FPGA-controlled Outphasing Modulator Using A Power Combining Antenna Bachelor degree project report in Electrical Engineering Jakob Gunnarsson, Christopher Ek & Simon Westergren Group: EENX16-VT25-0033 DEPARTMENT OF ELECTRICAL ENGINEERING CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden 2025 www.chalmers.se www.chalmers.se Bachelor degree project report 2025 FPGA-controlled Outphasing Modulator Using A Power Combining Antenna Jakob Gunnarsson, Christopher Ek & Simon Westergren Department of Electrical Engineering Chalmers University of Technology Gothenburg, Sweden 2025 FPGA-controlled Outphasing Modulator Using A Power Combining Antenna Jakob Gunnarsson, Christopher Ek & Simon Westergren © Jakob Gunnarsson, Christopher Ek & Simon Westergren, 2025. Supervisors: Rob Maaskant & Iaroslav Shilinkov, Department of Electrical Engi- neering Examiner: Erik Ström, Department of Electrical Engineering Bachelor degree project report 2025 Department of Electrical Engineering Chalmers University of Technology SE-412 96 Gothenburg Sweden Telephone +46 31 772 1000 Cover: Illustration of an outphasing system with a two-element patch antenna array as the power combiner, where the phase modulated inputs generate an amplitude modulated output. Typeset in LATEX, template by Kyriaki Antoniadou-Plytaria Gothenburg, Sweden 2025 iv FPGA-controlled Outphasing Modulator Using A Power Combining Antenna Jakob Gunnarsson, Christopher Ek & Simon Westergren Department of Electrical Engineering Chalmers University of Technology Abstract Coupling between antenna elements is often an undesired characteristic in antenna arrays, due to its distortion of radiation patterns and degradation of beamform- ing accuracy. However, if this coupling could be exploited in outphasing through load modulation, it has the potential to improve total system efficiency. This project aimed to design a high-efficiency outphasing system for communication applications, consisting of two power amplifiers (PAs) and a power combining antenna array. To evaluate how different load impedances affect PA performance, a custom ac- tive vector-receiver load-pull setup was constructed and calibrated using an FPGA board. This setup enabled precise control over the presented load impedance to the PAs and was critical for measuring power added efficiency and output power under dynamic loading conditions. The resulting load-pull data informed the selection of ideal 2-port S-parameters for the power combiner. Based on these, a two-element patch antenna array was designed to serve as the combiner. Separate matching net- works were implemented to match the antenna ports to the desired S-parameters. Two types of matching networks were considered: using lumped components and using microstrip lines. Using lumped components, the desired S-parameters were able to be matched quite well, yielding an error of around 9% whereas the microstrip line network was unable to provide sufficient matching in its current configuration. Using the PA load-pull data and the S-parameters of the designed antenna, the performance of the outphasing system was tested through simulations in both MAT- LAB and CST. The results confirmed that outphasing was achievable with this setup, where amplitude modulation was realized by steering the antenna beam away from the receiver. Additionally, the simulations indicated that implementing an appro- priate matching network could enhance the overall system efficiency. Keywords: antenna, load modulation, antenna array, outphasing, power amplifiers, load-pull, FPGA, matching network. v Sammanfattning Koppling mellan antennelement är ofta en oönskad egenskap i gruppantenner, då den kan orsaka distorsion i strålningsmönster och försämra precisionen i beamform- ing. Om denna koppling istället kan utnyttjas i outphasing genom lastmodulering, kan systemets verkningsgrad potentiellt förbättras. Syftet med projektet var att konstruera ett outphasingsystem med hög verkningsgrad för kommunikationsapp- likationer, bestående av två effektförstärkare och en gruppantenn som används som effektkombinator. För att utvärdera hur olika lastimpedanser påverkar förstärkarnas prestanda, kon- struerades och kalibrerades en egenutvecklad aktiv vektor-mottagare för load-pull mätningar med hjälp av ett FPGA-kort. Denna uppställning möjliggjorde nog- grann styrning av den presenterade lastimpedansen till effektförstärkarna och var avgörande för mätning av både power added efficiency och uteffekt under dynamiska belastningsförhållanden. Den uppmätta load-pull-datan låg till grund för valet av optimala tvåports S-parametrar för effektkombinatorn. Utifrån detta designades en gruppantenn bestående av patchantenner för att fungera som kombinator. Separata matchningsnätverk implementerades för att matcha antennportarna till de önskade S-parametrarna. Två typer av matchningsnätverk utvärderades: ett baserat på diskreta komponenter och ett baserat på mikrostripledare. Med diskreta kompo- nenter kunde de önskade S-parametrarna uppnås med en felmarginal på cirka 9 %, medan nätverket bestående av mikrostripledare inte lyckades uppnå den önskade matchningen i sin nuvarande uppsättning. Med hjälp av förstärkarnas load-pull-data och de uppmätta S-parametrarna för den designade antennen, testades outphasing-systemets prestanda genom simuleringar i både MATLAB och CST. Resultaten bekräftade att outphasing kunde uppnås med denna uppsättning, där amplitudmodulering realiserades genom att styra an- tennens lob bort från mottagarantennen. Simuleringarna visade dessutom att im- plementeringen av ett lämpligt matchningsnätverk skulle förbättra systemets totala verkningsgrad ytterligare. vi Acknowledgements We would like to extend our sincere thanks to Dr. Gregor Lasser for his expertise and the numerous discussions regarding the characterization of the power amplifiers. Furthermore, we would like to thank our supervisors Dr. Rob Maaskant and Iaroslav Shilinkov. Their consistent availability, constructive feedback, and timely responses to questions were deeply appreciated and were essential for the progress of the project. Jakob Gunnarsson, Christopher Ek and Simon Westergren, Gothenburg, May 2025 vii List of Acronyms Below is the list of acronyms that have been used throughout this thesis listed in alphabetical order: ADC Analog-to-Digital Converter ASK Amplitude Shift Keying DAC Digital-to-Analog Converter DC Direct Current DUT Device Under Test FPGA Field-Programmable Gate Array FSK Frequency Shift Keying PA Power Amplifier PAE Power Added Efficiency PSK Phase Shift Keying PWM Pulse Width Modulation QAM Quadrature Amplitude Modulation RF Radio Frequency SOL Short Open Load SOLT Short Open Load Through VNA Vector Network Analyzer ix Nomenclature Below is the nomenclature of indices, parameters, and variables that have been used throughout this thesis. Indices i, j Port indices used in the S-parameter matrix (input/output ports) Parameters Z0 Characteristic impedance, typically 50 Ω λ0 Free space wavelength A0 Constant amplitude of the decomposed outphasing signals Sij S-parameter from port j to i ∆θ Difference in outphasing angle between intersections of outphasing circles L Length of the patch antenna W Width of the patch antenna x0 Distance between feed point and center of the first patch antenna x1 Distance between feed point and center of the second patch antenna dx Distance between antenna elements εr Dielectric material of antenna substrate h Height of dielectric substrate t Thickness of metal patch L1, L2 Lumped component inductance in matching network at ports 1 and 2 C1, C2 Lumped component capacitance in matching network at ports 1 and 2 xi Variables a1, a2, a3 Forward traveling waves into port 1, 2 and 3 b1, b2, b3 Reflected or outgoing waves at ports 1, 2, and 3 Pin Input power Pout Output power PDC Consumed DC power PAE Power Added Efficiency Γ Reflection coefficient Γin Input reflection coefficient ΓL Load reflection coefficient ΓPA1 , ΓP A2 Load reflection coefficient seen by PA 1 and 2 in outphasing ZL Load impedance S(t) Original signal to be transmitted S1(t), S2(t) Constant envelope signals created from S(t) θ Outphasing angle xii Contents List of Acronyms ix Nomenclature xi List of Figures xiv List of Tables xvi 1 Introduction 3 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Theory 7 2.1 Power Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Digital Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Load-pull PA Characterization . . . . . . . . . . . . . . . . . . . . . . 10 2.4 Outphasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4.1 Load Modulation . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4.2 Combiner Design . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4.3 Power Combining Antennas . . . . . . . . . . . . . . . . . . . 18 2.5 Patch Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.5.1 Microstrip Line . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.5.2 Antenna Array . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.5.3 Impedance Matching . . . . . . . . . . . . . . . . . . . . . . . 20 2.5.4 Gain and Friis’ Equation . . . . . . . . . . . . . . . . . . . . . 21 3 Methods 23 3.1 Load-Pull Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.1.1 Generating Impedances And Measuring DUT . . . . . . . . . 25 3.1.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.1.3 Parameter Calculations . . . . . . . . . . . . . . . . . . . . . . 26 3.1.4 Measurement Region Adjustments . . . . . . . . . . . . . . . . 27 3.2 Analytical Combiner S-parameter Calculations . . . . . . . . . . . . . 27 3.3 Antenna Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3.1 Matching Network . . . . . . . . . . . . . . . . . . . . . . . . 31 xiii Contents 3.3.2 Exploratory Designs . . . . . . . . . . . . . . . . . . . . . . . 32 3.4 Outphasing Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.4.1 Analytical S-parameter Simulations . . . . . . . . . . . . . . . 33 3.4.2 Antenna Combiner Simulations . . . . . . . . . . . . . . . . . 34 4 Results 35 4.1 Load-Pull . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.2 Optimal Combiner S-parameters . . . . . . . . . . . . . . . . . . . . . 36 4.3 Antenna Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.3.1 Lumped Component Matching Network . . . . . . . . . . . . . 39 4.3.2 Microstrip Line Matching Network . . . . . . . . . . . . . . . 40 4.4 Outphasing Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.4.1 Resulting Load Modulation on the PAs . . . . . . . . . . . . . 41 4.4.2 Radiation Patterns at Outphasing . . . . . . . . . . . . . . . . 42 4.4.3 Total Power and PAE . . . . . . . . . . . . . . . . . . . . . . 44 5 Discussion 47 5.1 Power Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5.2 Load-Pull Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5.3 Antenna Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.4 Outphasing Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 49 6 Conclusion 51 A Appendix I A.1 Exploratory Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . I A.2 CST Outphasing Simulation Data . . . . . . . . . . . . . . . . . . . . II xiv List of Figures 2.1 The 1 dB compression point illustrated where the actual output power of the PA diverges from the linear approximation by 1 dB. . . . . . . 7 2.2 Diagram of how different PA classes operate in relation to the transis- tor cutoff voltage (right). Transistor showing the gate-source voltage VGS, drain-source voltage VDS, and drain current IDS (left). The wave- forms shown here are the input signals, where some classes operate with parts of the signal wave in cutoff. . . . . . . . . . . . . . . . . . 8 2.3 Simplified schematic of a power amplifier as the DUT in a traditional passive load-pull setup. . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4 Simplified schematic of a power amplifier as the DUT in a passive vector-receiver load-pull setup. . . . . . . . . . . . . . . . . . . . . . . 11 2.5 Simplified schematic of a power amplifier as the DUT in an active vector-receiver load-pull setup. . . . . . . . . . . . . . . . . . . . . . . 12 2.6 Synthesized examples of how load-pull contour plots can look for ar- bitrary parameters 1 and 2 (output power or PAE for example). . . 