### Transmission Lines - Solved Numericals / Problems - 2.

Q.4) A 70 Ω lossless line has s = 1.6 and θΓ = 300o. If the line is 0.6λ long, obtain
(a) Γ, ZL, Zin
(b) The distance of the first minimum voltage from the load

a) Using the smith chart, locate S at s = 1.6. Draw a circle of radius OS. Locate P where θΓ = 300o . At P,

| Γ | = OP / OQ = 2.1 cm / 9.2 cm = 0.228

Γ = 0.228 ∠300o

Also at P, ZL = 1.15 – j0.48,

ZL = ZZL = 70 (1.15 – j0.48) = 80.5 – j33.6 Ω

l = 0.6 λ = 0.6 x 720o = 432o = 360o + 72o

From P, move 432o to R. At R, Zin = 0.68 – j0.25

Zin = ZZin = 70 (0.68 – j0.25) = 47.6 – j17.5 Ω

b) The maximum voltage (the only one) occurs at θΓ = 180o ; its distance from the load is
(180 – 60) λ / 720  =   λ / 6  =   0.1667 Ω

Q.5) A lossless 60 Ω line is terminated by a 60 + j60 Ω load.
(a) Find Γ and s. If Zin = 120 - j60 Ω, how far (in terms of wavelengths) is the load from the generator? Solve this without using the Smith chart.
(b) Solve the problem in (a) using the Smith chart. Calculate Zmax and Zin,min . How far (in terms of λ) is the first maximum voltage from the load?

a)

b)