UNIT-3. Ans: Arrays of two point sources with equal amplitude and opposite phase:

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1 `` UNIT-3 1. Derive the field components and draw the field pattern for two point source with spacing of λ/2 and fed with current of equal n magnitude but out of phase by 180 0? Ans: Arrays of two point sources with equal amplitude and opposite phase: In this, point source 1 is out of phase or opposite phase (180 ) to source 2 i.e. when there is maximum in source 1 at one particular instant, and then there is minimum in source 2 at that instant and vice-versa. Referring to Fig.1.1 the total far field at distant point P, is given by E = (-E ie - φ j/2 ) + (+ E 2 e + φ i/2 ) But Then E 1 =E 2 =E 0 (say) E=E 0 2j E=2jE 0 sinφ/2. (1.1a) E=2jE 0 sin cosθ. (1.1b) Let d = λ/2 and 2E 0 j = 1 Enorm, = sin (π/2 COS θ).. (1.2) Maximum directions: Maximum value of sine function is ± 1 sin (π/2 cosθ) = ± 1 (П/2 cosθ max ) = ± (2 n + 1) n / 2 where n = 0, 1, 2 (cosθ max ) = ± 1 if n = 0 θ max = 0 and (1.3 a) Minima directions: Minimum value of a sine function is 0 sin (π/2 cosθ) = 0 π/2 cosθmin = ± nπ where n = 0, 1, 2.. COS θmin = 0 Therefore θmin= 90 and (1.3b) Half power point directions: sin (П /2 cosθ) = ± П/2 cosθ HPPD = ± (2n+ 1) π/4 П/2 cosθ HPPD = ± π /4 if n = 0 cosθ HPPD = ± θ HPPD = 60, ± 120 (1.3c) GRIET/ECE 1

2 From these, it is possible to draw the field pattern which is as shown in Fig.1.2 It is seen that maxima have shifted 90 along X-axis in comparison to in-phase field pattern. The figure is horizontal figure of 8 and 3-dimensional space pattern is obtained by rotating it along X -axis. Once the arrangement gives maxima along line joining the two sources and hence this is one of the simplest type of "End fire" 'Array'. 2. What is the necessity of an array? Explain the three different types of array with regard to beam pointing direction Ans: Antenna Array This is one of the common methods of combining the radiations from a group of similar antennas in which the wave-interference phenomenon is involved. The field strength can be increased in preferred directions by properly exciting group or array of antennas simultaneously, such as arrangement is known as antenna array. Array of antenna is an arrangement, of several individual antennas so spaced and phased that their individual contributions coming in one preferred direction and cancel in all other directions, which will be going to increase the directivity of the system. The different types of arrays with regard to beam pointing direction are as follows, 1. Broadside array 2. End fire array 3. Collinear array. 1. Broadside Array Broadside array is one of the most commonly used antenna array in practice. The array in which a number of identical parallel antennas are arranged along a line perpendicular to the line of array axis is known as broadside array, which is shown in figure (2.1). In this, the individual antennas are equally spaced along a line and each element is fed with current of equal magnitude, all in the same phase. GRIET/ECE 2

4 Where E - Total field E0(θ,φ) = Field pattern of individual source Ei(θ,φ) = Field pattern of array of isotropic point source Epi(θ,φ)= Phase pattern of individual source Epa(θ,φ)= Phase pattern of array of isotropic point sources. Hence, θ and φ are polar and azimuth angles respectively. The principle of multiplication of pattern is best suited for any number of similar sources. Considering a two dimensional case, the resulting pattern is given by the equation, E = 2 E 0 cosφ /2 E = 2 E 1 sinθ cosφ /2. E = E (θ) cosφ /2 It can be seen that E0 is a function of E (θ). In the above equation the total field pattern is equal to the product of primary pattern E (θ) and a secondary pattern cosφ/2. Effect of Earth on the Radiation Pattern The effect of earth on the radiation pattern can be obtained by using an image principle. In image principle, earth is considered as an image antenna of same length and current as shown in the figure (3.1). For vertical antenna, currents in actual and image antennas are equal and have same direction, whereas opposite direction for horizontal antenna. The resultant field is obtained by the addition of field of an image antenna to that of an actual antenna. The shape of the vertical pattern is affected more than the horizontal pattern GRIET/ECE 4

5 Effect of Earth on the Radiation Pattern of Vertical Antenna The ground-effect factor of a perfectly conducting earth is given as, 2cos П sinφ Where, h = Height of the center of antenna above earth φ = Elevation angle above horizontal. But, for the case of finite conducting of earth, the above given expression is valid for large angles of φ0. Whereas, for low angles of φ 0, less than 15 known as "Pseudo-Brewster angle", the phase of the reflection factor is nearer to 180 than it is to 0 and the use of above equation would lead to erroneous result. The effect of earth on radiation pattern can be explained by taking different cases of conductivities (σ). The function n is defined as, n = Where, x=σ/ω σ = conductivity of the earth in mho/meter =15, Relative dielectric of the earth.\ The vertical radiation pattern of a vertical dipole is a shown in the fig 3.2 GRIET/ECE 5

