adio Technology Metopolia/A. Koivumäki Antenna fundamentals: With answes to questions and poblems (See also Chapte 9 in the textbook.) 1. a) Make up a definition fo the tem "antenna". Answe: One definition: Antenna is a device which moves electomagnetic enegy fom two dimensional space to thee dimensional space and vice vesa. Anothe definition: A conducto by which electomagnetic waves ae sent out o eceived. Othe definitions may be found fom the web. b) Make a list of diffeent types of antennas you know. Answe: One list: http://www.antenna-theoy.com/antennas/main.php. Anothe list: http://en.wikipedia.og/wiki/categoy:adio_fequency_antenna_types. c) An antenna can tansmit and/o eceive adio waves. It can be shown that an antenna is a ecipocal device. This means that the popeties of an antenna do not depend on whethe it opeates as a eceive antenna o as a tansmit antenna. It follows fom ecipocity e.g. that in antenna measuements the antenna unde test can be eithe the eceiving antenna o the tansmitting antenna, whicheve is easie to ealize. The measuement esult is valid fo both eceive mode and tansmit mode of the antenna. Fo instance, it is vey easy to measue the impedance of an antenna by using the antenna as a tansmit antenna (i.e. a signal is fed into the antenna) and then measuing the signal eflecting back fom the antenna. If the antenna unde test is used as a eceive antenna, it is almost impossible to measue its impedance. d) Why does a tansmit antenna adiate an electomagnetic field? The answe comes fom the physics of atomic paticles: when a chaged paticle is acceleated o deceleated, it adiates an electomagnetic field. The accleation of chaged paticles is ealized by causing a F cuent to flow on the oute suface of a conducting object. The suface cuent is geneated by feeding a F signal fom a tansmitte into the antenna. And the othe way ound: When an F electomagnetic field hits a conducting suface, an F cuent will stat flowing on the suface. Then this suface cuent geneates a signal into a cable attaced to the antenna, and the signal goes into a ecieve. e) Some impotant electical popeties of antennas ae: gain, diectivity, adiation patten, sidelobe level, beamwidth, polaization, coss-polaization, impedance, losses, efficiency, bandwidth etc. And because of ecipocity, the value of each fo a given antenna does not depend on whethe the antenna eceives o tansmits.. adiation patten. See Chapte 9.1 in adio Engineeing fo Wieless Communication and Senso Applications. 3. Isotopic antenna is an antenna which adiates at an equal stength to all diections. Sketch the adiation patten of an isotopic antenna. a) in pola co-odinate system b) in ectangula co-odinate system Answe: a) Cicle: θ
b) Hoizontal line: P( θ)/db θ 4. If signal powe P T is input into an isotopic antenna, what will be the powe density of the adiated field at distance? You can deduce the answe in these six steps: What does powe density mean? (b) So, what is the unit of powe density? (c) How is the tansmit powe P T distibuted between diffeent diections? (d) If we think that the antenna is at the cente of a sphee with adius, how will the tansmit powe P T be distibuted on the suface of this sphee? (e) What is the aea of a sphee of adius? (f) So, what will be the powe density caused by the isotopic tansmit antenna at distance fom the antenna? Answe: S = 5. Signal powe of P T is input to an isotopic tansmit antenna. Make an Excel woksheet to calculate powe density S, electic field stength E and magnetic field stength H at distance. Then calculate values of S, E and H fo a) P T = 1 W, = 1 m b) P T = 1 W, = 1 km c) P T = 1 W, = 1 km d) P T = 1 W, = 1 km Answe: Using S = and EH E H Z S = = = and Z = 377 Ω. Z a) S = 79.6 µw/m E = 45 mv/m H = 65 µa/m b) S = 796 nw/m E = 4.5 mv/m H = 65. µa/m c) S = 7.96 nw/m E =.45 mv/m H = 6.5 µa/m d) S = 79.6 nw/m E = 7.75 mv/m H =.5 µa/m 6. Gain is one of the most impotant popeties of an antenna. Something to contemplate about gain: (b) (c) (d) If the gain of an amplifie is 3 db and a signal powe of 1 mw is input to the amplifie, what is the output powe? Answe: 3 dbm = 1 W Whee does the additional signal powe come fom? Not fom thin ai, o what do you think? Answe: It comes fom the powe souce of the amplifie. Do you think antenna gain means the same thing as amplifie gain? Answe: No If the gain of a tansmit antenna is 3 db, and a signal powe of 1 mw is input to the antenna, what is the powe adiated fom the antenna to the atmosphee? emembe that basically an antenna is just a piece of conducting mateial shaped in a pope way. Answe: adiated
