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Antenna array(as point source concept)Bablu K. Ghosh

Antennas

Wires passing an alternating current emit, or radiate, electromagnetic energy. The shape and size of the current carrying structure determines how much energy is radiated as well as the direction of radiation. Transmitting Antenna: Any structure designed to efficiently radiate electromagnetic radiation in a preferred direction is called a transmitting antenna. We also know that an electromagnetic field will induce current in a wire. The shape and size of the structure determines how efficiently the field is converted into current, The shape and size also determines from which direction the radiation is preferentially captured. Receiving Antenna: Any structure designed to efficiently receive electromagnetic radiation is called a transmitting antenna

Antenna parameters6. Friis transmission equation.

Assuming that both antennas are in the far field region and that antenna A transmit to antenna B. The gain of the antenna A in the direction of B is Gt, therefore the average power density at the receiving antenna B is

The power received by the antenna B is:

The Friis transmission equation (ignoring polarization and impedance mismatch) is:

Near and far field

Antennas Directivity

The directive gain,, of an antenna is the ratio of the normalized power in a particular direction to the average normalized power, or

The directivity, Dmax, is the maximum directive gain,

Directivity:

Where the normalized powers average value taken over the entire spherical solid angle is

Using

Resolution and DirectivityDirectivity and resolution: Usually resolution of an antenna is it`s half the BW between first nulls.Often FNBW/2 Resolution and it is approximately equal to HPBWSo, A = ( FNBW/2) ( FNBW/2) two planes of the fieldIf number of point source N, the receiving antenna can resolve, N= 4/ A, Directivity, D= 4/ A, so number of point source in the sky is equal to directivity of the antenna.

Antenna Arrays

Antenna arrays are characterized by their array factor which is given by the formula

Antenna arrays are formed by assembling identical (in most cases) radiating elements such as dipoles for example.

In the diagram below is shown an antenna array with its elements along the z axis such that the distance between each two successive elements is equal to d.

Antenna Arrays: BenefitsPossibilities to control electronically Direction of maximum radiationDirections (positions) of nullsBeam-widthDirectivityLevels of side lobesusing standard antennas (or antenna collections) independently of their radiation patternsAntenna elements can be distributed along straight lines, arcs, squares, circles, etc.

Antenna arraysConsist of multiple (usually identical) antennas (elements) collaborating to synthesize radiation characteristics not available with a single antenna. They are ableto match the radiation pattern to the desired coverage area to change the radiation pattern electronically (electronic scanning) through the control of the phase and the amplitude of the signal fed to each elementto adapt to changing signal conditionsto increase transmission capacity by better use of the radio resources and reducing interference

Complex & costly

Antenna arraysIt is not always possible to design a single antenna with the radiation pattern needed. An antenna array is a cluster of antennas arranged in a specific physical configuration (line, grid, etc.). Each individual antenna is called an element of the array. The excitation (both amplitude and phase) applied to each individual element may differ. The far field radiation from the array in a linear medium can be computed by the superposition of the EM fields generated by the array elements.Say, a linear array (elements are located in a straight line) consisting of two elements excited by the signals with the same amplitude but with phases shifted by .

Antenna arrays

The individual elements are characterized by their element patterns F1(,).i.. At an arbitrary point P, taking into account the phase difference due to physical separation and difference in excitation, the total far zone electric field is:

Field due to antenna 1Field due to antenna 2Here:

The phase center is assumed at the array center. Since the elements are identical

Relocating the phase center point only changes the phase of the result but not its amplitude.whereE1=E2

arrayIf no phase difference then, =0, then = kd Cos. To normalized or to make a maximum value unity; 2E1(r) = 1, Then E (r) = Cos{(kd Cos)/2}; if the source is /2 apart or d= /2, then

E (r) = Cos( /2Cos) , since k=2/, wave vector.

The plot of the field pattern of E versus is represented as follows in fig-a. The parallel shift of the point source to maintain respective distance thesame will show the same pattern

arrayii. But when the source of one ref. E1 and other E1 ej the total field from the two sources as given

E = E1 + E1 ej = 2E1 ej/2 Cos/2 where = kd Cos

Now normalizing the value 2E1 =1, we get E= ej/2 Cos/2 = Cos/2 angle(/2)

iii. But when they are in opposite phase the previous equ. Become

E = E1 ej/2 - E1 e-j/2 = 2jE1 Sin {(kd Cos)/2} ; Now normalized or to make a maximum value unity; 2E1 = 1, j operator shows 90 shift from the reference field as shown in fig.(b) in previous page.

then

ArrayThen E = Cos{(kd Cos)/2}; if the source is /2 apart or d= /2, then E = Sin( /2Cos) The direction of field pattern, m maximum field are obtained when /2 Cos m = (2k +1)/2 where k= 0,1,2 .. For k=0 and m = 0 and 180 , the null direction 0 are given by

/2 Cos m = k

For k=0 and = 90 , the half power direction are given by

/2 Cos = (2k +1)/4,

For k=0 and = 60 , 120 , the figure for field pattern is shown before in fig-b.

