6. Short-distance link design, Fresnel ellipsoide. Topic 5: Radio wave propagation and safety issues A 6. 10-km Short-distance link system, link see design, figures Fresnel 1) and 3) ellipsoide. below, operates at 6 GHz. Problem 5.1: Fresnel zones and obstruction losses a. A Figure 10-km 2) link shows system, the see relative figures electric 1) and field 3) below, strength operates E B (in at comparison 6 GHz. to the field strength when r = ) as a a. function Figure 2) of shows r calculated the relative using numerical electric field integration. strength EExplain B (in comparison the curve to and the its field shape. strength when r = ) as a b. Based function the of r curve calculated for the using relative numerical E B in figure integration. 2) estimate Explain roughly the curve the needed and its shape. radius r for the space that b. should Based be on preserved the curve for empty the relative so that Ethe B in radio figure wave 2) estimate propagates roughly without the needed any extra radius loss r for caused the space by the that should be preserved empty so that the radio wave propagates without any extra loss caused by the c. Estimate the same radius as in b. based on the first Fresnel ellipsoid (figure 3)) i.e., calculate h F. A 10-km link system, see Figures 1(a) and 1(c) below, operates at 6 GHz. a) Figure obstacles. 1(b) shows the relative electric field strength at the RX E B when there is an infinitesimally obstacles. large absorbing screen deployed in the middle of the link. The absorbing screen has a hole of Compare radiusand r, where discuss theh F and center the value of ther chosen circle coincides b. with the line between the TX and RX. The value Compare E B is and normalized discuss h F and with the respect value r chosen to that in of b. r =, i.e., when hole radius is infinitesimallywithout large meaning any extra loss? that Neglect the screen the ground does not reflection exist. and Explain the radius whyof the curve Earth. has very low values at small without r andany then extra converges loss? Neglect to 0the dbground with reflection small fluctuation and the radius as rof increases. the Earth. c. Estimate the same radius as in b. based on the first Fresnel ellipsoid (figure 3)) i.e., calculate h F. d. Based on b. and c. what should be the height h of the antenna towers when the radio wave propagates d. Based on b. and c. what should be the height h of the antenna towers when the radio wave propagates Circular hole Absorbing screen TX r RX 5 km 5 km (a) (b) (c) Figure 1: (a) 10 km link, (b) Relative field strength at the RX and (c) First Fresnel ellipsoid. b) Based on the curve for the relative E B in Figure 1(c) estimate roughly the needed radius r for the space that should be kept free of obstacles so that the radio wave propagates without any extra loss caused by the obstacles. c) Estimate the same radius as in b) based on the first Fresnel ellipsoid. Refer to Figure 1(c), i.e., calculate h F. Compare and discuss h F and the value r chosen in b). d) Based on b) and c), what should be the height h of the antenna towers when the radio wave propagates without any extra loss? Neglect the ground reflection and the radius of the Earth.
Topic 5: Radio wave propagation and safety issues Problem 5.2: Atmospheric attenuation The purpose of this exercise is to familiarize students with effects of atmospheric losses in radio link budget. a) Using the Friis free space transmission equation and the parameters given below, estimate the free space path loss of the signal. Note that there is a clear line-of-sight between the two antennas and they are perfectly aligned; we do not consider losses due to matching, cables of the transceivers and polarization. Table 1: Link properties. Parameters Gain of transmit antenna, G t Gain of receive antenna, G r Power fed to the transmit antenna, P t Radio frequency, f Transmit-receive distance, d Values 2 dbi 19 dbi 17 dbm 60 GHz 200 m b) The diagram in Fig. 2 indicates the excess atmospheric loss with respect to radio frequency in db/km. Estimate the atmospheric loss of the link mentioned in part a). Interpret the results keeping in mind the applications of 60 GHz frequency band for 5G cellular network. Figure 2: Attenuation in clear atmosphere verses frequency. Curve A at the sea level (T = 20 C, water vapor density 7.5 g/m 3 ). Curve B: at altitude of 4 km (T = 0 C, water vapor density 1 g/m 3 ). c) An empirical formula of radio wave attenuation due to rain is A = ar b db/km, (2.1)
where R is the rain rate in millimeters per hour and a and b are constants that depend on frequency and temperature of the rain. Parameters a and b can be computed using the below formulae: a = G a f Ea (f in GHz), (2.2) where G a = 6.39 10 5, G a = 4.21 10 5, G a = 4.09 10 2, G a = 3.38, E a = 2.03 (f < 2.9 GHz), E a = 2.42 (2.9 f < 54 GHz), E a = 0.699 (54 f < 180 GHz), E a = 0.151 (180 GHz f), and where b = G b f E b (f in GHz), (2.3) G b = 0.851, G b = 1.41, G b = 2.63, G b = 0.616, E b = 0.158 (f < 8.5 GHz), E b = 0.0779 (8.5 f < 25 GHz), E b = 0.272 (25 f < 164 GHz), E b = 0.0126 (164 GHz f). Use Eqs. (2.1), (2.2) and (2.3) to calculate the attenuation in decibels per kilometer for signals with i) f = 20 GHz, ii) f = 60 GHz and iii) f = 2 GHz at moderate rain of 6 mm/h. What is the attenuation at a heavy rate of 20 mm/h? Make a table of calculated values and discuss the rain effects in current cellular radio systems operation and future fifth-generation network which may operate at millimeter waves.