12 2.7 Block diagram of the outphasing process . . . . . . . . . . . . . . . . 13 2.8 Complex vector representation of signal decomposition with differen- tial phase shift θ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.9 Schematics of a general 3-port circuit-based power combiner, where the two input ports (ports 1 and 2) combine in the output port (port 3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.10 Example of load modulation circle placement from [6], Copyright © 2015 IEEE. Reproduced with permission . . . . . . . . . . . . . . . . 17 2.11 Power combining antenna array configuration where the original sig- nal is reproduced in free space. . . . . . . . . . . . . . . . . . . . . . 18 2.12 Schematic of a patch antenna, showing both a top-down view (left) and a cross-section (right). . . . . . . . . . . . . . . . . . . . . . . . . 19 3.1 Picture of the load-pull setup in the lab with labeled components and instruments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2 The load-pull setup schematic, illustrating the uncalibrated measured waves denoted with sub-index m which correspond to the incoming and reflected waves at the ports of the DUT. . . . . . . . . . . . . . . 24 3.3 The antenna design schematic showing the dimension parameters for patch element i. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 xv List of Figures 3.4 Schematic of the lumped components matching network for antenna element i. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.5 Schematic of the microstrip line matching network for antenna ele- ment i. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.1 Load-pull results illustrating how the parameters PAE and Pout change depending on the load impedance presented to the PA, with an aver- age input power of 3.93 dBm. . . . . . . . . . . . . . . . . . . . . . . 35 4.2 Analytical outphasing load modulation circles overlaid on PAE and Pout contours. The figure illustrates the placement of the circles rela- tive to the PA characteristics. The dots mark the point corresponding to θ = 0◦, and as θ increases, the load impedances trace the circles in the direction of the arrows. . . . . . . . . . . . . . . . . . . . . . . . . 36 4.3 Normalized Power added efficiency vs. back-off power level for the 4 different picks of S-parameters where 0◦ < θ < 90◦. . . . . . . . . . . 37 4.4 S-parameters and co-polar embedded element pattern for the antenna array without matching networks for the ports. . . . . . . . . . . . . 39 4.5 Predicted load modulation circles for the different antenna feeding configurations compared against the target design. The dots indicate the point of maximum system output power. As θ increases, the load on the PAs traject along the circles in the direction of the arrows. . . 41 4.6 Output waves of the PAs at different outphasing angles which corre- sponds to the magnitude of the input waves of the antenna combiner, |a1,comb| and |a2,comb|. . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.7 Total radiation patterns (φ constant) for the antenna with the lumped component matching network for the lowest, intermediate, and max- imum gain in broadside. . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.8 Total radiation patterns (φ constant) for the antenna with the mi- crostrip line matching network for the lowest, intermediate, and max- imum gain in broadside. . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.9 IEEE Gain of the antennas at broadside as a function of the outphas- ing angle θ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.10 Normalized received power at broadside against the outphasing angle θ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.11 Normalized total PAE versus back-off power level in dB for 0◦ < θ < 180◦. As θ increases, the plots trace the curve in the direction indicated by the arrows. . . . . . . . . . . . . . . . . . . . . . . . . . 45 A.1 Schematic of single patch antenna with two orthogonally polarized feed-lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II xvi List of Tables 4.1 S-parameters for the selected combiner design in rectangular and po- lar form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.2 Dimensions for the patch antenna elements without matching network. 38 4.3 Values for the lumped component matching networks at ports 1 and 2. 39 4.4 S-parameters of the antenna with lumped component matching net- work in rectangular and polar form. . . . . . . . . . . . . . . . . . . . 40 4.5 Dimensions of the microstrip line matching networks at ports 1 and 2. 40 4.6 S-parameters of the antenna with microstrip matching network in rectangular and polar form. . . . . . . . . . . . . . . . . . . . . . . . 40 A.1 CST outphasing simulation results using lumped component match- ing network. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II A.2 CST outphasing simulation results using microstrip matching network. III 1 List of Tables 2 1 Introduction 1.1 Background As the evolution of wireless connectivity continues to advance, the demand for higher data rates and more bandwidth increases. When designing these highly efficient com- munication systems, reducing the total power consumption becomes a crucial factor. This comes with the need for more efficient systems and improved power amplifica- tion techniques [1]. The approach explored in this project is by integrating nonlinear, highly efficient power amplifiers (PAs) using a technique known as outphasing [2]. This technique enables more efficient power utilization during amplitude modula- tion, particularly for high-order modulation schemes such as Quadrature Amplitude Modulation (QAM) [3]. The outphasing technique, first introduced by Chirex in 1935, involves generating two constant amplitude signals with a differential phase shift, θ [4]. These constant amplitude signals are then amplified separately using two highly efficient, nonlinear PAs. Finally, the two signals are combined using a power combiner, where the dif- ferential phase shift is translated into amplitude modulation of the output signal. A crucial feature of outphasing is the use of a non-isolated power combiner, which introduces electrical coupling between its input ports. This coupling dynamically varies the load impedance seen by each PA as the differential phase shift between the two branches changes [5]. The nature of this modulation depends on the Scattering Parameters (S-parameters) of the combiner. The benefit of this is the fact that PA performance metrics, such as output power and power-added efficiency (PAE), are sensitive to load impedance. The coupling between the ports can thus be used to help modulate the amplitude of the signal. If utilized optimally, this effect, known as load modulation, can significantly improve the efficiency of the system, especially at power levels below the peak output, commonly referred to as power back-off. To utilize load modulation effectively, the PA’s performance dependence on load impedance must be characterized [6]. This is achieved through a technique called load-pull, in which the PA is systematically subjected to a range of load impedances while its performance is measured at each impedance [7]. These measurements allow for the prediction of the desired load modulation behavior, enabling the design of a power combiner that optimally leverages both load modulation and outphasing for maximized efficiency. 3 1. Introduction Traditionally, outphasing in wireless communication systems is implemented us- ing a circuit-based power combiner before the signal is radiated by an antenna [3]. This however comes with the drawback of resistive losses in the combiner circuit. A possible work-around presented in more recent studies show that incorporating the power combiner into the antenna structure itself is a possibility. In this approach, the two signals recombine in free space, eliminating resistive losses in the combiner circuit. This integration, however, introduces new design considerations, particu- larly the role of mutual coupling between antenna elements in array configurations, which typically is an undesired effect, due to its distortion of radiation patterns and degradation of beamforming accuracy [8]. 1.2 Purpose This project explores a potential advantage of the inherent coupling between antenna array elements. Specifically, it investigates the use of a two-element antenna array as both a radiator and a power combiner in an outphasing architecture. In this configuration, the coupling between the elements may be exploited to achieve load modulation in free space, potentially improving efficiency of outphasing while also eliminating resistive losses associated with conventional circuit-combiners. 1.3 Problem To fulfill the purpose, there were several problems that needed to be assessed. The main problems that are addressed in this project are the following: • How can an active load-pull measurement setup be constructed and calibrated with the use of an FPGA board? • By measuring the PAs with the load-pull setup, how does the Power Added Efficiency (PAE) and the output power depend on the load impedance? • Using the results from the load-pull measurements, how should the antenna array be designed regarding input impedance and coupling to enable optimal outphasing performance? • How can an outphasing system with an antenna array as the power combiner be designed to improve efficiency? 1.4 Scope Due mainly to time constraints, the project was subject to a few limitations. Firstly, the designed power combining antenna was only simulated and not manufactured and measured. Therefore, the complete outphasing system performance was not 4 1. Introduction tested with physical measurements, but rather simulated in order to estimate the performance. The patch antenna was the only type of antenna investigated as a combiner for this system. When characterizing the PAs, they were assumed to be identical. Consequently, only one of the amplifiers was characterized. This assumption was made for simplicity when simulating the PA performance during the outphasing simulations. 5 1. Introduction 6 2 Theory In this chapter, relevant theory behind the main parts of the project is presented. This includes theory regarding the linearity and efficiency of power amplifiers, load- pull methods, outphasing, and patch antennas. 2.1 Power Amplifiers In a transmitting RF communication system, the PA is mainly used to amplify the transmission signal to reach a large enough signal strength at the receiver [9]. For this application, two common but conflicting PA design goals are linearity and efficiency. The linearity of a PA can be described as how well the shape of an input waveform is preserved at the output. This is highly dependent on the region in which it operates. A common measurement for the linear operation capability of a PA is the 1 dB compression point [4]. This point indicates at which output power the PA no longer follows a linear relation to the input power. This is illustrated in Fig. 2.1. Figure 2.1: The 1 dB compression point illustrated where the actual output power of the PA diverges from the linear approximation by 1 dB. Linear amplifiers are designed to be driven in the linear region, and the 1 dB com- pression point becomes the output limit for linear amplification. However, the lin- 7 2. Theory earity of a PA is not only dependent on how it is driven with input but also on how it is designed. It is common for the linearity of a PA to be categorized in classes such as class A, AB, B, C, D, and so on, where class A is the most linear but also the least efficient [10]. Fig. 2.2 illustrates how the classes are designed to operate compared to each other. Figure 2.2: Diagram of how different PA classes operate in relation to the transistor cutoff voltage (right). Transistor showing the gate-source voltage VGS, drain-source voltage VDS, and drain current IDS (left). The waveforms shown here are the input signals, where some classes operate with parts of the signal wave in cutoff. The class A amplifier conducts throughout the 360 degrees of the input signal’s wavelength [11]. This is done by applying a constant bias gate voltage to ensure the transistor operates in the linear region for a given input signal. This results in low distortion, but it also ensures that the transistor is always conducting drain current from the DC supply. Therefore, the class A amplifier consumes power even if there is no input signal, resulting in lower efficiency. The class A has a theoretical maximum efficiency of 50 %, but in practice it is typically around 40 to 45 % or lower [12]. Other classes can improve the efficiency by lowering or removing the bias voltage, but this creates problems with distortion and quality of the output signal. 