Spring 2019 Midterm 1_Q1-3.pdf - ECE 333 UMass Amherst Spring 2019 Midterm 1 questions 1-3 with slight modifications 1[25 pts The voltage wave along a

Spring 2019 Midterm 1_Q1-3.pdf - ECE 333 UMass Amherst...

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ECE 333 UMass Amherst 1 Spring 2019 Midterm 1, questions 1-3 with slight modifications 1. [25 pts] The voltage wave along a transmission line has the following expression. 𝑣𝑣 ( 𝑧𝑧 , 𝑡𝑡 ) = cos(6 𝜋𝜋 × 10 8 𝑡𝑡 + 4 𝜋𝜋𝑧𝑧 ) − √ 2 sin 6 𝜋𝜋 × 10 8 𝑡𝑡 + 4 𝜋𝜋𝑧𝑧 − 𝜋𝜋 4 (V) (a) [8 pts] Find the direction of propagation (i.e., the + 𝑧𝑧 or −𝑧𝑧 direction), the frequency 𝑓𝑓 in Hz, the wavelength 𝜆𝜆 in meters, and the phase velocity 𝑢𝑢 𝑝𝑝 in m/s. (b) [10 pts] Find the expression for the phasor 𝑉𝑉 ( 𝑧𝑧 ) in polar form. (c) [7 pts] At time 𝑡𝑡 = 0 , find the locations in 𝑧𝑧 where the voltage is equal to zero. 2. [25 pts] The cross-section of a coaxial cable with a purely resistive characteristic impedance that operates at 𝑓𝑓 = 10 GHz is shown in the following figure. The line has a per-meter resistance of 𝑅𝑅 = 5 ( Ω /m) , and the insulating material has a conductivity of 𝜎𝜎 = 2 × 10 −4 (S/m)

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