Dr. Hugh Blanton ENTC 4307/ENTC 5307 TELECOMMUNICATIONS Dr. Hugh Blanton ENTC 4307/ENTC 5307

Solutions to Test 1

1. Definitions RF—Implies the frequencies where the wavelength, l, becomes equal or smaller than the physical components in the circuits. Continuous—A signal which can take an infinite number of different values between a minimum and a maximum. Dr. Blanton - ENTC 4307 - Solution_Test_1 3

Discrete—A signal which can take only a finite number of different value. Wireless—A term used to describe telecommunications in which electromagnetic waves (rather than some form of wire) carry the signal over part or all of the communication path. Dr. Blanton - ENTC 4307 - Solution_Test_1 4

Random—A rule that assigns one and only one numerical value to each sample point in a random experiment. Deterministic—A model where a set inputs always produce the same outputs. Dr. Blanton - ENTC 4307 - Solution_Test_1 5

2. Complex Numbers a. Express z1 and z2 in polar form. b. Find | z1 | and | z2 | and calculate the product z1  z2 and the ratio z1 / z2 in polar form. Dr. Blanton - ENTC 4307 - Solution_Test_1 6

3. RF The presence of the transmission line can be ignored when: a. l = 0.1 m, f = 1 GHz transmission line cannot be ignored! b. l = 1 m, f = 1.8 GHz transmission line cannot be ignored! Dr. Blanton - ENTC 4307 - Solution_Test_1 7

3. RF c. l = 0.01 m, f = 0.9 GHz transmission line cannot be ignored! d. l = 5 cm, f = 5.4 GHz transmission line cannot be ignored! Dr. Blanton - ENTC 4307 - Solution_Test_1 8

4. Smith Chart a. Reflection coefficient (G): b. Standing wave ratio (SWR): c. Input impedance (ZIN): Dr. Blanton - ENTC 4307 - Solution_Test_1 9

4. Smith Chart d. Input admittance (YIN): e. Shortest line length Dr. Blanton - ENTC 4307 - Solution_Test_1 10

4. Smith Chart 0.144l 0.494l Dr. Blanton - ENTC 4307 - Solution_Test_1 11

5. Stub Tuning Dr. Blanton - ENTC 4307 - Solution_Test_1 12

6. Uniform Distribution Dr. Blanton - ENTC 4307 - Solution_Test_1 13

7. PDF Dr. Blanton - ENTC 4307 - Solution_Test_1 14 pX(x) x ½ ⅜ ⅛ 1 2

8. Signal r(t) = s(t) + n(t) s(t) = 5 cos(2p x 1000t )+ 10cos (2p x 1100t) noise n(t) is white noise with power No = 0.05 watt/Hz passband between 990 Hz and 1100 Hz Dr. Blanton - ENTC 4307 - Solution_Test_1 15

9. RC The output power spectral density is the input density multiplied by the square of the magnitude of the transfer function: Note the Fourier transform pair: x(t) R C Dr. Blanton - ENTC 4307 - Solution_Test_1 16

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10. Ideal Filter Dr. Blanton - ENTC 4307 - Solution_Test_1 19 H(f) f fm -fm 1 Dr. Blanton - ENTC 4307 - Solution_Test_1 19