Automation of Antenna Isolation Modeling Master’s thesis in Information and Communication Technology SRI SAI SATYANARAYANA DAMARAJU DEPARTMENT OF ELECTRICAL ENGINEERING CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden 2025 www.chalmers.se www.chalmers.se Master’s thesis 2025 Automation of Antenna Isolation Modeling A Master of Science thesis in the Information and Communication Technology Master’s Programme SRI SAI SATYANARAYANA DAMARAJU Department of Electrical Engineering Division of Communications, Antennas, and Optical Networks Chalmers University of Technology Gothenburg, Sweden 2025 Automation of Antenna Isolation Modeling A Master of Science thesis in the Information and Communication Technology Mas- ter’s Programme (MPICT ) SRI SAI SATYANARAYANA DAMARAJU © SRI SAI SATYANARAYANA DAMARAJU, 2025. Supervisor: Dr. Ola Tageman, Expert mm-wave Integrated Sub-Systems, Ericsson Research, Gothenburg, Sweden Examiner: Prof. Dr. Jian Yang, Communications, Antennas and Optical Networks Division, Department of Electrical Engineering, Chalmers University of Technology, Gothenburg, Sweden Master’s Thesis 2025 Department of Electrical Engineering Chalmers University of Technology SE-412 96 Gothenburg Telephone +46 31 772 1000 Cover: Antenna design constructed in Ansys HFSS showing a 4x4 array separated with a 120-degree angle and isolation, and mutual coupling between elements. Typeset in LATEX, template by Kyriaki Antoniadou-Plytaria Printed by Chalmers Reproservice Gothenburg, Sweden 2025 iv Automation of Antenna Isolation Modeling SRI SAI SATYANARAYANA DAMARAJU Department of Electrical Engineering Chalmers University of Technology Abstract This thesis enhances an existing Python-based automation framework for an- tenna isolation modeling in large-scale antenna arrays, developed by Ericsson Re- search. The framework utilizes ANSYS HFSS via the PyAEDT API for automating electromagnetic workflows, enabling systematic variation of antenna array parame- ters including geometry, element spacing, polarization configurations, etc. which are loaded for model creation. This builds a complete 3D antenna array model in HFSS with proper excitation and boundary conditions, which then extracts comprehen- sive S-parameter data from simulation results and provides visualization capabilities with mathematical error metrics for evaluating mesh convergence and simulation re- liability. This work extends the framework with advanced performance evaluation and additional comparative analysis capabilities. Key contributions include the develop- ment of simulation performance evaluation tools that systematically analyze HFSS log files to extract information as resource utilization and convergence behavior, esti- mating error-free dynamic range and computational efficiency enabling quantitative comparison of simulation performance across different array configurations and com- putational runs. This is critical for optimizing simulation workflow and validating result accuracy in large-scale antenna modeling. Additionally, the extended frame- work provides comprehensive S-parameter comparison tools that perform quantita- tive analysis between different antenna simulations facilitating systematic evaluation of design variation and isolation performance characteristics. Keywords: Antenna Isolation, HFSS Automation, Performance Evaluation, PyAEDT, S-Parameter Analysis. v Acknowledgements First and foremost, I would like to express my deepest gratitude to Dr. Ola Tageman at Ericsson for his unwavering support, insightful guidance, and construc- tive feedback throughout the course of my thesis. Under his mentorship, I discovered the powerful capabilities of Python in the antenna field—an eye-opening experience that significantly shaped my work. I am sincerely thankful to Dr. Parisa Aghdam at Ericsson for her pivotal role in facilitating this project; her leadership in ensuring access to necessary tools and her strategic guidance in resource management were instrumental to the seamless execution of my research. I am also grateful to Vinnova for their generous fund- ing, which enabled this research and supported the pursuit of innovation with the potential for meaningful societal impact. Additionally, I extend my thanks to my colleagues at Ericsson for their valuable insights and camaraderie, as their diverse perspectives and collaborative spirit greatly enriched my research journey. A special note of appreciation goes to Professor Dr. Jian Yang, my university supervisor, whose rigorous academic scrutiny and valuable feedback consistently pushed me to refine my hypotheses and elevate the quality of my analysis. Lastly, my heartfelt thanks go to Rohith Virinchi. His constant encouragement and belief in me have been a source of strength and resilience throughout this aca- demic endeavor. I am truly grateful for his presence and support during my thesis. Sri Sai Satyanarayana Damaraju Gothenburg May 2025 vii List of Acronyms Below is the list of acronyms that have been used throughout this thesis listed in alphabetical order: AEDT Ansys Electronics Desktop API Application Programming Interface CCM Convergence Cost Metric COM Component Object Model CPU Central Processing Unit CST Computer Simulation Technology CSV Comma-Separated Values DDM Domain Decomposition Method E-field Electric Field EM Electromagnetic FEBI Finite Element Boundary Integral FEM Finite Element Method GPU Graphics Processing Unit GUI Graphical User Interface H-Field Magnetic Field HFSS High Frequency Structure Simulator HPC High-Performance Computing ISAC Integrated Sensing and Communication JSON JavaScript Object Notation MCA Multiple Component Array MIMO Multiple-Input Multiple-Output MoM Method of Moments PyAEDT Python Ansys Electronics Desktop RAM Random Access Memory SRD Simulation Resource Density S-parameter Scattering Parameter VSWR Voltage Standing Wave Ratio Z-parameter Impedance Parameter ix Nomenclature Below is the nomenclature of indices, parameters, and variables that have been used throughout this thesis. Indices i,j Indices for antenna array elements and S-parameter matrix posi- tions k Index for frequency points n Index for mesh refinement passes Parameters ϵ Small numerical value to prevent logarithmic singularities λ Wavelength at operating frequency [m] ϕij Phase of S-parameter between ports i and j [rad] θ Array rotation angle [rad] τg Group delay [s] ω Angular frequency [rad/s] dx, dy Element spacing in x and y directions [m] f Frequency [Hz] l Dipole antenna length [m] nx, ny Number of array elements in x and y directions Nports Total number of antenna ports NS−parameters Total number of S-parameters in matrix Rrad Radiation resistance [Ω] Z0 Reference impedance (typically 50 Ω) xi Variables Sij Scattering parameter from port i to port j |Sij| Magnitude of S-parameter Zij Impedance parameter between ports i and j [Ω] ∆|Sij| Change in S-parameter magnitude between mesh refinement passes e1-e6 Error metrics for convergence analysis VSWR Voltage Standing Wave Ratio [I] Identity matrix [S] S-parameter matrix [Z] Z-parameter matrix Pfinal Final position vector of antenna element after transformations [m] Tcenter, Tgrid, TarrayTranslation vectors for array positioning [m] Ry(θ) Rotation matrix about y-axis S(fk) S-parameter matrix at frequency point k xii Contents List of Acronyms ix Nomenclature xi List of Figures xv List of Tables xvii Listings xix 1 Introduction 1 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Purpose and Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 Purpose and Need for Automated Analysis . . . . . . . . . . . 2 1.2.2 Research Goal and Framework Enhancement . . . . . . . . . . 2 1.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Theoretical Background 5 2.1 Antenna Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 Antenna Types and Classification . . . . . . . . . . . . . . . . 5 2.1.2 Dipole and Cross-Dipole Antenna . . . . . . . . . . . . . . . . 5 2.1.3 Antenna Performance Parameters . . . . . . . . . . . . . . . . 6 2.1.3.1 S-Parameters . . . . . . . . . . . . . . . . . . . . . . 6 2.1.3.2 Z-Parameters . . . . . . . . . . . . . . . . . . . . . . 7 2.1.3.3 Return Loss . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.3.4 Voltage Standing Wave Ratio (VSWR) . . . . . . . . 8 2.1.3.5 Group Delay . . . . . . . . . . . . . . . . . . . . . . 8 2.1.4 Antenna Arrays and Element Spacing . . . . . . . . . . . . . . 8 2.1.5 Mutual Coupling in Antenna Arrays . . . . . . . . . . . . . . 9 2.2 Computational Electromagnetics Methods . . . . . . . . . . . . . . . 10 2.2.1 Finite Element-Boundary Integral (FEBI) Method . . . . . . . 11 2.3 HFSS Software and Modeling . . . . . . . . . . . . . . . . . . . . . . 11 2.3.1 Multiple Component Arrays in HFSS . . . . . . . . . . . . . . 11 2.4 Automation in Electromagnetic Modeling . . . . . . . . . . . . . . . . 13 2.4.1 PyAEDT Interface for HFSS . . . . . . . . . . . . . . . . . . . 13 xiii Contents 2.4.2 Advantages of Programmatic Approach over Traditional GUI Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Confidentiality Notice 17 7 Results 19 7.1 Testing Environment and Software Configuration . . . . . . . . . . . 19 7.2 Automated Model Creation Result . . . . . . . . . . . . . . . . . . . 19 7.3 Data Extraction Results . . . . . . . . . . . . . . . . . . . . . . . . . 