TRANSMISSION LINE RESONATORS. ENEE 482 Spring 20012 Series and Parallel Resonator Circuits L R T Z...

TRANSMISSION LINE RESONATORS

ENEE 482 Spring 2001 2

Series and Parallel Resonator Circuits

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Parallel Resonant Circuit

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TRANSMISSION LINE RESONATORS

• LENGTHS OF T.L TERMINATED IN SHORT CIRCUITS

ZinZ0

20gn

l

T

L

RT

Zin

00

0

0

for /2/

1 , tanh

tanhtan1

tantanh

p

ppp

in

v

vvv

j

jZZ

C


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2

ZL ,1

2

1

)/(1

)/(

tantantan

0

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WAVEGUIDE RESONATORS

• RECTANGULAR WAVEGUIDE RESONATORSRESONANT FREQUENCIES OF TEl,m,n OR Tml,m,n

GHz IN IS

INCHES IN ARE

82.34

,...3,2,1,

)()(

2

2222

222

f

a, b, c

c

abn

b

am

a

clabf

db

n

a

mk

mn

mn

Z

X

Y

a

b

c


MODE CHART OF RECTANGULAR RESONATOR WITH A/B=2

0

50

100

150

200

250

300

350

400

450

500

0 0.5 1 1.5 2 2.5 3 3.5 4

a^2/c^2

f^2a

^2

[G

Hz

In.]

^2

TE101

TM110

TE011

TE111,TM111

TE012

TM210

TM112,TE112

TE211,TM211

TE212,TM212


CYLINDRICAL RESONATORS

z

D

Lr

• CYLINDRICAL WAVEGUIDE RESONATORSRESONANT FREQUENCIES OF TEl,m,n OR Tml,m,n

22

,22

23.139 LnDx

Df ml

WHERE:

INCHESIN ARE AND

GHz in is

MODES-TM FOR0 OF ROOT th

MODES-TE FOR0 OF ROOT th

,

',

LD

f

xJmx

xJmx

lml

lml


C

Le+

-

Zin

rZo

MEASUREMENTS OF CAVITY COUPLING SYSTEM PARAMETERS

CAVITY EQUIVALENT CIRCUITNEAR ONE OF THE RESONANCES


RESONATOR’S Q-FACTORS

2 ENERGY STORED

Q =

ENERGY DISSIPATED PER CYCLE

UNLOADED Q: Qu = 2 fo (L I2/2)/(r I2/2) = o L/r

LOADED Q : QL = o L/(r + Zo) = Qu/(1+ Zo/r)

COUPLING PARAMETER : Zo/r ; Qu = (1+ QL

EXTERNAL Q : QE = Qu/ QL = Qu + QE

LOADED Q: INCLUDES ALL DISSIPATION SOURCES

UNLOADED Q: INCLUDES ONLY INTERIOR DISSIPATION SOURCES TO CAVITY COUPLING SYSTEM


LC

C

LZ

ZjrZ

CLjrZ

o

o

o

ooin

in

1

ˆ

:where

ˆ

1

CIRCUIT PARAMETERS AND DEFINITIONS


o

oo

o

o

oo

o

o

ooo

o

ooo

oin

oinin

jZ

Zr

jZ

Zr

ZjZr

ZjZr

ZZ

ZZ

ˆ

ˆ

ˆ

ˆ

RESONATOR’S INPUT REFLECTION COEFFICIENT


111

ˆ11

ˆ11

ˆ11

uEL

o

o

ooo

oE

o

o

ooo

oL

oou

QQQ

Z

Z

ZC

L

Z

L

LCZ

LQ

Zr

Z

ZrC

L

Zr

L

LCZr

LQ

r

Z

rC

L

r

L

LCr

LQ

DEFINITIONS AND RELATIONSHIPSAMONG THE RESONATOR’S Q’S


11

11

22

22

2

o

oEu

o

oEuin

QQ

QQ

AMPLITUDE MEASUREMENTS

Magnitude of the reflection coefficient is:

11

11

o

oEu

o

oEuin

jQQ

jQQ

The reflection coefficient is:


11

11

Eu

Euo

QQ

QQ

Reflection Coefficient At Resonance :

111

2

2

2

EuLL

o

o

L

QQQ

At Angular Frequency L Where:

2

1

2

1

112

11

2

1

1111

1111

2

2

2

22

22

2

o

Eu

Eu

EuEu

EuEuL

QQ

QQ

QQQQ

QQQQ

The Reflection Coefficient is Given By:


• 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 QL FROM : QLo L

L o

2 2

L o

2 21

2

1

2

L

• CALCULATE QE FROM:

QQ

EL

O

2

1 • THE SIGN TO USE IS DETERMINED FROM THE PHASE OF 0 USE +VE SIGN FOR r < Z0 AND -VE SIGN FOR r < Z0


LOCUS OF CAVITY IMPEDANCE ON SMITH CHART NEAR RESONANCE

r < ZOr > ZO

r = ZO


R.L. at fLVs. R.L. at fo

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0.0 5.0 10.0 15.0 20.0 25.0 30.0

Return Loss at fo [dB]

Retu

rn L

oss

at fl

[dB]


Reflection Coefficient for Amplitude Measurements

0.500.550.600.650.700.750.800.850.900.951.00

0.00 0.20 0.40 0.60 0.80 1.00

(Magnitude of Roh at fo)^2

(Mag

nitu

de o

f Roh

at

fL)^

2


Fig. 2 Magnitude of Ref. Coeff. Squared Vs. Freq.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.985 0.990 0.995 1.000 1.005 1.010 1.015

Normalized Freq.

|roh|

^2


Fig. 4 Reflection Coeff. Magnitude & Phase for Qu>QE

-360.00

-310.00

-260.00

-210.00

-160.00

-110.00

-60.00

-10.00

0.985 0.990 0.995 1.000 1.005 1.010 1.015

Normalized Frequency

Ph

as

e (

De

gre

es

)

0.000.100.200.300.400.500.600.700.800.901.00

Am

plit

ud

e o

f R

efl

. Co

eff

Sq

ua

red


Fig. 3 Reflection Coeff. Magnitude & Phase for QE>Qu

-30.00

-20.00

-10.00

0.00

10.00

20.00

30.00

0.985 0.990 0.995 1.000 1.005 1.010 1.015

Normalized Frequency

Ph

as

e (

De

gre

es

)

0.000.100.200.300.400.500.600.700.800.901.00

Am

op

litu

de

of

Re

fl. C

oe

ff

Sq

ua

red


PHASE MEASUREMENTS

• MORE SUITABLE FOR LOW Q ( TIGHTLY COUPLED ) SYSTEMS

• AT FREQUENCY SHIFT u = fo / (2 Qu ) , THE IMPEDANCE IS: Zu = r + j r

• INTERSECTION OF THE LOCUS OF Zu WITH THE LOCUS OF THE CAVITY IMPEDANCE DETERMINES A POINT Pu

• MEASUREMENT OF u AND THE RESONANT FREQUENCY fo YIELDS THE VALUE OF Qu = fo /( 2 u )

• AT FREQUENCY SHIFT L = fo / (2 QL ) , THE IMPEDANCE IS: ZL

= r + j(Zo + r )

• INTERSECTION OF THE LOCUS OF ZL WITH THE LOCUS OF THE CAVITY IMPEDANCE DETERMINES A POINT PL

• MEASUREMENT OF L AND THE RESONANT FREQUENCY fo YIELDS THE VALUE OF QL = fo /( 2 L )


PHASE MEASUREMENTS (ctd.)

• LOCUS OF Zu ON THE SMITH CHART CAN BE SHOWN TO HAVE THE EQUATION:

X2 + ( Y + 1 ) 2 = 2

WHERE X = Re Y = Im LOCUS OF Zu IS A CIRCLE OF CENTER (0,-1) AND RADIUS (2)1/2

• LOCUS OF ZL 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)


ˆ

o

ooin ZjrZ

Phase Measurements

Locus of Zin

Locus of ZU

Zo

r = 0 r = 8

Pu

PLLocus of ZL

TRANSMISSION LINE RESONATORS. ENEE 482 Spring 20012 Series and Parallel Resonator Circuits L R T Z...

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Transcript of TRANSMISSION LINE RESONATORS. ENEE 482 Spring 20012 Series and Parallel Resonator Circuits L R T Z...