Antenna arraysThe radiation pattern can be written as a product of the radiation pattern of an individual element and the radiation pattern of the array (array pattern):

where the array factor is:

Here is the phase difference between two antennas. The array factor depends on the array geometry and amplitude and phase of the excitation of individual antennas. If no phase difference then, =0The total far-field radiation pattern |E| of the array (array pattern) consists of the original radiation pattern of a single Hertzian dipole multiplying with the magnitude of the array factor |AF|. This is a general property of antenna arrays and is called the principle of pattern multiplication.

Antenna arrays: ExampleExample 10.7: Find and plot the array factor for 3 two-element antenna arrays, that differ only by the separation difference between the elements, which are isotropic radiators. Antennas are separated by 5, 10, and 20 cm and each antenna is excited in phase. The signals frequency is 1.5 GHz.The separation between elements is normalized by the wavelength via

The free space wavelength:

Normalized separations are /4, /2, and . Since phase difference is zero ( = 0) and the element patterns are uniform (isotropic radiators), the total radiation pattern F() = Fa().

Antenna arraysAnother method of modifying the radiation pattern of the array is to change electronically the phase parameter of the excitation. In this situation, it is possible to change direction of the main lobe in a wide range: the antenna is scanning through certain region of space. Such structure is called a phased-array antenna.We consider next an antenna array with more identical elements.

There is a linearly progressive phase shift in the excitation signal that feeds N elements.

The total field is:Utilizing the following relation:

Antenna arraysthe total radiated electric field is

Considering the magnitude of the electric field only and using

we arrive at

where

is the progressive phase difference between the elements. When = 0:

Antenna arraysThe normalized array factor:

The angles where the first null occur in the numerator of above equation define the beam width of the main lobe. This happens when

Similarly, zeros in the denominator will yield maxima in the pattern.

Antenna arrays

Field patterns of a four-element (N = 4) phased-array with the physical separation of the isotropic elements d = /2 and various phase shift.

The antenna radiation pattern can be changed considerably by changing the phase of the excitation.

Antenna arraysAnother method to analyze behavior of a phase-array is by considering a non-uniform excitation of its elements.

Let us consider a three-element array shown. The elements are excited in phase ( = 0) but the excitation amplitude for the center element is twice the amplitude of the other elements. This system is called a binomial array.Because of this type of excitation, we can assume that this three-element array is equivalent to 2 two-element arrays (both with uniform excitation of their elements) displaced by /2 from each other. Each two-element array will have a radiation pattern:

Antenna arraysNext, we consider the initial three-element binomial array as an equivalent two-element array consisting of elements displaced by /2 with radiation patterns of previous equ. The array factor for the new equivalent array is also represented by the equ. Therefore, the magnitude of the radiated field in the far-zone for the considered structure is:

Element pattern F1()Array factor FA()Antenna pattern F()No sidelobes!!

Antenna arrays (Example)Example 10.8: Using the concept of multiplication of patterns (the one we just used), find the radiation pattern of the array of four elements shown below.

This array can be replaced with an array of two elements containing three sub-elements (with excitation 1:2:1). The initial array will have an excitation 1:3:3:1 and will have a radiation pattern as:

Element patternAntenna array patternArray factor

Alternative-N element array

N element

N element.

N element array.

N array contd.

N array contd.

N array contd.

array

Array

Antenna arraysContinuing the process of adding elements, it is possible to synthesize a radiation pattern with arbitrary high directivity and no side lobes if the excitation amplitudes of array elements correspond to the coefficients of binomial series. This implies that the amplitude of the kth source in the N-element binomial array is calculated as

It can be seen that this array will be symmetrically excited:

Therefore, the resulting radiation pattern of the binomial array of N elements separated by a half wavelength is

Antenna arrays-impedanceDuring the analysis considered so far, the effect of mutual coupling between the elements of the antenna array was ignored. In the reality, however, fields generated by one antenna element will affect currents and, therefore, radiation of other elements.