21 7.4 JSON Data Analysis and Visualization Results . . . . . . . . . . . . . 22 7.4.1 S-Parameter Frequency Response Analysis . . . . . . . . . . . 22 7.4.2 S-Parameter Convergence Across Refinement Passes . . . . . . 23 7.4.3 Three-Dimensional Error Analysis . . . . . . . . . . . . . . . . 23 7.4.4 Final Pass Convergence Assessment . . . . . . . . . . . . . . . 24 7.4.5 Basic Simulation Performance Analysis . . . . . . . . . . . . . 25 7.4.6 Advanced Simulation Performance Metrics . . . . . . . . . . . 26 7.5 Touchstone File Analysis and Visualization Results . . . . . . . . . . 27 7.5.1 Return Loss Analysis . . . . . . . . . . . . . . . . . . . . . . . 27 7.5.2 Group Delay Analysis . . . . . . . . . . . . . . . . . . . . . . 28 7.5.3 Three-Dimensional S-Parameter Visualization . . . . . . . . . 28 7.5.4 Smith Chart Impedance Analysis . . . . . . . . . . . . . . . . 29 7.6 Comparative Analysis Results . . . . . . . . . . . . . . . . . . . . . . 30 7.6.1 Return Loss and VSWR Comparison . . . . . . . . . . . . . . 30 7.6.2 Impedance Parameter Comparison . . . . . . . . . . . . . . . 31 7.6.3 S-Parameter Coupling Heatmap Analysis . . . . . . . . . . . . 31 7.6.4 Maximum Relative Difference Assessment . . . . . . . . . . . 32 7.6.5 Three-Dimensional Relative Difference Visualization . . . . . . 32 7.6.6 Comparative sNp Relative Error Analysis . . . . . . . . . . . 33 8 Conclusion and Future Scope 35 8.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 8.2 Future Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Bibliography 37 A Appendix: Software Configuration and Setup I A.1 Python Library Dependencies . . . . . . . . . . . . . . . . . . . . . . I A.2 File Naming Conventions . . . . . . . . . . . . . . . . . . . . . . . . . I xiv List of Figures 2.1 Cross-dipole antenna configuration showing orthogonal dipole ele- ments perpendicular to each other. . . . . . . . . . . . . . . . . . . . 6 2.2 Rectangular antenna array geometry showing element spacing for 6× 6 + 6 × 6 configuration with coordinate system. . . . . . . . . . . . . 9 2.3 Mutual coupling illustration between two antenna elements showing electromagnetic field interaction and induced currents[5]. . . . . . . . 10 2.4 HFSS Array Tool interface demonstrating multiple component array configuration for systematic antenna array modeling. . . . . . . . . . 12 2.5 Simple dipole antenna geometry created using PyAEDT script show- ing the programmatic modeling. . . . . . . . . . . . . . . . . . . . . . 14 7.1 Generated 3D model of Dipole Array, Rev 15_2, 3×3+3×3, AntArr - 8236 as Table 7.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 7.2 S-parameter magnitude versus frequency showing electromagnetic cou- pling behavior across the 3.15-3.85 GHz range . . . . . . . . . . . . . 23 7.3 S-parameter magnitude convergence across adaptive mesh refinement passes showing solution stability . . . . . . . . . . . . . . . . . . . . . 23 7.4 3D visualization of absolute convergence errors (deltaS in dB) across mesh refinement passes and final coupling levels . . . . . . . . . . . . 24 7.5 Convergence check showing deltaS/S vs. final coupling strength with binned statistical analysis and reference thresholds . . . . . . . . . . . 24 7.6 Basic simulation performance analysis showing time allocation, fre- quency solve duration, adaptive pass duration, and error trends . . . 25 7.7 Advanced simulation performance metrics including adaptive mesh convergence analysis, normalized simulation cost, and memory usage progression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 7.8 Return loss versus frequency for reflection coefficients showing impedance matching characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 27 7.9 Group delay versus frequency showing phase linearity characteristics across the 3.15-3.85 GHz range . . . . . . . . . . . . . . . . . . . . . 28 7.10 3D visualization of S-parameters showing magnitude relationships across frequency and center frequency reference . . . . . . . . . . . . 29 7.11 Smith chart visualization showing complex impedance characteristics at 50-ohm reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 xv List of Figures 7.12 Return loss and VSWR comparison between AntArr_3 and AntArr_4 showing impedance matching characteristics . . . . . . . . . . . . . . 30 7.13 Z-parameter comparison showing complex impedance characteristics for both antenna configurations . . . . . . . . . . . . . . . . . . . . . 31 7.14 S-parameter coupling heatmap comparison showing magnitude differ- ences and vector distances at center frequency . . . . . . . . . . . . . 31 7.15 Maximum relative difference heatmap showing normalized coupling variations across the S-parameter matrix . . . . . . . . . . . . . . . . 32 7.16 3D visualization of S-parameter relative differences showing coupling variations across frequency and magnitude dimensions . . . . . . . . . 33 7.17 Comparative relative error analysis showing ∆S/Savg vs S-parameter magnitude at 3.500 GHz . . . . . . . . . . . . . . . . . . . . . . . . . 33 xvi List of Tables 7.1 Antenna Array Configuration Parameters for Test Case: AntArr - 8236 19 xvii List of Tables xviii Listings 2.1 PyAEDT script for creating a simple dipole antenna . . . . . . . . . . 13 7.1 Sample JSON data structure showing extracted S-parameter imagi- nary components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 7.2 Sample Touchstone file header and data showing industry-standard S-parameter format . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 xix Listings xx 1 Introduction 1.1 Background The rapid evolution of wireless communication systems has fundamentally trans- formed the requirements for antenna design and antenna analysis. Modern commu- nication technologies such as full duplex communication, Integrated Sensing and Communication(ISAC), and antenna co-location scenarios will demand a sophisti- cated antenna arrays with hundreds or thousands of elements which are operating in a close proximity. Full duplex systems enable simultaneous transmission and reception on the same frequency with a requirement of stringent isolation between transmitting and receiving antennas to prevent self-interference [2]. Integrated Sens- ing and Communication (ISAC) systems combine radar sensing and communication functionalities, requiring careful electromagnetic isolation to preserve sensing accu- racy and communication quality [3]. Co-location scenarios involve multiple antenna systems sharing limited installation space which require sufficient isolation to pre- vent mutual interference between different services. Antenna isolation, to be defined as the electromagnetic decoupling between dif- ferent antenna elements which has become a critical design parameter within wireless systems. Achieving adequate isolation will present a significant practical challenges due to its physical size constraints that limit separation distances which would make electromagnetic coupling inevitable. This would result in the complexity of accu- rately modeling large antenna arrays creating computational bottlenecks where each simulation can require hours or days of processing time limiting iterative design op- timization. Traditional approaches to antenna isolation analysis have largely relied on man- ual design process using electromagnetic simulation software through a graphical user interface(GUI). While this works well and provides accurate results for small- scale problems, its increasingly impractical as array sizes grows, as extensive repet- itive modeling tasks, time-intensive parameter sweeps, and error-prone data ex- traction process of engineering effort for arrays containing all the elements. These challenges of manual modeling complexity, computational requirements, and compu- tational analysis needs emphasize the critical requirement for automated workflows that can systematically generate models, execute simulations, and extract relevant performance data for analysis and comparison. Recent developments in software automation frameworks, particularly the Python- Ansys Electronics Desktop(PyAEDT) interface for HFSS(High-Frequency Structure Simulator), have created new opportunities for addressing these challenges, which 1 1. Introduction enables programmatic control of electromagnetic simulation software to automat- ing workflow. However, the effective implementation of such automation systems require careful consideration of software architecture, model parameterization strate- gies, and validation procedures. 