II-3HOII-3. Scattering Matrix (1) Normalized Voltage Waves-(1) 1-port NW : to/from the Load V + ( x) = Z 0 a( x) V ( x) = Z 0 b( x) Normalized Waves v( x) ≡ V ( x) Z0 V + ( x) Z0 V ( x) Z0 1 x Incident wave to the Load i ( x) ≡ Z 0 I ( x) a ( x) ≡ b( x ) ≡ ∴ v ( x ) = a ( x ) + b( x ) i ( x) = a ( x ) b( x ) (4) (5) Ae jβx ≡ V ( x) + Reflected wave from the Load Be + jβx ≡ V ( x) Then the voltage and current waves are V ( x) = V ( x) + V ( x) I ( x) = I ( x) I ( x) V + ( x) V ( x) = Z0 Z0 + + and (1) (2) a ( x) = b( x) = b( x ) = Γ ( x) a ( x ) (6) The normalized incident and reflected v. w.s are Also, the reflection coefficients are V ( x) Γ( x) = + (3) V ( x) 1 [v( x) + i( x)] = 1 [V ( x) + Z 0 I ( x)] 2 2 Z0 (7) (8) 1 [v( x) i( x)] = 1 [V ( x) Z 0 I ( x)……