Consider The Circuit Drawn In Figure 3 Below Matching Network Type 1 Cables Rg 50 12 Mo Vg Type 1 201 500 Er1 1 (88 KiB) Viewed 30 times
Consider The Circuit Drawn In Figure 3 Below Matching Network Type 1 Cables Rg 50 12 Mo Vg Type 1 201 500 Er1 2 (61.17 KiB) Viewed 30 times
Consider the circuit drawn in Figure 3 below: matching network (type-1 cables) RG = 50 12 MO VG "type-1" 201 = 500 er1 = 2 o "type-2" Zo2 = 751 6,2 = 3 O O Z = 150 - 300 1 = 1.5 m Figure 3 A load impedance Z = 150 - 130 is connected to a lossless cable of length ly = 1.5 m and characteristic impedance 202 = 75 2. The cable has a dielectric with relative dielectric constant Er2 = 3. The 1.5 m cable with Zo2 = 75 A is an integral part of the circuit and cannot be removed. We will call this cable "type-2". We wish to connect this system of load + type-2 cable to a distant generator, which produces a steady-state sinusoidal signal at frequency f = 500 MHz. The generator needs to be connected to the rest of the circuit with a cable having characteristic impedance Zo1 = 50 N and a relative dielectric constant €1 = 2. We will call this cable "type-1". The aim of this exercise is to design a circuit that matches the "load + type-2 cable to the generator, using pieces of type-1 cable. In all the questions below, you must obtain the results using a Smith chart. (0) Using the Smith chart, calculate the reflection coefficient r, at the load. [4 marks] (ii) Using the Smith chart, calculate the Voltage Standing Wave Ratio (VSWR) in the type-2 cable. [2 mark] (iii) Calculate the distance between maxima of the standing wave along the type-2 cable. [3 marks] (iv) Using the Smith chart, calculate the impedance seen at point J (see drawing above). looking towards the load. (5 marks]
(v) Using the Smith chart, design a single short-circuited stub that matches the load to the characteristic impedance of the type-1 cable (you may assume that you can cut the coaxial cable at any point and insert a perfect T-piece to connect the stub). Explain in words each step you take to arrive at the result. Once you have obtained the result, describe the stub in terms of its length I, and its distance d from point J. Quote these lengths relative to the signal wavelength (Note: the whole matching circuit is made of type-1 cable). [16 marks] (vi) Now assume you replace the piece of type-2 cable with a different one, that has Er2 = 4, but the same characteristic impedance Zo2 = 75 2. With this new cable, is the stub geometry you designed at point (v) still effective at matching the system? Explain clearly the for your answer. [5 marks) For all the questions that required using a Smith chart, clearly mark on the chart all the relevant points, explain in the text of your assignment paper how you found every point, and include a scan of the Smith chart with your submitted pdf file. reas
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