1.2 Purpose and Goal 1.2.1 Purpose and Need for Automated Analysis The analysis of antenna isolation in large-scale arrays presents significant prac- tical challenges that extend beyond the electromagnetic complexity itself. Modern antenna arrays containing hundreds or thousands of elements generate thousands of S-parameters that must be systematically evaluated across multiple frequency points and configuration scenarios. For a typical dual-array system with 36 ports, each simulation produces 1,296 S-parameter relationships, requiring comprehensive analysis to extract meaningful design insights for isolation characterization. Traditional manual approaches to such analysis involve repetitive modeling tasks through graphical user interfaces, time-intensive parameter sweeps, and complex data processing workflows. The iterative nature of antenna design compounds these challenges, as each design modification requires complete re-simulation including model creation, mesh generation, solution convergence, and post-processing analy- sis. For large antenna arrays, this manual workflow can require weeks of effort per design iteration, making systematic design optimization and comparative studies impractical within realistic project timelines. Furthermore, validating simulation reliability becomes increasingly complex as array sizes grow. Evaluating computational efficiency, and ensuring solution accu- racy across millions of S-parameters requires systematic analysis of simulation data. The manual interpretation of convergence metrics and performance characteristics across multiple simulation attempts introduces both time delays and potential for analysis inconsistencies, emphasizing the critical need for automated validation and comparison frameworks that can systematically process and evaluate simulation re- sults. 1.2.2 Research Goal and Framework Enhancement While electromagnetic simulation tools like HFSS provide powerful capabilities for antenna analysis, the manual approach to large-scale antenna array modeling presents significant bottlenecks that limit design efficiency and systematic opti- mization. An existing automation framework developed at Ericsson Research ad- dresses the fundamental challenge of programmatic antenna array generation using PyAEDT, providing a solid foundation that enables systematic analysis of large antenna arrays through automated model creation and simulation execution. Building upon this established framework, this thesis enhances the existing au- tomation system to address gaps in simulation reliability assessment and perfor- mance evaluation. The primary goal focuses on developing comprehensive methods to evaluate simulation efficiency by quantifying the relationship between compu- 2 1. Introduction tational effort and achieved electromagnetic precision, enabling optimal resource allocation while maintaining sufficient solution accuracy. This work addresses the following research questions: How can simulation ac- curacy be systematically estimated and validated for large antenna arrays? How can simulation efficiency be quantified by considering both electromagnetic preci- sion and computational resource requirements? How can simulation performance be systematically compared between different modeling configurations to optimize computational approaches? How can S-parameters for two different model config- urations be compared in detail to facilitate the evaluation of various model sim- plification attempts aimed at reducing simulation time? Through addressing these questions, the enhanced framework transforms from a basic automation tool into a comprehensive analysis platform that enables systematic antenna isolation studies while ensuring both computational efficiency and solution reliability. 1.3 Thesis Outline The remainder of this thesis is organized as follows: • Chapter 2: Theoretical Background establishes the fundamental con- cepts of antenna theory, computational electromagnetics, and automation ap- proaches. • Chapter 3: Automated Antenna Array Modeling System details the five-stage automation framework architecture, including antenna model pa- rameterization, automated model generation using PyAEDT, array popula- tion algorithms, and HFSS configuration management for large-scale antenna arrays. • Chapter 4: Simulation Data Extraction presents the data extraction methodology from HFSS simulation results, including model validation, multi- domain S-parameter processing, convergence analysis, and custom data stor- age architectures for electromagnetic simulation data. • Chapter 5: Data Analysis and Visualization Framework describes the automated data processing system, S-parameter visualization methods, con- vergence analysis techniques, simulation performance evaluation, and Touch- stone file analysis capabilities. • Chapter 6: Comparative Analysis and Performance Evaluation out- lines the systematic evaluation framework for multiple antenna array configu- rations, including electromagnetic parameter comparison methods, quantita- tive S-parameter difference analysis, and simulation performance benchmark- ing. • Chapter 7: Results presents comprehensive case studiy and analyses of antenna array models processed through the automation framework, demon- strating isolation characteristics, computational performance metrics, and val- idation of the automated modeling approach. • Chapter 8: Conclusion and Future Scope summarizes the key enhance- ments made to the existing automation framework and outlines future research directions. 3 1. Introduction 4 2 Theoretical Background This chapter establishes the theoretical background to understand the frame- work exploring fundamental concepts of antenna theory, computational electromag- netics and principles that form the basis for efficient antenna isolation analysis. 2.1 Antenna Fundamentals An antenna is a transducer that converts electrical energy into ElectroMag- netic(EM) waves for transmission, or conversely converts electromagnetic waves into electrical energy for reception serving as a interface between guided waves in trans- mission lines and free-space electromagnetic waves enabling wireless communication across various distances and applications. 2.1.1 Antenna Types and Classification Antennas can be broadly classified into several categories based on their physical structure and radiation characteristics. The primary classifications include: • Wire Antennas: Include dipoles, monopoles, and loop antennas, represent- ing the most fundamental antenna types due to their simple structure and well-understood radiation properties • Aperture Antennas: Such as horn antennas and parabolic reflectors, which radiate electromagnetic energy through a defined aperture area • Microstrip Antennas: Consist of metallic patches printed on dielectric sub- strates, widely used in modern communication systems due to their low profile and ease of integration • Reflector Antennas: Employ curved conducting surfaces to focus electro- magnetic energy, achieving high directional gain • Antenna Arrays: Multiple antenna elements arranged in specific patterns to achieve enhanced performance characteristics Among these categories, wire antennas and specifically dipole configurations form the foundation for understanding antenna arrays used in modern communi- cation systems, where multiple elements work together to achieve enhanced perfor- mance characteristics. 2.1.2 Dipole and Cross-Dipole Antenna The basic dipole antenna consists of two conducting elements separated by a small gap, typically fed at the center having a physical length l = λ/2, where the 5 2. Theoretical Background current distribution follows a sinusoidal pattern with maximum current at the center and zero current at the ends. The radiation pattern exhibits a characteristic toroidal shape with maximum radiation perpendicular to antenna axis. Whereas, a cross-dipole antenna extends the basic dipole by incorporating two orthogonal dipole elements positioned perpendicular to each other enabling dual- polarized operation where each dipole element can independently transmit or receive electromagnetic waves providing horizontal or vertical polarization, or alternatively ±45-degree slant polarizations depending on the orientation. Figure 2.1: Cross-dipole antenna configuration showing orthogonal dipole elements perpendicular to each other. The radiation resistance of a short dipole antenna (i.e., when the dipole length l ≪ λ) can be approximated by[4]: Rrad = 20π2 ( l λ )2 [Ω] (2.1) where l is the dipole length in meters and λ is the wavelength in meters. 2.1.3 Antenna Performance Parameters Understanding antenna performance requires the familiarity with several key parameters that characterize the electromagnetic behavior providing quantitative measure for antenna design optimization and system integration [4]. 2.1.3.1 S-Parameters S-parameters, or scattering parameters, describe the relationship between inci- dent and reflected electromagnetic waves at antenna ports. For a two-port network, the S-parameter matrix relates input and output wave amplitudes: 6 2. Theoretical Background [ b1 b2 ] = [ S11 S12 S21 S22 ] [ a1 a2 ] (2.2) where ai represents incident wave amplitudes and bi represents reflected wave amplitudes. The reflection coefficient S11 represents the ratio of reflected power to incident power at port 1, while S21 characterizes the transmission from port 1 to port 2. S-parameters are complex quantities that can be represented in different forms: • Magnitude and Phase Representation: Sij = |Sij|ejϕij (2.3) where |Sij| is the magnitude (dimensionless) and ϕij is the phase in radians. • Real and Imaginary Representation: Sij = Re(Sij) + jIm(Sij) (2.4) where Re(Sij) and Im(Sij) are the real and imaginary components (dimension- less). The conversion between (magnitude/phase) and (real/imaginary) forms follows: |Sij| = √ [Re(Sij)]2 + [Im(Sij)]2 (2.5) ϕij = arctan ( Im(Sij) Re(Sij) ) [rad] (2.6) S-parameters are typically expressed in decibels for magnitude representation: Sij [dB] = 20 log10 |Sij| (2.7) When S-parameters are given in real and imaginary form, the magnitude must first be calculated before conversion to decibels, while the phase is expressed in degrees as: ϕij [deg] = 180 π arctan ( Im(Sij) Re(Sij) ) (2.8) 2.1.3.2 Z-Parameters Z-parameters describe antenna impedance characteristics through the impedance matrix relating voltages and currents:[ V1 V2 ] = [ Z11 Z12 Z21 Z22 ] [ I1 I2 ] (2.9) where Vi represents port voltages in volts [V], Ii represents port currents in amperes [A], and Zij represents impedance elements in ohms [Ω]. Z-parameters are complex quantities that can be calculated from S-parameters using conversion relationships. For a general N-port network with characteristic impedance Z0, the conversion follows: 7 2. Theoretical Background [Z] = Z0([I] + [S])([I] − [S])−1 (2.10) where [I] is the identity matrix, [S] is the S-parameter matrix, and [Z] is the Z-parameter matrix, Z0 is the reference impedance, typically 50 Ω for antenna mea- surements. 