hint :for small circular antennahθ= e sin θ, sin θdθ jkr

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5 yıl önce
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1 4- Deive the expessions of the powe adiated, adiation esistance, diectivity, gain and effective apetue fo a small cicula electical cuent loop antenna whee S is the loop aea. kis π jk 3 4 hint :fo small cicula antennahθ= e sin θ, sin θdθ 3 4π =

2 1- Mekezi oijinde xy düzlemindeki N saimlik a yaıçaplı bi loop antenin elektik alanı aşağıda veilmekti. a) Toplam yayılan gücü hesaplayın. b) Anten kazancını hesaplayın. c) 4 3 Radyasyon diencini bulun. d) N= 1 ve a= 1 λ olsun. Bu antenin tek saimlik antene göe avantajı nedi? 1- An AM adio antenna consists of a pefectly conducting coil of adius a, whee both the adius and length ae much smalle than the wavelength. In the following use the fact that when an N tuns loop of the coil is excited with a cuent I, the adiated E-field is given by jk e πa Eφ= NIM sinθ, whee M= η. λ a) Find the total adiated powe. Use b) Find the Gain. (assume no losses) c) Find the adiation esistance. 4 d) Conside a coil with N= 1 and π 3 sin xdx= 43 3 a 1 λ ove a single loop antenna of the same adius? =. What is the advantage of this coil antenna N I M sin θ π π πn I M π 3 4πN I M a) S= P sin sin ad= S θdd θ φ θdθ η = η = 3η S 3 b) G= 4π = sin θ P 1 c) P = I R R = N d) N= 1, a= 1 λ M= 377π 1 R = 31 Ω. Fo a single coil R ad ad ad ad M η 8π 3 ad 8 will be less by a facto N = 1 (much too small fo a pactical impedance match). Thus though the coil and single loop have identical gain (1.5sin θ) the R of 31Ω is much 7 moe pactical than Ω.

3 - Öz empedansı ohm olan bi iletim hattı ile beslenen mükemmel iletken elektiksel olaak küçük bi loop anten vasayalım. Empedansı uyumlandımak için loop antenin giiş empedansı (adyasyon dienci) ohm olsun. a) f = 1 MHz te bu empedans uyumunun sağlanması için loop un yaıçapı ne olmalıdı? b) loop 1 döngüden oluşuyosa yaıçap ne olmalıdı? - A small, pefectly conducting loop antenna is to be fed with a ohm tansmission line. To achieve a good impedance match, assume that the eal pat of the input impedance of the loop (the adiation esistance) should be ohms. (a) Detemine the adius of the loop equied to achieve the equied input esistance if f = 1 MHz. (b) Repeat (a) if 1 tuns of the loop ae to be used. c R = k a = a= f= = = a= f ( π ).9 λ, 1MHz λ 3m.7m N= R = Nkπa = a= λ λ= a= 1 ( ).85, 3 m.85 m