8 2. Theory Class B amplifiers, for example, do not have a bias DC voltage, and the transis- tors only conduct around 180 degrees of the signal wavelength [11]. By using two opposite-type transistors, both the negative and positive half-wavelengths can be amplified and combined at the output. However, this also creates some distortion around the zero voltage point of the output signal. This is due to the cutoff voltage on both transistors that cuts off the input at voltages near zero. The class AB amplifier counteracts this distortion by adding a small bias voltage, which results in a more linear amplifier with slightly lower efficiency than class B. In general, the trade-off when designing a linear amplifier is lower efficiency [10]. The same is true the other way around. The most efficient amplifiers are categorized as switched-mode amplifiers and class D is one of these. Also referred to as class S for RF and microwave frequencies [10]. Here, the transistor is used as a switch, to switch “on” or “off” the output voltage. In class D and S, the switch is used to pulse width modulate (PWM) a desired out- put signal. A low-pass or “reconstruction” filter is placed at the output to smooth out the PWM signal into the modulated waveform. This way the transistors will only conduct current when a signal is being sent. And as seen in Fig. 2.2 when the input is switched “on”, the drain current ID is equal to ID, max while the drain- source voltage is zero. And when the input is switched “off”, ID is equal to zero while VDS = VDS,max = VCC. Then, an ideal switched-mode amplifier would not pull current and voltage from the DC supply at the same time, resulting in no power con- sumption. Therefore, the theoretical efficiency of a perfect switched-mode amplifier is 100 % [4]. In reality, it will be lower due to non-instantaneous switching. De- pending on the application, it can be desirable to use these highly efficient amplifiers despite the nonlinearity. For example, in linear systems that can utilize nonlinear components, such as an outphasing system. 2.2 Digital Modulation In most telecommunication systems, such as 5G, WiFi, and fiber optics, digital data must be transmitted over physical channels. However, these channels are inherently analog. To enable the transmission of digital information, a digital modulation tech- nique is employed to encode the discrete data into a continuous waveform that can propagate effectively through the medium [13]. This is done by producing a so-called carrier signal of a high frequency. The digital data is embedded into this carrier by dividing the signal into discrete elements called symbols. Each symbol corresponds to a specific configuration of the wave’s properties, namely its amplitude, phase, or frequency. Modulating these properties enables the creation of various digital modulation schemes, such as Amplitude Shift Keying (ASK), Frequency Shift Keying (FSK), and Phase Shift Keying (PSK). Among these, a particularly efficient and widely adopted tech- nique is Quadrature Amplitude Modulation (QAM), which combines both amplitude and phase modulation [14]. This hybrid approach allows multiple bits to be trans- mitted per symbol, dramatically improving spectral efficiency and making QAM 9 2. Theory especially valuable in high-data-rate communication systems where bandwidth is limited. Due to the varying amplitudes of the signals, QAM schemes put some key require- ments on the power amplifiers used in these systems. Most importantly, linearity is essential, as the information is encoded into the shape of the signal waveform. Non-linear amplification will distort the shape and, consequently, the transmitted information. Additionally, the power amplifiers need to operate below their peak output power. This condition, known as power back-off, often leads to reduced ef- ficiency [10]. As a result, evaluating efficiency at power back-off becomes a crucial parameter when analyzing the performance of power amplifier systems designed for amplitude-modulated signals. 2.3 Load-pull PA Characterization Load-pull is a method to characterize a nonlinear active device under test (DUT). Characterization in this context can be described as the mapping of DUT parame- ters for a variety of impedances at the ports of the DUT. Often used to characterize RF power amplifiers, the method can be used to model how a PA’s performance changes depending on the impedance at the input or output [7]. This makes it pos- sible to find the impedances that optimize the parameters of a PA, which can then be used to design matching networks for the transistor. Load-pull measurements are performed by measuring the parameters of the PA for many different source and output impedances. However, there are different ways to conduct these measure- ments. Load-pull measurement setups can generally be categorized as either active or pas- sive [15]. This refers to the way of generating impedances at the ports of the DUT, with either active or passive components. But there are also different methods to measure the DUT during load-pull. Two ways of measuring the DUT are referred to as traditional and vector-receiver [16]. A traditional passive load-pull of an ampli- fier is performed with passive impedance tuners at the input and output of the PA, as seen in Fig. 2.3. This method uses power sensors to measure the power at the impedance tuners. The measurements are then de-embedded from the components in the setup to get the power at the input and output of the DUT. The parameters input power Pin and output power Pout are then given from these results. Figure 2.3: Simplified schematic of a power amplifier as the DUT in a traditional passive load-pull setup. 10 2. Theory Figure 2.4: Simplified schematic of a power amplifier as the DUT in a passive vector-receiver load-pull setup. Load-pull can also be performed by measuring the incoming and reflected power waves at the input and output. Measuring power waves in this way is referred to as vector-receiver load-pull, and it relies on low-loss bi-directional couplers connected to the DUT that allow measurements of the a and b waves, as seen in Fig. 2.4 [7], [16]. The variables a and b refer to power waves [17]. These measured waves can then be used to calculate the input impedance of the PA and the load impedance seen by the PA. Using the same notation for the waves as in Fig. 2.4, the input impedance is given by the reflection coefficient Γin Γin = b1 a1 (2.1) and the load impedance is given by the reflection coefficient ΓL ΓL = a2 b2 . (2.2) The corresponding impedance is then given by Z = Z0 1 + Γ 1 − Γ (2.3) where Z0 is the characteristic impedance (50 Ω) and Γ is substituted for the cor- responding reflection coefficient. Parameters of the DUT such as input and output power can also be derived from the measured waves [16]. Input power is Pin = 1 2 ( |a1|2 − |b1|2 ) (2.4) and output power is given by Pout = 1 2 ( |b2|2 − |a2|2 ) . (2.5) To characterize the parameter PAE (Power Added Efficiency), the DC power con- sumed by the PA would also have to be measured during the load-pull. PAE is then given by PAE = Pout − Pin PDC (2.6) where PDC is the consumed DC power. These equations show that the load impedance is only dependent on the a and b waves measured in the setup. This makes it pos- sible to create a load impedance by generating a reflected a2 wave with a signal 11 2. Theory generator, rather than letting the b2 wave reflect off of the passive output tuner, as seen in Fig. 2.4. Generating a load impedance like this is referred to as active load-pull and is illustrated in Fig. 2.5 [15]. Figure 2.5: Simplified schematic of a power amplifier as the DUT in an active vector-receiver load-pull setup. The generated signal a2 in this setup can be specified digitally before being sent by the generator. And since the b2 wave can be determined by the source signal, it is possible to generate any reflection coefficient using (2.2). Thereby generating any load impedance. After load-pull measurements have been conducted, the collected parameter data is often visualized as a contour plot on the Smith chart. Each parameter data point can be associated with the load impedance that was presented to the DUT during the time of measurement. The measured load impedance can then be plotted on the Smith chart, and the value of the arbitrary parameter can be visualized with a contour plot. A fabricated example of such a plot, for an arbitrary DUT parameter, can be seen in Fig. 2.6. (a) Gradient contour with optimal load impedance marked for the parameter. (b) Contour plots of two parameters with maximums marked. Figure 2.6: Synthesized examples of how load-pull contour plots can look for arbitrary parameters 1 and 2 (output power or PAE for example). 12 2. Theory The plots assist in analyzing how the parameters of the PA behave for different loads. The data collected can also be used to approximate the value of a parameter between points by interpolation, which provides an approximate mapping of the PA parameters. Thereby characterizing the PA in the region of the Smith chart where measurements were taken. 2.4 Outphasing When maximizing efficiency in power amplifiers it comes with the drawback of non- linear amplification [10]. This makes them unfit for communication applications as linearity is essential to preserve the information in amplitude-modulated signals. One possible way to work around this is through a technique called outphasing. First introduced in 1935, the outphasing technique aims to utilize nonlinear, highly efficient PAs in linear power amplification systems [4, pp. 303–309], [18]. The aim of this is to improve efficiency and reduce the driving cost of RF power amplifica- tion systems. An outphasing system consists of two similar PAs that are driven in parallel at a fixed power level. The output of the two PAs are then added together through a power combiner to create the desired output signal. A simplified setup is presented in Fig. 2.7 below. Figure 2.7: Block diagram of the outphasing process In principle, the system works as follows: Suppose a phase and amplitude-modulated signal S(t) = A(t) · cos(ωt + ϕ(t)) (2.7) is to be amplified. The idea of outphasing is then to convert the amplitude mod- ulation A(t) into a differential phase shift θ(t) between the two PA branches by creating two signals with constant amplitude S1(t) and S2(t) (also referred to as constant-envelope signals) such that S1(t) + S2(t) = S(t) [18]. This would produce the sub-signals S1(t) = A0 · cos[ωt + ϕ(t) + θ(t)] S2(t) = A0 · cos[ωt + ϕ(t) − θ(t)], (2.8) 13 Erik Ström Erik Ström 2. Theory where A(t) = 2A0 cos(θ(t)) =⇒ θ(t) = cos−1 ( A(t) 2A0 ) . (2.9) This process of decomposing the signal is depicted in the complex vector represen- tation in Fig. 2.8. For simplicity, the phase modulation ϕ(t) is set to zero but can be any value and pass through the system unchanged. Figure 2.8: Complex vector representation of signal decomposition with differential phase shift θ. S1(t) and S2(t) are then amplified separately by the two PAs. As the signals are of constant amplitude, they will be amplified without distortion despite the nonlinear- ity of the amplifiers. Thereafter S1(t) and S2(t) are added together at the output using a power combiner. Assume a perfectly isolated combiner, meaning the two input ports are electrically isolated and all the input power is transferred to the output port, is used. Also, let each PA have a voltage gain of G, the output signal is then theoretically given by Sout(t) = G · S1(t) + G · S2(t) = G · (S1(t) + S2(t)) = G · S(t). (2.10) Thus, linearity is achieved [4, pp. 303–309]. Although this system presents almost perfect linearity and makes use of highly effi- cient PAs some further improvements can be made. When using a perfectly isolated combiner as assumed in Fig. 2.7 the PAs consume the same power regardless of the outphasing angle and system output power. This means a lot of power will be lost at lower system output amplitudes when two branches combine out of phase. To improve the efficiency, a non-isolated combiner is used instead [5], [18]. This intro- duces electrical coupling between the two PA branches resulting in a phenomenon known as load modulation. 