2.1.3.3 Return Loss Return loss quantifies the power reflected from an antenna port relative to the incident power, expressed as: Return Loss [dB] = −20 log10 |S11| (2.11) A well-matched antenna exhibits high return loss values, indicating efficient power transfer and minimal reflection. 2.1.3.4 Voltage Standing Wave Ratio (VSWR) VSWR describes the impedance mismatch between the antenna and transmis- sion line: VSWR = 1 + |S11| 1 − |S11| (2.12) VSWR is dimensionless, with ideal matching corresponding to VSWR = 1 and practical systems typically requiring VSWR < 2. 2.1.3.5 Group Delay Group delay characterizes the frequency-dependent phase response of antennas. Variations in such can cause signal distortion in communication systems. τg = −dϕ dω [s] (2.13) where ϕ is the phase in radians and ω is the angular frequency in rad/s. 2.1.4 Antenna Arrays and Element Spacing Antenna arrays consist of multiple antenna elements arranged in a specific ge- ometric patterns to achieve a desired radiation characteristics which couldn’t be obtained with single-element antennas offering other advantages like increased di- rectional gain, beam steering and improved spatial selectivity through constructive or destructive interference of electromagnetic fields. The fundamental principle of array operation is that EM waves from individual elements within, combine in space creating enhanced radiation in desired directions enabling higher gain, better direc- tivity for modern communication systems[6]. 8 2. Theoretical Background Figure 2.2: Rectangular antenna array geometry showing element spacing for 6 × 6 + 6 × 6 configuration with coordinate system. Other important design parameter is the spacing between array elements that directly affects the array performance. Element spacing is usually expressed in terms of wavelengths and significantly influences radiation pattern characteristics, mutual coupling levels. and overall array efficiency. From figure 2.2, rectangular arrays arrange elements in rows and columns with uniform spacing in both horizontal and vertical directions as per the array size. Maintaining proper spacing selection pre- vents unwanted radiation lobes(grating lobes) while maintaining acceptable coupling between adjacent elements. The relationship between element spacing and array performance establishes fundamental design trade-offs in antenna engineering. While closer spacing reduces grading lobes and enables wider scan angles but increases mutual coupling between elements that can degrade individual element performance, conversely larger spac- ing reduces coupling effects but may introduce grating lobes that created unwanted radiation directions reducing the array efficiency. Modern array designs are to be carefully balancing these competing requirements while also considering other prac- tical constraints. 2.1.5 Mutual Coupling in Antenna Arrays Mutual coupling refers to the electromagnetic interaction between adjacent an- tenna elements within array configuration. This phenomenon occurs when the electromagnetic field radiated by one element induces currents in neighboring ele- ments affecting the impedance and radiation characteristics. The coupling strength depends on several factors such as element spacing, antenna geometry, operat- ing frequency, etc. The operating frequency affects coupling through wavelength- dependent near-field interactions. While mutual coupling typically involves near- 9 2. Theoretical Background neighbor interactions, in the context of this work, the focus is on long-range coupling effects between separate arrays. Figure 2.3: Mutual coupling illustration between two antenna elements showing electromagnetic field interaction and induced currents[5]. The effects of mutual coupling include impedance variations across array el- ements, altered radiation patterns, and reduced antenna efficiency. In communi- cation systems, excessive mutual coupling can lead to signal correlation, reduced spatial diversity, and compromised system capacity. Understanding and controlling mutual coupling is essential for optimizing antenna array performance in practical applications[6]. 2.2 Computational Electromagnetics Methods When faced with real-world antenna problems, we quickly discover that Maxwell’s equations, while elegant and complete, become nearly impossible to solve analyti- cally for anything beyond the simplest geometries. Consider trying to calculate the radiation pattern of a smartphone antenna surrounded by a metal case, or determin- ing how closely we can place antenna elements in an array before mutual coupling becomes problematic. These practical questions require numerical solutions because the mathematical complexity exceeds what can be handled with pencil and paper. Computational electromagnetics provides the bridge between electromagnetic theory and practical antenna design. Rather than attempting to find exact analytical solutions, these methods break down complex problems into smaller, manageable pieces that computers can solve numerically. Think of it as solving a large jigsaw puzzle by working on small sections at a time, then assembling the complete picture. The fundamental approach involves converting Maxwell’s differential equations into systems of algebraic equations that computers can solve efficiently. This trans- formation process, called discretization, represents continuous electromagnetic fields 10 2. Theoretical Background using discrete values at specific points or over small regions in space. Different com- putational methods employ various discretization strategies, each with particular strengths and limitations depending on the problem characteristics. 2.2.1 Finite Element-Boundary Integral (FEBI) Method The Finite Element-Boundary Integral (FEBI) method represents a powerful hybrid approach that combines geometric flexibility of FEM with computational effi- ciency of Boundary Integral techniques for open-region electro-magnetics addressing the limitations of individual methods by utilizing finite elements to model complex geometries and material properties within near-field region, while employing bound- ary integral equations to handle radiation and scattering in the unbounded far-field region. This method is particularly well-suited for antenna and array analysis, where accurate modeling of both detailed antenna structures and radiation into free space is essential. FEBI divides the computational domain into two regions: an inner finite element region containing the antenna structures, and an outer region extending to infinity that is handled using boundary integral formulations. By doing such, this eliminates the need of artificial absorbing boundaries providing accurate solutions for radiation problems while maintaining computational efficiency, make it an attractive choice for large-scale antenna array simulations. For the same, this method has become a standard approach in commercial electromagnetic simulation software for antenna design and analysis applications[7]. However, this method can experience conver- gence difficulties when dealing with electrically large structures with high mutual coupling, requiring careful mesh generation and solver parameter optimization. 2.3 HFSS Software and Modeling ANSYS HFSS (High Frequency Structure Simulator) represents a comprehensive electromagnetic simulation environment that implements the finite element method to solve Maxwell’s equations in three-dimensional structures. Understanding how this software operates and its modeling capabilities provides insight into practical electromagnetic analysis workflows and the computational implementation of the theoretical concepts discussed in previous sections. Rather than requiring users to implement complex mathematical formulations manually, HFSS provides an integrated environment where electromagnetic prob- lems can be set up, solved, and analyzed through a combination of graphical inter- faces and programmatic controls. The software handles the underlying mathematical complexity while allowing users to focus on problem definition, geometry creation, and results interpretation [8]. 