6 Effect of Earth on the Radiation Pattern of Horizontal Antenna The effect of ground is obtained by multiplying free-space pattern and ground factor, i.e. 2cos П sinφ The first maxima in this pattern occurs at, sinφ = λ/4h (h> λ/4) The effect of earth on the vertical pattern perpendicular to the axis of dipole is as shown in figure3.4. GRIET/ECE 6

8 Then according to multiplicity of pattern. The resultant radiation pattern of 4 elements is obtained by multiplying the radiation pattern of individual element Fig 4.3 (b) and array of two units spaced λ. In place of isotropic (non-directional) if the array is replaced by an non-isotropic (i.e. directional) antennas, then the radiation pattern Fig. 4.2 must be accordingly modified. Radiation pattern of 8-isotropic elements fed in phase, spaced λ/2 apart. As above the principle can be applied to broad-side linear array of 8-isotropic elements also as shown in Fig. 4.5 In this case 4- isotropic elements are assumed to be one unit and then to find the radiation pattern of two such units paced a distance 2λ apart. The radiation pattern of isotropic element is just seen in Fig. 4.4 GRIET/ECE 8

10 3. Cancel out interference from a particular set of directions. 4."Steer" the array so that it is more sensitive in a particular direction. 5. Determines the direction of arrival of the incoming signals. 6. It maximize the Signal to Interference plus Noise ratio Disadvantages 1. Ray deflection only in a single plane possible. 2. Complicated arrangement and more electronically controlled phase shifter needed. ; 3. Field view is restricted. 4. Considerable minor lobes are formed. 5. Large power loss due to current flowing in all elements. 6. Overall efficiency decreases. 7. Costly to implement. 6. What is the optimum spacing in parasitic array? why? Ans: The simplest case of a parasitic array is one driven element and one parasitic element and this may be considered as two element array. A parasitic array consists of one or more driven element and a number of parasitic elements. Hence in parasitic arrays there are one or more parasitic elements and at least one driven element to introduce power in the array. GRIET/ECE 10

11 A parasitic array with linear half-wave dipole as elements is normally called as "Yagi- Uda" or simply "Yagi" antenna after the name of inventor S.Uda (Japanese) and H. Yagi (English). The amplitude and phase of the current introduced in a parasitic element depends on its tuning and the spacing between parasitic element and driven element to which it is coupled. A variation in the distance between driven element and parasitic element changes the relative phases and this proves to be very convenient. It helps in making the radiation pattern unidirectional. A distance of λ/4 and phase difference of П/2 radian (or 90 ), for example, provides a unidirectional pattern. 7. What is linear array? Compare Broad side array and End fire array? Ans : Linear arrays: The arrays in which the individual antennas (called as elements) are equally spaced along a straight line are called as linear arrays. Thus, linear antenna array is a system of equally spaced elements. GRIET/ECE 11

12 Broad side array End fire array GRIET/ECE 12

14 8. What are the various difference between binomial and linear arrays? Ans: Binomial Array 1. The binomial array is one in which all the elements are fed with currents of non-uniform amplitude. 2. Elements are fed with unequal amplitude. 3. We use Pascal triangle to select the coefficient or amplitudes of elements. 4. Principle of multiplication of pattern is used for derivation of pattern. 5. Secondary lobes does not appear in the radiation pattern. 6. HPBW increases and directivity decreases. For Example: For 5 element array with λ/2 spacing HPBW = 31 Linear Array 1. In antenna array if the individual antennas are equal spaced in a straight line, then it is said to be linear array. 2. If elements are fed with equal amplitude, it is called as uniform linear array. 3. We do not use Pascal triangle, 4. Principle of multiplication of pattern is used for derivation of pattern. 5.Secondary lobes appear in the radiation pattern 6. HPBW is less compared to binomial array. For Example: For 5 "element array with λ/2 spacing HPBW= Design is complex for large array due to large amplitude ratio. 7. Design is simple for large array due to uniform amplitude 9. Explain the concept of scanning arrays and What the requirement of tapering of arrays is Ans: In broad side (or) end fire array, the maximum radiation occurs in a specific direction. In broad side array, the direction of radiation pattern is perpendicular to the array axis whereas in end fire array radiation pattern is normal, to the array axis. It is possible to change the orientation of maximum radiation in any direction with the help of scanning (or) phased arrays Let, θ 0 =Orientation angle Therefore Phase difference (α) can be calculated by, GRIET/ECE 14

16 4. The field strength readings and direction of the secondary half wave dipole antenna with respect to primary half wave dipole antenna are recorded along the circle at different points. 5. Finally, using the readings of field strengths at a number of points the plot of radiation pattern of primary half wave dipole antenna is made either in rectangular form or in polar form. GRIET/ECE 16

17 GRIET/ECE 17

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