4 - Tek saımlı daiesel bi loop anten f= 13.5MHz te çalışmakta olup adyasyon dienci R =.4Ω du. Bu anten yaıçapı 5 mm olan bi sonsuz iletken telden yapılmaktadı. a) Loop antenin yaıçapını hesaplayın. b) Loop un elektiksel olaak küçük olduğunu vasayaak eactance ( X A) değeini bulun. c) Loop anten alıcı konumunda 3 ohmm luk bi yüke bağlanacak olup anten ile yük aasındaki yansımlaı enaza indigemek geekeceğinden ilk aşamada anten empedansının eel kısmının 3 ohm olması için antenin sagı sayısını bulun. d) c şıkkındaki sagı sayısıyla anten empedansının sanal kısmını hesaplayın. L(n) = L(1)n (L(1) bi saımlık loop un indüktansıdı.) e) Empedans uyumlandımayı tam temin edebilmek için n saımlı loop anten ile yük aasındaki kondansatö değeini hesaplayın. - A single tun infinitesimally small lossless cicula loop antenna in ai opeating at e=f= 13.5 MHz has R =.4Ω. The loop is made fom a wie of adius a= 5mm. (a) Detemine the adius of the infinitesimal loop. 4 ( S) λr S= πb, R = 31,171 b=.75 m 4 = λ π 31, (b) Detemine the eactance ( X A) of the loop assuming that the loop is electically small. XA= ω( Le+ Li), Li= (wie lossless), XA= ωle ωµ b ln(8ba ), Le= 4.797µ H (c) Assume that the loop is to be connected to a 3 Ω load. To minimize the eflections between the loop and the load, detemine the numbe of intege tuns the loop must have (Real pat of input impedance closest to load esistance). Once you detemine the numbe of tuns, calculate the new input impedance. Hint: Assume that inductance of n tun loop is given by L e (n) = L e (1)n whee L e (1) is the inductance of a loop with a single tun. R = R n n= R = R = = Ω (1) 3 (1) 7.4(7) 91.6 L = 4.797(7) = 3497.µ H X = πfl = K Z = j Ω 3 e A e A (d) Add a shunt capacito between the antenna and the load to cancel the eactance of the antenna. Detemine the capacitance of this capacito. 1 j Zɶ L= 3+ = 3, ZA= RA+ XA, = C= F jωc ωc ωc X A

5 3- A single loop antenna of adius a (πa << l) caies a cuent I. If θ is the angle fom the z- axis which is also the axis of the loop, the adiated magnetic field is: k( Iπa ) jk Hθ= e sinθ 4π a) What is the adiated electic field vecto? (in spheical coodinates) b) What is antenna gain at position (,θ,φ)? [ use π sin 3 x dx = 4 3 ] c) What is the adiation esistance? Consideing the loop as an inducto fo use at 1MHz, what is the lagest adius loop that you could use and keep the adiative loss esistance less than.1 ohms.

7 1- Calculate the seies esistance and adiation esistance of a 1 MHz AM loop antenna of 1 tuns wound aound a Sandust coe of μ = 1 and μe = 4 and having a diamete of 1 cm. The wie diamete is μm and the conductivity of coppe is 5.8 x 1 7 Ω -1 m -1. What is the efficiency of this eceiving antenna? Compae with the pefomance of a typical λ/4 long and mm diamete FM monopole (cente fequency of 98 MHz) if this monopole is to be used at 1 MHz fo AM eception. (Do not foget to take into account the skin depth in you calculations.)

8 1- A shot cente-fed dipole of length l is located at the cente of a small cicula loop of aea S, and is oiented pependicula to the plane of the loop. Deive the elation that is equied between the dipole length, loop aea, wavelength and antenna cuents fo the adiated fa field to be ight-hand ciculaly polaized. You may ignoe ohmic losses in the antennas. Include a sketch of the antennas denoting the efeence diections of the cuents.

10 - A half-wave dipole antenna and a 1-tun cicula loop antenna of adius a = 1 cm ae used to fom a tansmit/eceive communication link at a fequency of f = 3 MHz. The wie used to make both antennas has a esistance of.5 Ω/m. a) Calculate the diectivity D, adiation esistance R, antenna esistance R A and gain G fo each antenna.

11 b) Sketch the mutual oientation of these antennas fo which the fa field of one is polaization matched to the othe. c) If the antennas ae sepaated by a distance = 1 km, and the tansmitting antenna is fed by a souce with available powe P t = 1 kw, find the maximum powe available to a load at the feed teminals of the eceiving antenna.

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hint :for small circular antennahθ= e sin θ, sin θdθ jkr

hint :for small circular antennahθ= e sin θ, sin θdθ jkr 4- Derive the expressions of the power radiated, radiation resistance, directivity, gain and effective aperture for a small circular electrical current loop antenna where S is the loop area. 2 kis 0 π