Final Examination. 22 April 2013, 9:30 12:00. Examiner: Prof. Sean V. Hum. All non-programmable electronic calculators are allowed.

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1 UNIVERSITY OF TORONTO FACULTY OF APPLIED SCIENCE AND ENGINEERING The Edward S. Rogers Sr. Department of Electrical and Computer Engineering ECE 422H1S RADIO AND MICROWAVE WIRELESS SYSTEMS Final Examination 22 April 2013, 9:30 12:00 Examiner: Prof. Sean V. Hum NAME: STUDENT NUMBER: TOTAL POINTS: 40 Notes: You can use one double-sided, letter-sized aid sheet. All non-programmable electronic calculators are allowed. Only answers that are fully justified will be given full credit. The last page has formula sheet which can be detached if you wish. GOOD LUCK! Problem 1 Problem 2 Problem 3 Problem 4 TOTAL /10 /10 /10 /10 /40

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3 ECE422 Final Examination Page 1 PROBLEM #1. [10 POINTS] A uniformly-excited parallel array of N half-wave dipole antennas along the x-axis shown in Figure 1 is to be used as a high gain antenna in a monostatic RADAR system. The element spacing is d = 0.75λ at f = 10 GHz. The array is centred at the origin. Figure 1: Antenna array for use as a RADAR a) Write the expression for the total electric field produced by an array with N = 6 elements, and plot the E-field pattern of the array on a polar plot in the H-plane, noting all null locations. [3 points]

4 ECE422 Final Examination Page 2 b) The EIRP of the RADAR system is 1 kw and an aircraft approaches the array from the broadside direction (φ = 90 ) at a distance of 50 km, as shown in Figure 2(a). If the RADAR echo from the aircraft has a power density of dbw/m 2 and a frequency of f = 10, 000, 018, 148 Hz, determine the radar cross section of the aircraft and its velocity. [2 points] array array (a) Single-target detection problem (b) Multiple-target problem detection Figure 2: RADAR system for aircraft detection

5 ECE422 Final Examination Page 3 c) Two aircraft at the same distance R are to be resolved as shown in Figure 2(b). The array is to be mechanically rotated in the xy plane to resolve the two targets. If the aircraft are separated by an angle of φ sep = 10, determine the minimum number of elements N required so that the two aircraft can be properly resolved as the array is rotated. Ignore sidelobes produced by the array. [3 points] d) It has been proposed that the beam from the array could be electronically scanned by introducing a phase gradient α between the elements. Assuming this can be implemented, explain any limitations that may arise given the target angular separation constraint given in part (c), and also the fact that the two aircraft could be located anywhere along the dashed circle shown in Figure 2(b). [2 points]

6 ECE422 Final Examination Page 4 PROBLEM #2. [10 POINTS] A satellite link is shown in Figure 3(a). The uplink operates at 28 GHz while the downlink operates at 14 GHz. downlink amplifier uplink active filter transmission line (a) Link geometry (b) Downlink receiver components Figure 3: Geosynchronous satellite communications system a) Consider the uplink first. If the ground station uses an impedance-matched transmitter with an output power of 100 W that is fed into a circular reflector antenna with a diameter of 3 m and an aperture efficiency of 70%, determine the power density produced at the satellite if it is in geosynchronous orbit at an altitude of H = 35, 795 km. The atmospheric losses at sea level are defined by α = 1 db/km, the scale height is 4 km, and the ground station is located at an elevation of 200 m. [2.5 points]

7 ECE422 Final Examination Page 5 b) Next, consider the downlink, which is characterized by atmospheric attenuation losses amounting to 1 db at a physical temperature of T 0a = 220 K and rain attenuation losses amount to 4 db at a physical temperature of T 0r = 260 K. The background sky temperature is T sky = 56 K. Determine the antenna temperature if the receiving antenna on the downlink has a radiation efficiency of 90%. Determine the receiver figure of merit if the gain of the downlink antenna is 50 dbi. [1.5 points] c) The front-end of the receiver is to be constructed from the components in Figure 3(b). Propose and draw connection of the components shown so that the overall noise figure of the receiver front-end is minimized, and determine the overall receiver and system temperatures. The characteristics of the components are as follows: [3 points] Amplifier, G = 10 db, F = 2 db Active filter, G = 20 db, F = 3 db Transmission line, L = 4 db

8 ECE422 Final Examination Page 6 d) If the downlink EIRP is 36 dbw and the minimum CNR required by the system is 8 db, determine the available link margin on the downlink. The elevation angle of the ground station antenna on the downlink is α = 30, and the bandwidth of the signal is 20 MHz. [3 points]

9 ECE422 Final Examination Page 7 PROBLEM #3. [10 POINTS] A terrestrial microwave point-to-point link is used for backhaul communications at 5 GHz. The link is at sea level. a) Aperture antennas are used on the transmitter and receiver, each with a radiated E-field defined by E θ (θ, φ) = { E0 e jβr r (sin θ cos 2 φ) 1/2 0 θ π, 0 φ π/2, 3π/2 φ 2π 0 elsewhere. Determine the directivity of the antenna. Note: cos 2 x = cos 2x; 2 2 sin2 x = 1 1 sin 2x 2 2 [3 points]