2.3.1 Multiple Component Arrays in HFSS When analyzing antenna arrays, the repetitive nature of array elements suggests that computational efficiency could be improved by avoiding redundant calculations. HFSS addresses this through its Multiple Component Array (MCA) functionality, 11 2. Theoretical Background which leverages the similarity between array elements to reduce both modeling com- plexity and computational requirements. Multiple Component Array Concept The MCA approach recognizes that identical array elements will have identical electromagnetic characteristics when placed in identical environments. By defining a single element as a reusable component, the software can replicate this element across the array geometry while maintaining proper electromagnetic coupling be- tween elements [8]. Figure 2.4: HFSS Array Tool interface demonstrating multiple component array configuration for systematic antenna array modeling. As illustrated in Figure 2.4, the Array Tool interface provides systematic controls for array generation and management. The interface allows specification of array dimensions, element spacing, and excitation patterns through structured parameter entry rather than manual element-by-element definition. Current Implementation Considerations While the MCA functionality offers clear advantages for array analysis, its im- plementation requires careful consideration of computational resources and analysis objectives. The initial setup and validation of component definitions may require substantial effort to ensure that the simplified model accurately represents the in- tended array behavior. Due to time constraints in the current work, the MCA approach was not explored for the array analyses presented in this study. Instead, individual element modeling was employed to maintain full control over the analysis process and to ensure that all electromagnetic interactions were explicitly captured without relying on software- specific optimization techniques. Future work could explore the MCA capabilities more thoroughly, particularly for large array analyses where computational efficiency becomes a limiting factor. The potential benefits in terms of reduced modeling time and computational require- 12 2. Theoretical Background ments make this approach attractive for extensive parametric studies or optimization investigations. 2.4 Automation in Electromagnetic Modeling The increasing complexity of modern electromagnetic systems has created a significant demand for automation in simulation workflows. Traditional electromag- netic modeling approaches rely heavily on manual processes through graphical user interfaces, which become increasingly time-consuming and error-prone as system complexity grows. For large-scale antenna arrays containing hundreds or thousands of elements, manual model creation, parameter sweeping, and data extraction can require weeks or months of engineering effort. This limitation has driven the develop- ment of automated simulation frameworks that can systematically generate models, execute simulations, and process results without extensive human intervention. Automation in electromagnetic modeling encompasses various aspects including model generation, batch simulation execution, systematic data extraction, and auto- mated result analysis. Modern automation frameworks define simulation templates and parameter sets that can be automatically instantiated across multiple design variations. These systems can execute complex design space explorations, perform statistical analysis, and generate comprehensive reports without manual oversight. The automation approach not only reduces simulation time and human effort but also improves result consistency and enables the generation of large datasets nec- essary for advanced analysis techniques. Furthermore, automated workflows facili- tate integration with optimization algorithms and design exploration tools, creating comprehensive design environments that can systematically improve antenna per- formance. 2.4.1 PyAEDT Interface for HFSS PyAEDT represents a comprehensive Python interface that provides program- matic access to ANSYS Electronics Desktop (AEDT) applications including HFSS. This interface enables to control HFSS functionality through python scripts for auto- mated model creation, execution, and post-processing operations. PyAEDT reduces the complexity of HFSS native scripting language while providing complete access to the full range of software capabilities including geometry creation, material as- signment, boundary condition specification , mesh control and solver configuration. The power of PyAEDT is demonstrated through its ability to create complex ge- ometries with minimal code. For example, a simple dipole antenna can be generated using the following Python script[9]: 1 from pyaedt import Hfss 2 hfss = Hfss( specified_version =" 2024.2 ", 3 non_graphical =False , 4 new_desktop_session =True) 5 6 arm_length = 1 7 gap = 0.2 8 radius = 0.2 13 2. Theoretical Background 9 10 hfss. modeler . create_cylinder ( cs_axis ="Z", 11 position =[0, 0, gap /2], 12 radius =radius , 13 height = arm_length ) 14 15 hfss. modeler . create_cylinder ( cs_axis ="Z", 16 position =[0, 0, -gap /2 - arm_length ], 17 radius =radius , 18 height = arm_length ) Listing 2.1: PyAEDT script for creating a simple dipole antenna Figure 2.5: Simple dipole antenna geometry created using PyAEDT script showing the programmatic modeling. The integration between pyAEDT and HFSS operate through the Component Object Model(COM) interface, allowing python scripts to communicate directly with the HFSS engine. As demonstrated in Listing 2.1 and Figure 2.5, which enables seamless automation of complex simulation workflows. PyAEDT provides object- oriented programming structures that mirror HFSS functionality, make it intuitive with electromagnetic modeling concepts supporting both local and remote simula- tion execution, enabling integration with high-performance computing resources and cluster environments. 14 2. Theoretical Background 2.4.2 Advantages of Programmatic Approach over Tradi- tional GUI Methods The programmatic approach to electromagnetic simulation offers substantial ad- vantages over traditional GUI-based workflows, particularly for complex and repet- itive modeling tasks. These advantages become increasingly significant as system complexity and analysis requirements grow: • Scalability and Efficiency: Automated scripts can generate large-scale models and execute extensive parameter sweeps without manual intervention and later processing large amounts of data after simulation. • Consistency and Reproducibility: Programmatic workflows eliminate hu- man errors and ensure identical modeling approaches across different designs, providing consistent and reproducible results essential for comparative analy- sis. • Integration Capabilities: Programmatic interfaces enable seamless integra- tion with external tools including optimization algorithms, statistical analysis packages, and machine learning frameworks, creating comprehensive design environments. • Parametric Design Exploration: Automated frameworks can systemat- ically explore large design spaces through parametric sweeps and sensitivity analysis, identifying optimal configurations that might be missed through man- ual approaches. • Batch Processing and Parallelization: Scripts can distribute simulations across multiple computing resources and execute batch processing operations, significantly reducing overall analysis time for complex projects. These advantages make programmatic approaches essential for modern electro- magnetic design workflows, where traditional GUI methods become limiting factors in achieving comprehensive analysis and optimization of complex antenna systems. 15 2. Theoretical Background 16 Confidentiality Notice Confidentiality Agreement As per Ericsson confidentiality Agreement, the information communi- cated in conjunction with the Assignment for Ericsson and that is not already generally known through publication shall be treated as being confidential and shall not be disclosed for any other purpose. Under this agreement: Chapters 3, 4, 5, 6 are not disclosed for public preview 17 2. Theoretical Background 18 7 Results This chapter presents the comprehensive results obtained from the enhanced automation framework for antenna isolation modeling demonstrating framework’s capabilities across the complete workflow (starting from Model generation to Model Compare). 