Main Content

rotmanLens

Create a Rotman Lens in microstrip form

Since R2024b

expand all in page

    Description

    Use the rotmanLens object to create a Rotman Lens in microstrip form.

    A Rotman Lens is a passive phase shifting network used with antenna arrays in beam forming and steering applications.

    The structure of a Rotman Lens consists several regions as shown in the figure below.

    Rotman Lens Regions

    • Input Beam Ports – The Input Beam Ports lie on a semi-circular arc along the perimeter of the Parallel Plate Region and provide connectivity between the RF excitation source (radio transmitter and/or receiver) . The array scan angle is controlled by selecting which beam port is connected to the excitation source. The number of beam ports determines the incremental change in the scan angle of the antenna array.

    • Parallel Plate Region – The Parallel Plate Region provides the phase delays between the Input Beam Ports and Output Ports of the lens. It consists of the lens and ground plane conductive layers and the dielectric substrate sandwiched between the conductive layers.

    • Output Ports – The Output Ports lie in a curved arc along the perimeter of the Parallel Plate Region exactly opposite the Input Beam Ports. The Output Ports are connected to the Delay Lines region of the lens. Each Output Port is connected to an individual delay line.

    • Delay Lines – The Delay Lines provide time delays and connectivity between the Output Ports and the Linear Array regions of the lens.

    • Linear Array – The Linear Array region lies along a straight line and provides connectivity from the Delay Lines to the antennas.

    • Dummy Ports – The Dummy Ports lie symmetrically along the two side walls of the lens. They are terminated with matching impedances to prevent reflections from occurring along the side walls of the lens.

    The design of the Rotman Lens is determined by its geometrical configuration as shown in the figure below.

    Rotman Lens Geometry

    • C – is the semi-circular arc of the beam inputs.

    • S1 – is the arc of the beam output.

    • S2 – is the line of the linear array

    • F0 – is the on-axis focal point of the lens located at the center of arc C.

    • F1 and F2 – are the off-axis foci points of the lens located equidistant from F0 on arc S.

    • d is the Array Port spacing along S2.

    • w0 – is the on-axis delay line electrical delay.

    • w – are the off-axis delay lines electrical delays.

    • α – is the Beam Port angle.

    • ψ – is the maximum scan angle of the array.

    Creation

    Syntax

    lens = rotmanLens
    lens = rotmanLens(name = value)

    Description

    lens = rotmanLens creates a default Rotman Lens.

    example

    lens = rotmanLens(name = value) sets Properties using one or more name-value arguments. For example, lens = rotmanLens(NumBeamPorts=4) creates a Rotman Lens with 4 beam ports. Properties not specified retain their default values.

    example

    Properties

    expand all

    The number of beam ports specified as a positive scalar.

    Example: lens = rotmanLens(NumBeamPorts = 4)

    Data Types: double

    The number of array ports specified as a positive scalar.

    Example: lens = rotmanLens(NumArrayPorts = 8)

    Data Types: double

    The number of dummy ports specified as a positive scalar less than 9.

    Example: lens = rotmanLens(NumDummyPorts = 4)

    Data Types: double

    The shape of the trace into the beam ports specified as a shape object

    Note

    Only tapered traces are supported.

    Data Types: object | char

    The trace into the array ports specified as a shape object.

    Note

    Only tapered traces are supported.

    Data Types: object | char

    The array port spacing specified in meters.

    Example: lens = rotmanLens(ArrayPortSpacing = 0.017)

    Data Types: double

    The angle of the beam ports specified in degrees.

    Note

    The supported range of beam angle is 25 < BeamPortAngle < 60.

    Example: lens = rotmanLens(BeamPortAngle = 35)

    Data Types: double

    The maximum scan (beam steering) angle specified in degrees.

    Note

    The supported range of scan angle is 5 < MaxScanAngle < 45.

    Example: lens = rotmanLens(MaxScanAngle = 25)

    Data Types: double

    The on-axis focal length specified in meters.

    Example: lens = rotmanLens(OnAxisFocalLength = 0.1095)

    Data Types: double

    The off-axis focal length specified in meters.

    Example: lens = RotmanLens(OffAxisFocalLength = 0.0961)

    Data Types: double

    Height of the Rotman Lens above the ground plane specified in meters.

    Example: lens = rotmanLens(Height = 0.499e-03)

    Data Types: double

    Type of metal specified as a metal object.

    Example: lens = rotmanLens(Conductor = metal('copper'))

    Data Types: string | char

    Type of substrate specified as a dielectric object.

    Example: lens = rotmanLens(Substrate = dielectric('FR4'))

    Data Types: char | string

    Object Functions

    currentCalculate and plot current distribution
    dgsCreate defected ground structure of PCB element
    feedCurrentCalculate current at feed port
    meshChange and view mesh properties of metal or dielectric in PCB component
    showDisplay PCB component structure or PCB shape
    layoutPlot all metal layers and board shape
    chargeCalculate and plot charge distribution
    shapesExtract all metal layer shapes of PCB component
    sparametersCalculate S-parameters for RF PCB objects

    Examples

    collapse all

    Open Live Script

    Create and visualize a Rotman Lens in stripline form.

