#### Antenna Theory

operates at 10 MHz. /30= ^/1000·시and wire radius bA single turn circular loop antenna with a = a) Find the radiation resistance of the loop. b) Find the input impedance of the loop. c) What capacitance should be put in parallel with the loop to resonate it? d) What is the radiation resistance of the loop if there are N = 4 turns?

(12 pts) Assume you have copper tube of diameter 2 cm. Design an antenna that operates at 300 MHz with maximum radiation at 0 = 0° (as near as you can). a) Does your loop have constant or non-uniform current? b) What is the radius of your loop? c) What is the radiation resistance of your loop? d) What is the directivity at theta= 0°? e) Is your loop self-resonant? If not, what capacitance (in parallel) or inductance (inseries) must be added to resonate the loop? f) Explain can you use a copper tube instead of a solid copper wire.

Design a uniform broadside linear array of N elements placed along the z-axis with a uniformspacing d = /10 between the elements. Determine the closest integer number of elementsso that in the elevation plane the (a) Half-power beam width of the array factor is approximately 60°. (b) First-null beam width of the array factor is 60°.

Design a five-element binomial array with elements placed along the z-axis. (a) Derive the excitation coefficients. (b) Write a simplified expression for the array factor. (c) For a spacing of d = 31/4, determine all the angles theta (in degrees) where the array factor possesses nulls. (d) For a spacing of d = 31/4, determine all the angles theta (in degrees) where the array factor possesses main maxima.

(4 pts) Design a constant current circular loop that has a null at 0 = 90° and two nulls above the plane of the loop. (Of course there will also be two nulls below the plane.) a) What is the radius of the loop? b) Where are the nulls (in the upper half-plane)?

1 (8 pts) Consider a constant current circular loop whose intensity vanishes at theta = 0° and theta = 60°. a) What is the radius of the loop (in terms of wavelength)? b) What is the direction of maximum radiation? c) What is the maximum directivity? d) What is the total power radiated by the antenna?

(4 pts) The far field E of a circular loop with non-uniform current and C = lambda is approximated as E_{\infty}=A_{0} \cos ^{2}(\theta) e^{-j k} / r 0^{\circ}<\theta<90^{\circ} \text { and } 0^{\circ}<\omega<360^{\circ} a) Find the maximum directivity of the loop. b) Estimate the input impedance of the loop.

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 constant current circular loop has radius a = 3 lambda/2 a) Where are the nulls in the field pattern? b) What is the direction of maximum radiation? c) What is the total power radiated by the antenna? d) What is the total power radiated by the antenna if the frequency is twice the design frequency?

(6 pts) Design a single turn circular loop operating at 10 MHz such that the radiationresistance is 0.73 Ohm. You may assume RLresonating capacitor.= 0 and that the antenna is in parallel with a a) What is the radius of the loop? b) What number of turns of the wire is necessary to match (as closely as possible) a300 Ohm feed line? c) Assume the number of turns given in your answer to part (c). An incident planewave is polarization matched to the antenna and has a power density S =10-6 w/m²-m2.What is the maximum power to the load?

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.

It is desired to design a uniform ordinary end-fire array of 6 elements with a maximum toward theta o = 0° and 0, = 180°, simultaneously. Determine the (a) smallest separation between the elements (in 1). (b) excitation progressive phase shift (in degrees) that should be used (d) relative value (in dB) of the magnitude of the array factor toward broadside (0, = 90°)compared to that toward the maximum (theta, = 0° or 180°). (c) approximate directivity of the array (dimensionless and in dB)

Design a uniform broadside linear array of N elements placed along the z-axis with a uniform spacing d = 1/10 between the elements. Determine the closest integer number of elements so that in the elevation plane the (a) Half-power beamwidth of the array factor is approximately 60°. (b) First-null beamwidth of the array factor is 60°.

(4 pts) A small circular loop operating at 300 MHz is placed a height h above an infinite PEC ground plane. a) What is the minimum height such that there will be a null in the pattern at 0 =30°? b) Where are the nulls in pattern when h = lambda?

). 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.

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

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.

71. A horizontal 1/50 infinitesimal dipole of constant current and length I is placed parallel tothe y-axis a distance h = 0.707A above an infinite electric ground plane. Find all the nullsformed by the antenna system in the o = 90° plane.%3D

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 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

8. A one-turn small circular loop is used as a radiating element for a VHF (f = 100 MHz) communications system. The circumference of the loop is C = 1/20 while the radius of the wire is 1/400. Determine, using a wire conductivity of o = 5.7 x 107 S/m, the (a) input resistance of the wire for a single turn. (b) input reactance of the loop. Is it inductive or capacitive? Be specific. (c) inductance (in henries) or capacitance (in farads) that can be placed in series with the loop at the feed to resonate the antenna at f = 100MHZ; choose the element that will accomplish the desired objective.

A very small circular loop of radius a(a < ^/6x) and constant current I, is symmetrically placed about the origin at x = 0 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

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

63. A vertical 1/2 dipole antenna is used as a ground-to-air, over-the-horizon communication antenna at the VHF band (f = 200 MHz). The antenna is elevated at a height h (measured from its center/feed point) above ground (assume the ground is flat, smooth, and perfect electric conductor extending to infinity). In order to avoid interference with other simultaneously operating communication systems, it is desired to place a null in the far-field amplitude pat-tern of the antenna system at an angle of 60° from the vertical.% Determine the three smallest physical/nontrivial heights (in meters at 200 MHz) above theground at which the antenna can be placed to meet the desired pattern specifications.