课程论文代写_工程课程作业代写：Bachelor and Master of Engineering

Examination for the Degrees of
Bachelor and Master of Engineering

工程课程作业代写 If a pair of identical antennas is used to transfer a radio signal from one place to another, ideally the antennas should be aligned

All questions carry 20 marks each
The maximum for this paper is 60 marks Calculators must have the Engineering Faculty seal of approval.

Q1  工程课程作业代写

(a) Maxwell’s equations, assuming phasor fields and sinusoidal sources, in vacuum are:  工程课程作业代写

Show that in a charge-free vacuum, the solution for electric field E obeys Helmholtz’s second-order differential equation:

(b) represents a plane wave travelling in the z direction. Show that this is a solution for Helmholtz’s equation (A is an arbitrary constant). (3 marks)

(c) Determine the magnetic field intensity, H, associated with the plane wave in part (b). (3 marks)

Plane waves do not, of course, have to travel along the axes of the co-ordinate system. Consider for the remainder of this question a plane wave travelling in the y-z plane at an angle  from the z-axis 工程课程作业代写

(d)represents the Electric field for this plane wave. Show that it, too, is a solution for Helmholtz’s equation. (6 marks)

(e) Determine the magnetic field intensity, H, associated with the plane wave of part (d). (5 marks)

Q 2

A 50 Ohm transmission line is terminated in a 70 Ohm resistive load, operated at a frequency of 1GHz. Assume for convenience in this question that the phase velocity on all transmission lines is the speed of light in vacuum (3×108 m/s).

(a) Design a quarter-wavelength transformer to eliminate the mismatch. (4 marks)

(b)

Find the reactances needed to achieve a loss-less (purely reactive) matching network, as shown in Figure Q2(b). (9 marks)

(c) Select components and their component values that give the required reactances for Figure Q2(b). (4 marks)
(d) Do these two matching methods work at frequencies away from the design frequency? Explain your answer. (3 marks)

Q 3  工程课程作业代写

The propagation constant for electromagnetic waves propagating in a uniform medium is defined as:

(a) Explain the role of the real and imaginary parts of this constant in the wave’s propagation. (2 marks)  工程课程作业代写
(b) The relative importance of losses (attenuation) caused by materials are often expressed as a loss tangent. Define loss tangent in terms of the quantities in the above equation. (2 marks)
(c) Wireless spectrum is a limited resource and expensive to acquire. An operator wishes to offer new data services to customers in their homes and has identified two available parts of spectrum:
 790-862MHz (frequencies previously-used for TV broadcast)
 59-64GHz

By estimating factors such as attenuation in the home environment, portability and bandwidth, discuss the advantages and disadvantages of these two bands for this application; include supporting calculations.

You will find the following facts useful:

You may also find it helpful to be reminded of De Moivre’s theorem:

If z is a complex number(16 marks)

Q 4

Helmholtz’s equation for the time domain Electric Field is

(a) Show that is a solution to this equation (where A is an arbitrary constant and(6 marks)

(b) This solution is called a “circularly polarised” plane wave since its angle of polarization rotates as it travels. Derive an expression for the angle (in radians) of its polarisation as a function of distance. (3 marks)
(c) Over a distance of half of one wavelength, by how many radians does the direction of polarisation change? (2 marks)
(d) What is the wave’s direction of propagation? Explain your answer.(2 marks)  工程课程作业代写

(e) If a pair of identical antennas is used to transfer a radio signal from one place to another, ideally the antennas should be aligned with each other. Explain why this is. (2 marks)
(f) It is possible to build antennas to transmit and receive circularlypolarised waves. This is commonly done in systems that communicate between the earth and a satellite in space. Suggest
why this is the case. (2 marks)
(g) The plane wave of part (a) travels from the negative-z direction and is incident on an infinitely-wide sheet of perfectly-conducting metal plane located at z=0. Derive an expression for the wave reflected from the metal plane. (3 marks)

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