0195136047.pdf

PROBLEMS 735

15.1.27An antenna has an aperture area of 10 m^2 ,an

aperture efficiency of 0.6, and negligible losses.

If it is used at 5 GHz, find:

(a) Its power gain.

(b) The maximum power density that the antenna

can generate at a distance of 20 km with an

input power of 2 kW.

15.1.28The power gain of an antenna is 10,000. If its input

power is 1 kW, calculate the maximum radiation

intensity that it can generate.

*15.1.29An antenna has beam widths of 3° and 10° in
orthogonal planes and has a radiation efficiency
factor of 0.6. Find the maximum radiation inten-
sity if 1 kW is applied to the antenna.
15.1.30The radiation pattern of a half-wave dipole an-
tenna [see Figure 15.1.7(a)] is given by

P(θ, φ)=

cos^2 [(π/ 2 )cosθ]

sin^2 θ

(a) Sketch the radiation pattern in the principal

plane ofxzcontaining angleθ.

(b) Determine the beam width between the−10-

dB points of its radiation pattern as well as the

half-power beamwidth.

15.1.31The effective area of a dipole is given byAe=

0.13λ^2. Find the effective area of a half-wave

dipole at 3 GHz.

15.1.32For a helical antenna [see Figure 15.1.7(c)], the

half-power beamwidth and directive gain are

given by

θB∼=

52 λ^3 /^2

C

√

NS

whereC=πD,N=L/S, andS=Ctanα,in

whichαis called the pitch angle, and

GD∼=

12 NC^2 S

λ^3

The input impedance seen by the transmission

line at pointP[Figure 15.1.7(c)] is almost purely

resistive, given byZa∼= 140 C/λ. Calculate the

antenna parameters of a 10-turn helix atf= 500

MHz by assuming thatC=λandα= 14 π/180.

15.1.33For a pyramidal-horn antenna [Figure 15.1.7(e)],

the maximum directive gain is given by

GD∼=

2. 05 πAB

λ^2

occurring when the aperture dimensions are√ A∼=

3 λLandB∼= 0. 81 A. The principal-plane beam-

widths for the optimum horn with maximum gain

are given byθB∼= 54 λ/Bin degrees in theyz-

plane, and byφB∼= 78 λ/Ain degrees in thexz-

plane. For a pyramidal horn, withA= 6 λandB

=4.86λ, at 6 GHz, findGD,θB, andφB. Comment

on whether this horn is optimum.

15.1.34A conical horn [Figure 15.1.7(f)] has a side view as

shown in Figure P15.1.34. The maximum value of

the directive gain is given byGD∼= 5. 13 (D/λ)^2 ,

whereD∼=

√

3. 33 λL 1 andL 1 ∼=L/( 1 −d/D),in

whichdis the inside diameter of the waveguide.

Beamwidths for the main beam directed along the

z-axis are given byθB∼= 60 λ/Din degrees in the

yz-plane, and byφB∼= 70 λ/Din degrees in thexz-

plane. Let the circular waveguide, with a 2.5-cm

inside diameter, be expanded by adding a conical

flare to have an aperture with an inside diameter

of 5.771λat 8 GHz. ForL 1 = 10 λ, find:

(a) The horn lengthL.

(b) The directive gain.

(c) The principal-plane beamwidths.

*15.1.35A paraboloidal antenna [Figure 15.1.7(g)] has an

aperture efficiency of 0.6 and a diameterD=

100 λat 6 GHz. Illumination by the feed is such

that the beamwidths of the principal-plane sec-

ondary patterns are equal. Determine the antenna’s

power gain and beamwidth. (Note that the ra-

diation pattern of the feed is called the primary

pattern, whereas that of the overall antenna is the

secondary pattern.)

15.1.36Two stations, located on mountain tops 40 km

apart, communicate with each other using two

L 1

L

Apex Aperture

Throat

D

d

z

Figure P15.1.34