# EIE 235 Class Test (1 hour working time for the total of - PolyU

Class Test – Answers and solutions True or false (2 marks per correct answer, -1 penalty for incorrect answers, total maximum of 20 marks) 1. True 2. True 3. False 4. False 5. True 6. False 7. True 8. False 9. False 10. True Short answers (3 marks per correct answer each, 15 marks total) 1. What is the channel capacity for a teleprinter channel with 300Hz bandwidth and SNR of 3dB where the noise is white thermal noise? SNRdB = 3 = 10logSNR, SNR = 100.3 = 1.995 C = B*log2(1+SNR)= 474.76 bit/s 2. How long will it take to transmit a block of data of 4MB on a distance of 10000km if average speed of the signal is 0.8c (speed of light c=3 * 108 m/s) and data rate is 500 bit/s. The dalay in sending a signal over distance d=10000km with a speed of v=0.8c=2.4*108 m/s is Equal to td = d/v = 1/24 s, Time to transmit 4MB data at a rate of 500bit/s tt = 4*106/500=8000 s Total time t = tt + td = 8000.04 s 3. Calculate the height of a radio antenna which could cover line of sight transmission in a circle of 100km diameter around it Radius of the circle around the mast R = 0.5 d = 50km = 3.57 √(4/3 * h) hence 2 h = 3/4 (R/3.57) = 147.11 m 4. 1GHz transmission with a signal power at the receiver of 0.1W experiences thermal noise of temperature T=800K. What is the theoretical channel capacity? Noise power at T=800K equals N = kTB = 1.38 * 10-23 J/K * 800 K * 109 1/s = 11.04 * 10 -12 W Channel capacity C = B*log2(1+P/N) = 33 * 109 5. What are the wave lengths of signals at frequencies of 60Hz and 1.8GHz? λ1 = c/f1 = 5000 km, λ2 = c/f2 = 16.66 cm Long answers (5 marks per correct answer each, 15 marks total, show full working and express all answers in appropriate units) 1. Calculate the mean value of a sinusoidal signal which passed through a detector/rectifier and at its output can be expressed as a function of time f(t)=∣Asin(2πt/T)∣. Mean value of the signal is equal to fmean = 1/T * 0 ∫T ∣Asin(2πt/T)∣dt = 2. 2A/T * 0 ∫T/2 sin (2πt/T)dt = A/π(1 – cosπ) = 2A/π A microwave transmitter has an output of 0.1W at 2GHz. Signal is transmitted by a parabolic antenna of 1.2m diameter over free space to a receiver which has a parabolic antenna with the same parameters. The distance between the stations is d=24km. Find the available signal power out from the receiving antenna. λ= c/f = 15cm, effective area of the antenna Ae=0.56A=0.56πR2 Gain of each antenna can be expressed as G = 4πAe /λ2 = 353.73 = 25.49dB Loss over d=24km free space can be expressed as L = 10log(4πd/λ) 2 = 126dB 3. Total loss is equal to L - 2*G =75dB which corresponds to the output power of the second antenna of P2 = 3.16 nW A digital system is required to operate at 9600bps. What would be the required channel bandwidth if each signal element encodes a 4bit word? What would be the answer in the case of 8bit words? Nyquist formula for channel capacity reads C=2Blog2M where B is the required bandwidth and M denotes number of signal elements. For 4bit words M=24=16 hence 9600=8B and B=1200Hz For 8bit words M=28=256 hence 9600=16B and B=600Hz

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