2.4.1 Load Modulation Load modulation is an important concept in designing outphasing PAs as it con- tributes significantly to improving the overall system efficiency [4, pp. 303–309]. The 14 2. Theory principle relies on using a non-isolated power combiner that connects the two PA branches such that parts of the signal from the output of PA 1 will be transmitted to the output of PA 2. In other words, the PAs are essentially performing load-pull on each other. As the outphasing angle θ varies, the PAs will be presented with dif- ferent impedances at their outputs, referred to as load impedances. When presented with larger load impedances, the output power of the PAs will decrease, since parts of the output wave reflect back from the load, as described by (2.2), (2.3) and (2.5). This enables amplitude modulation of the combined output signal by varying the load impedance of the PAs, hence the term Load Modulation. An additional benefit of this is that high-efficiency PAs draw less DC supply power at higher loads. To take full advantage of this, the combiner should be designed such that the PAs are presented with higher load impedances as the outphasing angle increases. In this way, amplitude modulation is performed by varying the out- phasing angle and presented load simultaneously, increasing the efficiency at power back-off. An important note is that load modulation introduces non-linearity into the outphasing system. However, with thorough analysis and characterization of the system through measurements, amplitude modulation can still be achieved in a controlled and predictable manner. To achieve the desired load modulation action, the load seen by the PAs as θ varies, ΓPA1(θ) and ΓPA2(θ), can be predicted using the S-parameters of the combiner [6]. Consider a general 3-port circuit-based power combiner as illustrated in Fig. 2.9. Figure 2.9: Schematics of a general 3-port circuit-based power combiner, where the two input ports (ports 1 and 2) combine in the output port (port 3). Here, the outputs of the two PA branches are connected to ports 1 and 2 and the combined output signal is extracted from port 3. S is the 3 × 3 S-parameter matrix of the combiner, where [17] Sij = bi aj ∣∣∣∣∣ ai̸=j=0 i, j ∈ {1, 2, 3}. (2.11) As a power combiner is a passive and reciprocal network, the S-matrix has cer- tain constraints. Firstly, passivity means no power is added to the system by the combiner i.e. ∑ |an|2 ≥ ∑ |bn|2, (2.12) 15 2. Theory which implies that the matrix (I) − (S)H(S) is positive definite. Here, (S)H is the complex conjugate transpose of S, and I is the identity matrix. Furthermore, reciprocity implies that Smn = Snm m, n ∈ {1, 2, 3}. (2.13) Once the S-parameters of the combiner are known, the presented load on each PA can be predicted through a small signal analysis of the combiner [6]. The output waves of the PAs, which become the incident waves to the combiner, a1 and a2, are expressed in a similar matter as in (2.8). With complex representation, the following expressions are obtained a1 = A1e jθ a2 = A2e −jθ. (2.14) Here, θ is the outphasing angle between the two branches, and A1 and A2 are the output amplitudes of each PA. Assuming there is no incident wave at the output port (a3 = 0), the reflected b-waves at the inputs can be calculated according to b1 = S11a1 + S12a2 b2 = S21a1 + S22a2. (2.15) Substituting (2.14) into (2.15) yields b1 = S11A1e jθ + S12A2e −jθ b2 = S22A2e −jθ + S21A1e jθ. (2.16) The reflection coefficient at each input of the combiner, corresponding to the load seen at the output of PA is then calculated as ΓPA1 = b1 a1 = S11 + A2 A1 S12e −j2θ ΓPA2 = b2 a2 = S22 + A1 A2 S21e j2θ, (2.17) which predicts the load modulation action on the PAs with respect to the outphasing angle θ. Going forward in this project, the amplitude A1 and A2 of the two branches are assumed to be equal and denoted as A. Thereby simplifying ΓPA1(θ) and ΓPA2(θ) as ΓPA1(θ) = S11 + S12e −j2θ ΓPA2(θ) = S22 + S21e j2θ. (2.18) From this, it can be observed that when sweeping the outphasing angle θ, the re- flection coefficients ΓPA1 and ΓPA2 will trace out circles on the Smith chart. These circles traject in opposite directions with origins in S11 and S22. The 2θ factor in the exponent indicates that the presented load on the PAs will be periodic with a period of 180◦. The coupling between the ports, S12 and S21 will determine the radius of the circles. As the combiner is a reciprocal network, S12 = S21 as stated in (2.13), thus the circles have equal radii. Going forward, the circles given by (2.18) will be 16 2. Theory referred to as Load Modulation Circles. Furthermore, the output signal b3 can also be predicted using the combiner S- parameters. Again, assuming that a3 = 0 the output is given by b3 = S31a1 + S32a2. (2.19) Expanding a bit and substitutiong the a1 and a2 waves into 2.19 yields b3 = |S31| ej∠S31Aejθ + |S32| ej∠S32Ae−jθ. (2.20) Consequently, the output signal will be dependent on both the phase and the am- plitude of S31 and S32 2.4.2 Combiner Design Optimizing the outphasing system then ultimately comes down to designing a com- biner with S-parameters that results in a desired load modulation action. At high powers, it is hard to predict the behavior of the PAs at different loads. Therefore, load-pull measurements are performed, which are then used to design the desired load modulation circles [6]. The goal of the combiner design is to have the circles intersect at the maximum PAE point at the same outphasing angle θ with output power decreasing as the outphasing angle increases. In addition to this, they should remain in the highest efficiency region possible. It is also desirable to have the same output power from both PAs, therefore the load modulation contours are to be balanced over the axis of output power symmetry. Fig. 2.10 presents an illustrative example of how this can look on the Smith chart for an outphasing system evaluated in [6]. Figure 2.10: Example of load modulation circle placement from [6], Copyright © 2015 IEEE. Reproduced with permission In traditional circuit-based combiners the physical design is based on connecting different lengths of series transmission lines and shunt reactances [18], [19]. The structure can then be tuned until the desired load modulation is achieved, using the small signal analysis from (2.18) to predict the load modulation. 17 2. Theory 2.4.3 Power Combining Antennas The conventional way of using outphasing PAs is to connect them to a circuit-based power combiner as discussed above. The combined signal can then be radiated through an antenna at the output of the combiner [2]. However, using a circuit- based combiner comes with the drawback of resistive losses in the circuit. Instead, if the combining step is integrated into the antenna structure itself, the losses in the combiner circuit could be eliminated. The combining step is then instead performed in free space via superposition of the radiated electromagnetic waveforms. This approach thus has the potential to reduce resistive losses and improve the overall efficiency of the outphasing system. The over-the-air power combining can be achieved by either using a radiator with two input ports [2], [3], or by using two (or more) single-port elements in an array configuration as is depicted in Fig. 2.11 [20]. Figure 2.11: Power combining antenna array configuration where the original signal is reproduced in free space. In this approach, the outputs of each PA branch are transmitted through individ- ual antenna elements and the original phase- and amplitude modulated signal is reproduced via superposition at a certain angle in free-space. 2.5 Patch Antennas In this project, a patch antenna array is used for power combining. The patch antenna is a low-profile narrow-band microstrip antenna. The antenna consists of a finite, very thin metal patch, with the thickness t ≪ λ0 (λ0 being the free- space wavelength), placed above a ground plane with a thin dielectric substrate εr, with the height h ≪ λ0, separating the ground plane and the patch. In contrast to microstrip lines, the patch antenna benefits from a larger substrate thickness and lower dielectric constant since fringing fields are necessary for the patch to radiate [21]. Fig. 2.12 illustrates the dimensions of a patch antenna. 18 2. Theory Figure 2.12: Schematic of a patch antenna, showing both a top-down view (left) and a cross-section (right). The patch antenna becomes resonant when the length of the patch is approximately half the wavelength inside the substrate. The fringing fields will extend beyond the patch resulting in the electric length of the antenna being larger than the physi- cal length. Therefore, the physical length is slightly shorter than half the wave- length [22]. To get an approximate value of the length, the following formula can be used L ≈ 0.49 λ0√ εr . (2.21) More precise formulas are available in both [21], [22] but are not necessary since the length has to be tweaked to find the optimal performance for the project anyway. Therefore,(2.21) provides a sufficient initial length The width is usually chosen to increase the bandwidth and simultaneously yield sufficient radiation efficiency. Usually, a trade-off has to be made between these two parameters. Furthermore, it will affect the dominant mode of the patch [22]. As an initial value for the width, the following equation is used W = λ0 2 √ 2 εr + 1 . (2.22) There are different methods to feed the patch antenna. The aperture-coupled feed has the benefit of enabling different thicknesses as well as dielectric constants of the dielectrics for the microstrip line and the patch antenna. The fringing fields for the microstrip lines can therefore be held small whilst being large for the antenna. Another common method to feed the patch antenna is a microstrip edge feed with an inset to the point yielding the necessary input impedance for matching to the wanted S11 coefficients [22]. 2.5.1 Microstrip Line Regardless of the matching method, a microstrip line has to be used. The microstrip line must be designed for a specified characteristic impedance Z0. The design for- 19 2. Theory mulas for the microstrip lines are the following [17] Wmicrostrip h =  8eA e2A−2 , for Wmicrostrip/h < 2 2 π { B − 1 − ln (2B − 1) + εr−1 2εr } ( ln(B − 1) + 0.39 − 0.61 εr ) , for Wmicrostrip/h > 2 (2.23) where A = Z0 60 √ εr + 1 2 + εr − 1 εr + 1 ( 0.23 + 0.11 εr ) (2.24) and B = 377π 2Z0 √ εr . (2.25) The characteristic impedance can be analytically verified using Z0 =  60√ εe ln ( 8h Wmicrostrip + Wmicrostrip 4h ) , for Wmicrostrip/h ≤ 1 120π√ εe[Wmicrostrip/h+1.393+0.667 ln (Wmicrostrip/h+1.444)] , for Wmicrostrip/h > 1 (2.26) where the effective dielectric constant is found by εe = εr + 1 2 + εr − 1 2 1√ 1 + 12h/Wmicrostrip . (2.27) The length of the microstrip line will affect the phase of the wave and therefore the phase of the reflection coefficients. 2.5.2 Antenna Array The antennas can be placed adjacent to one another with a distance dx between the elements. Since the antennas are in the reactive near-field, the antennas will be coupled which affects the input impedance. By changing the distance between the elements the coupling coefficients Sij (where i ̸= j) will change. Due to the distance dx between the elements, a small phase shift will occur between the two transmitted signals. This is due to the traveling distances of the signals not necessarily being the same due to the spatial difference; for a receiver placed between the two elements in broadside, the distance will be identical and no phase shift will occur [22]. 