# Antenna Magus Array Synthesis

Antenna Array Design Made Easy

## The Antenna Magus Array Synthesis Tool

The array synthesis tool helps with the initial stages of array design. It assists engineers in synthesizing arrays of various shapes, such as linear, planar and circular with different excitation distributions and radiating elements. The array synthesis tool contains several design algorithms that determine the required array parameters for given objectives. Users can also import array layouts into Antenna Magus and modify the layouts using operators.

A useful application for the array synthesis tool is the distribution matrix (DM) import functionality. It allows users to specify customized array layouts using tab-separated value (tsv) files. Antenna Magus reads each element's spacing (x,y,z), amplitude and phase and calculates the synthesized array using the specified element pattern.

## Antenna Array Types

The Antenna Magus information browser provides more information about how to use the array synthesis in: Antenna Array Synthesis in Antenna Magus and in Help: How do I use the Array Synthesis tool?  The latter article also describes the different excitation tapers in more detail, and provides references for further research.

### Broadside with Default Taper

This synthesis algorithm designs a linear array for a specified directivity or beamwidth. Antenna Magus arranges the elements of the array along the x-axis, with the resulting pattern being symmetrical around the x-axis and the peak directivity in the y-z plane (broadside).

This design algorithm sets the inter-element spacing always at 0.49 λ. The specification of a directivity of less than 20 dB, or a beamwidth of greater than 20°, results in all the side-lobes to be equal or -20 dB below the main beam directivity [Dolph-Chebychev excitation taper]. For higher gain designs, the first five side lobes are -20 dB below the main beam directivity [Villeneuve excitation taper].

### Broadside Directivity and Scan Angle

This synthesis algorithm designs a linear array for a specified directivity or beamwidth and a scan angle. Antenna Magus arranges the elements of the array along the x-axis. The resulting pattern being rotationally symmetric around the x-axis and the peak directivity being at the specified scan angle away from the y-z plane.

This design algorithm sets the inter-element spacing always at 0.49 λ. The specification of a directivity of less than 20 dB, or a beamwidth of greater than 20°, results in all the side-lobes to be equal or -20 dB below the main beam directivity [Dolph-Chebychev excitation taper]. For higher gain designs, the first five side lobes are -20 dB below the main beam directivity [Villeneuve excitation taper]. The specification of the scan angle introduces an inter-element phase offset in the excitation.

### Broadside Directivity and Excitation Taper

This synthesis algorithm designs a linear array for a specified directivity or beamwidth and a scan angle. Antenna Magus arranges the elements of the array along the x-axis. The resulting pattern is rotationally symmetric around the x-axis and the peak directivity is at the specified scan angle away from the y-z plane.

This design algorithm sets the inter-element spacing always at 0.5 λ. Antenna Magus enables the selection of the excitation taper between equal excitation [Uniform], uniform side lobe level [Dolph-Chebychev] and first few side lobes uniform [Villeneuve]. Then they can specify side lobe level and number of side lobes, where applicable.

### Broadside Directivity, Scan Angle and Taper

This synthesis algorithm designs a linear array for a specified directivity or beamwidth, scan angle and excitation taper. The user can specify the excitation taper to control the sidelobes while using the scan angle (specified from broadside) to design an array that squints at a specific angle. Antenna Magus can design this array can with the elements arranged along any of the three major axes. The resulting pattern is rotationally symmetric around the chosen axis and the peak directivity is at the specified scan angle away from the plane normal to this axis.

This design algorithm can use the inter-element spacing as an input. Values between 0 λ and 5 λ are possible. A spacing of over 0.5 λ can lead to unwanted grating lobes appearing together with the required main lobe. Hence, the peak directivity could be lower than designed for. The energy in the grating lobe can be compensated for in the design requirements of the main lobe. The direction of the main lobe can be specified between -90° and 90 degrees. Users can select the excitation taper to be equal excitation [Uniform], uniform side lobe level [Dolph-Chebychev] and first few side lobes uniform [Villeneuve]. Then they can specify side lobe level and number of side lobes, where applicable.

### End-Fire Directivity or Beamwidth

This synthesis algorithm designs a linear array for a specified directivity or beamwidth. Antenna Magus arranges the elements of the array along the x-axis. The main lobe of the resulting pattern is a body of rotation about the x-axis, with the peak directivity in the +x direction.

The inter-element spacing is always 0.49 λ when this design algorithm is used. If a directivity of less than 20 dB, or a beamwidth of greater than 20°, is specified, all the side-lobes are equal and -20 dB below the main beam directivity [Dolph-Chebychev excitation taper]. For higher gain designs, the first five side lobes are -20 dB below the main beam directivity [Villeneuve excitation taper]. The specification of the scan angle introduces an inter-element phase offset in the excitation.

### End-fire Directivity and Excitation Taper

This synthesis algorithm designs a linear array for a specified directivity or beamwidth and excitation taper. The direction of peak directivity can be set to any of the Cartesian axis directions. The specification of the excitation taper controls the sidelobes. The resulting pattern of this array is always rotationally symmetric around the chosen axis.

This design algorithm can use the inter-element spacing as an input. Values between 0 λ and 5 λ are possible. If a spacing of over 0.5 λ is used, unwanted grating lobes are present together with the required main lobe. Therefore, the peak directivity could be lower than designed for. The energy in the grating lobe can be compensated for in the design requirements of the main lobe. Users can select the excitation taper to be equal excitation [Uniform], uniform side lobe level [Dolph-Chebychev] and first few side lobes uniform [Villeneuve]. Then they can specify side lobe level and number of side lobes, where applicable

### Broadside Null with Directivity and Taper

This synthesis algorithm designs a linear array that has a broadside null, with a specified directivity either side of the null and excitation taper. The specification of the excitation taper allows the sidelobes to be controlled. Antenna Magus can design this array with the elements arranged along any of the three major axes. The resulting pattern is rotationally symmetric around the chosen axis and the null is in the plane normal to that axis.

The inter-element spacing designed by this algorithm is always 0.5 λ. Users can select the excitation taper to be equal excitation [Uniform] and near-in side-lobes at quasi-uniform specified level [Bayliss]. The side lobe level and number of side lobes can be set when using the Bayliss taper.

### Specify the Layout Directly

This algorithm allows the specification of the array and its excitation directly. Antenna Magus does not adjust the array layout at all to achieve specific electrical objectives. Therefore, users can evaluate a custom array layout, using the array routines in Antenna Magus.

The array orientation, the inter-element spacing, the spacing method and the excitation taper can all be specified. Users can select the excitation taper to be equal excitation [Uniform], uniform side lobe level [Dolph-Chebychev] and first few side lobes uniform [Villeneuve]. Then they can specify side lobe level and number of side lobes, where applicable.

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