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

**Q.4) A 70 Ω lossless line has s = 1.6 and θ**

_{Γ}= 300^{o}. If the line is 0.6λ long, obtain**(a) Γ, Z**

_{L}, Z_{in}**(b) The distance of the first minimum voltage from the load**

**Answer:**

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

_{Γ}= 300

^{o}. At P,

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

Γ = 0.228 ∠300

^{o}

Also at P, Z

_{L}= 1.15 – j0.48,

Z

_{L}= Z

_{o }Z

_{L}= 70 (1.15 – j0.48) = 80.5 – j33.6 Ω

l = 0.6 λ = 0.6 x 720

^{o}= 432

^{o}= 360

^{o}+ 72

^{o}

From P, move 432

^{o}to R. At R, Z

_{in}= 0.68 – j0.25

Z

_{in}= Z

_{o }Z

_{in}= 70 (0.68 – j0.25) = 47.6 – j17.5 Ω

b)

**The maximum voltage (the only one) occurs**at θ

_{Γ}= 180

^{o}; 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 Z**

_{in}= 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 Z**

_{max}and Z_{in,min}. How far (in terms of λ) is the first maximum voltage from the load?

**Answer:**

a)

b)

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