2.5.3 Impedance Matching The antennas should operate in the optimal region found from the load-pull. This is achieved by matching the S-parameters to the desired values. By changing the inset of the feed on the patch antenna, the input impedance can be slightly altered. If the necessary reflection coefficients for the port cannot be realized by only changing the inset feed, a matching network has to be designed. The simplest method of matching is using an L-network. This is done by connecting an inductance in series and a capacitance in parallel (or vice-versa) with the load. The matching network 20 2. Theory also has to match the phase for the coupling coefficients which could complicate the matching of the reflection coefficients and alter the magnitude of the coupling. The necessary values for these can be found manually using the Smith chart or by simulations. Thereafter, the corresponding microstrip line can be calculated using Richard’s Transformation [17]. 2.5.4 Gain and Friis’ Equation The gain of an antenna is a measure that takes into account both the directional characteristics and the efficiency of an antenna. It is defined as the ratio of the radiation intensity for the antenna in a given direction to the isotropic power inten- sity [21]. The relative gain is calculated by GIEEE(θ, φ) = 4πU(θ, φ) Pin (2.28) where U(θ, φ) is the radiation intensity and Pin is the accepted input power. Com- monly when the direction is not stated, the gain is taken for the maximum radiation point [21]. However, in this project, it will be taken as the gain in the broadside direction. The IEEE gain does not include reflection losses or polarization losses. When two antennas are placed in direct Line-Of-Sight at a distance in the farfield region, the electromagnetic waves transmitted from an antenna are approximately a plane wave [21], [22]. The Friis Transmission Equation is used to find the received power from the transmitted power, for antennas in the farfield [21], and is found by Pr = ( λ 4πR )2 GtGrPin. (2.29) For an isotropic radiator, the gain is unity; approximating the receiver as an isotropic radiator then results in Gr = 1. If the distance between the antennas is fixed and only one frequency is considered, the received power is proportional to Pr ∝ GtPin. (2.30) This proportionality can be used to investigate the shape, and the relative value, of the received power for different outphasing angles. 21 2. Theory 22 3 Methods This chapter presents the methods used throughout the project. The methods be- hind the load-pull measurements, analytical calculations of combiner S-parameters, antenna design, and outphasing simulations are described here. 3.1 Load-Pull Setup To design a suitable antenna combiner for the two QPA9501 power amplifiers, they were characterized using an active vector-receiver load-pull setup. This is to deter- mine what S-parameters the antenna combiner should present to the amplifiers for best performance in the outphasing system. The PAs were characterized for the parameters output power and PAE. The ZCU216 RFSoC FPGA board was used to generate and measure the signals in the setup. For this, the board’s digital- to-analog converters (DACs) and analog-to-digital converters (ADCs) were used. Fig. 3.1 shows a labeled picture of the setup in the lab and Fig. 3.2 shows the schematic of the setup. Figure 3.1: Picture of the load-pull setup in the lab with labeled components and instruments. 23 3. Methods Figure 3.2: The load-pull setup schematic, illustrating the uncalibrated measured waves denoted with sub-index m which correspond to the incoming and reflected waves at the ports of the DUT. The components used in the setup were filters, pre-amps, low-loss bi-directional cou- plers, and attenuators. The purpose of the filters, at the output of DAC 0 and 1, was to filter out harmonics from the DACs before reaching the pre-amps. The pre-amps then amplified the DAC signal to an appropriate power level of approximately 3.9 dBm for the input of the PAs. The output power of PA 2 was then reduced by 3 dB with the 3 dB attenuator before reaching PA 1. This was done to constrain the a2 wave to always be lower in amplitude than the b2 wave. Thereby constraining the load reflection coefficient to be lower than one. This was a safety precaution for the PAs since shorting the PAs could be damaging to them. Attenuators and filters were also used at ADC 2 and 3 to remove harmonics and reduce the large power levels generated by the PAs, avoiding damage to the ADCs. Finally, as this was a vector-receiver setup, it relied on the couplers at the input and output of the DUT to measure incoming and reflected waves separately. MATLAB was then used to conduct these measurements. The board was controlled from MATLAB in order to control the signals from the DACs and save the measurements from the ADCs. The DC power consumption of the DUT was measured with an INA260 power sensor connected to an Arduino Uno. The DC measurements were then sent to MATLAB by the Arduino. In order to test the DUT for multiple load impedances, a script was written in MATLAB to generate different reflection coefficients. 24 3. Methods 3.1.1 Generating Impedances And Measuring DUT The load impedance seen by the DUT was generated by fixing the input a1 wave and changing the generated reflected a2 wave. Then, by measuring the a2 and b2 waves, the reflection coefficient ΓL is given by (2.2). The load impedance presented to the DUT could then be specified by changing the DAC 0 signal relative to the DAC 1 signal in Fig. 3.2. To specify which impedances would be measured, a function was created to place a circle inside the Smith chart with a given radius and center. The function then placed evenly spaced points inside the circle, which corresponded to the impedances that would be generated. The points were then converted from Cartesian coordi- nates to amplitudes and phases, which then could be sent by DAC 0. This way, a chosen region of the Smith chart could be measured with a specified number of points. Each data point corresponded to a load impedance, and the saved data for a point were the measured waves a1m, b1m, a2m, b2m and the consumed DC power. Calibration was then applied to this data before calculating the parameters output power and PAE. 3.1.2 Calibration Before load-pull measurements were performed, the two ports of the setup were cali- brated using an 8-term Short Open Load Through (SOLT) calibration, as presented in [23]. This method uses known short, open, load, and a standard through connec- tion to conduct seven measurements, providing an 8-term error model for relative calibration. Later, a power sweep was performed to calibrate the absolute power measurements of the setup. Firstly, the four calibration standards were measured with a calibrated Vector Net- work Analyzer (VNA). These measurements gave known values for the reflection coefficients of the short, open, and load standards, denoted as, ΓShort, ΓOpen ΓLoad as well as the full 2 × 2 S-parameter matrix of the thru standard, Sij,through. The calibration of the load pull setup was then performed by first conducting a one-port Short Open Load (SOL) calibration on both ports separately, followed by a through calibration between the two ports. The SOL calibration was done by first connecting the short to the first port, then sending a wave through that port and measuring the incoming and reflected wave with the ADCs. The uncalibrated measured reflection coefficient ΓmShort was then calculated for the short. The subscript mS indicates that the reflection coefficient is an uncalibrated measurement of the short calibration standard. The same process was done for the open and load, giving ΓmOpen and ΓmLoad. Then, the error terms for the first port, β′ 1, γ′ 1 and δ′ 1, were calculated as follows  β′ 1 γ′ 1 δ′ 1  =  −ΓmShort · ΓShort 1 ΓmShort −ΓmOpen · ΓOpen 1 ΓmOpen −ΓmLoad · ΓLoad 1 ΓmLoad  −1  ΓShort ΓOpen ΓLoad  . (3.1) 25 3. Methods The same process was then repeated for the second port, giving the error terms β′ 2, γ′ 2 and δ′ 2. The SOL calibration of the two ports gives six of the eight error terms needed for the full two-port calibration in [23]. The completely calibrated waves, ai and bi for port i are given by[ ai bi ] = αi · [ 1 β′ i γ′ i δ′ i ] [ ai m bi m ] (3.2) where i can be substituted for 1 or 2, and αi represents the last two error terms in the calibration. But by using only the six error terms, the waves can be partially calibrated using [ āi b̄i ] = [ 1 β′ i γ′ i δ′ i ] [ ai m bi m ] (3.3) where āi and b̄i are the partially calibrated waves. These are related to the fully calibrated waves with { ai = αiāi bi = αib̄i. (3.4) Then to calibrate the ports in relation to each other, the two ports were connected with the through standard. A signal was then sent from port 1, and all waves (a1m, b1m, a2m and b2m) were measured. The partially calibrated waves (ā1, b̄1, ā2 and b̄2) were then calculated from these measurements using (3.3). The error term α2 could then be calculated with α2 = (b̄2 − S22,throughā2)−1ā1S21,through (3.5) where S22,through and S21,through are the S-parameters of the through connector ac- quired from the VNA measurements. Since the calibration was a relative calibration, the error term α1 = 1. To calibrate power measurements with the setup, a power sweep was performed. The power at port 1 was measured with a R&S NRP332N power sensor, for several different amplitudes sent by port 1. The difference in power, between the SOLT calibration of the waves and the power meter measurements, was assumed to be linear. Following this, the relation was modeled as a single coefficient that scaled the power measurements by the setup. By measuring the power with both the setup and the power meter at the same time, the constant coefficient ρ was calculated by dividing the two measurements. This constant was then applied when calculating the input power and output power. 3.1.3 Parameter Calculations After the raw measured waves had been calibrated, they were used in the equations presented in Section 2.3. For every measured point, the load reflection coefficient was calculated with (2.2). When the input and output power were calculated, the constant power-calibration-coefficient ρ was multiplied to (2.4) and (2.5), which gives 26 3. Methods Pin = 1 2 ( |a1|2 − |b1|2 ) ρ (3.6) and Pout = 1 2 ( |b2|2 − |a2|2 ) ρ. (3.7) The Pin and Pout from these equations were then used in (2.6) to calculate PAE, where PDC is the measured DC power for the data point. The calculated parame- ters for all reflection coefficients were then saved in MATLAB to be visualized as contour plots in the Smith chart. These plots were then used to decide how the load modulation circles should be placed, and in turn, determine the desired 2-port S-parameters of the antenna combiner. 3.1.4 Measurement Region Adjustments After a load-pull measurement, it was observed that the measurement region in the Smith chart had been shifted in some direction from the region specified in the MAT- LAB script. It was theorized that this was caused by constructive and destructive interference between the outputs of PA 1 and PA 2. Considering that the b2 reflects at the PA 2 output, the b2 reflection then adds to the a2 wave when traveling back to the PA 1 output. This addition of the waves, going in the a2 direction, would then interfere constructively or destructively depending on the phase difference between them. This phase difference was determined by the phase difference between a2 and b2, but also the travel length between the outputs of PA 1 and PA 2. Depending on the type of interference, the total reflected wave seen by the DUT could either be larger or smaller. Causing the measured load reflection coefficient ΓL to be larger or smaller in amplitude based on the phase of ΓL. This could cause the measured region to shift in the direction of a certain phase in the Smith chart. By controlling the phase at which constructive/destructive interference occurs, the measured region of the Smith chart could be rotated into a region of interest. This was done by adding a through connection at the output of PA 2 in order to change the travel length between the PAs, and thereby change the phase that shifts the measured region. Different lengths of this through were tested to find a desirable region which could be used for outphasing. 