Scattering Matrix

초고주파공학

조용희

 Voltage: electric field

 Current: magnetic field

 ^



12 1

E d l

V

 ^



H d l I



 Voltage-current definition

 Power-voltage definition

 Power-current definition

I V Z

 /





2

0

V / P 2

Z 

2 av

0

2 P / I Z 



TEM line

Non-TEM line The definition of Z is not unique except for TEM line



 Power delivered to a network

 Power in terms of V and I

 Input impedance





S

E H d s P

j W W

P  ₂ ¹  

   ^{2 } 

*

2 1 VI P 



 

in 2

5 . 0 2

I

W W

j P

I jX V

R

Z    

 



 Voltage

 Current









n

V V

V











n

I I

I

 Matrix definition: open load

 

 





 

 





 

 





 

 







 

 





 

 





N NN

N N

N N

N

I

I I

Z Z

Z

Z Z

Z Z

Z

V V

V













2 1

2 1

2 21

1 12

11 2

1



     ^{V  Z I} _ ^{Z  V}

 Matrix definition: short load

 

 





 

 





 

 





 

 







 

 





 

 





N NN

N N

N N

N

V

V V

Y Y

Y

Y Y

Y Y

Y

I I

I













2 1

2 1

2 21

1 12

11 2

1



     ^{I  Y V}

j i ij

V Y I





 

 Matrix definition: matched load

 

 







 

 







 

 





 

 







 

 







 

 



















NN N N

N

N N

N

V

V V

S S

S

S S

S S

S

V V V













2 1

2 1

2 21

1 12

11 2

1



  ^V

^{   S}   ^V

_ ^{S  V}

 Matched T-shaped 3 dB attenuator with Z₀ = 50 Ohms, R₁ = R₂ = 8.56 Ohms, and R₃ = 141.8 Ohms



 Matrix definition: matched load

gain :

isolation :

reflection :

, where

21 12

22 11

2 1 22

21

12 11

2 1

S S

S S

V V S

S

S S

V

V 



 



 



 



 

 

 















 Power gain

 Available gain: conj. matched source and load

 Transducer power gain: conj. matched source

network the

input to Power

load the

to delivered

Power

IN



 P G

P



source the

from available

Power

network the

from available

Power

AVS AVN



 P G

P

source the

from available

Power

load the

to delivered

Power

AVS



 P

G

P