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1. The normalized far-zone electric field radiated by a small square loop of uniform current Io is given

by

where C is a constant. Determine the:

a) Vector radiated power density (Watts/m)

b) Radiated power (Watts)

c) Radiation resistance Rr (ohms)

d) Maximum directivity (dimensionless and in dB)

e) Maximum effective area (in )

2. It is desired to design a Binomial array with a uniform spacing between the elements of placed along the z - axis,

and with an elevation half-power beamwidth for its array factor of 15.18 degrees. To accomplish this, determine the:

a) Number of elements

b) Directivity (dimensionless and in dB)

c) Sidelobe level of the array factor (in dB)

3. It is desired to design a Dolph-Tschebyscheff nonuniform linear broadside array. The desired array should have

20 elements with a uniform spacing between them. The required sidelobe level -40 dB down from the maximum.

Determine the

a) Maximum uniform spacing that can be used between the elements and still maintain a constant sidelobe level of

-40 dB for all minor lobes

b) Half-power beamwidth (in degrees) of a uniform linear array of the same number of elements and spacing as the

Dolph-Tschebyscheff array. Assume d = .

c) Half-power beamwidth (in degrees) of the Dolph-Tschebyscheff array with d =

d) Directivity of the Dolph-Tschebyscheff array of d = (dimensionless and in dB)

e) Directivity of the uniform array of d = (dimensionless and in dB)

4. It is desired to synthesize a linear array of elements with spacing d = 3/8. It is important that the array factor

(AF) exhibits nulls along = 0, 90 and 180 degrees. Assume there is no initial progressive phase excitation

between the elements (i.e., = 0). To achieve this design, determine:

a) The number of elements

b) The excitation coefficients (amplitude and phase)

If the design allows the progressive phase shift ( ) to change, while maintaining the spacing constant (d = 3/8),

c) What would it be the range of possible values for the progressive phase shift to cause the null at = 90 degrees

disappear (to place its corresponding root outside the visible region)?

1. Two identical dipoles are placed in a side-by-side arrangement. The separation between

the dipoles is 0.375. When one of the dipoles is connected to a 50-ohm transmission line,

determine at the load the:

a. input reflection coefficient and VSWR when one of the dipoles is radiating in free space

in the absence of the other.

b. input reflection coefficient and VSWR when one of the dipoles is radiating in free space

in the presence of the other.

1. A folded dipole antenna operating at 100 MHz, with identical wires in both arms whose overall

length of each is 0.48, is connected to a 300-ohm twin-lead line. The radius of each wire

is while the center-to-center separation is . Determine the:

a. approximate length (in ) of the regular dipole, at the first resonance, in the absence

of the other wire.

b. input impedance of the single wire resonant regular dipole.

c. input impedance of the folded dipole at the length of the first resonance of the single

element.

d. capacitance (in f/m) or inductance (in h/m), whichever is appropriate, that must be placed

in series with the element at the feed to resonate the folded dipole. To keep the element

balanced, place 2 elements, one in each arm.

e. VSWR of the resonant folded dipole.

3. It is desired to design an optimum end-fire helical antenna radiating in the axial mode at

100 MHz whose polarization axial ratio is 1.1. Determine the:

a. directivity (dimensionless and in dB).

b. half-power beamwidth (in degrees).

c. input impedance.

d. VSWR when connected to a 50-ohm line.

e. wave velocity of the wave traveling along the helix for an ordinary end-fire radiation

(in m/sec).

4. A rectangular X-band (8.2 - 12.4 GHz) waveguide (with inside dimensions of 0.9 in by 0.4 in),

operating in the dominant mode at 10 GHz, is mounted on an infinite ground plane, and

it is used as a receiving antenna. This antenna is connected to a matched lossless transmission

line and a matched load attached to the transmission line. Determine the:

a. directivity (dimensionless and in dB) using:

1. most accurate formula that is available to you in class.

2. Kraus' formula.

b. maximum power (in watts) that can be delivered to the load when a uniform plane wave, with a

power density of 10 mwatts/cm, is incident upon the antenna at normal incidence. Neglect

any losses.

1. It is desired to design a very small, 100% efficient, antenna whose largest fractional bandwidth is 10%.

Determine:

a. The smallest possible quality factor (Q).

b. Its overall largest dimensions (in ).

2. A circular waveguide of radius a, NOT mounted on an infinite Perfect Electric Conductor (PEC), and

operating in the dominant mode, is used as a transmitting antenna. Based on the approximate

equivalent, determine the far zone electric and magnetic radiated fields (you do NOT have to derive them).

3. It is desired to design an optimum directivity conical horn antenna of circular cross section whose overall

slanted length l is 10. Determine the:

a. Geometrical dimensions of the conical horn [radius (in ), diameter (in ), total flare angle (in

degrees)].

b. Aperture efficiency of the horn (in %).

c. Directivity of the horn (dimensionless and in dB).

* To get full credit, you must do all the math and show all the work; do not just write the answers.

4. Design a rectangular microstrip antenna to resonate at 9 GHz using a substrate with a dielectric constant

of 2.56. Determine the:

a. Directivity of a single radiating slot (dimensionless and in dB). Use the cavity model.

b. Approximate directivity of the entire patch (dimensions and in dB). Use the cavity model and neglect

coupling between the two slots.

5. The diameter of an educational TV station reflector is 10 meters. It is desired to design the reflector at

1 GHz with a f/d ratio of 0.5. The pattern of the feed is given by

Assume a symmetrical pattern in the ' direction. Determine the:

a. Total subtended angle of the reflector (in degrees)

b. Aperture efficiency (in %)

c. Directivity of the reflector (dimensionless and in dB).