Respuesta :
The characteristic impedance, the phase constant, the velocity on the line, and the input impedance are respectively;
A) Z_o = 40.82 Ω
B) β = 11.543 rad/m
C) v_p = 2.72 × 10^(8) m/s
D) Z_in = 115.91 Ω
We are given;
Inductance; L = 0.15 μH/m = 0.15 × 10^(-6) H/m
Capacitance; C = 90 pf/m = 90 × 10^(-12) f/m
Frequency; f = 500 MHz = 500 × 10^(6) Hz
Load impedance; Z_l = 80 Ω
Length of transmission line; l = 80cm = 0.8m
A) Formula for characteristic impedance is;
Z_o = √(L/C)
Thus;
Z_o = √((0.15 × 10^(-6))/(90 × 10^(-12)))
Z_o = 40.82 Ω
B) Formula for the phase constant is;
β = ω√(LC)
Where;
ω = 2πf
Thus;
β = (2π × 500 × 10^(6))√(0.15 × 10^(-6) × 90 × 10^(-12))
β = 11.543 rad/m
C) Formula for phase velocity is;
v_p = ω/β
v_p = (2π × 500 × 10^(6))/11.543
v_p = 2.72 × 10^(8) m/s
D) Formula for the input impedance is;
Z_in = Z_o[(Z_l + Z_o*tanβl)/(Z_o + Z_l*tanβl)]
Z_in = 40.82[(80 + 40.82*tan(11.543*0.8))/(40.82 + 80*tan(11.543*0.8))]
Z_in = 40.82(72.1335/25.4031)
Z_in = 115.91 Ω
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