2. Model the geometry in FEKO. To do so, take the same frequency as in question 1, and select the

An array of 10 isotropic elements are placed along the z-axis a distance d apart. Assum-ing uniform distribution, find the progressive phase (in degrees), half-power beam width (in degrees), first-null beam width (in degrees), first side lobe level maximum beam width (indegrees), relative side lobe level maximum (in dB), and directivity (in dB) (using equations and the computer program Directivity of Chapter 2, and compare) for (a) broadside (b) ordinary end-fire (c) Hansen-Woodyard end-fire

A very small loop antenna (a « /30) of constant current is placed a height h above a flat,perfectly conducting ground plane of infinite extent. The area plane of the loop is parallel to the interface (x-y plane). For far-field observations (a) find the total electric field radiated by the loop in the presence of the ground plane b) all the angles (in degrees) from the vertical to the interface where the total field will vanish when the height is (c) the smallest nonzero height (in 2) such that the total far-zone field exhibits a null at an angle of 60° from the vertical

2.16. The normalized radiation intensity of an antenna is rotationally symmetric in , and it is represented by U= 0° ≤ 0 < 30° 0.5 30° 0 < 60° 0.1 60° ≤0 < 90° 0 90° ≤ 0 ≤ 180° (a) What is the directivity (above isotropic) of the antenna (in dB)? (b) What is the directivity (above an infinitesimal dipole) of the antenna (in dB)?

A small circular loop with a uniform current distribution, and with its classical omnidirectional pattern, is used as a receiving antenna. Determine the maximum directivity (dimensionless and in dB) using: (a) Exact method. (b) An approximate method appropriate for this pattern. Specify the method used. (c) Another approximate method appropriate for this pattern. Specify the method used.

A small circular loop with circumference C < 1/20 is used as a receiving antenna. A uniformplane wave traveling along the x-axis and toward the positive (+).x direction (as shown in the figure), whose electric field is given by \mathbf{E}_{w}^{i}=\left(\hat{q}_{y}+2 \hat{q}_{z}\right) e^{-j k x} is incident upon the antenna. Determine the (a) polarization of the incident wave. Justify your answer. (b) axial ratio of the polarization ellipse of the incident wave. (c) polarization of the loop antenna toward the x-axis. (d) polarization loss factor (dimensionless and in dB). (e) maximum power at 1 GHz that can be delivered to a load connected to the antenna,E.if the power density of the above incident wave is 5 m watts/cm². Assume no other losses \text { Hint: } \hat{\mathbf{a}}_{\phi}=-\hat{\mathbf{a}}_{x} \sin \phi+\hat{a}_{y} \cos \phi

4.51. Determine the smallest height that an infinitesimal vertical electric dipole of I = /50 must be placed above an electric ground plane so that its pattern has only one null (aside from the null toward the vertical), and it occurs at 30° from the vertical. For that height, find the directivity and radiation resistance.

A three-element array of isotropic sources has the phase and magnitude relationships shown.The spacing between the elements is d = /2. (a) Find the array factor. (b) Find all the nulls.

2.12. The normalized radiation intensity of a given antenna is given by (a) U = sin sin (b) U = sin 0 sin² (d) U = sin²0 sin (f) U = sin² 0 sin³ (c) U = sin 0 sin³ (e) U = sin²0 sin² The intensity exists only in the 0 ≤ 0 ≤ π,0 ≤ ≤ region, and it is zero elsewhere. Find the (a) exact directivity (dimensionless and in dB). (b) azimuthal and elevation plane half-power beamwidths (in degrees).

). Design a 10 × 8 (10 in the x-direction and 8 in the y) element uniform planar array so that the main maximum is oriented along thetag = 10°, phi o = 90°. For a spacing of d, = d, = 1/8between the elements, find the (a) progressive phase shift between the elements in the x and y directions (b) directivity of the array (c) half-power beamwidths (in two perpendicular planes) of the array.

2.10. In target-search ground-mapping radars it is desirable to have echo power received from a target, of constant cross section, to be independent of its range. For one such application, the desirable radiation intensity of the antenna is given by U(0,4)= 1 0.342 csc(0) 0 {0.34 0° ≤ 0 <20° 20° ≤ 0 < 60° 60° ≤ 0 ≤ 180° Find the directivity (in dB) using the exact formula. 1 0 5 0° ≤ ≤ 360°