# Application Note 3: Designing A Slot-Coupled Patch Antenna Array With A Corporate Feed Network Using EM.Picasso

## Contents

## Introduction

EM.Picasso can be used to analyze large and fairly complex multilayer planar structures. In this application note, we will show how to use EM.Picasso to design a 4 × 4 slot-coupled patch antenna array with a microstrip corporate feed network. The design process involves three steps: design of the slot-couple patch element, design of the power divider, and finally, construction of the 16-element array. The first two steps are the subject of two of EM.Picasso's tutorial lessons.

## Designing the Patch Radiating Element

The operating frequency of the patch array is f = 2.4GHz. At this frequency, the free-space wavelength is λ_{0} = 125mm. The patch radiators will be spaced at half free-space wavelength: S_{x} = S_{y} = λ_{0}/2 = 62.5mm. The design of the slot-coupled patch antenna is described in detail in EM.Picasso Tutorial Lesson 7: Designing A Slot-Coupled Patch Antenna. The substrate consists of two finite-thickness dielectric layers with ε_{r} = 3.38, σ = 0, separated by a perfect electric conductor (PEC) ground plane of infinite lateral extents. The table below summarizes the substrate stackup's layer hierarchy:

Substrate Object Label | Substrate Object Type | Function | Material | Thickness |
---|---|---|---|---|

THS | Half-Space Medium | Top Substrate Termination | Vacuum | Infinite |

PEC_1 | PEC Trace | Patch Plane | PEC | 0 |

Layer_1 | Substrate Layer | Patch Substrate | ROGER RO4003C | 2mm |

PMC_1 | Slot Trace | Slot Plane | PMC | 0 |

Layer_2 | Substrate Layer | Feed Substrate | ROGER RO4003C | 0.787mm |

PEC_2 | PEC Trace | Microstrip Feed Plane | PEC | 0 |

BHS | Half-Space Medium | Bottom Substrate Termination | Vacuum | Infinite |

The design variables in this problem include the side dimensions of the square patch radiator, length and width of the coupling slot and the length of the open microstrip stub extended beyond the coupling slot. The width of the mircostrip feed line is chosen to be w_{f} = 2.4mm to yield a characteristic impedance of Z_{0} = 50Ω.

Design Variable Name | Optimal value |
---|---|

patch_len | 39.5mm |

slot_len | 12mm |

slot_wid | 1.5mm |

stub_len | 21mm |

## Designing the Wilkinson Power Divider

The input signal power must be divided equally among 16 patch radiating elements. In other words, a 1:16 power distribution network is needed for this project. The design of a Wilkinson power divider is described in detail in EM.Picasso Tutorial Lesson 9: Designing a Microstrip Wilkinson Power Divider. An Ω-shaped microstrip ring is used to create a three-port network. The input and output microstrip lines all have a width of 2.4mm with Z_{0} = 50Ω. The microstrip partial ring has a width of √2Z_{0} = 70.7Ω and serves as the two quarter-wave arms of the Wilkinson power divider. It is determined that if a lumped 100Ω resistor is connected between the two output arms of this divider, better return loss and isolation levels are achieved. The figure below shows the geometry of the optimized 1:2 Wilkinson power divider.

## Constructing a Four-Element Patch Sub-Array

A binary H-tree structure is used to construct a 1:4 Wilkinson power divider network as shown in the figures below. In this case, the network involves three ring-type Wilkinson power dividers.

The multilayer structure is parameterized with the design variables listed in the table below. Of these variables, only the open stub length needs to be changed to 18.5mm, and rest of them retain their original value for the best input impedance match.

Design Variable Name | Optimal value |
---|---|

patch_len | 39.5mm |

slot_len | 12mm |

slot_wid | 1.5mm |

stub_len | 18.5mm |

resistance | 100 Ohms |

The figure below shows the planar mesh of the sub-array. The patch and slot elements are discretized with a mesh density of 30 cells per effective wavelength, while the corporate feed network requires a higher mesh density of 50 cells per effective wavelength due to the narrow line hosting the lumped resistors.

The 4-element slot-coupled patch sub-array is simulated using EM.Picasso's planar method of moments (MoM) solver. An adaptive frequency sweep is performed to compute the frequency response of the structure over the frequency range [2.2GHz - 2.6GHz]. The figures below show the variation of the sub-array's return loss with frequency and its 3D far-field radiation pattern computed at 2.4GHz.

## Constructing a 16-Element Patch Array

The binary H-tree structure described earlier is expanded to construct a 1:16 Wilkinson power divider network as shown in the figures below. In this case, the network involves 15 ring-type Wilkinson power dividers.

Using the same mesh densities as before, the planar mesh shown in the figure below is generated for the 16-element patch array.

The matrix size for this planar MoM simulation is N = 10,771. EM.Picasso's LU solver was used to solver the linear system. The total computation time including the LU decomposition, back-substitution and computation of the full 3D far-field radiation pattern at an angular resolution of 1° along both the azimuth and elevation directions was 150 seconds. At the end of the planar MoM simulation, the following port characteristics are reported:

S11: 0.447781 + 0.118984j

S11(dB): -6.682387

Z11: 123.053609 + 37.286922j

Y11: 0.007443 - 0.002255j

The figures below show the 3D far-field radiation pattern as well as 2D Cartesian radiation pattern cuts in the principal YZ and ZX planes computed at 2.4GHz. A directivity of D_{0} = 17.3dB is predicted for this array.

The figures below show the surface electric current distribution maps on the patch and feed planes, as well as the surface magnetic current distribution map on the middle ground plane, all computed at 2.4GHz.