    Create Lens

    Create a Rotman Lens.

    lens = rotmanLens
    lens = 
  rotmanLens with properties:

          NumBeamPorts: 6
             BeamTaper: [1×1 traceTapered]
         BeamPortAngle: 30
         NumDummyPorts: 2
         NumArrayPorts: 6
            ArrayTaper: [1×1 traceTapered]
      ArrayPortSpacing: 0.0167
          MaxScanAngle: 20
     OnaxisFocalLength: 0.1099
    OffaxisFocalLength: 0.0962
                Height: 5.0800e-04
             Substrate: [1×1 dielectric]
             Conductor: [1×1 metal]

    Visualize the Lens

    Use the show and layout functions to visualize the PCB and port numbers.

    show(lens)

    Figure contains an axes object. The axes object with title rotmanLens element, xlabel x (mm), ylabel y (mm) contains 24 objects of type patch, surface. These objects represent PEC, feed, Teflon, load.

    layout(lens)

    Figure contains an axes object. The axes object with title rotmanLens Layout, xlabel x (m), ylabel y (m) contains 17 objects of type line, text. One or more of the lines displays its values using only markers These objects represent Board Shape, Layer1, Layer3, Feed, Via.

    Open Live Script

    Create, visualize, and analyze a Rotman lens with user defined properties.

    Create Lens

    Create a Rotman lens with 4 beam ports, 4 array ports, 4 dummy ports, 40 degree beam port angle, 30 degree maximum scan angle, and copper conducting layer.

    lens = rotmanLens(NumBeamPorts=4,NumArrayPorts=4,NumDummyPorts=4,BeamPortAngle=40,MaxScanAngle=30,Conductor=metal('copper'))
    lens = 
  rotmanLens with properties:

          NumBeamPorts: 4
             BeamTaper: [1x1 traceTapered]
         BeamPortAngle: 40
         NumDummyPorts: 4
         NumArrayPorts: 4
            ArrayTaper: [1x1 traceTapered]
      ArrayPortSpacing: 0.0167
          MaxScanAngle: 30
     OnaxisFocalLength: 0.1099
    OffaxisFocalLength: 0.0962
                Height: 5.0800e-04
             Substrate: [1x1 dielectric]
             Conductor: [1x1 metal]

    Visualize Lens

    Use the show and layout functions to visualize the PCB and port configuration.

    show(lens)

    Figure contains an axes object. The axes object with title rotmanLens element, xlabel x (mm), ylabel y (mm) contains 28 objects of type patch, surface. These objects represent Copper, feed, Teflon, load.

    layout(lens)

    Figure contains an axes object. The axes object with title rotmanLens Layout, xlabel x (m), ylabel y (m) contains 13 objects of type line, text. One or more of the lines displays its values using only markers These objects represent Board Shape, Layer1, Layer3, Feed, Via.

    Analyze the lens at 5.8 GHz

    Look at the s-parameters of the created lens using the sparameters function.

    s = sparameters(lens,5.8e09)
    s = 
  sparameters with properties:

      Impedance: 50
       NumPorts: 8
     Parameters: [8x8 double]
    Frequencies: 5.8000e+09


    s.Parameters
    ans = 8×8 complex

  -0.2406 + 0.0714i   0.1550 + 0.3123i  -0.0068 - 0.0329i   0.1169 - 0.0305i  -0.0548 + 0.0995i  -0.0102 + 0.1841i   0.0669 + 0.1715i   0.1621 + 0.0605i
   0.1550 + 0.3123i  -0.6264 + 0.0309i   0.0331 - 0.3224i  -0.0060 - 0.0422i  -0.0727 - 0.0483i  -0.1132 - 0.0140i  -0.1419 - 0.0080i  -0.1420 - 0.0272i
  -0.0068 - 0.0329i   0.0331 - 0.3224i  -0.6262 + 0.0356i   0.1449 + 0.3100i  -0.1448 - 0.0262i  -0.1392 - 0.0069i  -0.1165 - 0.0181i  -0.0694 - 0.0491i
   0.1169 - 0.0305i  -0.0060 - 0.0422i   0.1449 + 0.3100i  -0.2386 + 0.0525i   0.1597 + 0.0566i   0.0669 + 0.1671i  -0.0115 + 0.1906i  -0.0523 + 0.1008i
  -0.0548 + 0.0995i  -0.0727 - 0.0483i  -0.1448 - 0.0262i   0.1597 + 0.0566i   0.8829 + 0.1010i  -0.0330 - 0.1625i  -0.0483 + 0.0026i  -0.0041 + 0.0630i
  -0.0102 + 0.1841i  -0.1132 - 0.0140i  -0.1392 - 0.0069i   0.0669 + 0.1671i  -0.0330 - 0.1625i   0.8020 + 0.2828i  -0.0545 - 0.1551i  -0.0506 + 0.0056i
   0.0669 + 0.1715i  -0.1419 - 0.0080i  -0.1165 - 0.0181i  -0.0115 + 0.1906i  -0.0483 + 0.0026i  -0.0545 - 0.1551i   0.7978 + 0.2803i  -0.0340 - 0.1652i
   0.1621 + 0.0605i  -0.1420 - 0.0272i  -0.0694 - 0.0491i  -0.0523 + 0.1008i  -0.0041 + 0.0630i  -0.0506 + 0.0056i  -0.0340 - 0.1652i   0.8834 + 0.1017i

    References

    [1] Hansen, R.C. Design Trades for Rotman Lenses IEEE Transaction on Antennas and Propagation, Vol. 39, No. 4, April 1991

    Version History

    Introduced in R2024b

    See Also