Antennas and Propagation (Assignment-II)

1. A horizontal infinitesimal electric dipole of constant current is placed symmetrically about the

origin and directed along the x-axis. Derive the

a) Far zone fields radiated by the dipole.

b) Directivity of the antenna

1b) Repeat this problem for a horizontal infinitesimal dipole directed along the y-axis.

2. An infinitesimal magnetic dipole of constant current and length is symmetrically placed about

the origin along the z-axis. Determine,

a) Spherical E and H field components radiated by the dipole in all space.

b) Directivity of the antenna.

3. For an antenna of maximum linear dimension D, determine the inner and outer boundaries of the

Fresnel region so that the maximum phase error does not exceed

a)

radians b) radians c) d)

4. The current distribution on a terminated and matched long linear antenna of length is given by

where is a constant. Derive expressions for

a) Far zone spherical electrical and magnetic field components.

b) Radiation power density.

5. A thin linear dipole of length is placed symmetrically about the z-axis. Find the far-zone

spherical electric and magnetic components radiated by the dipole whose current distribution

can be approximated by

a)

b ) (

6. A center fed electric dipole of length is attached to a balanced lossless transmission line whose

characteristic impedance is 50 ohms. Assuming the dipole is resonant at the given length, find

the input VSWR when a) b) c) .

7. The radiation field of a particular antenna is given by,

The values of and depend on the antenna geometry. Obtain an expression for the radiation

resistance. Determine the polarization of the antenna.

8. Determine the far zone electric and magnetic fields radiated by a magnetic dipole of length

aligned with the z-axis. Assume a sinusoidal current with maximum value .

9. A center fed electric dipole of length `l’ is attached to a balanced loss less transmission line

whose characteristic impedance is 50 ohms. Assuming the dipole to be resonant at the given

length, find the input VSWR when a)

10. A resonant center-fed dipole is connected to q 50-ohm line. It is desired to maintain the input

VSWR=2.

a) What should be the largest input resistance of the dipole to maintain VSWR=2?

b) What should be the length (in wavelengths) of the dipole to meet the specification?

c) What is the radiation resistance of the dipole?

11. Determine the smallest height that an infinitesimal vertical electric dipole of length

must

be placed above the ground plane so that its pattern has only one null (aside from the null

towards the vertical), and it occurs at from the vertical. For that height, find the directivity

and radiation resistance.

12. A very short

vertical electric dipole is mounted at a height `h’ above the ground, which is

assumed to be flat, perfectly conducting and of infinite extent. The dipole is used as a

transmitting antenna in a VHF ( ground-to-air communication system. In order for

the communication system transmitting antenna not to interfere with a nearby radio station, it

is necessary to place a null in the vertical dipole system at an angle of with the vertical.

What should be the shortest height (in meters) of the dipole to achieve the desired

specifications?

13. Write the fields of an infinitesimal linear magnetic dipole of constant current length

positioned along the z-axis. Use the fields of an infinitesimal dipole ( as

determined for an infinitesimal electric dipole and apply the principle of duality. Compare these

results with the fields obtained for a small electric loop.

14. Design a loss less resonant circular loop operating at 10 Mhz so that its single turn radiation

resistance is 0.73 ohms. The resonant loop is to be connected to a balanced ``twin-wire’’ 300-

ohm transmission line.

a) Determine the radius of the loop in meters and wavelengths.

b) Closest integer number of turns the loop must have to minimize the reflections at the loop

transmission line interface.

c) For the loop of part b), determine the maximum power that can be expected to be delivered

to a matched load if the incident wave is polarization matched to the loss less resonant loop.

The power density of the wave is

15. A very small circular loop of radius and constant current is symmetrically placed

about the origin at and with the plane of its area parallel to the y-z plane. Find the

a) Spherical E and H-field components radiated by the loop in the far zone.

b) Directivity of the antenna.

16. Three isotropic sources with a spacing `d’ between them, are placed along the z-axis. The

excitation coefficient of each outside element is unity while that of the center element is 2. For

spacing of between the elements, find the

a) array factor

b) angles (in degrees) where the nulls and the maxima of the pattern occur.

17. A three element array of isotropic elements has the following phase and magnitude relationships:

Element -1 (top element):-1, Element -2 (middle element):-j, Element -3 (bottom element):+1

(elements are arranged along z axis).

a) Find the array factor

b) Find all the nulls.

18. Repeat the above problem when the excitation coefficients for the three elements are respectively

+1, +j and –j.

19. Show that in order for a uniform array of N elements not to have any minor lobes, the spacing and

the progressive phase shift between the elements must be

a)

for a broad side array.

b)

for an ordinary end-fire array.

20. Show that a three element binomial array with a spacing of

between the elements does not

have a side lobe.

21. Five isotropic sources are placed symmetrically placed along the z-axis, each separated from its

neighbor by an electrical distance

. For a binomial array, find the

a) excitation coefficients

b) array factor

22. Design a four element -40 dB side lobe level Dolph-Tschebyscheff array of isotropic elements placed

symmetrically about the z-axis. Find the

a) amplitude excitation coefficients

b) array factor

c) angles where the nulls occur for

.

23. Repeat the design of problem 22. For a six element -20 dB Dolph-Tschebyscheff array.

24. Design a element uniform planar array so that

the main maximum is directed along = . For a spacing of

between th

elements, find the

a) Progressive phase shift between the elements in the x and y directions.

b) Directivity of the array.

c) half-power beam-widths (in two perpendicular planes) of the array.