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1 Fields and Signals in Coupled Coaxial and Cylindrical Cavities John C. Young Chalmers M. Butler Clemson University

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2 Clemson University / Applied Electromagnetics Group Introduction Sample Structures Integral Equation Motivation Data and Observations

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3 Clemson University / Applied Electromagnetics Group Sample Structures

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4 Clemson University / Applied Electromagnetics Group Sample Structures

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5 Clemson University / Applied Electromagnetics Group Structure and Sections

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6 Clemson University / Applied Electromagnetics Group Integral Equation Definitions

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7 Clemson University / Applied Electromagnetics Group Integral Equation Definitions

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8 Clemson University / Applied Electromagnetics Group Integral Equation Definitions

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9 Clemson University / Applied Electromagnetics Group Integral Equation

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10 Clemson University / Applied Electromagnetics Group Integral Equation

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11 Clemson University / Applied Electromagnetics Group Integral Equation Definitions

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12 Clemson University / Applied Electromagnetics Group Integral Equation

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13 Clemson University / Applied Electromagnetics Group Solution Technique Pulse Expansion/Point Matching – matrix equation Kummer’s transformation – acceleration of convergence Fields at points in cavity can be found from knowledge of aperture fields

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14 Experimental Setup

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16 Clemson University / Applied Electromagnetics Group Input Admittance

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17 Reflection Coefficient Clemson University / Applied Electromagnetics Group

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18 Input Admittance Clemson University / Applied Electromagnetics Group

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19 Reflection Coefficient Clemson University / Applied Electromagnetics Group

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20 Input Admittance Clemson University / Applied Electromagnetics Group

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21 Clemson University / Applied Electromagnetics Group Sample Frequency Domain Data Radial Cutoff Frequencies Section 1 Section GHz 1.58 GHz 14.9 GHz 3.27 GHz Axial Resonant Frequencies TEM Mode Section GHz 3.00 GHz TM 01 Mode Section GHz 3.39 GHz

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22 Clemson University / Applied Electromagnetics Group Sample Frequency Domain Data Radial Cutoff Frequencies Section 1 Section GHz 1.58 GHz 14.9 GHz 3.27 GHz

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23 Clemson University / Applied Electromagnetics Group Sample Frequency Domain Data Axial Resonant Frequencies TEM Mode Section 2 Section GHz 1.50 GHz TM 01 Mode Section 2 Section GHz 7.54 GHz Radial Cutoff Frequencies Section 1 Section 2 Section GHz 1.58 GHz 7.39 GHz 14.9 GHz 3.27 GHz 14.9 GHz

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24 Clemson University / Applied Electromagnetics Group Sample Frequency Domain Data Axial Resonant Frequencies TEM Mode Section GHz 3.00 GHz TM 01 Mode Section GHz 3.39 GHz Radial Cutoff Frequencies Section 1 Section 2 Section GHz 1.58 GHz 7.39 GHz 14.9 GHz 3.27 GHz 14.9 GHz

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25 Clemson University / Applied Electromagnetics Group Sample Frequency Domain Data Radial Cutoff Frequencies Section 1 Section 2 Section GHz 1.58 GHz 7.39 GHz 14.9 GHz 3.27 GHz 14.9 GHz Axial Resonant Frequencies TEM Mode Section 2 Section GHz 1.87 GHz 2.50 GHz 3.75 GHz TM 01 Mode Section 2 Section GHz 7.62 GHz

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26 Clemson University / Applied Electromagnetics Group Preliminary Time Domain Data

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27 Preliminary Time Domain Data Clemson University / Applied Electromagnetics Group

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28 Clemson University / Applied Electromagnetics Group Disadvantages of frequency domain analysis Advantages of time domain analysis Provides direct physical interpretation Gives intuitive idea of meaning of frequency domain data Difficult to interpret data Very complicated for complex structures

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29 Clemson University / Applied Electromagnetics Group Fast Fourier Transform (FFT) Easy to use with existing frequency domain analysis For signals with frequency content below the cutoff frequencies of all the cavities, transmission line analysis provides a very good approximation Requires knowledge of dc fields in the guide

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30 Clemson University / Applied Electromagnetics Group Conclusions Fields in cascaded cavities can be determined Frequency domain data is often difficult to interpret, even for relatively simple structures Time domain analysis is easier to interpret physically and helps in understanding frequency domain data

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