (mU) for 9 cm loops ! !" ! (mU) for 5 cm loops 30° misalignment 60° misalignment Analysis For both the 9 cm and 5 cm loops: 1. Calculate the deNembedded input resistance at the measured distances at ! ! . At ! ! , only the magnitude of the reflection coefficient is needed. 2. Using eq. (5.4), calculate the mutual inductance at these distances. Resistances ! ! and ! ! are the loop resistances calculated in Experiment 4.3. The load resistance ! ! is the impedance presented by the network analyzer, which is 50 Ω. 3. Calculate the mutual inductance for the system of loops that are misaligned by 30° or 60°. 4. Calculate the power transfer efficiency at each distance using the transmission coefficient ! !" . ( Note : These efficiency values correspond to an unmatched system.)

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96 Questions 1. How do the measured mutual inductance values compare with the plots of Fig. 5.3 and Fig. 5.4.? Why might the experiment not match exactly the two plots? ( Hint : What assumption are made in eq. (5.1)?) 2. What happened to the mutual inductance in the case that the loops were misaligned? Why? VI. Experiment 5.2: Strong and Weak Coupling Setup If the network analyzer is not already calibrated for both reflection and transmission measurements, perform the necessary calibrations as described in the Setup of Experiment 5.1. Procedure 1. Connect a 9 cm loop to each of the patch cords attached to the reflection and transmission ports of the network analyzer. 2. Begin with the loops far apart (i.e. in weak coupling), but axiallyNaligned on the graduated PVC pipe. Decrease the coupling distance while maintaining axial alignment. Measure the critical coupling distance ( Hint : At critical coupling, a transition occurs from a single resonance to two resonances: the even and odd mode resonances.) 3. Bring the loops even closer together in order to enter strong coupling. Observe the behavior of the resonant frequencies as the loops are moved closer together. Does the behavior follow the same trend as Fig. 5.7? 4. Repeat the same procedure using 5 cm loops. Measured Data Copy the following into your lab notebook and fill in the measured data. If you are missing any data, please repeat the necessary parts of this experiment before proceeding. Loop Experimental critical coupling distance Theoretical critical coupling distance (from Analysis 1) 9 cm 5 cm Analysis
97 1. Use the plots of Fig. 5.3 and Fig. 5.4 as well as eq. (5.7) to determine the theoretical critical coupling distance for both the 9cm and 5 cm loops.
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• Winter '08
• RAND
• BNC

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