3.2 Analytical Combiner S-parameter Calculations The approach for designing the power combining antenna was to first perform analyt- ical calculations based on the load-pull data to determine the combiner S-parameters that yield the desired load modulation behavior for maximized efficiency. There- after the antenna combiner was designed in CST with the aim to match these S- parameters. The design was based on the load-pull results for a fixed high input power, at which the system is intended to operate. The objective was to meet the design goals outlined in Section 2.4.2; however, other designs were also evaluated to validate the chosen approach. 27 3. Methods To calculate the S-parameters of the combiner based on a given placement of the load modulation circles, the following approach was used: Let S1 and S2 represent the complex impedance points on the Smith chart where the load modulation cir- cles intersect. For both points, the outphasing angle θ must be identical to ensure consistent phase alignment. Specifically, S1 corresponds to the point of maximum PAE, achieved at a low outphasing angle θ0, while S2 corresponds to lower output power at a higher outphasing angle θ1. Using (2.18), these conditions are translated into the following system of equations S11 + S12e −2jθ0 = S1 S22 + S21e j2θ0 = S1 S11 + S12e −j2θ1 = S2 S22 + S21e j2θ1 = S2. (3.8) Then, let θ1 = θ0 + ∆θ, where ∆θ is a parameter that needs to be optimized. Additionally, using the fact that the combiner is reciprocal, meaning S12 = S21, and substituting into (3.8) results in S11 + S12e −j2θ0 = S1 S22 + S12e j2θ0 = S1 S11 + S12e −j2(θ0+∆θ) = S2 S22 + S12e j2(θ0+∆θ) = S2. (3.9) Subtracting the first equation in (3.9) with the third and the second equation with the fourth yields S12 ( ej2θ0 − ej2(θ0+∆θ) ) = S1 − S2 S12 ( e−j2θ0 − e−j2(θ0+∆θ) ) = S1 − S2. (3.10) Dividing these two equations gives S12 ( ej2θ0 − ej2(θ0+∆θ) ) S12 (e−j2θ0 − e−j2(θ0+∆θ)) = ej2θ0 − ej2(θ0+∆θ) e−j2θ0 − e−j2(θ0+∆θ) = 1, which implies ej2θ0 − e−j2θ0 = ej2(θ0+∆θ) − e−j2(θ0+∆θ). (3.11) Recall the trigonometric identity sin(θ) = ejθ − e−jθ j2 , thus, (3.11) can be written in terms of sine-functions sin (2θ0) = sin (2(θ0 + ∆θ)). (3.12) Solving for θ0 given that 0 < 2θ0 < 2π results in 2 cases, firstly 2θ0 = 2(θ0 + ∆θ), (3.13) 28 3. Methods which has no non-trivial solutions, and secondly 2θ0 = π − 2(θ0 + ∆θ) =⇒ θ0 = π − 2∆θ 4 . (3.14) Substituting the resulting θ0 into (3.10) and solving for S12 gives S12 = S1 − S2 e−j2θ0 − e−j2(θ0+∆θ) . (3.15) Then, substitution (3.15) into the original expressions in (3.8) and solving for S11 and S22 yields the resulting S-parameters S11 = S1 − S12e j2θ0 S22 = S1 − S12e −2jθ0 S12 = S1 − S2 e−j2θ0 − e−j2(θ0+∆θ) S21 = S12. (3.16) By carefully choosing the phase difference ∆θ and the optimal points {S1, S2} for the PAs resulting in the highest efficiency; the S-parameters for the power combiner’s two input ports are found using (3.14) and substituting into (3.16). These equations give the desired load modulation circles, however, the output signal is also dependent on how the input waves combine in the third port. The output is given by (2.19). From this, it can be seen that the phase of S32 and S31 determines when maximum outphasing action occurs. This is when the two terms add up in phase a1 · S31 = a2 · S32 =⇒ θ + S31 = −θ + S32. (3.17) Ideally, this should occur at the maximum PAE point where the two circles intersect, i.e where θ = θ0; θ0 + S31 = −θ0 + S32 =⇒ S32 − S31 = 2θ0. (3.18) This gives maximum efficiency at the maximum output power as seen in Fig. 2.10, maximizing the system efficiency. To evaluate the outphasing performance using the calculated S-parameters, sim- ulations based on the load-pull data were conducted in MATLAB. By varying the phase difference ∆θ and testing different intersection points S1, S2, the relative per- formance of each configuration was analyzed. This enabled the identification of the optimal load modulation circle placement. Details of the simulation process are provided in Section 3.4. After determining the optimal S-parameters for the combiner, the objective was to design an antenna that matches the S-parameters defined in (3.16) and ideally also produces an output that satisfies the phase condition given in (3.18). Achiev- ing an exact match for all these criteria may not be entirely feasible, so the design process involves finding the best possible compromise with the proposed antenna structure. As such, certain trade-offs may be necessary to balance performance and practical implementation. 29 3. Methods 3.3 Antenna Design Before trying specific designs, a patch antenna with a center frequency of 5.4 GHz was designed. Firstly, the thickness t of the metal sheet, the height h of the substrate, and the dielectric material εr were chosen based on the PCBs that were available for manufacturing on Eurocircuits. Thereafter, the wavelength in free space was calculated using λ0 = c0/f and then the dimensions L and W of the patch were retrieved using (2.21) and (2.22). Fig. 3.3 shows the dimensions of the patch antenna. The parameters denoted with subindex i refer to antenna element i (1 or 2). This notation also applies to Fig 3.4 and Fig 3.5. Figure 3.3: The antenna design schematic showing the dimension parameters for patch element i. Using the parameters L, W , h, t and εr, the patch antenna was modeled and sim- ulated in CST. Before defining any ports, the Eigenvalue Solver was used to verify that a resonance peak was present at 5.4 GHz; the length L of the patch had to be slightly altered to place the resonance peak at the center frequency. Thereafter, the Time Domain Solver was used to simulate the antenna by first placing a single discrete port on the symmetrical axis from the ground plane to the patch with a distance xi from the center. Furthermore, the parameter xi was swept from the edge to the center of the patch. The point corresponding to the lowest S11 value was taken as the inset point. The width of the microstrip lines Wmicrostrip was calculated using (2.23)–(2.25) and the characteristic impedance Z0 was verified analytically using (2.26) and (2.27). The microstrip line was also verified by simulating in CST for an arbitrary length Lmicrostrip,i. The waveguide ports were constructed using the Calculate port exten- sion coefficient macro and then the characteristic impedance of the port could be verified from the port information. After verifying the feed lines, the microstrip line was connected to the patch. The inset was designed by removing a thin strip of the metal patch next to the feed point where the microstrip line was connected. 30 3. Methods Thereafter, the optimizer was run for the inset point xi to minimize the reflection coefficient S11 at 5.4 GHz to match the port to 50 Ω. The final design consisted of an antenna array with two elements. The two ele- ments were placed on the same PCB with a center-to-center distance dx between the elements. As mentioned in Section 2.5.2 this will affect the input impedance. Since the design of a single element is, in isolation, matched and resonant at 5.4 GHz, the optimizer can quickly be used on multiple parameters simultaneously. There- after, the optimizer was run for the parameters {L, W, x1, x2, dx} with the goal to minimize S11 and S22 and to match the magnitude of the S12-parameter to the |S12| from the load-pull measurements. 3.3.1 Matching Network A matching network was designed to match the S-parameters of the antenna to the S-parameters retrieved from the load-pull measurements. This was using an L-network containing an inductance L in series and a parallel conductance C with the antenna port. The values of these were found using the optimizer in CST for schematic simulations. The reference plane was set to the edge of the patch and transmission lines were added to the antenna ports to match the phase of the S12 parameters. Thereafter, the L-network, shown in Fig 3.4, was placed at the antenna ports. Figure 3.4: Schematic of the lumped components matching network for antenna element i. To achieve the inductances and capacitances required for the matching, microstrip lines were used. The dimensions of these were found by setting a fixed width, WC and WL, of the microstrip lines for the capacitances and the inductances. Then by letting the optimizer find the length corresponding to the wanted impedances, lCi and lLi were found. The microstrip line for the capacitances was connected as open- circuit stubs, and the microstrip lines for the inductances were added in series; a simple T-junction was used to connect the three transmission lines. A layout of the microstrip line matching network for one antenna element is illustrated in Fig. 3.5. 31 3. Methods Figure 3.5: Schematic of the microstrip line matching network for antenna element i. 3.3.2 Exploratory Designs Different patch antenna designs were modeled and simulated in CST. Firstly, the antenna proposed in [1] was modeled in CST in order to try to recreate the simula- tion results. Since this antenna only used one antenna with two feed lines and also used aperture-coupled feeds, the design could be flexible. If the simulation results could be recreated, then the antenna would be used for the wanted performance derived from the load-pull measurements. Another design that was attempted was a single patch antenna with orthogonally polarized inset feed lines. This consisted of designing a patch as described above. The inset points were found by optimizing both the offset from the symmetrical axis {y0, x1} and the offset from the center toward the edge {x0, y1}. The optimization goals were min |S11| and min |S22| at the frequency 5.4 GHz. Thereafter, the mi- crostrip lines were connected with an inset at these points. Finally, an attempt to match this to 50 Ω was made using the optimizer. Further discussion regarding the exploratory designs can be found in Appendix A.1. 3.4 Outphasing Simulations To evaluate the performance of the outphasing system, simulations based on the load-pull results and antenna designs were performed in MATLAB and CST. The simulations were carried out in two stages. Firstly, as mentioned at the end of Sec- tion 3.2 they were used to help determine the optimal selection of the analytically calculated S-parameters. Secondly, the simulations were repeated using the realized antenna design models in CST, evaluating the practical performance of the system. Since the load-pull results consisted of discrete data points, interpolation was re- quired to enable continuous analysis over the Smith chart. The interpolation was performed using the MATLAB griddata function, giving a piecewise linear approx- imation of the measured parameter values across the entire measured region on the Smith chart. 32 3. Methods Using the 2-port S-parameters of the combiner inputs, the load modulation circles, ΓPA1 and ΓPA2 were predicted using (2.18) as described in Section 2.4.1. By sweeping the outphasing angle, parameter values were extracted from the interpolated data along the circles. This data was then used to analyze the system’s output power Pout,tot, and total PAE as a function of the outphasing angle. The PAE was also evaluated as a function of power back-off levels to assess the outphasing system’s efficiency in scenarios involving amplitude modulation, such as in QAM systems. To evaluate the output of the system, the magnitude of the input waves to the combiner at each outphasing angle was obtained from the interpolated load-pull data. It is important to note that this magnitude is not equivalent to √ 2 · Pout,PA, as that expression includes both the forward and reflected components from the load, see (2.5). Instead, the magnitude of the measured output wave from the PAs (denoted as the b2 wave in Fig. 3.2) was used for each predicted load impedance. Applying the differential outphasing angle θ as in (2.14), the inputs to the combiner were given by a1,comb = |b2,PA1(θ)| · ejθ, a2,comb = |b2,PA2(θ)| · e−jθ. (3.19) Power back-off is given in dB and defined as PBack-off,dB(θ) = 10 · log10 ( Pout,tot(θ) max (Pout,tot(θ)) ) . (3.20) The total power-added efficiency for the outphasing system is computed as PAEtot(θ) = Pout,tot(θ) − 2Pin,PA PDC1(θ) + PDC2(θ) . (3.21) Here, both the input RF power and DC power consumption of the two amplifier branches are included. Determining the output power level and thus total PAE of the system when using an antenna as a combiner is however not straightforward. Since power combining oc- curs in free space, the received power decreases with distance from the transmitters, following Friis’ equation (2.29). As a result, the measured output power depends on the position of the receiving antenna. To account for this, the system was evaluated using normalized output power and PAE levels, which provide a relative measure of how the output power and efficiency vary with the outphasing angle, independent of distance. 