Topic 5: Radio wave propagation and safety issues Problem 5.3: Two-path model of ground reflection Radio transmitter (TX) and receiver (RX) are deployed on a flat smooth ground as illustrated in Figure 3. The TX and RX are equipped with idealistic omni-directional lossless antennas with heights of h 1 = 300 and h 2 = 10 m operating at f = 500 MHz. The TX feeds a unit power to the antenna, which emits a parallel-polarized wave to the ground. The RX antenna receives the same polarization. Figure 3: Radio propagation involving direct wave and reflection from the ground; h 1 = 300 m, h 2 = 10 m and f = 500 MHz. a) Given the separation distance between the TX and RX d, derive a formula of complex voltage at the RX antenna port, E. Raisanen, Antti, and Lehto, Arto. Radio Engineering for Wireless Communication and Sensor Applications. Norwood, MA, USA: Artech House, 2003. ProQuest ebrary. Web. 23 December 2015. Copyright 2003. Artech House. All rights reserved. Hint: the Friis formula we covered in Problem 4.4 provides the complex voltage at the RX antenna port for a unit TX power as E = λ 4πd e jβd, (3.1) when the separation distance between the TX and RX antennas is d and there is no reflection from the surrounding environment; λ is wavelength of a radio wave and β is a wavenumber. b) Reproduce Figure 4, which corresponds to Figure 10.11(a) of Räisänen and Lehto, using the formula obtained in a). In the figure E 0 denotes a magnitude of the voltage at the RX antenna for the direct wave propagating from the TX to RX. c) The magnitude of the voltage at the RX antenna, E/E 0, in Figure 4 sees maxima and minima in an alternating manner as d grows. Write down the conditions leading to these minima and maxima.
d) According to Figure 4, E/E 0 seems to have the last maximum at d = 20 km as d increases. Discuss how E/E 0 behaves beyond this distance. Is there any way to estimate the distance according to the concept of Fresnel zone? Figure 4: Voltage at the RX antenna port for varying TX-RX separation distance; h 1 = 300 m, h 2 = 10 m and f = 500 MHz. Raisanen, Antti, and Lehto, Arto. Radio Engineering for Wireless Communication and Sensor Applications. Norwood, MA, USA: Artech House, 2003. ProQuest ebrary. Web. 23 December 2015. Copyright 2003. Artech House. All rights reserved.
Topic 5: Radio wave propagation and safety issues Problem 5.4: Radiation safety [Note: this is a bonus problem and is not eligible as a problem of minimum return.] Let us assume that you live in a suburb area. A local mobile operator is planning to build a new base station in the area. A person, who is very concerned about the health risks of the radio waves transmitted by the base station, collects names to a petition in order to prevent the building of the base station. Write a short (e.g., half A4) opinion to a local newspaper in order to clarify the health effects of the radio waves. Write understandable way! Choose your perspective freely, but your opinion is based on scientific research results. Pay attention to the legibility of your text and use good linguistic form. You can, for instance, use the article Radiowaves and our environment.