Let us consider an array of two dipoles with lengths L1 and L2. The first dipole is driven by a voltage V1 while the second dipole is passive. We assume that the currents in both terminals are I1 and I2 and the following circuit relations hold:

where Z11 and Z22 are the self-impedances of antennas (1) and (2) and Z12 = Z21 are the mutual impedances between the elements. If we further assume that the dipoles are equal, the self-impedances will be equal too.

Antenna arrays

In the case of thin half-wavelength dipoles, the self-impedance is

The dependence of the mutual impedance between two identical thin half-wavelength dipoles is shown. When separation between antennas d 0, mutual impedance approaches the self-impedance.For the 2M+1 identical array elements separated by /2, the directivity is:

Antenna arrays: ExampleExample 10.9: Compare the directivities of two arrays consisting of three identical elements separated by a half wavelength for the:Uniform array: I-1 = I0 = I1 = 1A;Binomial array: I-1 = I1 = 1A; I0 = 2A.We compute from (10.51.1):Uniform array:Binomial array:The directivity of a uniform array is higher than of a binomial array.

Array of isotropic point sources beam shaping

Antenna Arrays

Antenna arrays are characterized by their array factor which is given by the formula

In the diagram below is shown an antenna array with its elements along the z axis such that the distance between each two successive elements is equal to d.

N the number of elements making the array, k = 2/ , is the polar angle and is the difference of phase between any two successive elements forming the array. The main objective is to explore how each of the parameters N, d and affect the radiating pattern of the array.

Antenna Arrays1 - Start the applet by clicking on the button "click here to start". On the left panel, you may use any of the sliders to change N the number of elements making the array, d the distance between the elements and the phase .

2 - Set d = 0.25 (this 0.25*wavelength) , to 0 and increase N slowly. Note that the array is more directional.

End-Fire Array 3 - Set N = 10, d = 0.25 (this is 0.25*wavelength) and = kd = 2*Pi*0.25 = 0.5Pi. The main beam (maximum radiation) is directed toward = 180 degrees along the z axis which is also the axis of the array. If you change to -0.5Pi, the main beam is directed toward 0 degrees along the z axis. For these values of we have end-fire radiation.

Endfire Array

Main Beam along the Array

x

Array of isotropic point sources end-fired

Antenna ArraysBroadside Array

4 - Set N = 10, d = 0.25 (this 0.25*wavelength) and = 0 . The main beam (maximum radiation) is directed toward = 90 degrees normal to the z axis which is also the axis of the array. For this value of we have broadside radiation.

Change Phase For Scanning

5 - Set N = 10, d = 0.25 (this 0.25*wavelength) and change slowly starting from 0. Note that the direction of maximum radiation changes. The maximum radiation can be oriented in any direction. This is the basic principle of electronic scanning using antenna arrays.

Broadside Array

xMain Beam orthogonal to the Array

Array of isotropic point sources centre-fed array

Pattern multiplicationThe total field pattern of an array of non-isotropic but similar point sourcesis the product of the individual source pattern and the pattern of an array of isotropic point sources having the same locations,relative amplitudes and phases as the non-isotropic point sources.

Patterns from line and area distributionsWhen the number of discrete elements in an array becomes large, it may be easier to consider the line or the aperture distribution ascontinuous. line source:

2-D aperture source:

Antenna Array PatternsET = F(,I0) (a0+a1ejkdcos+a2ej2kdcos + ) = EF*AFElement Factor (EF) is the field of a lone element.Only Array Factor (AF) can be controlled electronically, by changing the magnitude and phase of {ai}.For a beam to look at direction , set:progressive phase = angle of. ai+1 angle of .ai = -kd cos()|ai| = 1

r1r221

kd cosPhase shift due tophysical separation.k=2/

d

Element FactorsCommon array elements: Dipole, PatchOther arrays: 2-dim. or even 3-dim. arraysElement is chosen to be isotropic over region of interestElement can be chosen for its properties in other dimensions

ParallelCollinearAF

AF

Examples: 16-Antenna ArrayUniform Array: mag.= 1, progressive phase = , uniform spacingWe only need phase shifters!

Phased: =-kd cos(60)

D=12 dBIsotropicradiators

D=12 dBN = 16kd = Broadside: = 0

Number of AntennasDirectivity = D0=Umax/U0 ~ AFmax2 = NHalf Power Beamwidth(HPBW) ~ 2*arccos(1-/Nd)Nulling of interferers reduces main beam gain (a little).Physical size of antenna array is not an issueCircuit complexity grows as N

HPBWD0

ND0HPBW46 dB2689 dB101210.8 dB91612 dB73215 dB3.5

(Uniform Array)