3.4.1 Analytical S-parameter Simulations To evaluate the system performance using the calculated S-parameters from Sec- tion 3.2 the relative output power was evaluated using approximations of the S31 and S32 parameters. Different configurations of ∆θ, S1 and S2 were tested, along with different phase differences between S32 and S31. These configurations were com- pared against each other and a fully isolated reference case matched to the maximum 33 3. Methods PAE point from the load-pull. In the fully isolated case, there exists no coupling between the two ports (S21 and S12 = 0) and thus no load modulation action occurs. As only relative power levels were considered, the magnitudes of S31 and S32 were set to arbitrary but equal values across all configurations, ensuring a fair comparison of the relative performance. The output b3 wave was then calculated using (2.19). The combined output power Pout,tot was calculated using the same approach as in (2.5), but since there is no incident wave at the output port (a3 = 0), it simplifies to Pout,tot = |b3|2 2 . (3.22) This was then normalized to the highest output power across all evaluated cases. Finally, the relative efficiency at different power back-off levels was assessed using (3.20) and (3.21). The configuration that yielded the highest overall and back-off efficiency was selected as the target S-parameters for the power combining antenna. 3.4.2 Antenna Combiner Simulations The outphasing simulations for the realized antenna designs were conducted in CST using the Schematic simulator. Using the a-coefficients as stated in (3.19) as the excitation coefficients for the two ports, the different outphasing angles could be simulated. The coefficients corresponding to an outphasing angle of 0 to 180◦ with a step size of 15◦ were used for both the lumped component matching network as well as the microstrip line matching network. The accepted input power was then calculated by Pin,ant = 1 2 [ aHa − (Sa)H(Sa) ] (3.23) where a is the 2 × 1 vector of the excitation coefficients and S is the 2 × 2 matrix for the simulated scattering parameters of the antenna with the matching network. The IEEE gain was retrieved from the CST simulation of the system for the different excitations by taking the broadside point in the linear scale for the φ-component. Using (2.30) the non-normalized proportionality of the received power in broadside was calculated. The received power values were then normalized by the maximum output power across both combiner designs. Thereafter, the relative efficiency at different power back-off levels was evaluated using (3.20) and (3.21), enabling a direct comparison of the designs’ performance, both in regards to total output power and efficiency at different back-off levels. 34 4 Results This chapter presents both the intermediate results used in the design of the out- phasing system and the simulation results evaluating its performance. The results from load-pull measurements, combiner S-parameter calculations, antenna design, and outphasing simulations are included here. 4.1 Load-Pull The characteristics of the PA parameters PAE and Pout are presented in Fig. 4.1. The plots indicate which load impedance yields the maximum value for each parameter and how they vary in the measured region of the Smith chart. (a) PAE [%] contour plot with maximum marked. (b) Pout [dBm] contour plot with maxi- mum marked. Figure 4.1: Load-pull results illustrating how the parameters PAE and Pout change depending on the load impedance presented to the PA, with an average input power of 3.93 dBm. These plots were used to determine the optimal placement of the load modulation circles for the PAs in outphasing. 35 4. Results 4.2 Optimal Combiner S-parameters This section presents the selection of the combiner S-parameters to which the an- tenna is matched. Based on the initial antenna design, it was observed that a maximum coupling of approximately −11 dB could be achieved. Consequently, the magnitudes of S12 and S21 were constrained to this value when determining the op- timal parameters. To determine the optimal parameters, the following cases were evaluated through the MATLAB simulations: 1. Circle placement along the symmetry line, as described in Section 2.4.2, with the phases of S31 and S32 set to 0◦. 2. Circle placement along the symmetry line, with the phases of S31 and S32 chosen according to (3.18). 3. Circle placement not centered on the symmetry line, with the phases of S31 and S32 set to 0◦. 4. A fully isolated reference case, matched to the maximum PAE point of the amplifiers. In this case, S21 = S12 = 0, resulting in no load modulation circles. Fig. 4.2 shows the different placement of the circles along with the load-pull data and an approximate line of output power symmetry. (a) Circle placement over the line of out- put power symmetry, case 1 and 2. (b) Off-symmetry placement of load mod- ulation circles, case 3. Figure 4.2: Analytical outphasing load modulation circles overlaid on PAE and Pout contours. The figure illustrates the placement of the circles relative to the PA characteristics. The dots mark the point corresponding to θ = 0◦, and as θ increases, the load impedances trace the circles in the direction of the arrows. The normalized power added efficiency for the four cases is plotted against the power back-off level in Fig. 4.3 below. 36 4. Results Figure 4.3: Normalized Power added efficiency vs. back-off power level for the 4 different picks of S-parameters where 0◦ < θ < 90◦. From this, it can be concluded that the circle fit in Fig. 4.2a with phase of S31 and S32 according to (3.18) results in the best efficiency at back-off. Therefore, this configuration was chosen for the final design. The resulting S-parameters for this circle placement are displayed in Table 4.1. Table 4.1: S-parameters for the selected combiner design in rectangular and polar form. Parameter Rectangular Form Polar Form S11 0.1131 + j0.3288 0.35 71.02◦ S12 0.1485 − j0.2298 0.27 −57.12◦ S21 0.1485 − j0.2298 0.27 −57.12◦ S22 −0.0319 + j0.2350 0.24 97.74◦ The corresponding θ0, from these S-parameters, where in-phase outphasing should occur is θ0 = 9.2◦. As a result, these S-parameters, along with the corresponding phase conditions for S31 and S32 as defined in (3.18) S32 − S31 = 2θ0 = 18.4◦ (4.1) were used as the target when designing the antenna. 4.3 Antenna Design The antenna elements, shown in Fig. 3.3, have the dimensions as presented in Ta- ble 4.2, where the dimensions Wmicrostrip, Lmicrostrip,1 and Lmicrostrip,2 of the microstrip feed were found after optimizing the lumped component matching network. The el- ements were placed with a distance of dx = 21.36 mm between the center of the two 37 4. Results ports. Furthermore, the patch antenna array was placed over a ground plate with the dimensions 62.954 × 41.592 mm2. Table 4.2: Dimensions for the patch antenna elements without matching network. Parameter Value [mm] L 13.842 W 16.218 Wnotch 0.570 Wmicrostrip 1.139 Lmicrostrip,1 1.670 Lmicrostrip,2 4.364 x1 1.597 x2 0.000 t 0.018 h 0.508 The S-parameters for the antenna array before connecting the matching network and the co-polar embedded element pattern for port 1 are shown in Fig. 4.4. The radiation pattern for the second element is anti-symmetrical to the first element pattern. 38 4. Results (a) S-parameters over frequency for the two-element antenna array without matching network. (b) Co-polar radiation pat- tern of the antenna without matching network. Figure 4.4: S-parameters and co-polar embedded element pattern for the antenna array without matching networks for the ports. As seen, the antenna ports are well matched to 50 Ω, reflection coefficients below -20 dB, and the coupling coefficients are approximately -11.4287 dB at 5.4 GHz. 4.3.1 Lumped Component Matching Network As described in Section 3.3.1 the matching network was first designed using lumped components in an L-network, as shown in Fig. 3.4. Running the optimizer resulted in the inductance L1 and capacitance C1 for port 1, along with L2 and C2 for port 2. These values are presented in Table 4.3. Table 4.3: Values for the lumped component matching networks at ports 1 and 2. Parameter Value L1 1.462 [nH] C1 0.173 [pF] L2 1.328 [nH] C2 0.310 [pF] 39 4. Results The resulting S-parameters are shown in Table 4.4. Table 4.4: S-parameters of the antenna with lumped component matching network in rectangular and polar form. Parameter Rectangular Form Polar Form S11 0.1131 + j0.3287 0.35 71.01◦ S12 0.1369 − j0.2051 0.25 −56.28◦ S21 0.1369 − j0.2051 0.25 −56.28◦ S22 −0.0319 + j0.2350 0.24 97.73◦ Comparing these results with the desired parameters in Table 4.1 it can be concluded that the matching using this approach was rather successful with S11 and S22 being matched almost perfectly, and S12 and S21 deviating by about 9%. 4.3.2 Microstrip Line Matching Network Running the optimizer, for the microstrip matching network shown in Fig. 3.5, gave the dimensions lL1, lC1, lL2 and lC2. Where the transmission line width for the inductance was fixed to WL = 0.1 mm and the width for the capacitance was fixed to WC = 3 mm. The dimension values are presented in Table 4.5. Table 4.5: Dimensions of the microstrip line matching networks at ports 1 and 2. Parameter Value [mm] WL 0.1 WC 3 lL1 0.819 lC1 0.509 lL2 0.873 lC2 1.145 The resulting S-parameters are presented in Table 4.6. Table 4.6: S-parameters of the antenna with microstrip matching network in rect- angular and polar form. Parameter Rectangular Form Polar Form S11 0.0226 + j0.0120 0.03 27.97◦ S12 −0.0395 + j0.2653 0.27 98.47◦ S21 −0.0395 + j0.2653 0.27 98.47◦ S22 0.0235 + j0.0530 0.06 66.09◦ In this case, the matching was less successful. Compared to the desired values in Table 4.1, the acquired S-parameters from the microstrip matching deviate a lot. 40 4. Results This is mainly due to the transmission lines not being able to achieve the impedance without unrealistic widths in the current type of matching network. 4.4 Outphasing Simulations In this section, the results from the outphasing simulations based on the CST an- tenna designs are presented. Firstly, the resulting load modulation on the PAs is evaluated based on the S-parameters of the two designed antenna combiners. There- after, radiation patterns and the antenna gain at broadside for different outphasing angles are presented. Finally, the overall power output and efficiency of the system are evaluated. 