Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 70

Thevenin's theorem is a very popular concept used in the analysis of the low‐frequency lumped element circuits. It is equally applicable to a transmission line network. At the output end of the line, the input source voltage and the line section are replaced by the equivalent Thevenin's voltage, with internal impedance, i.e. the Thevenin's impedance Z_TH [B.12]. Figure (2.8d) shows it. The distance is measured from the load end. Thevenin's voltage is an open‐circuit voltage at the load end. In the case of the open‐circuited load, Z_L → ∞, equation (2.1.86) provides a reflection coefficient Γ_L = 1. Thevenin's voltage is obtained from equations (2.1.88a) and (2.1.97):

(2.98)

On replacing Γ_g from equation (2.1.96), Thevenin's voltage is

(2.1.99)

Thevenin's impedance Z_TH is obtained from equation (2.1.88b) by computing Norton current, i.e. the short‐circuit current at x = 0. Under the short‐circuited load condition at x = 0, Γ_L = − 1, and the Norton current is

(2.1.100)

Thevenin's impedance is obtained as follows:

(2.1.101)