7.1 Testing Environment and Software Configu- ration The automation framework was developed and tested using testing environment consisted of the following software versions: • Python: Version 3.11.1 • ANSYS HFSS: Version 2024.2 • PyAEDT: Version 0.15.3 7.2 Automated Model Creation Result The automated model creation process utilizes a comprehensive set of parame- ters. This section presents the specific parameter configuration used for generating the test case: "Dipole Array, Rev 15_2, 3x3+3x3, AntArr - 8236" as follows: Table 7.1: Antenna Array Configuration Parameters for Test Case: AntArr - 8236 Parameter Category Configuration Details Array Geometry and Structure Array Configuration Dual array system (single_array = False) Array Dimensions 3×3 + 3×3 configuration (nx1=3, ny1=3, nx2=3, ny2=3) Total Elements 18 antenna elements (9 elements per array) Total Ports 36 ports (2 polarizations per element) Element Type Cross-dipole antennas with dual polarization capability Spatial Positioning and Orientation Horizontal Separation 2 wavelengths (xseparation = 2) Vertical Separation 0 wavelengths (yseparation = 0) Angular Orientation 120-degree separation (yangle = ‘120deg’) 19 7. Results Table 7.1 – continued from previous page Parameter Category Configuration Details Reference Radius 6 wavelengths (radius = 6) Positioning Mode Normalized positioning (=True) Excitation and Polarization Configuration Polarization Type Horizontal linear polarization Excitation Element Center element of Array 1 (Element_1_5) Source Configuration Dual-port excitation (X and Y polarizations) Element Distribution Mapping Array 1 Buildmap All active elements (buildmap1.all_active) Array 2 Buildmap All active elements (buildmap2.all_active) Active Elements Full electromagnetic participation with X and Y ports Load/Lumped/Void Ele- ments Not utilized in this configuration Frequency and Analysis Parameters Reference Frequency 3.5 GHz (fref = 3.5e9) Frequency Range 3.15 - 3.85 GHz (fstart = 3.15, fstop = 3.85) Frequency Points 15 discrete points (fpoints = 15) Mesh Frequency 3.5 GHz optimization Element Spacing Wavelength-normalized based on reference frequency Simulation Accuracy and Solver Configuration Speed Level Level 3 (balanced approach for most simulations) Maximum Passes 6 adaptive refinement iterations Solver Type FEBI Template and Component Configuration HFSS Template DAP15_2_template_for_GDP16 (dual array) Project File Dipole Array, Rev 15_2.aedt Active Components GDP16.a3dcomp (cross-dipole elements) Component Parameters Predefined geometry and design variables 20 7. Results This parameter configuration generates a representative dual-array antenna sys- tem from framework as follows: Figure 7.1: Generated 3D model of Dipole Array, Rev 15_2, 3×3+3×3, AntArr - 8236 as Table 7.1 7.3 Data Extraction Results The data extraction process follows the methodology, systematically retrieving S-parameter data from HFSS simulation results and processing them into structured formats. The following listings demonstrate a small part of extracted data formats(JSON and sNp) for the test case "AntArr - 8236": 1 " data_freq ": { 2 " discrete_sweep ": { 3 " extractmap_inter_1sparse_2sparse ": { 4 " convention ": " Element_array (1 or 2) _elementnumber ( row first) _polarization (X-red -neg45 or Y-blue -pos45)", 5 " imagdata ": [ 6 { 7 " entry_key ": S( Element_1_1_X , Element_2_1_X ) 8 " freq_entries ": [ 9 { 10 "freq": 3.15 , 11 "imag": 0.000845538476039103 12 }, 13 { 14 "freq": 3.2, 15 "imag": 0.0005797380915756188 16 }, 17 { 18 "freq": 3.4, 19 "imag": -0.0010324536887846751 20 }, 21 7. Results 21 { 22 "freq": 3.85 , 23 "imag": -0.00047922947472753063 24 } Listing 7.1: Sample JSON data structure showing extracted S-parameter imaginary components 1 ! Touchstone file exported from HFSS 2024.2.1 2 ! File: R:/ HFSS from cluster /64159/ Dipole_Array , _Rev_15_2 ,_3x3 +3x3 ,_AntArr_ -_8236.aedt 3 ! Generated : 12:24:28 AM May 24, 2025 4 ! Design : DAP15_2_3x3 +3x3 5 ! Project : Dipole_Array ,_Rev_15_2 ,_3x3 +3x3 ,_AntArr_ - _8236 6 ! Setup: Setup1 7 ! Solution : SweepDiscrete 8 # GHz S MA R 50.000000 9 ! Terminal data exported 10 3.15 0.400810440579014 -36.7120325159593 0.0432075134977711 -147.267869696324 0.0874160468592595 89.217237227437 0.0663313140287666 -178.956574450542 11 0.0156699220218193 -133.441081717354 0.0224999127213456 -27.042240243007 0.185876796156664 136.276584386435 0.14423257176528 34.0936740973737 12 0.0376144844528315 122.813646107233 0.0145951865617113 115.324285156829 0.0131667545314536 -99.6345285627282 0.0122167328767924 -69.7332183776987 Listing 7.2: Sample Touchstone file header and data showing industry-standard S-parameter format 7.4 JSON Data Analysis and Visualization Re- sults The JSON data analysis and visualization results demonstrate the comprehen- sive analytical capabilities of the enhanced framework, following the methodologies. 7.4.1 S-Parameter Frequency Response Analysis Figure 7.2 presents the frequency-domain S-parameter analysis using the dis- crete sweep data extracted from HFSS simulation, plotting S-parameter magnitudes in decibels across the 3.15-3.85 GHz frequency range for the inter-array sparse cou- pling map (extractmap_inter_1sparse_2sparse). Each trace represents electromag- netic coupling between elements in arrays which demonstrates the isolation char- acteristics of dual-array configuration with variations across the bandwidth, where stronger couplin (higher magnitude values) occur at specific frequencies due to the resonance effects and EM interactions between arrays which are positioned at 120- degree angular separation. 22 7. Results Figure 7.2: S-parameter magnitude versus frequency showing electromagnetic cou- pling behavior across the 3.15-3.85 GHz range 7.4.2 S-Parameter Convergence Across Refinement Passes Figure 7.3: S-parameter magnitude convergence across adaptive mesh refinement passes showing solution stability Figure 7.3 demonstrates the primary convergence visualization showing S-parameter magnitudes in decibels versus mesh refinement pass numbers. The plot reveals that most S-parameters stabilize after a initial refinement passes having minimal varia- tions in subsequent iterations. This convergence behavior indicates successful adap- tive mesh refinement, where the EM solution reaches stable values as finite element mesh is progressively refined capturing field gradients accurately. 7.4.3 Three-Dimensional Error Analysis Figure 7.4 illustrates the 3D convergence metric, displaying the absolute conver- gence errors in 3D, as x-axis representing the final S-parameter coupling strength, 23 7. Results Figure 7.4: 3D visualization of absolute convergence errors (deltaS in dB) across mesh refinement passes and final coupling levels y-axis shows the mesh refinement pass number, and the z-axis indicates the absolute delta-S magnitude in decibels. This visualization enables identification of system- atic convergence patterns and reveals how different coupling levels behave during adaptive mesh refinement and reference lines 0 dB and -18 dB act as indicators for error assessment to identify which S-parameters require additional refinement passes to achieve acceptable accuracy. 7.4.4 Final Pass Convergence Assessment Figure 7.5: Convergence check showing deltaS/S vs. final coupling strength with binned statistical analysis and reference thresholds Figure 7.5 presents the final pass convergence assessment visualization methods. The plot combines raw scatter data (individual S-parameter convergence values) with a binned staircase representation that applies statistical smoothing using the 24 7. Results 99th percentile within each magnitude bin. The horizontal reference line at -79 dB represents the 1dB-error range, meaning all the S-parameters weaker than -79 dB have converged to within 1 dB accuracy. 7.4.5 Basic Simulation Performance Analysis Figure 7.6: Basic simulation performance analysis showing time allocation, fre- quency solve duration, adaptive pass duration, and error trends Figure 7.6 illustrates the fundamental performance characteristics extracted from the HFSS simulation log analysis. The analysis provides a comprehensive view of computational efficiency and convergence behavior across four key metrics: • Sweep Performance Breakdown (Subplot 1): Time allocation analysis reveals that adaptive meshing consumes 1729 seconds, significantly exceeding the discrete sweep duration of 966 seconds, with remaining operations account- ing for 1354 seconds. This distribution is characteristic of complex antenna array simulations where iterative mesh refinement dominates computational overhead, particularly for 36-port systems requiring high accuracy. • Frequency Solve Duration for Discrete Sweep (Subplot 2): Individual frequency point processing times exhibit substantial variation across the 3.2- 3.8 GHz range, with an average solve time of 1012.55 seconds per frequency point. The oscillating pattern between approximately 700-1200 seconds in- dicates frequency-dependent convergence complexity, where certain frequency points require additional computational effort due to resonance effects or field distribution complexity. • Adaptive Pass Duration (Subplot 3): The step-wise progression shows increasing computational requirements for successive mesh refinement passes, escalating from approximately 110 seconds for Pass 1 to 390 seconds for Pass 6. This exponential growth pattern reflects the increasing mesh density and computational complexity as the adaptive algorithm refines critical regions to achieve the specified convergence criteria. • S-Matrix Error Trend (Subplot 4): Convergence reliability assessment demonstrates generally stable error levels below the 0.5% threshold across most frequency points, with a notable exception at approximately 3.5 GHz where 25 7. Results the error exceeds 35%. This anomaly suggests potential convergence diffi- culties at this specific frequency, possibly indicating insufficient mesh density or numerical instabilities requiring additional refinement passes or modified solver settings. 