4.4.1 Resulting Load Modulation on the PAs The corresponding load modulation circles for the antenna with the lumped com- ponent matching network and the microstrip line matching network are shown in Fig. 4.5. Quite a large discrepancy can be seen between the two cases due to the microstrip line matching network not being able to achieve the wanted S-parameters with the current design of the matching network. (a) Resulting load modulation circles of the lumped component matching antenna (b) Resulting load modulation circles of the microstrip matching antenna Figure 4.5: Predicted load modulation circles for the different antenna feeding configurations compared against the target design. The dots indicate the point of maximum system output power. As θ increases, the load on the PAs traject along the circles in the direction of the arrows. The maximum system output power is achieved at θ = 165◦ ±180 ·n for the lumped component antenna and at θ = 135◦ ± 180 · n (n ∈ N) for the microstrip antenna (note that the output power is periodic with a period of 180◦). The resulting output waves from the PAs along the predicted load modulation circles in Fig. 4.5 are plotted as a function of the outphasing angle in Fig. 4.6 below. From this data, values were sampled at 15◦ intervals and used as the excitation signals for 41 4. Results the antenna in CST, following the formulation in (3.19). The specific values used for exciting the antenna ports are provided in Appendix A.2. (a) Magnitude of the output waves the PAs using the lumped component an- tenna (b) Magnitude of the output waves the PAs using the microstrip antenna Figure 4.6: Output waves of the PAs at different outphasing angles which corre- sponds to the magnitude of the input waves of the antenna combiner, |a1,comb| and |a2,comb|. It can be seen that the lumped component antenna satisfies the condition of equal output powers quite well, whereas in the microstrip case, the magnitude of the output waves from the PAs deviates quite a bit from each other. 4.4.2 Radiation Patterns at Outphasing For the antenna array with lumped components matching network, the lowest gain at broadside was achieved for the outphasing angle θ = 75◦ and the highest gain was received at θ = 165◦, the maximum gain is also expected at θ = −15◦ due to the periodicity of outphasing. The radiation patterns at different outphasing angles for the lumped component antenna are presented in Fig. 4.7. 42 4. Results (a) Total radiation pat- tern for the outphasing angle θ = 75◦. (b) Total radiation pattern for the outphasing angle θ = 90◦. (c) Total radiation pattern for the outphasing angle θ = 165◦. Figure 4.7: Total radiation patterns (φ constant) for the antenna with the lumped component matching network for the lowest, intermediate, and maximum gain in broadside. The total radiation patterns, shown in Fig. 4.8, for the microstrip line matching antenna the lowest and highest gain were at θ = 60◦ and θ = 150◦ respectively. The maximum gain is also expected at θ = −30◦ due to symmetry. (a) Total radiation pat- tern for the outphasing angle θ = 60◦. (b) Total radiation pat- tern for the outphasing angle θ = 90◦. (c) Total radiation pattern for the outphasing angle θ = 150◦. Figure 4.8: Total radiation patterns (φ constant) for the antenna with the mi- crostrip line matching network for the lowest, intermediate, and maximum gain in broadside. The difference in the outphasing angles compared to the lumped component case is due to the deviating S-parameters. Consequently, the excitations are different which results in the angles for maximum and minimum gain being shifted by a few degrees. The antenna IEEE gain at broadside for the antennas with the two different matching networks is presented in Fig. 4.9. 43 4. Results Figure 4.9: IEEE Gain of the antennas at broadside as a function of the outphasing angle θ. Due to the low resolution of 15◦, the full notch for the microstrip line matched antenna is not shown in the figure. The gain is expected to reach the same maximum gain value before θ = 0 as well but is not shown in the figure due to only 0 ≤ θ ≤ 180◦ being investigated. 4.4.3 Total Power and PAE The normalized received power, shown in Fig. 4.10, varies periodically in an approx- imate sinusoidal shape. This is due to the beam being steered away from broadside and low power being transmitted in broadside. For larger scan angles, this results in a side lobe which increases in intensity until finally becoming the main beam and then being steered back to broadside. Figure 4.10: Normalized received power at broadside against the outphasing angle θ. The lumped component matching network resulted in a higher received power than the microstrip line case. As shown in the tables in Appendix A.2 the peak power 44 4. Results from the PAs to the inputs of the antennas is lower for the microstrip line case compared to the lumped component case for the angles where the beam is steered to broadside, which is the reason for the lower received power level. Fig. 4.11 shows the total PAE of the system compared to the power back-off level. As seen in Fig. 4.10, the same power level is achieved twice as θ sweeps from 0◦ to 180◦, resulting in a curve that loops back on itself. Figure 4.11: Normalized total PAE versus back-off power level in dB for 0◦ < θ < 180◦. As θ increases, the plots trace the curve in the direction indicated by the arrows. Overall, the efficiency is higher for the better-matched lumped component case com- pared to the microstrip case. Furthermore, it can be observed that the maximum efficiency points appear at the same outphasing angle as the maximum antenna gain. This occurs because, at these angles, the two signals combine in-phase at broadside, and maximum outphasing action is achieved. Consequently, less power is lost in the combining step, resulting in improved overall system efficiency at this angle. As previously discussed, the goal was to achieve this at the maximum PAE point, where θ = θ0 = 9.2◦. However, none of the current antenna designs fully met this criterion, with the lumped component case coming closest, deviating by 24.2◦. 45 4. Results 46 5 Discussion The results from the project, and some of the methods used, are discussed in this chapter. Discussions on the PAs, load-pull setup, antenna design, and outphasing simulations are held here. Suggestions for future work in these areas are presented as well. 5.1 Power Amplifiers The QPA9501 PAs were used to show the potential benefits of using the outphasing technique presented in this project. However, they were not ideal for this purpose. As mentioned previously, the outphasing technique can take advantage of highly efficient nonlinear amplifiers. However the PAs in this project behave pretty lin- early, and only some nonlinear effects were caused by driving them with a large input power. This is because the PAs operate mostly in the linear region as seen in the datasheet, where the 1 dB compression point occurs near the maximum output power of the amplifiers [24]. This could also explain the low efficiency seen in the PAE results in Fig. 4.1a, where the maximum PAE is 29.7 %. To accurately eval- uate the performance potential of outphasing with nonlinear amplifiers, PAs with stronger nonlinearities and higher efficiencies may be more suitable. The amplifiers are designed for 50 Ω, which also can be seen in the plots of Fig. 4.1. This means that they are mismatched during load modulation, which results in a decrease in the efficiency of the system. Ideally, to achieve the maximum efficiency from the amplifiers in an outphasing system, the PAs should be co-designed with the antenna. 5.2 Load-Pull Setup The load-pull setup was constructed only to fulfill the purposes of this project, as presented in Section 3.1. However, there are some potential areas of improvement if measurements need to be conducted with more control and precision when testing a load. One aspect is the influence that the DUT exerts on the setup. During the measurements, PA 2 was not isolated from the output signal of the DUT. This caused PA 2 to be load modulated in the same way as the DUT. Thus, PA 2 was presented with a large load impedance when sending the generated reflected wave. Which in turn altered the output of the PA, similar to how the DUT changes 47 5. Discussion output as seen in Fig. 4.1b. This alteration was not accounted for when picking points on the Smith chart and is different from the shift presented in Section 3.1.4. Therefore, the measured load impedances were slightly different and not as evenly spaced as the ones picked in MATLAB. This relatively small change can be seen in the load-pull results. However, this did not affect the measured characteristics. Isolating PA 2 from the DUT output could improve the precision and control of generating loads. One way to do this could be to add a circulator at the output of PA 2, which would divert the output of the DUT from PA 2 to a termination. This could also fix the shift of the measurement region as presented in Section 3.1.4. 5.3 Antenna Design The antenna array was only modeled to be used for simulations, this was mainly due to exploratory designs not yielding the wanted results and other time constraints. This made it possible to use more precise values for the circuit components and not having to investigate the effect of tolerances in the dimensions. Therefore, the results in connection with the antenna are aimed at proof-of-concept and risk being too ideal. Large discrepancies can be seen between the matching network composed of lumped components and the network consisting of microstrip lines. This can possibly be remedied by utilizing a more sophisticated matching network, such as a multi-stub network or other techniques to construct the required inductances and capacitances instead of the proposed microstrip line matching network. Furthermore, the lumped component network might be hard to realize at this frequency band due to the reso- nance frequency of commercially used components usually being well below 5.4 GHz. The very specific values of the inductance and capacitance required for the matching can generally not be found for commercially available components. In this project, only patch antennas have been analyzed. Other antenna types might be more suited for this type of application. In [3] a half-loop antenna was used for outphasing, but monopoles and dipoles could also be possible; aperture antennas might also be suitable but might result in a physically larger array compared to the other cases. Since the antenna was not manufactured and measured in an anechoic chamber, the non-idealities e.g. the dielectric material and conductors could not be considered. The tolerances for the dimensions of the antenna might also change the resonance frequency. These factors might significantly alter the S-parameters for the antenna as well as add ohmic losses not considered. Furthermore, a receive antenna will be required for measurements. This antenna has its own gain that has to be taken into account and will also introduce re-radiation and further power losses. Furthermore, the matching network might also differ due to the aforementioned tolerances. 48 5. Discussion 5.4 Outphasing Simulations From the results, it can be concluded that using an antenna array as a power com- biner in an outphasing modulator system is possible. However, some improvements could be made to increase its efficiency. Firstly, it can be seen from Fig. 4.11 that better matched S-parameters do result in higher efficiency. Thus, a better match- ing network using microstrip lines needs to be explored for better implementation at higher frequencies. Furthermore, as can be seen in Fig. 4.7 and Fig. 4.8, the outphas- ing angles for maximum and minimum power deviate from the desired angles θ = θ0 and θ = θ0 + 90◦ respectively. A possible solution could be to increase the trans- mission line length Lmicrostrip,1 and decrease the length Lmicrostrip,2 to compensate for the deviation in outphasing angle without radically changing the phase of S21, this should then satisfy (3.18). For the antenna with the lumped component matching network, approximately θ0 + 15◦ has to be compensated. For the antenna with mi- crostrip matching, approximately θ0 + 30◦ has to be compensated. As previously stated, the resolution should be increased to resolve the ambiguity before changing the transmission line length. It is important to verify that the other S-parameters are unaffected by this change in length. Furthermore, a length corresponding to half a wavelength could be added to make room for sockets for physical ports. For the gain over outphasing angle plot in Fig. 4.9, there is some ambiguity for the outphasing angles resulting in the notch in the gain. There could exist a lower value for the antenna with the microstrip matching network between the outphasing angle 60◦ and 75◦ that is not shown. The remedy could be to increase the resolu- tion to 1◦. This was not done due to the amount of time to either simulate it by manually entering the excitations in CST or implement a MATLAB script, using a CST interface such as TCSTInter