1 EXAMPLE !!!! COMS4104/COMS7104 Mid-semester Exam Sample Instructions: For Questions 1-2: On the left hand side, adjacent to the statement, draw a little circle for a correct statement and a little cross for an incorrect statement. For Questions 3-4 write your solution in the provided space. -------------------------------------------------------------------------------------------------------------- Q1. Microstrip, stripline and slotline transmission lines (a) A microstrip line is a two-conductor transmission line and hence it can support pure TEM mode. (False) (b) A microstrip is a non-TEM transmission line because it is surrounded by a composite dielectric material. (True) (c) The stripline operating at TEM mode is non-dispersive because its phase velocity does not vary with frequency. (False) (d) For its proper operation the slotline requires one sheet of conductor with a longitudinal slot and the other sheet of conductor for a ground plane like a microstrip. (False) (e) The three definitions as given by voltage-current ratio, voltage squared-power ratio or power- current squared ratio lead to the same value of characteristic impedance for the pure TEM transmission line such as stripline or coaxial line. (True) (f) For a lossless stripline its characteristic impedance can be determined using the value of relative dielectric constant (of a dielectric substrate material) and the capacitance per unit length. (True) (g) The difficulty of realizing a microstrip with the characteristic impedance of 10ohm using a typical dielectric substrate is due to the fact that the width of the strip will be large and the resulting transmission line will support propagation of higher order modes. (True) Q2. Passive Microwave Devices (a) For a TEM transmission line, scattering matrix parameters provide suitable relationships between forward and backward traveling voltage waves. The complex voltage magnitudes need to be scaled by the square root of the characteristic impedance so that: 2 (i) The squared magnitudes of normalized voltage can represent power carried by forward and backward traveling waves (True) (ii) The scattering matrix parameters Sik=Ski for i≠k for passive reciprocal circuits (True) (b) The reason for introducing the ABCD matrix parameters for microwave circuits is because (i) They are more convenient to use when dealing with series and parallel connections of microwave components (False) (ii) They are more convenient to use when dealing with cascaded circuits (True) (iii) They are more useful than S parameters because they provide measure of power densities for waves traveling in microwave networks (False) (c) At a given frequency, the relationship between the input reflection coefficient and a load reflection coefficient of a two-port network is fully described by: (i) Two complex numbers (False) (ii) Three complex numbers (True) (iii) Four complex numbers (False) (e) The property of an N-section binomial impedance transformer is that (i) It provides an input reflection coefficient with N-1 ripples in the pass-band (False) (ii) It provides a flat characteristic of the input reflection coefficient with a 0-value at the centre frequency of a given band (True) (iii) It provides an input reflection coefficient with maximum return loss at the centre frequency of a given band (False) 3 Q3. Show that ABCD matrices for the chosen circuits are as follows (a) For impedance Z connected in series with a transmission line: 10 1 Z (b) For admittance Y connected in parallel with a transmission line: 1 01 Y 4 Q4. Show that for an non-ideal 4-port reflectometer represented by an ideal reflectometer and a two-port error characterized by the scattering parameters {eik}, the relationship between the measured reflection coefficient Γm and the actual reflection coefficient Γa is given by the following expression: a a m e eee Γ− Γ +=Γ 22 2112 11 1
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