7.4.6 Advanced Simulation Performance Metrics Figure 7.7: Advanced simulation performance metrics including adaptive mesh convergence analysis, normalized simulation cost, and memory usage progression Figure 7.7 presents the advanced performance evaluation metrics extracted from comprehensive HFSS log file analysis, providing deeper insights into simulation ef- ficiency and resource utilization: • Adaptive Mesh: Convergence by Pass (Subplot 1): The convergence progression analysis shows the relationship between mesh refinement passes and achieved accuracy. The bar chart displays maximum magnitude Delta S values decreasing from 1.0 to approximately 0.15 across six adaptive passes, while the overlaid curve represents tetrahedral count growth reaching over 200k elements. The 0.01 threshold line indicates the target convergence crite- rion, demonstrating that convergence is achieved by Pass 4, with subsequent passes providing marginal accuracy improvements at significantly increased computational cost. • Normalized Simulation Cost vs No. of Ports (Subplot 2): This scat- ter plot quantifies computational efficiency using the Normalized Simulation Cost (NSC) metric, calculated as the ratio of total computation time to the product of frequency points and port count. For the 36-port AntArr_1 config- uration, the NSC value of approximately 1.0 indicates balanced computational efficiency relative to the problem complexity. This metric enables direct com- parison between different antenna array configurations and guides optimization strategies for large-scale simulations. • Memory Usage Progression Timeline (Subplot 3): The comprehensive memory utilization profile tracks resource consumption throughout the entire simulation workflow. Peak memory usage reaches 11.4GB during FEBI (Finite Element Boundary Integral) solving at 3.5 GHz iterations, as highlighted by 26 7. Results the yellow annotation box. The timeline reveals distinct phases: initial setup with minimal memory footprint, progressive memory allocation during adap- tive meshing (0-25 minutes), peak utilization during frequency sweep solving (25-30 minutes), followed by memory deallocation and final processing phases (65-70 minutes). The multiple colored markers represent different simulation phases, enabling identification of memory bottlenecks and optimization oppor- tunities for large antenna array simulations. The advanced metrics collectively demonstrate that while the simulation achieves acceptable convergence levels, the significant memory requirements and extended processing times for frequency-dependent solving highlight the computational in- tensity inherent in high-fidelity antenna array modeling. These insights are crucial for scaling simulations to larger array configurations and optimizing computational resource allocation. 7.5 Touchstone File Analysis and Visualization Results The Touchstone file analysis and visualization results demonstrate the frame- work’s capabilities for processing industry-standard S-parameter data. 7.5.1 Return Loss Analysis Figure 7.8: Return loss versus frequency for reflection coefficients showing impedance matching characteristics Figure 7.8 illustrates the return loss characteristics calculated exclusively for diagonal S-parameters using equation (2.11). The plot shows return loss values ranging from approximately 8 to 12.5 dB across the frequency range. The curved response pattern with peak values around the center frequency indicates reasonable impedance matching at the design frequency of 3.5 GHz. Higher return loss values 27 7. Results (approaching 12-13 dB) suggest better matching, while the frequency variation re- veals the bandwidth characteristics of the antenna elements within the dual-array configuration. 7.5.2 Group Delay Analysis Figure 7.9: Group delay versus frequency showing phase linearity characteristics across the 3.15-3.85 GHz range Figure 7.9 presents the group delay analysis computed using equation (2.13) through numerical differentiation of the phase response with phase unwrapping. The plot reveals the frequency-dependent phase response characteristics of the an- tenna array S-parameters. Most of the S-parameters do exhibit relatively stable group delay values between 0-4 nanoseconds across the frequency range indicating good phase linearity but some parameters do show significant variations particularly observed at higher frequencies within range that indicates a frequency-dependent phase distortion affecting signal integrity. 7.5.3 Three-Dimensional S-Parameter Visualization Figure 7.10 presents the three-dimensional S-parameter visualization system that displays magnitude relationships across multiple dimensions, as x-axis rep- resenting frequency variation across the simulation bandwidth, the y-axis shows the magnitude at center frequency (3.5 GHz) providing a reference coupling level, and the z-axis represents the actual S-parameter magnitude in decibels. This plot enables identification of frequency-dependent coupling variations and assessment of how different S-parameters relate to each other across the operating bandwidth. The 3D representation reveals systematic patterns in electromagnetic coupling behavior, helping identify which parameter combinations exhibit similar frequency responses and coupling strengths relative to their center frequency reference values. 28 7. Results Figure 7.10: 3D visualization of S-parameters showing magnitude relationships across frequency and center frequency reference 7.5.4 Smith Chart Impedance Analysis Figure 7.11: Smith chart visualization showing complex impedance characteristics at 50-ohm reference Figure 7.11 provides impedance-based analysis through Smith chart visualiza- tion, transforming S-parameter data into complex representation. The plotted tra- 29 7. Results jectories show the frequency-dependent impedance behavior of S-parameters, with points near the chart center indicating good matching (low reflection) and points toward the periphery indicating impedance mismatches or reflection coefficients. 7.6 Comparative Analysis Results The goal of the comparative analysis is to evaluate how two modeling approaches differ by examining all S-parameters. It serves two purposes: first, to visualize the differences through plots for easier troubleshooting; and second, to generate a single numerical score that summarizes the overall error across all S-parameters and fre- quencies. This score helps guide automated processes, such as adjusting simulations to balance accuracy and efficiency. A similar approach can be applied to NSC for consistent evaluation throughout multiple models. The following subsections present the comparative analysis results for AntArr_3 versus AntArr_4: 7.6.1 Return Loss and VSWR Comparison Figure 7.12: Return loss and VSWR comparison between AntArr_3 and An- tArr_4 showing impedance matching characteristics Figure 7.12 presents the return loss and VSWR analysis following the mathemat- ical foundations. The upper subplot shows return loss comparison calculated, while the lower subplot displays VSWR characteristics computed using equation (2.12). Both antenna configurations exhibit similar return loss patterns ranging from 8-12 dB across the frequency band, with peak matching around 3.5 GHz. The VSWR comparison shows values between 1.5-2.5, with both configurations achieving VSWR < 2 around the center frequency, indicating acceptable impedance matching. The close agreement between the two configurations suggests consistent antenna design characteristics despite potential differences in array positioning or element varia- tions. 30 7. Results 7.6.2 Impedance Parameter Comparison Figure 7.13: Z-parameter comparison showing complex impedance characteristics for both antenna configurations Figure 7.13 illustrates the impedance parameter analysis following the Z-parameter. The plots show both real and imaginary components of diagonal Z-parameters (self- impedance characteristics) for both antenna configurations across the frequency range. AntArr_3 and AntArr_4 demonstrate very similar impedance behavior, with real parts ranging from approximately 20-80 ohms and imaginary parts vary- ing from -60 to +20 ohms. 7.6.3 S-Parameter Coupling Heatmap Analysis Figure 7.14: S-parameter coupling heatmap comparison showing magnitude dif- ferences and vector distances at center frequency Figure 7.14 presents the heatmap-based coupling analysis, focusing on center frequency assessment at 3.5 GHz: 31 7. Results • Magnitude Difference Heatmap (Left Subplot): Shows the magnitude difference calculation, revealing variations ranging from -60 to 0 dB across the port matrix. Darker blue regions indicating smaller differences and lighter regions showing larger variations. • Vector Distance Heatmap (Right Subplot): Displays the vector distance computation, providing linear-scale analysis showing distances up to 0.006 between complex S-parameters. 7.6.4 Maximum Relative Difference Assessment Figure 7.15: Maximum relative difference heatmap showing normalized coupling variations across the S-parameter matrix Figure 7.15 illustrates the relative difference calculation, where S-parameter dif- ferences are normalized by the average magnitude to provide magnitude-independent assessment. The heatmap reveals systematic patterns related to the antenna array structure, with inter-array coupling elements (cross-block regions) showing different relative difference characteristics compared to intra-array coupling elements (diago- nal blocks) enabling identification of which coupling paths exhibit the most signifi- cant variations between the two antenna configurations. 