Voltage @z=−l | | V i n c | = 2 Z 0 ⋅ P i n c | V r e f l e c t e d = V i n c ⋅ Γ L ⋅ e − 2 j β l | V r e f l e c t e d | = 2 Z 0 P i n c ⋅ | Γ L | | | V i n | = 2 P i n R e ( 1 Z i n * ) = 2 P i n c ( 1 − | Γ L | 2 ) ⋅ R e ( 1 Z i n * ) |
Current @z=−l | | I i n c | = 2 ⋅ P i n c Z 0 | I r e f l e c t e d = V i n c ⋅ Γ L ⋅ e − 2 j β l − Z 0 | I r e f l e c t e d | = 2 P i n c Z 0 ⋅ | Γ L | | | I i n | = 2 P i n R e ( Z i n ) = 2 P i n c ( 1 − | Γ L | 2 ) ⋅ R e ( Z i n ) |
Power @z=−l | P i n c = 1 2 R e ( V i n c ⋅ I i n c * ) | P r e f l e c t e d = 1 2 R e ( V r e f l e c t e d ⋅ I r e f l e c t e d * ) = 1 2 R e ( V r e f l e c t e d ⋅ ( − V r e f l e c t e d Z 0 ) ) = − | V r e f l e c t e d | 2 2 Z 0 = − P i n c ⋅ | Γ L | 2 | P i n = 1 2 R e ( V i n ⋅ I i n * ) = 1 2 | V i n | 2 R e ( 1 Z i n * ) ≡ 1 2 | I i n | 2 R e ( Z i n ) |