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 jkr 3 4 hint :for small circular antennahθ= e sin θ, sin θdθ 3 4πr = 0
2- Öz empedansı 20 ohm olan bir iletim hattı ile beslenen mükemmel iletken elektriksel olarak küçük bir loop anten varsayalım. Empedansı uyumlandırmak için loop antenin giriş empedansı (radyasyon direnci) 20 ohm olsun. a) f = 100 MHz te bu empedans uyumunun sağlanması için loop un yarıçapı ne olmalıdır? b) loop 10 döngüden oluşuyorsa yarıçap ne olmalıdır? 2- A small, perfectly conducting loop antenna is to be fed with a 20 ohm transmission line. To achieve a good impedance match, assume that the real part of the input impedance of the loop (the radiation resistance) should be 20 ohms. (a) Determine the radius of the loop required to achieve the required input resistance if f = 100 MHz. (b) Repeat (a) if 10 turns of the loop are to be used. c Rr = k a = a= f= = = a= f 2 2 2 20( π ) 20 0.09 λ, 100MHz λ 3m 0.27m N= R = Nkπa = a= λ λ= a= 2 2 2 10 r 20( ) 20 0.0285, 3 m 0.085 m
2- Tek sarımlı dairesel bir loop anten f= 13.5MHz te çalışmakta olup radyasyon direnci R = 0.4Ω dur. Bu anten yarıçapı 5 mm olan bir sonsuz iletken telden yapılmaktadır. r a) Loop antenin yarıçapını hesaplayın. b) Loop un elektriksel olarak küçük olduğunu varsayarak reactance ( X A) değerini bulun. c) Loop anten alıcı konumunda 300 ohmm luk bir yüke bağlanacak olup anten ile yük arasındaki yansımları enaza indirgemek gerekeceğinden ilk aşamada anten empedansının reel kısmının 300 ohm olması için antenin sargı sayısını bulun. d) c şıkkındaki sargı sayısıyla anten empedansının sanal kısmını hesaplayın. L(n) = L(1)n 2 (L(1) bir sarımlık loop un indüktansıdır.) e) Empedans uyumlandırmayı tam temin edebilmek için n sarımlı loop anten ile yük arasındaki kondansatör değerini hesaplayın. 2- A single turn infinitesimally small lossless circular loop antenna in air operating at e=f= 13.5 MHz has R = 0.4Ω. The loop is made from a wire of radius a= 5mm. r (a) Determine the radius of the infinitesimal loop. 2 4 2 ( S) λr r S= πb, Rr = 31,171 b= 0.75 m 4 = 2 λ π 31,171 14 (b) Determine the reactance ( X A) of the loop assuming that the loop is electrically small. XA= ω( Le+ Li), Li= 0(wire lossless), XA= ωle ωµ 0b ln(8ba 2), Le= 4.797µ H (c) Assume that the loop is to be connected to a 300 Ω load. To minimize the reflections between the loop and the load, determine the number of integer turns the loop must have (Real part of input impedance closest to load resistance). Once you determine the number of turns, calculate the new input impedance. Hint: Assume that inductance of n turn loop is given by L e (n) = L e (1)n 2 where L e (1) is the inductance of a loop with a single turn. R = R n n= R = R = = Ω 2 2 r r(1) 300 r(1) 27 r 0.4(27) 291.6 L = 4.797(27) = 3497.22µ H X = 2πfL = 296.645 K Z = 291.6+ j 296.645 10 Ω 2 3 e A e A (d) Add a shunt capacitor between the antenna and the load to cancel the reactance of the antenna. Determine the capacitance of this capacitor. 1 j Zɶ 1 1 14 L= 300+ = 300, ZA= RA+ XA, = C= 3.974 10 F jωc ωc ωc X A
3- A single loop antenna of radius a (2πa << l) carries a current I. If θ is the angle from the z- axis which is also the axis of the loop, the radiated magnetic field is: 2 2 k( I0πa ) jkr Hθ= e sinθ 4πr a) What is the radiated electric field vector? (in spherical coordinates) b) What is antenna gain at position (r,θ,φ)? [ use π sin 3 x dx = 4 3 0 ] c) What is the radiation resistance? Considering the loop as an inductor for use at 100MHz, what is the largest radius loop that you could use and keep the radiative loss resistance less than 0.01 ohms.
1- Calculate the series resistance and radiation resistance of a 1 MHz AM loop antenna of 100 turns wound around a Sandust core of μr = 100 and μe = 40 and having a diameter of 1 cm. The wire diameter is 200 μm and the conductivity of copper is 5.8 x 10 7 Ω -1 m -1. What is the efficiency of this receiving antenna? Compare with the performance of a typical λ/4 long and 2 mm diameter FM monopole (center frequency of 98 MHz) if this monopole is to be used at 1 MHz for AM reception. (Do not forget to take into account the skin depth in your calculations.)
1- A short center-fed dipole of length l is located at the center of a small circular loop of area S, and is oriented perpendicular to the plane of the loop. Derive the relation that is required between the dipole length, loop area, wavelength and antenna currents for the radiated far field to be right-hand circularly polarized. You may ignore ohmic losses in the antennas. Include a sketch of the antennas denoting the reference directions of the currents.
2- A half-wave dipole antenna and a 100-turn circular loop antenna of radius a = 10 cm are used to form a transmit/receive communication link at a frequency of f = 30 MHz. The wire used to make both antennas has a resistance of 0.05 Ω/m. a) Calculate the directivity D, radiation resistance R r, antenna resistance R A and gain G for each antenna.
b) Sketch the mutual orientation of these antennas for which the far field of one is polarization matched to the other. c) If the antennas are separated by a distance r = 1 km, and the transmitting antenna is fed by a source with available power P t = 1 kw, find the maximum power available to a load at the feed terminals of the receiving antenna.