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Microwave Engineering CHO, Yong Heui Resonator

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(1)

Microwave Engineering

CHO, Yong Heui

(2)

EM Wave Lab

2

 Filter

 Oscillator

 Frequency meter

 Tuned amplifier

(3)

 Input impedance

 Input power

 Resonant frequency: Wm = We

C L j

j

Z

in

   

 

 

 

C

L j j

I I

Z VI

P

in * in 2 2

 

2 1 2

1 2

1

LC

 1

(4)

EM Wave Lab

4

 R, L, C

 Input impedance

 Input power

 Resonant frequency

C L j

j R

Z

in

    

 

 

  

C

L j j

R I

I Z

VI

P

in * in 2 2

 

2 1 2

1 2

1

LC

 1

(5)

 Definition

 3 dB bandwidth

 Q in terms of R, L, C

d loss/secon Energy

stored energe

Average

Q

BW f

0

Q

RC R

L P

Q W

l m

0 0

0

2 1

   

(6)

EM Wave Lab

6

 Input impedance

 

     

 

 

R j L R j L

Z

2

2

2 0 2

in

(7)

 R, L, C

 Input admittance

 Input power

 Resonant frequency

C L j

j

Y R

 1

in

 

 

  

j C

L j V R

V Y

VI

P

 1

2 1 2

1 2

1

* 2 2

in

* in

LC

 1

(8)

EM Wave Lab

8

 Q in terms of R, L, C

L RC R

P Q W

l m

0 0

0

2 

   

(9)

 Input admittance

 

     

 

 

j C

C R R j

Y 1 1 2

2 2 0 2

in

(10)

EM Wave Lab

10

 Unloaded Q: resonant circuit itself

 Loaded Q: External load resistor

Q Q

Q

L e

1 1

1  

(11)

 Transmission line

 Input impedance: lossy medium

 

) tanh(

) tan(

1

) tan(

) tanh(

tanh

0

0 in

l l

j

l j

Z l

l j

Z Z

 

(12)

EM Wave Lab

12

 Low-loss transmission line

 Phase:

l l

 )  tanh(

2 /

0

 , 

    l

0 0

) tan(

)

tan( 



 

l    

(13)

 Input impedance

 Quality factor

 





 

 

 

 

 

jL R

j l

l Z j

j Z l

Z

2

) /

( 1

) /

(

0 0

0 0 0

in

2 2

0

 

R l

Q L

(14)

EM Wave Lab

14

 Transmission line

 Input impedance: lossy medium

 

) tan(

) tanh(

) tanh(

) tan(

1

coth

0

0 in

l j

l

l l

Z j

l j

Z Z

 

(15)

 Low-loss transmission line

 Phase:

l l

 )  tanh(

2 /

0

 , 

    l

0 0

) tan(

)

tan( 



 

l    

(16)

EM Wave Lab

16

 Input impedance

 Quality factor







 

 

 

jC R

j l

Z j

l

l Z j

Z

2 /

1

1

) /

( )

/ (

) /

( 1

0 0

0 0 0

in

 

2

0

 2 

RC l

Q

(17)

 Metallic wall

 Propagation constant

 Resonant condition

2 2

2

 

 

 

 

 

b

n a

k m

mn

 

mn

dl

(18)

EM Wave Lab

18

 Resonant wavenumber

 TE101 mode and TM110 mode

 Q of cavity

2 2 2

 

 

 

 

 

 

 

 

 

d l b

n a

k

mnl

m   

l e

P Q 2 W

0

(19)

 Metallic wall

 Propagation constant

 Resonant condition

 TE111 mode and TM110 mode

mn

dl

(20)

EM Wave Lab

20

 High Q

 Fringing field

 High permittivity: magnetic wall

 Mechanical tuning

 TE01d mode

 Notation

1 /

2 

L

g

d

(21)

 Two mirrors

 High Q

 Laser

 Millimeter and optical applications

참조

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