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

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

3. 3 Clemson University / Applied Electromagnetics Group Sample Structures

4. 4 Clemson University / Applied Electromagnetics Group Sample Structures

5. 5 Clemson University / Applied Electromagnetics Group Structure and Sections

6. 6 Clemson University / Applied Electromagnetics Group Integral Equation Definitions

7. 7 Clemson University / Applied Electromagnetics Group Integral Equation Definitions

8. 8 Clemson University / Applied Electromagnetics Group Integral Equation Definitions

9. 9 Clemson University / Applied Electromagnetics Group Integral Equation

10. 10 Clemson University / Applied Electromagnetics Group Integral Equation

11. 11 Clemson University / Applied Electromagnetics Group Integral Equation Definitions

12. 12 Clemson University / Applied Electromagnetics Group Integral Equation

13. 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

14. 14 Experimental Setup

15. 15

16. 16 Clemson University / Applied Electromagnetics Group Input Admittance

17. 17 Reflection Coefficient Clemson University / Applied Electromagnetics Group

18. 18 Input Admittance Clemson University / Applied Electromagnetics Group

19. 19 Reflection Coefficient Clemson University / Applied Electromagnetics Group

20. 20 Input Admittance Clemson University / Applied Electromagnetics Group

21. 21 Clemson University / Applied Electromagnetics Group Sample Frequency Domain Data Radial Cutoff Frequencies Section 1 Section 2 7.39 GHz 1.58 GHz 14.9 GHz 3.27 GHz Axial Resonant Frequencies TEM Mode Section 2 1.50 GHz 3.00 GHz TM 01 Mode Section 2 2.18 GHz 3.39 GHz

22. 22 Clemson University / Applied Electromagnetics Group Sample Frequency Domain Data Radial Cutoff Frequencies Section 1 Section 2 7.39 GHz 1.58 GHz 14.9 GHz 3.27 GHz

23. 23 Clemson University / Applied Electromagnetics Group Sample Frequency Domain Data Axial Resonant Frequencies TEM Mode Section 2 Section 3 1.50 GHz 1.50 GHz TM 01 Mode Section 2 Section 3 2.18 GHz 7.54 GHz Radial Cutoff Frequencies Section 1 Section 2 Section 3 7.39 GHz 1.58 GHz 7.39 GHz 14.9 GHz 3.27 GHz 14.9 GHz

24. 24 Clemson University / Applied Electromagnetics Group Sample Frequency Domain Data Axial Resonant Frequencies TEM Mode Section 2 1.50 GHz 3.00 GHz TM 01 Mode Section 2 2.18 GHz 3.39 GHz Radial Cutoff Frequencies Section 1 Section 2 Section 3 7.39 GHz 1.58 GHz 7.39 GHz 14.9 GHz 3.27 GHz 14.9 GHz

25. 25 Clemson University / Applied Electromagnetics Group Sample Frequency Domain Data Radial Cutoff Frequencies Section 1 Section 2 Section 3 7.39 GHz 1.58 GHz 7.39 GHz 14.9 GHz 3.27 GHz 14.9 GHz Axial Resonant Frequencies TEM Mode Section 2 Section 3 1.25 GHz 1.87 GHz 2.50 GHz 3.75 GHz TM 01 Mode Section 2 Section 3 2.02 GHz 7.62 GHz

26. 26 Clemson University / Applied Electromagnetics Group Preliminary Time Domain Data

27. 27 Preliminary Time Domain Data Clemson University / Applied Electromagnetics Group

28. 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

29. 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

30. 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