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