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