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Array Modeling and Analysis

This example shows how to construct, visualize, and analyze an antenna array from the Antenna Toolbox.

Create Antenna Array Using Antenna Elements

Create a default rectangular antenna array using the rectangularArray element in the array library. By default, the array uses the dipole as an antenna element.

ra = rectangularArray
ra = 
  rectangularArray with properties:

           Element: [1x1 dipole]
              Size: [2 2]
        RowSpacing: 2
     ColumnSpacing: 2
           Lattice: 'Rectangular'
    AmplitudeTaper: 1
        PhaseShift: 0
              Tilt: 0
          TiltAxis: [1 0 0]

Visualize Layout of Array

Use the layout function to plot the position of array elements in the x-y plane. By default, the rectangular array is a 4-element dipole array in a 2x2 rectangular lattice.

layout(ra)

Figure contains an axes object. The axes object with title Array layout contains 5 objects of type scatter, text.

Visualize Geometry of Array

Use the show function to view the structure of the rectangular antenna array.

show(ra)

Figure contains an axes object. The axes object with title rectangularArray of dipole antennas contains 12 objects of type patch, surface. These objects represent PEC, feed.

Plot Radiation Pattern of Array

Use the pattern function to plot the radiation pattern of the rectangular array. The radiation pattern is the spatial distribution of the power of an array. The pattern displays the directivity or gain of the array. By default, the pattern function plots the directivity of the array.

pattern(ra,70e6)

Figure contains an axes object and other objects of type uicontrol. The axes object contains 12 objects of type patch, surface.

Plot Azimuth and Elevation Pattern of Array

Use patternAzimuth and patternElevation functions to plot the azimuth and elevation pattern of the rectangular array. These two patterns are the 2D radiation pattern of the array at a specified frequency.

patternAzimuth(ra,70e6)

Figure contains an object of type uicontainer.

figure
patternElevation(ra,70e6)

Figure contains an object of type uicontainer.

Calculate the Directivity of Array

Directivity is the ability of an array to radiate power in a particular direction. It can be defined as the ratio of the maximum radiation intensity in the desired direction to the average radiation intensity in all other directions. Use the pattern function to calculate the directivity of the rectangular array.

[Directivity] = pattern(ra,70e6,0,90)
Directivity = -39.2495

Calculate EH Fields of Array

Use the EHfields function to calculate the EH fields of the rectangular array. EH fields are the x, y, and z components of the electric and magnetic fields of an array. These components are measured at a specific frequency and at specified points in space.

[E,H] = EHfields(ra,70e6,[0;0;1])
E = 3×1 complex

   0.0000 + 0.0000i
   0.0009 + 0.0015i
  -1.3393 - 0.0711i

H = 3×1 complex
10-5 ×

  -0.1016 - 0.1843i
   0.0000 + 0.0000i
   0.0000 + 0.0000i

Plot Different Polarizations of Array

Use the Polarization name-value pair in the pattern function to plot the different polarization patterns of the rectangular array. Polarization is the orientation of the electric field, or E-field, of an array. Polarization is classified as elliptical, linear, or circular. This example shows the left-hand circularly polarized (LHCP) radiation pattern of the rectangular array.

pattern(ra,70e6,'Polarization','LHCP')

Figure contains an axes object and other objects of type uicontrol. The axes object contains 12 objects of type patch, surface.

Calculate Beamwidth of Array

Use the beamwidth function to calculate the beamwidth of the rectangular array. The beamwidth of an array is the angular measure of the array pattern coverage. The beamwidth angle is measured in the plane that contains the direction of main lobe of the array.

[bw,angles] = beamwidth(ra,70e6,0,1:1:360)
bw = 2×1

   44.0000
   44.0000

angles = 2×2

    28    72
   108   152

Calculate Scan Impedance of Array

Use the impedance function to calculate and plot the input impedance of rectangular array. Active impedance, or scan impedance, is the input impedance of each antenna element in an array, when all elements are excited.

impedance(ra,60e6:1e6:70e6)

Figure contains an axes object and other objects of type uicontrol. The axes object with title Active Impedance contains 2 objects of type line. These objects represent Resistance element 1, Reactance element 1.

You can also view the impedance of all four elements by changing the number of elements on the plot from 1 to 1:4. See figure.

Calculate Reflection Coefficient of Array

Use the sparameters function to calculate the S11 value of the rectangular array. S11 value gives the reflection coefficient of the array.

S = sparameters(ra,60e6:1e6:70e6,72)
S = 
  sparameters: S-parameters object

       NumPorts: 4
    Frequencies: [11x1 double]
     Parameters: [4x4x11 double]
      Impedance: 72

  rfparam(obj,i,j) returns S-parameter Sij

rfplot(S)

Figure contains an axes object and other objects of type uicontrol. The axes object contains 16 objects of type line. These objects represent dB(S_{11}), dB(S_{21}), dB(S_{31}), dB(S_{41}), dB(S_{12}), dB(S_{22}), dB(S_{32}), dB(S_{42}), dB(S_{13}), dB(S_{23}), dB(S_{33}), dB(S_{43}), dB(S_{14}), dB(S_{24}), dB(S_{34}), dB(S_{44}).

Calculate Return Loss of Array

Use the returnLoss function to calculate and plot the return loss of the rectangular array.

returnLoss(ra,60e6:1e6:70e6,72)

Figure contains an axes object and other objects of type uicontrol. The axes object with title Active Return Loss contains an object of type line. This object represents element 1.

You can also view the return loss of all four elements by changing the number of elements on the plot from 1 to 1:4. See figure.

Calculate Charge and Current Distribution Of Array

Use the charge and current functions to calculate the charge and current distribution on the rectangular array surface.

charge(ra,70e6)

Figure contains an axes object. The axes object with title Charge distribution contains 9 objects of type patch.

figure
current(ra,70e6)

Figure contains an axes object. The axes object with title Current distribution contains 9 objects of type patch.

Calculate Correlation Coefficient of Array

Use the correlation to calculate the correlation coefficient of the rectangular array. The correlation coefficient is the relationship between the incoming signals at the antenna ports in an array.

correlation(ra,60e6:1e6:70e6,1,2)

Figure contains an axes object. The axes object with title Correlation coefficient (Element1, Element2) contains an object of type line.

Change Size of Array and Visualize Layout

Use the 'Size' property of the rectangular array to change it to a 16-element dipole array.

ra.Size = [4 4];
show(ra)

Figure contains an axes object. The axes object with title rectangularArray of dipole antennas contains 48 objects of type patch, surface. These objects represent PEC, feed.

Change Array Elements Spacing To Nonuniform

Use the 'RowSpacing' and 'ColumnSpacing' properties of rectangular array to change the spacing between the antenna elements.

ra.RowSpacing = [ 1.1 2 1.2];
ra.ColumnSpacing =[0.5 1.4 2]
ra = 
  rectangularArray with properties:

           Element: [1x1 dipole]
              Size: [4 4]
        RowSpacing: [1.1000 2 1.2000]
     ColumnSpacing: [0.5000 1.4000 2]
           Lattice: 'Rectangular'
    AmplitudeTaper: 1
        PhaseShift: 0
              Tilt: 0
          TiltAxis: [1 0 0]

show(ra)

Figure contains an axes object. The axes object with title rectangularArray of dipole antennas contains 48 objects of type patch, surface. These objects represent PEC, feed.

References

[1] Balanis, C.A. "Antenna Theory. Analysis and Design", p. 514, Wiley, New York, 3rd Edition, 2005.

See Also