Exam_Main-2009

Tshwane University of Technology November 2009 Internal Examination - First Examination

Radio Engineering IV Code (RAE 411T) Duration: 3hours

Special requirements: None Only non programmable calculators are allowed Answer all the questions Full marks: 100

Number of of pages:

5

Appendix:

Yes

Course:

Radio Engineering IV

First examiner:

Mr. O.J. Oyedapo

Moderator:

Prof. K. Djouani

QUESTION 1 Marks]

[20

1.1 Differentiate between large scale and small scale propagation models (1) 1.2 What is the Fraunhofer distance df ? (1) 1.3 List three main mechanisms of propagation and the corresponding models based on those propagation models. (3) 1.4 What do you understand by the close in distance ‘d0’ of a propagation model?(1) 1.5 Explain the dependence of surface roughness on the frequency and angle of incidence. (3) 1.6 Answer the following questions: 1.6.1 Explain the advantages and the disadvantages of the two-ray ground reflection model in the analysis of path loss. (3) 1.6.2 What insight does the two-ray model provide about large-scale path loss that was disregarded when cellular systems used very large cells? (2) 1.7 Show that the Brewster angle (case where Γ || = 0 ) is given by θ i where (4) sin θ i

1.8

=

ε r  ε r 

−

1

2 −

1

If Pt=10 W, Gt= 0dB, Gr= 0 dB, and f c = 900 MHz, find Pr in Watts at free space distance of 1 km. (2)

QUESTION 2 Marks]

[30

Assuming a receiver is located 10 km from a 50 W transmitter.  The carrier frequency is 1900 MHz, free space propagation is assumed, Gt=1, Gr = 2. 2.1.1. Find the power at the receiver. (2) 1.2.2 Find the magnitude of the E-field at the receiver antenna. (1) 2.1

Radio Engineering IV (RAE411T) November 2009

Main Examinations

2

Find the open-circuit rms voltage applied the receiver input assuming that the receiver antenna has purely real impedance of  50 Ω and is matched to the receiver. (1) 2.1.4 Find the received power at the mobile using two-ray ground reflection model assuming the height of the transmitting antenna is 50 m, receiving antenna is 1.5 m above the ground, and the ground reflection is -1. (4) 2.2 A general design rule for microwave links is 55% clearance of the first Fresnel zone. For a 1 km link at 2.5 GHz, what is the minimum first Fresnel zone radius? What clearance is required for this system? (5) 2.3 If Pt=10 W, Gt= 10 dB, Gr = 3 dB and L=1 dB , compute the received power for the knife-edge geometry shown in Figure 1. Compare this value with the theoretical free space received power if an obstruction did not exist. What is the path loss due to diffraction for this case when: (17) 2.3.1 f=50 MHz. 2.3.2 f=1900 MHz. 2.1.3

Mountain may be modeled as conducting knife edge

60 m

400 m

5m 3 km

2 km Figure 1:Knife-edge geometry

QUESTION 3 Marks] 3.1

3.1.1

[14

Determine the maximum and minimum spectra frequencies received from a stationary GSM transmitter that has a centre frequency of exactly 1950.000000 MHz, assuming that the receiver is travelling at speeds of: 1km/hr. (3)

Radio Engineering IV (RAE411T) November 2009

Main Examinations

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3.1.2 3.1.3 3.1.4

5km/hr. 100 km/hr. 1000km/hr.

(3) (3) (3)

3.2

Describe the physical circumstances that relate to a stationary transmitting and a moving receiver such that the Doppler shift at the receiver is equal to 0 Hz. (2)

QUESTION 4 Marks]

[22

 Table 1 below represents a cellular system with a 9 cell (nine) cluster size with the cluster covering an area of 7500 km 2. The traffic intensity in Erlangs in each of the 9 (nine) cells are shown. It is known that each user generates an average traffic of 0.08 Erlangs per hour with a mean holding time of 120 seconds. This system is designed for 0.005 Erlangs B GOS with a total of 560 channels available to the entire system.

Cell Numb er  Traffic Erlang

1

2

3

4

5

6

7

8

9

35

68

52

48

30.6

42

37

33.8

64

Determine: 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8

The number of subscribers in each cell. (2) The number of calls per hour per subscriber. (2) The number of calls per hour in each cell. (3) The number of channels in each cell. (2) The total number of subscribers (or users) in the system. (2) The average number of subscribers (or users) per channel. (2) The subscriber density per km2. (2) The total traffic in Erlangs for this system. (2)

Radio Engineering IV (RAE411T) November 2009

Main Examinations

4

The traffic intensity in Erlangs per km2. (2) 4.10 The radius of a cell in this system. (3) 4.9

QUESTION 5 Marks]

[14

5.1 Show that the frequency reuse factor for a cellular system is given by k/S, where k is the average number of channels per cell and S is the total number of channels available to the cellular service provider. (3) 5.2

5.2.1 5.2.2 5.2.3 5.2.4

A cellular service provider decides to use a digital TDMA scheme which can tolerate signal-to-interference ratio of 15 dB in the worst case. Find the optimal value of N for: Ominidirectional antennas. (3) 120° sectoring. (3) 60° sectoring (3) Should sectoring be used? (2)

Radio Engineering IV (RAE411T) November 2009

Main Examinations

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USEFUL FORMULAS Q

=

S 

=

 I 

 D

=

 R

3 N 

S  io

∑ I 

i

i

=1

−n

 P r 

  d    =  P        d    o

o

  d   d 

 P r  (dBm ) =  P o (dBm ) −10 n log   S   I   Au

       

o

= (20) −

n

= λ  H   A = UA  A = UA / C  u

c

u

C 

 A C !

 P r  [blocking  ] =

∑ k ! k 

 P r  [delay

= GOS 

 A k 

C 

=0

 A C 

> 0] =

−1

 A k 

=0

k !

C 

 A

C 

+ C !(1 − )∑  A C 

k 

 D

= Pr[ delay > 0]

t 

 P r (d) =

Γ 

⊥

=

C  −  A

 G G λ 2   P     2  d 2 ( 4 ) π   L    

 P r (d) =

 P r (d) =

 H 

 P d  Ae

(V  / 2) 2  Rant 

− sin θ  +

r 

t 

= =

 E 

120π  V 

2

2

 Ae

=

 P t Gt Gr λ 

(4π )

2

2

d 

=

ε r 

i

ε r 

r 

November 2009

(W )

− cos 2 θ  − cos 2 θ 

i

i

sin θ i i

480π 

2

+ ε  − cos 2 θ  Γ  || = 2 ε  sin θ  + ε  − cos θ  2(d 1 + d 2 ) 2d 1d 2 h = α  Radio Engineering IV (RAE411T) λ d 1d 2 λ (d 1 + d 2 ) r 

2

 E  Gr λ 

4Rant 

sin θ i

− ε 

2

r 

r 

i

i

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v=

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