Workshop08Lossy

Workshop08Lossy - ECE 3030 Electromagnetic Fields and Waves...

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Unformatted text preview: ECE 3030: Electromagnetic Fields and Waves Fall 2009 WORKSHOP 8 INSTRUCTOR NOTES: Transmission Lines Reminder: Prelim 2 next Tuesday: no Homework 8. Date: Thursday 10/22 1. Problem 13.26: An unknown load is connected to a sinusoidal voltage source via a transmission line, as shown in Figure 1. The maximum amplitude (single-sided, not Figure 1: Unknown load fed by a transmission line from a sinusoidal source. peak-to-peak) of voltage oscillations V ( z,t ) on the transmission line are measured at each location on the transmission line during operation and plotted plotted in Figure 2. a. What is the frequency of the voltage source in Hz? b. What is the magnitude | Γ L | of the load-reflection coef- ficient? c. What is the phase of the load-reflection coefficient Γ L ? Give a numerical value in de- grees. d. What is the magnitude | I + | of the forward current wave on the transmission line? e. What is the value of the load impedance Z L ? Figure 2: Standing-wave pattern along the transmission line of Figure 1. Solution: The plot of the maximum voltage of a standing wave pattern as a function of distance along the transmission line is functionally given by | V ( z ) | = | V + | p 1 + | Γ L | 2 + 2 | Γ L | cos(2 kz + φ ) where V ( z ) = V + £ e- jkz + Γ L e + jkz / and Γ L = | Γ L | e jφ . a. The variations in the plot have a periodicity of half the wavelength, and so λ = 8 mm, corresponding to a frequency of f = c/λ = 37 . 5 GHz. b. SWR = V max V min = 3 = 1 + | Γ L | 1- | Γ L | = ⇒ | Γ L | = 1 2 . c. The first minimum in | V ( z ) | occurs when 2 kz + φ = ± π in | V ( z ) | = | V + | p 1 + | Γ L | 2 + 2 | Γ L | cos(2 kz + φ ) CORNELL UNIVERSITY c WES SWARTZ (09/8/14) 8–1 ECE 3030: Electromagnetic Fields and Waves Fall 2009 WORKSHOP 8 INSTRUCTOR NOTES: Transmission Lines or- 2 2 π λ ¶ . 003+ φ = ± π = ⇒- 3 π 2 + φ = ± π = ⇒ φ = π 2 = ⇒ Γ L = j 1 2 . d. | I + | = | V + | Z . Get | V + | from | V + | = | V max | 1 + | Γ L | = 6 1 + 1 2 = 4 Volts....
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Workshop08Lossy - ECE 3030 Electromagnetic Fields and Waves...

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