Answer Happy

[35 Marks] Question 2 - Impedance matching Consider the circuit drawn in Figure 3 below: matching network (type-1 cables) RG = 502 "type-1" Zo1 = 502 "type-2" Z02 = 75Ω VG ZL = 150 - 302 Eri = 2 62 = 3 12 = 1.5 m = Figure 3 A load impedance 2 = 150 - 230 N is connected to a lossless cable of length 12 = 1.5 m and characteristic impedance Zo2 = 75 2. The cable has a dielectric with relative dielectric constant Er2 = 3. The 1.5 m cable with Zo2 = 75 n 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 201 50 N and a relative dielectric constant Er1 = 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. (i) Using the Smith chart, calculate the reflection coefficient Ty 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]