TRANSMISSION LINE RESONATORS

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

ENEE 482 Spring 20013

4

5 Parallel Resonant Circuit

ENEE 482 Spring 20016

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

ENEE 482 Spring 20018

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

ENEE 482 Spring

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

ENEE 482 Spring

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

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

ENEE 482 Spring 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

ENEE 482 Spring CIRCUIT PARAMETERS AND DEFINITIONS

ENEE 482 Spring RESONATOR’S INPUT REFLECTION COEFFICIENT

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

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

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

ENEE 482 Spring 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

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

ENEE 482 Spring

ENEE 482 Spring

ENEE 482 Spring

ENEE 482 Spring

ENEE 482 Spring

ENEE 482 Spring 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 )

ENEE 482 Spring 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)

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