rotmanLens

Create a Rotman Lens in microstrip form

Since R2024b

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.

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.

Properties

NumBeamPorts — Number of beam ports in the Rotman Lens

6 (default) | 3 | 4 | 5 | 6 | 7 | 8 | positive scalar

The number of beam ports specified as a positive scalar.

Example: lens = rotmanLens(NumBeamPorts = 4)

Data Types: double

NumArrayPorts — Number of array ports in the Rotman Lens

6 (default) | 4 | 5 | 6 | 7 | 8 | positive scalar

The number of array ports specified as a positive scalar.

Example: lens = rotmanLens(NumArrayPorts = 8)

Data Types: double

NumDummyPorts — The number of dummy ports in the Rotman Lens

2 (default) | positive scalar

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

Example: lens = rotmanLens(NumDummyPorts = 4)

Data Types: double

BeamTaper — The shape of the conductive traces into the beam ports of the Rotman Lens

traceTapered (default) | shape object

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

Note

Only tapered traces are supported.

Data Types: object | char

ArrayTaper — The shape of the conductive traces into the array ports

traceTapered (default) | shape object

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

Note

Only tapered traces are supported.

Data Types: object | char

ArrayPortSpacing — The spacing between array ports

0.0167 (default) |

The array port spacing specified in meters.

Example: lens = rotmanLens(ArrayPortSpacing = 0.017)

Data Types: double

BeamPortAngle — The angle of the beam ports

30 (default) | positive scalar

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

MaxScanAngle — The maximum scan (beam steering) angle of the Rotman Lens

20 (default) | positive scalar

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

OnAxisFocalLength — Value of the on-axis focal length

0.1099 (default) | positive scaler

The on-axis focal length specified in meters.

Example: lens = rotmanLens(OnAxisFocalLength = 0.1095)

Data Types: double

OffAxisFocalLength — Value of the off-axis foci

0.0962 (default) | positive scalar

The off-axis focal length specified in meters.

Example: lens = RotmanLens(OffAxisFocalLength = 0.0961)

Data Types: double

Height — Height of the Rotman Lens from the ground plane

0.508e-03 (default) | positive scalar

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

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

Data Types: double

Conductor — Type of metal used for the conducting layers

PEC (default) | metal object

Type of metal specified as a metal object.

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

Data Types: string | char

Substrate — Type of dielectric material

Teflon (default) | dielectric object

Type of substrate specified as a dielectric object.

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

Data Types: char | string

Object Functions

current	Calculate and plot current distribution
dgs	Create defected ground structure of PCB element
feedCurrent	Calculate current at feed port
mesh	Change and view mesh properties of metal or dielectric in PCB component
show	Display PCB component structure or PCB shape
layout	Plot all metal layers and board shape
charge	Calculate and plot charge distribution
shapes	Extract all metal layer shapes of PCB component
sparameters	Calculate S-parameters for RF PCB objects

Examples

Create and Visualize a Default Rotman Lens

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)

layout(lens)

Create Rotman Lens with Defined Properties

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)

layout(lens)

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

  -0.1173 - 0.2060i  -0.1891 + 0.2725i  -0.0554 - 0.2198i  -0.0052 - 0.3561i  -0.1956 + 0.1203i   0.0022 + 0.1406i   0.1784 + 0.1065i   0.3097 + 0.0460i
  -0.1891 + 0.2725i  -0.6311 - 0.0703i  -0.0387 - 0.2839i  -0.0759 - 0.1793i   0.0270 + 0.0008i  -0.0624 - 0.0532i  -0.1925 - 0.1067i  -0.2654 - 0.1403i
  -0.0554 - 0.2198i  -0.0387 - 0.2839i  -0.5975 - 0.1100i  -0.1955 + 0.3023i  -0.2646 - 0.1957i  -0.1697 - 0.0987i  -0.0477 - 0.0454i   0.0175 + 0.0109i
  -0.0052 - 0.3561i  -0.0759 - 0.1793i  -0.1955 + 0.3023i  -0.1795 - 0.1837i   0.3368 + 0.0395i   0.1705 + 0.0642i  -0.0053 + 0.1545i  -0.1969 + 0.1600i
  -0.1956 + 0.1203i   0.0270 + 0.0008i  -0.2646 - 0.1957i   0.3368 + 0.0395i   0.5481 + 0.1652i   0.0322 - 0.3050i  -0.0048 + 0.0831i   0.1623 + 0.2962i
   0.0022 + 0.1406i  -0.0624 - 0.0532i  -0.1697 - 0.0987i   0.1705 + 0.0642i   0.0322 - 0.3050i   0.5941 + 0.5305i   0.1736 - 0.1734i  -0.0242 + 0.0879i
   0.1784 + 0.1065i  -0.1925 - 0.1067i  -0.0477 - 0.0454i  -0.0053 + 0.1545i  -0.0048 + 0.0831i   0.1736 - 0.1734i   0.5471 + 0.5601i   0.0193 - 0.3174i
   0.3097 + 0.0460i  -0.2654 - 0.1403i   0.0175 + 0.0109i  -0.1969 + 0.1600i   0.1623 + 0.2962i  -0.0242 + 0.0879i   0.0193 - 0.3174i   0.5634 + 0.1670i

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