Sample problems 3.pdf - ECE 333 UMass Amherst Sample problems 3 1 Two-wire line The cross-section of a two-wire transmission line in air is shown below

Sample problems 3.pdf - ECE 333 UMass Amherst Sample...

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ECE 333 UMass Amherst Sample problems 3 1. Two-wire line. The cross-section of a two-wire transmission line in air is shown below. The parameters are d = 0.812 mm, σ c = 5.813 × 10 7 S/m, D = 7.5 mm. At 𝑓𝑓 =200 MHz, find (a) R ′, L ′, G ′, and C ′. (b) γ and Z 0 . d D air µ c , σ c
ECE 333 UMass Amherst 2. Coaxial cable. A coaxial cable with 𝑍𝑍 0 = 50Ω is shown in the following figure and operates at 𝑓𝑓 = 8 GHz. (a) Find the per-meter resistance R ′, inductance L ′, conductance G , and capacitance 𝐶𝐶 for this line. (b) Find the complex propagation constant 𝛾𝛾 . How the amplitude of a voltage wave attenuates when it propagates 10m along this cable? 𝜖𝜖 𝑟𝑟 = 2.1, 𝜇𝜇 𝑟𝑟 = 1, 𝜎𝜎 = 5 × 10 −4 S/m
ECE 333 UMass Amherst 3. Low-loss line. For a low-loss transmission line characterized by 𝑅𝑅 ≪ 𝜔𝜔𝐿𝐿 and 𝐺𝐺 ≪ 𝜔𝜔𝐶𝐶 , show that the attenuation 𝛼𝛼 , the phase constant 𝛽𝛽 , and the characteristic impedance 𝑍𝑍 0 are given by

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