Example Scattering Parameters
Example Scattering Parameters
Example Scattering Parameters
Example: Scattering
Parameters
Consider a two-port device with a scattering matrix (at some
specific frequency ω0 ):
⎡ 0.1 j 0.7 ⎤
S ( ω = ω0 ) = ⎢
⎣ j 0.7 −0.2 ⎥⎦
and Z 0 = 50Ω .
V1 + ( z1 ) = − j 2 e − j β z 1
where z1P = z 2P = 0 .
Determine:
V1 + ( z1 ) = − j 2 e − j β z 1
V1 + ( z1 = z1P ) = − j 2 e − j β z P 1
= − j 2 e − j β (0)
= −j 2
V2+ ( z 2 = z 2P ) = 0
And also:
I 1 ( z 1 = z 1 P ) = I 1+ ( z 1 = z 1 P ) − I 1− ( z 1 = z 1 P )
V1 + ( z1 = z1P ) V1 − ( z1 = z1P )
= −
Z0 Z0
2.0 0.2
= −j +j
50 50
1.8
= −j
50
= − j 0.036
−jπ 2
= 0.036 e
and:
∆P1 = P1 + − P1 −
2 2
V01+ V01−
= −
2Z 0 2Z 0
2 2
(2 ) − ( 0.2 )
=
2 ( 50 )
= 0.0396 Watts