1. TRANSMISSION LINE RESONATORS

2. ENEE 482 Spring 20012 Series and Parallel Resonator Circuits L R T Z in C V

3. ENEE 482 Spring 20013

4. 4

5. 5 Parallel Resonant Circuit

6. ENEE 482 Spring 20016

7. 7 TRANSMISSION LINE RESONATORS LENGTHS OF T.L TERMINATED IN SHORT CIRCUITS Z in Z0Z0 T L R T C

8. ENEE 482 Spring 20018

9. 9 Open Circuited line T Y0Y0 Z in L C T T G

10. ENEE 482 Spring 200110

11. ENEE 482 Spring 200111 WAVEGUIDE RESONATORS RECTANGULAR WAVEGUIDE RESONATORS RESONANT FREQUENCIES OF TE l,m,n OR Tm l,m,n Z X Y a b c

12. ENEE 482 Spring 200112

13. ENEE 482 Spring 200113 CYLINDRICAL RESONATORS z D L r  CYLINDRICAL WAVEGUIDE RESONATORS RESONANT FREQUENCIES OF TE l,m,n OR Tm l,m,n WHERE:

14. ENEE 482 Spring 200114 C L e + - Z in r ZoZo MEASUREMENTS OF CAVITY COUPLING SYSTEM PARAMETERS CAVITY EQUIVALENT CIRCUIT NEAR ONE OF THE RESONANCES

15. ENEE 482 Spring 200115 RESONATOR’S Q-FACTORS 2  ENERGY STORED Q = ENERGY DISSIPATED PER CYCLE UNLOADED Q: Q u = 2  f o (L I 2 /2)/(r I 2 /2) =  o L/r LOADED Q : Q L =  o L/(r + Z o ) = Q u /(1+ Z o /r) COUPLING PARAMETER :  Z o /r ; Q u = (1+  Q L EXTERNAL Q : Q E = Q u /  Q L =  Q u +  Q E LOADED Q: INCLUDES ALL DISSIPATION SOURCES UNLOADED Q: INCLUDES ONLY INTERIOR DISSIPATION SOURCES TO CAVITY COUPLING SYSTEM

16. ENEE 482 Spring 200116 CIRCUIT PARAMETERS AND DEFINITIONS

17. ENEE 482 Spring 200117 RESONATOR’S INPUT REFLECTION COEFFICIENT

18. ENEE 482 Spring 200118 DEFINITIONS AND RELATIONSHIPS AMONG THE RESONATOR’S Q’S

19. ENEE 482 Spring 200119 AMPLITUDE MEASUREMENTS Magnitude of the reflection coefficient is: The reflection coefficient is:

20. ENEE 482 Spring 200120 Reflection Coefficient At Resonance : At Angular Frequency  L Where: The Reflection Coefficient is Given By:

21. ENEE 482 Spring 200121 MEASURE REFLECTION COEFFICIENT  0 AT RESONANCE DETERMINE  L FROM: OR USE CURVE OF  L IN dB VS.  o IN dB TO FIND  L MEASURE THE FREQUENCIES FOR WHICH THE REFLECTION COEFFICIENT IS EQUAL TO  L CALCULAT Q L FROM : CALCULATE Q E FROM: THE SIGN TO USE IS DETERMINED FROM THE PHASE OF  0 USE +VE SIGN FOR r < Z 0 AND -VE SIGN FOR r < Z 0

22. ENEE 482 Spring 200122 LOCUS OF CAVITY IMPEDANCE ON SMITH CHART NEAR RESONANCE r < Z O r > Z O r = Z O

23. ENEE 482 Spring 200123

24. ENEE 482 Spring 200124

25. ENEE 482 Spring 200125

26. ENEE 482 Spring 200126

27. ENEE 482 Spring 200127

28. ENEE 482 Spring 200128 PHASE MEASUREMENTS MORE SUITABLE FOR LOW Q ( TIGHTLY COUPLED ) SYSTEMS AT FREQUENCY SHIFT  u = f o / (2 Q u ), THE IMPEDANCE IS: Z u = r + j r INTERSECTION OF THE LOCUS OF Z u WITH THE LOCUS OF THE CAVITY IMPEDANCE DETERMINES A POINT P u MEASUREMENT OF  u AND THE RESONANT FREQUENCY f o YIELDS THE VALUE OF Q u = f o /( 2  u ) AT FREQUENCY SHIFT  L = f o / (2 Q L ), THE IMPEDANCE IS: Z L = r + j(Z o + r ) INTERSECTION OF THE LOCUS OF Z L WITH THE LOCUS OF THE CAVITY IMPEDANCE DETERMINES A POINT P L MEASUREMENT OF  L AND THE RESONANT FREQUENCY f o YIELDS THE VALUE OF Q L = f o /( 2  L )

29. ENEE 482 Spring 200129 PHASE MEASUREMENTS (ctd.) LOCUS OF Z u ON THE SMITH CHART CAN BE SHOWN TO HAVE THE EQUATION: X 2 + ( Y + 1 ) 2 = 2 WHERE X = Re  Y = Im  LOCUS OF Z u IS A CIRCLE OF CENTER (0,-1) AND RADIUS (2) 1/2 LOCUS OF Z L ON THE SMITH CHART CAN BE SHOWN TO HAVE THE EQUATION: X + Y = 1 WHICH IS A STRAIGHT LINE OF SLOPE -1, PASSING THROUGH THE POINTS (1,0) AND (0,1)

30. ENEE 482 Spring 200130 Phase Measurements Locus of Z in Locus of Z U ZoZo r = 0r = 8 PuPu PLPL Locus of Z L