10 ECE422 Final Examination Page 8 b) The refractivity of the atmosphere is described according to N(h) = h km h 2 km, where h km is the altitude in km. Determine the maximum distance the transmitter and receiver could be separated if h t = 150 m and the top of the tower is at an elevation of h = 400 m, without being obstructed by the earth. [2 points] c) Next, ignore atmospheric refraction and assume a planar earth. If the transmitter and receiver are separated by 42 km, determine the transmitter height h t near 150 m so that the reflection from the earth produces constructive interference with the line-of-sight path at the receiver location, if h r = 100 m. [2 points]

11 ECE422 Final Examination Page 9 d) The minimum required CNR of the link is 10 db. The receiver is mounted on a tower of height h r = 100 m. If the receiving antenna temperature is 310 K, determine the maximum noise figure of the receiver to maintain a required link margin of 5 db, when atmospheric and rain losses are zero. The transmitter height used is that from part (c), the bandwidth of the signal is 10 MHz, and the transmitter power into the antenna is 2 W. Assume the transmitter and receiver antenna gains are 5 dbi if you were unable to complete part (a). [3 points]

12 ECE422 Final Examination Page 10 PROBLEM #4. [10 POINTS] Two infinitesimal dipoles are placed in a crossed arrangement as shown in Figure 4. The dipoles are identical with dipole 1 oriented along the x-axis and dipole 2 along the y-axis. The antennas do not touch or electrically interact with each other. In the transmitting mode, the currents I 1 and I 2 are excited on each of the antennas. Figure 4: Crossed-dipole arrangement a) Write an expression for the vector effective length of the entire radiating system of antennas if I 1 = I and I 2 = j2i. [2 points]

13 ECE422 Final Examination Page 11 b) Write an expression for unit vector ˆl eff of the antenna system evaluated at a point P (0, 0, z) along the z-axis (z > 0). Express your answer in terms of Cartesian unit vectors. What is the polarization of the antenna? What is its axial ratio? [2 points] c) An incoming plane wave travelling in the z direction impinges upon the antenna. At z = 0 the electric field strength is E i = 30ˆx j40ŷ V/m. Describe the polarization of the incoming wave and its axial ratio. [2 points]

14 d) What is the magnitude of received open-circuit voltage produced across the terminals of dipole 1? dipole 2? [2 points] e) In the receiving mode, signals received by each dipole are phased and combined in a process that is reciprocal to the transmitting mode. Using your answer from part (b), determine the polarization loss factor between the antenna system and the incoming wave. Express your answer in db. [2 points]

15 ECE422 Final Examination Page 13 USEFUL FORMULAE Free space impedance: η = 120π 377 Ω Free space wavenumber: β = 2π λ Far field from a half-wave dipole at the origin: E θ = jηi 0 2π Time-average Poynting (power density) vector: P = 1 2 E H Radiation intensity: U(θ, φ) = P r r 2 Average radiation intensity: U avg = 1 4π 2π π 0 0 U(θ, φ) sin θdθdφ = W t 4π. Maximum antenna gain: G m = 4πr2 Pr max W rad +W loss = 4πUmax W rad +W loss Conversion from gain in db to gain in linear scale: G db = 10 log 10 G AF of uniform linear array: f = sin(n ψ/2)/n sin(ψ/2) Aperture antennas: θ 1 θ 2 D = 4π Friis formula in free space in linear scale: Wr W t exp( jβr) cos( π 1 cos θ) r 2 sin θ = G t G r ( λ 4πr) 2 P LF (1 Γt 2 )(1 Γ r 2 ) Friis formula in free space in db: W r (dbw or dbm) = ( ) 4πR W t (dbw or dbm) + G t (db) + G r (db) 20 log λ +10 log(p LF ) + 10 log(1 Γ r 2 ) + 10 log(1 Γ t 2 ) Friis formula with plane-earth reflection: Wr W t 2(d Fresnel-Kirchoff coefficient: v = h 1 +d 2 ) λd 1 d 2 Lee approximation: g diff (db) = ( = G t G λ r 4πR = α 2d 1 d 2 λ(d 1 +d 2 ) ) ( 2 ) 4 sin 2 2πh 1 h 2 λr 0 v 1 20 log( v) 1 v 0 20 log(0.5 exp( 0.95v)) 0 v 1 20 log( ( v) 2 1 v log ( v Refractivity of air: N = 10 6 (n 1) = 77.6 T in mb, e = water vapour pressure in mb ) v > 2.4 ( ) p e T, T = temperature in K, p = pressure

16 ECE422 Final Examination Page 14 Radius of the earth: R e = 6368 km Atmospheric refraction: 1 K = 1 + R e dn dh Atmospheric attenuation constants in db/km: a o = { [ a w = [ ] fghz (f GHz f 2 57) GHz f GHz < 57 a o (57) + 1.5(f GHz 57) f GHz ρ (f GHz 325.4) Geosynchronous orbit altitude: 6.61 earth radii Boltzmann s constant: k = J/K Noise figure: F = 1 + Te T (f GHz 22.2) (f GHz 183.3) ] fghz 2 ρ f < 350 Noise temperature of passive network (with respect to input): T e = (L 1)T g Cascaded noise temperature: T e = T e1 + T e2 G 1 Sky temperature: Link budgets: [ C N 0 ] U RCS: σ = 4πR 2 Pr P i + T e3 G 1 G T en G 1 G 2 G N 1 T sky = T sky + (L a 1)T 0a + (L r 1)T 0r L a L r L a L r L r = EIRP G F SL U L U + G S T S (units: db-hz) Radar range equation (monostatic RADAR): W r = A eff,r P r = A eff,rw t G t σ (4πR 2 l) 2

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