powe is less than 1 mw. In ideal case (no powe losses in antenna) it would be exactly 1 mw. 7. So, obviously, the gain of an antenna does not mean the same as the gain of an amplifie. (b) (c) (d) Let's assume that signal powe P T is input to an (imaginay) isotopic tansmit antenna. Then this isotopic antenna will geneate powe density S i at distance fom the antenna. Accoding to section 4, this powe density is S i =. Next, let's eplace the isotopic antenna with a eal wold antenna. The same signal powe P T is input into this antenna. If this eal antenna geneates powe density S at distance in the diection of the main beam of its adiation patten, the gain of the antenna is defined to be S G = S i (e) In othe wods: An antenna with gain G will geneate at a given distance a powe density which is G times as lage as would be the powe density geneated by an isotopic antenna with same input powe at the same distance. S (f) Nomally, antenna gain is given in decibels: G (db) = 1 log db. P T S i (g) (h) (i) (j) (k) Often, dbi is used as the unit of antenna gain. dbi is ead e.g. "decibel ove isotopic". Anothe db unit of antenna gain sometimes used is dbd, "decibel ove dipole". dbd value of gain shows, how many Half wave dipole: db the gain is lage than the gain of a half wave dipole is. The gain of a half wave dipole can be shown to be.15 dbi. So, if the gain of a cetain antenna is said to be x dbd, then it could as well be said to be (x +.15) dbi. How many dbi and dbd is the gain of an isotopic antenna? Answe: dbi =.15 dbd CABLE λ/ How many dbd is the gain of a half wave dipole antenna? Answe: dbd 8. Enhance the Excel sheet you made in section 5 by adding antenna gain in dbi as a new vaiable. Then calculate values of S, E and H fo a) G = 15 dbi, P T = 1 W, = 1 m b) G = 4 dbd, P T = 1 W, = 1 km G EH E H Z Answe: Using S = and S = = = and Z = 377 Ω. Z a) In the fomula we use G = 1 1.5 S =.5 mw/m E = 1.38 V/m H = 3.65 ma/m b) G = 4 dbd = 6.15 dbi, so we use G = 1.615 S = 3.8 µw/m E = 49.7 mv/m H = 13 µa/m 9. The diectivity of an antenna is almost the same thing as the gain, but not quite. (b) Gain is a popety of the antenna. Diectivity is a popety of the adiation patten of the antenna.
(c) If the adiation patten of the antenna is P( θ, ϕ ), its diectivity can be calculated as follows: 4 π D = P( θ, ϕ) dω So, diectivity is the atio of the maximun powe density to the aveage powe density adiated by the antenna. (d) Fo a totally lossless antenna (meaning that all signal powe fed into the antenna is adiated to the atmosphee), diectivity is equal to gain, D = G. (e) A pactical antenna always has losses (due to the esistivity of the antenna mateial, nonmatched antenna impedance, polaization impefections etc.). So, in pactice, always G < D. (f) If antenna losses ae L db, G (db) = D (db) L. (g) (h) The diectivity of an isotopic antenna is always 1 (o db), but if it is lossy, it has a gain of < 1 (o < db) In eal life, a small antenna (compaed to wavelength) often has quite high losses, so often it has a gain of < db, even if it may have a diectional adiation patten (with D > db). 1. Both gain and diectivity indicate, how effectively the antenna diects its adiation to the diection of the main lobe of its patten. So: The smalle the beamwidth of the antenna, the lage is the gain and diectivity of the antenna. (b) The highe the sidelobes of the antenna, the smalle is the gain and diectivity of the antenna. Why? Answe: Smalle beamwidth means that less powe is adiated outside the main beam, so moe powe goes into the diection of the main beam. Highe sidelobes mean that less powe is adiated into the diection of main beam. 11. Captue aea (effective aea) of an antenna We can think that a ecieve antenna functions by captuing all the signal powe fom a cetain aea aound the antenna. This aea is called the captue aea, o effective aea of the antenna, and it is denoted by A e. (b) It can be shown that captue aea depends on the gain of the antenna and on the wavelength of λ G the incoming adio wave as follows: Ae = (Hee G is not in db.) (c) If an antenna with captue aea A e is in an incoming electomagnetic field with powe density S, the signal powe ecieved by the antenna is P = Ae S. (d) Make an Excel woksheet to calculate the powe eceived (dbm), when fequency f (MHz), eceive antenna gain G (db) and electic field stength E (dbµv/m) ae given. Then calculate P fo a) f = 1 MHz, G = 8 db, E = 54 dbµv/m (FM adio eception) b) f = 1 GHz, G = 38 db, E = dbµv/m (satellite TV eception) c) f = 9 MHz, G = 1 dbd, E = 4 dbµv/m (GSM eception) Answe: Using E S = and A Z e = λ G and P = A S : a) λ = 3 m G = 1.8 E = 1 54/ µv/m P = 58. dbm b) λ = 5 mm G = 1 3.8 E = 1 / µv/m P = 13.8 dbm c) λ = 333.3 m G = 1.315 E = 1 4/ µv/m P = 96. dbm (e) Thee is a 9 MHz whip antenna of length λ/4 and of gain dbi on the oof of a ca. What is the captue aea of the antenna? Compae this aea to the physical size of the antenna. e