7.6.5 Three-Dimensional Relative Difference Visualization Figure 7.16 presents the three-dimensional relative difference visualization ex- tending the analysis across frequency and magnitude dimensions, where x-axis rep- resents the average magnitude at center frequency, the y-axis shows frequency variation, and the z-axis displays the relative difference in decibels. This plot enables identification of frequency-dependent coupling variations and reveals how S-parameter differences vary with both coupling strength and frequency, showing that most relative differences cluster around -20 to -40 dB range, indicating good agreement between the two antenna configurations. 32 7. Results Figure 7.16: 3D visualization of S-parameter relative differences showing coupling variations across frequency and magnitude dimensions 7.6.6 Comparative sNp Relative Error Analysis Figure 7.17: Comparative relative error analysis showing ∆S/Savg vs S-parameter magnitude at 3.500 GHz Figure 7.17 shows a relative error analysis comparing two antenna array config- urations at 3.500 GHz across 36 ports. The analysis calculates the relative difference between the two designs and plots it against S-parameter magnitude to assess how well the two configurations agree with each other. The scatter plot shows that weaker S-parameters (those with lower magnitudes, e.g., below –40 dB) tend to have smaller absolute differences (∆S) between the two antenna designs, but larger relative differences (∆S/S). This indicates that even small absolute changes in weak coupling paths can result in high relative variation. The blue histogram overlay shows the distribution of relative errors across dif- ferent S-parameter strength levels, with analysis revealing a maximum error of -8.60 dB and average error of -35.09 dB. With 37 out of 1296 total S-parameters exceed- ing the error threshold and a 1dB dynamic range spanning 64.0 dB, the results demonstrate good overall agreement between the two antenna configurations. 33 7. Results 34 8 Conclusion and Future Scope 8.1 Conclusion This thesis presents a collaborative effort with Ericsson research to extend an existing antenna array modeling framework into a comprehensive analysis platform. The work focused on enhancing simulation reliability, computational efficiency, and evaluation capabilities through three main areas: simulation accuracy analysis, touchstone file processing for S-parameter extraction, and comparative analysis be- tween different antenna models. The existing approach involved analyzing the code base from Ericsson Research to understand modeling and data extraction mecha- nisms, which was then extended with new methods for simulation evaluation and comparative analysis. The implementation addressed several technical challenges, particularly main- taining compatibility with the existing framework structure while introducing new analytical capabilities and correcting unforeseen complements in framework. The project successfully integrated touchstone file processing for detailed S-parameter analysis and developed tools to interpret simulation data in meaningful ways for practical antenna design decisions. While exploring the integration of multiple com- ponent arrays from HFSS showed promise as a potential simplification method, time constraints prevented full implementation of this approach into the framework, leav- ing it as a foundation for future development. The resulting platform demonstrates how existing frameworks can be thoughtfully extended to meet evolving research needs in antenna design while providing evaluation tools for the field. 8.2 Future Scope In this thesis, I’ve focused on developing the most essential automation features due to time constraints. Future work could explore: • Computational Method Integration: The current framework relies pri- marily on FEBI as the default solver method. Incorporating additional com- putational methods like SBR+ will provide result comparison between solvers, aiding in cases of uncertain reliability. • Large-Scale Array Optimization: One significant limitation was the in- ability to investigate simulation approaches for arrays with several hundred elements. The underlying research question of determining optimal simula- tion methods, settings, and simplifications for large-scale arrays remains un- addressed, particularly finding the right balance between speed and accuracy 35 8. Conclusion and Future Scope when dealing with complex coupling effects. • Automated Design Optimization: While the framework can build and analyze predetermined array configurations, it lacks capability for automated optimization where an optimizer could instruct the framework on which models to build and evaluate iteratively. • Extended Element Library: The framework currently supports cross-dipole configurations, but expanding to include other antenna element types like patch antennas or slots would broaden its applicability and address practical limitations encountered when modeling certain array architectures requiring different element geometries. 36 Bibliography [1] T. L. Marzetta, E. G. Larsson, H. Yang, and H. Q. Ngo, Fundamentals of Massive MIMO, Cambridge, UK: Cambridge University Press, 2016. [2] A. Sabharwal, P. Schniter, D. Guo, D. W. Bliss, S. Rangarajan, and R. Wich- man, “In-band full-duplex wireless: Challenges and opportunities,” IEEE Jour- nal on Selected Areas in Communications, vol. 32, no. 9, pp. 1637–1652, Sep. 2014. [3] F. Liu, C. Masouros, A. P. Petropulu, H. Griffiths, and L. Hanzo, “Integrated sensing and communications: Toward dual-functional wireless networks for 6G and beyond,” IEEE Journal on Selected Areas in Communications, vol. 40, no. 6, pp. 1728–1767, Jun. 2022. [4] C. A. Balanis, Antenna Theory: Analysis and Design, 4th ed., Hoboken, NJ: John Wiley & Sons, 2016. [5] OpenAI, “AI-generated image illustrating mutual coupling between antennas, generated by ChatGPT in response to user prompt,” ChatGPT, OpenAI, 2025. [Online]. Available: https://chat.openai.com/ [6] R. C. Hansen, Phased Array Antennas, 2nd ed., Hoboken, NJ: John Wiley & Sons, 2009. [7] J.-M. Jin, The Finite Element Method in Electromagnetics, 3rd ed., Piscataway, NJ: IEEE Press/Wiley, 2014. [8] ANSYS Inc., ANSYS HFSS User Guide, Release 2024.2, Canonsburg, PA: AN- SYS Inc., 2024. [9] Ansys, Inc., “PyAEDT Documentation,” Ansys Electronics Desktop Python API, 2024. [Online]. Available: https://aedt.docs.pyansys.com/ 37 https://chat.openai.com/ https://aedt.docs.pyansys.com/ Bibliography 38 A Appendix: Software Configuration and Setup A.1 Python Library Dependencies The framework requires the following Python libraries with their primary func- tions: • ansys.aedt.core • plotly • pandas • numpy • scikit-rf • pathlib • json • os, sys • shutil • random • re A.2 File Naming Conventions The framework implements standardized file naming conventions to ensure con- sistency and traceability: • HFSS Project Files: [Template_Name], [Array_Dimensions], [Model_Family] - [Random_ID].aedt • Configuration Files: [Base_Name], config.json • Data Files: [Base_Name], data.json • Touchstone Files: [Base_Name], touchstone.s[N]p • Performance Files: [Model_Tag]_Simlog.json Example complete filename: Dipole Array, Rev 15_2, 3x3+3x3, AntArr - 8236.aedt I DEPARTMENT OF SOME SUBJECT OR TECHNOLOGY CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden www.chalmers.se www.chalmers.se List of Acronyms Nomenclature List of Figures List of Tables Listings Introduction Background Purpose and Goal Purpose and Need for Automated Analysis Research Goal and Framework Enhancement Thesis Outline Theoretical Background Antenna Fundamentals Antenna Types and Classification Dipole and Cross-Dipole Antenna Antenna Performance Parameters S-Parameters Z-Parameters Return Loss Voltage Standing Wave Ratio (VSWR) Group Delay Antenna Arrays and Element Spacing Mutual Coupling in Antenna Arrays Computational Electromagnetics Methods Finite Element-Boundary Integral (FEBI) Method HFSS Software and Modeling Multiple Component Arrays in HFSS Automation in Electromagnetic Modeling PyAEDT Interface for HFSS Advantages of Programmatic Approach over Traditional GUI Methods Confidentiality Notice Results Testing Environment and Software Configuration Automated Model Creation Result Data Extraction Results JSON Data Analysis and Visualization Results S-Parameter Frequency Response Analysis S-Parameter Convergence Across Refinement Passes Three-Dimensional Error Analysis Final Pass Convergence Assessment Basic Simulation Performance Analysis Advanced Simulation Performance Metrics Touchstone File Analysis and Visualization Results Return Loss Analysis Group Delay Analysis Three-Dimensional S-Parameter Visualization Smith Chart Impedance Analysis Comparative Analysis Results Return Loss and VSWR Comparison Impedance Parameter Comparison S-Parameter Coupling Heatmap Analysis Maximum Relative Difference Assessment Three-Dimensional Relative Difference Visualization Comparative sNp Relative Error Analysis Conclusion and Future Scope Conclusion Future Scope Bibliography Appendix: Software Configuration and Setup Python Library Dependencies File Naming Conventions