. λ G (33.3 cm) 1 Answe: A e = = = 139.9 cm If the captue aea is imagined to be a squae, its sides ae 11.8 cm. Since λ = 33.3 cm, the length of the antenna is 8.3 cm. So, the antenna fits well inside the captue aea. (f) The captue aea of a eflecto antenna (dish antenna, paabolic antenna) is given by =η A, A e whee A is the actual aea of the eflecto (i.e. the aea defined by the im of the eflecto) and η is the apetue efficiency (also known as suface efficiency) of the antenna. If the eflecto is cicula with diamete D, then of couse πd A e = η. 4 The value of η is nomally between.5....7 and the most typical value fo pactical eflecto antennas is pehaps η =.6, which can be used, if no othe value is given. (g) Deive an equation fo the gain of a eflecto antenna when the diamete D of the eflecto, apetue efficiency η of the antenna and wavelength λ of the adio wave adiated ae given. π Answe: = η D π G. In decibels: G = 1 log η D dbi. λ (h) Make an Excel sheet to calculate the gain of a eflecto antenna, when fequency f (GHz), eflecto diamete D (m) and apetue efficiency η (%) ae given. Then calculate G (db) fo f = 1 GHz, η = 7 % and D = 3cm, 6 cm, 1 m, m, 5 m, and 1 m. Answe: Fo given eflecto sizes we get these gains: 9.98 db, 36. db, 4.44 db, 46.46 db, 54.41 db, 6.44 db 1. adio link If signal powe P T is fed into a tansmit antenna with gain G T, powe density at distance will G be S = T P T. (See. 7e ja 4f.) (b) If thee is a eceive antenna with gain G at distance, it has a captue aea of λ G A e =, so it eceives a signal powe of (c) P = λ G G P G G P A. T T T T e S = = λ ( ) / In this way we have deived the basic link budget equation, which is nomally given as GT G P = L whee L = is called the fee space loss of the adio link. λ (d) Link budget equation with decibels: P ( dbm) ( dbm) ( db) + G ( db) L( db) (e) Make an Excel woksheet to calculate P of a adio link, when tansmit powe P T (dbw), antenna gains G T and G (db), fequency f (MHz) and distance (km) ae given. Then solve these: a) The tansmit powe of a TV satellite is 4 W and the diamete of the eflecto of the tansmit antenna is 8 cm. The diamete of the eceive antenna is on 1 cm. Distance fom the satellite to Finland is 4 km, fequency is 11.5 GHz. How many dbm is the signal eceived by the eceive antenna?
b) A satellite link has a fequency of 1 GHz. The satellite antenna eflecto size is 1 m, the gound station has a m antenna. The apetue efficiency of each antenna is 7%. The powe eceived by the gound station (i.e. the input signal powe to the eceive) must be 75 dbm. What must be the tansmit powe of the satellite tansmitte (dbw)? c) Same poblem with f = 4 GHz. Suppose that the apetue efficiency of the antennas is still 7%. (This calls fo cetain changes in the antennas, when the fequency is doubled, but is a valid assumption). d) Make conclusions fom the answes to b) and c) beaing in mind that the fequencies used in satellite communication will get highe in the futue. Answes: a) Link budget equation: P L + G. 4 W Values: Tansmit powe P T = 4 W = 1 log dbm = 46. dbm 1mW 8 c 3 1 m/s Wavelength: λ = = =.61m f 9 11.5 1 Hz πd.8 m T π Gain of tansmit antenna: G T = 1 log η db = 1 log.7 db =.61 m πd 1. m π Gain of eceive antenna: G = 1 log η db = 1 log.7 db =.61 m (Apetue efficiencies of the antennas wee not given, hee η =.7 is used fo both antennas.) Path loss = fee space loss: 3 4 1 m L = 1 log db = log db = log db = 5.7 db.61 m λ So, eceived signal powe is P L + G = 46. dbm + 38.13 db 5.7 db + 41.65 db = 79.9 dbm. 38.13 db 41.65 db b) Link budget equation: P L + G. Now tansmit powe P T is unknown, we get it with = P GT + L G. Values with same equations as above: λ =.5 m, P = 75 dbm, G T = 4.44 db, G = 46.46 db, L = 6.7 db. 44.17 /1 equied tansmit powe is P T = 44.17 dbm = ˆ 1 mw = 6.16 W c) New wavelength: λ =.15 m. antenna gains and path loss incease by 6. db: G T = 46.46.44 db, G = 5.48 db, L = 1.9 db. equied tansmit powe is P T = 38.16 dbm = ˆ 1 38.16 /1 mw = 6.54 W d) Fequency is doubled wavelength is halved both tansmit and eceive antenna gains ae inceased by 6 db (if apetue efficiency can be maintained, and it can with pope antenna engineeing); fee space loss is also inceased by 6 db. Because thee ae two antenna gains but only one path loss, the net incease of eceived signal powe is 6 db, if tansmit powe is not changed. We can decease tansmit powe by 6 db, if we want the eceived powe to emain the same.