Técnicas de Reducción de Efectos Parásitos en Elementos Inductivos de Filtros EMI

Proyecto Fin de Carrera Ingeniería de Telecomunicación Formato de Publicación de la Escuela Técnica Superior de Ingeniería Autor: F. Javier Payán Somet Tutor: Juan José Murillo Fuentes Dep. Teoría de la Señal y Comunicaciones Escuela Técnica Superior de Ingeniería Universidad de Sevilla Sevilla, 2013 Trabajo Fin de Máster Máster en Ingeniería Aeronáutica Técnicas de Reducción de Efectos Parásitos en Elementos Inductivos de Filtros EMI Autor: Pablo Ruiz Morales Tutor: Joaquín Bernal Méndez Dpto. Física Aplicada III Escuela Técnica Superior de Ingeniería Universidad de Sevilla Sevilla, 2024 Trabajo Fin de Máster Máster en Ingeniería Aeronáutica Técnicas de Reducción de Efectos Parásitos en Elementos Inductivos de Filtros EMI Autor: Pablo Ruiz Morales Tutor: Joaquín Bernal Méndez Catedrático de Universidad Dpto. Física Aplicada III Escuela Técnica Superior de Ingeniería Universidad de Sevilla Sevilla, 2024 Trabajo Fin de Máster: Técnicas de Reducción de Efectos Parásitos en Elementos Inductivos de Filtros EMI Autor: Pablo Ruiz Morales Tutor: Joaquín Bernal Méndez El tribunal nombrado para juzgar el trabajo arriba indicado, compuesto por los siguientes profesores: Presidente: Vocal/es: Secretario: acuerdan otorgarle la calificación de: El Secretario del Tribunal Fecha: Agradecimientos Q uiero aprovechar estas líneas para expresar mi agradecimiento a todas aquellas personas que han contribuido, de una forma u otra, a hacer posible este trabajo fin de máster. A mi familia, su respaldo incondicional y presencia constante han sido factores claves en esta y en todas las etapas de mi vida. A mi tutor Joaquín y a María Ángeles, por su guía, sus valiosos aportes y la confianza depositada en mí durante todo el proceso. A mis compañeros y amigos del grupo de investigación, con quienes he tenido el placer de trabajar codo a codo. Por vuestra colaboración, los buenos momentos y por todo lo que me habéis enseñado. A todos, mi más sincera gratitud por formar parte de esta etapa y hacer posible este proyecto. Pablo Ruiz Morales Sevilla, 2024 I Resumen E n este trabajo se investiga el impacto de los efectos parásitos en inductores y chokes de modo común, utilizados en aplicaciones de interferencia electromagnética, con el objetivo principal de mejorar el rendimiento de los filtros EMI en sistemas electrónicos. Al centrarse en la capacidad parásita que afecta intrínsecamente a estos componentes, el estudio proporciona información útil y directrices prácticas dirigidas a los ingenieros con el fin de mejorar el diseño y la eficacia de soluciones de filtrado. Los efectos parásitos, en particular la capacidad parásita, pueden degradar significativamente el rendimiento de los inductores y chokes, especialmente a altas frecuencias. Estos efectos no deseados pueden conducir a una reducción de la eficiencia de filtrado y a problemas de cumplimiento de normativa en los dispositivos electrónicos. El objetivo de este trabajo es comprender mejor estos elementos parásitos y desarrollar estrategias para mitigar sus efectos adversos. En primer lugar, se examinan los inductores de núcleo anular, cruciales para las aplicaciones EMI de alta frecuencia. Mediante un análisis detallado, se demuestra que la permitividad del material del núcleo y la configuración del devanado desempeñan un papel fundamental en la determinación del nivel de capacidad parásita. Este hallazgo es fundamental para diseñar inductores que funcionen de forma óptima en entornos de alta frecuencia. Asimismo, al estudiar los chokes en modo común, este trabajo también pone de relieve cómo influyen las distintas estrategias de bobinado en la capacidad parásita. Se ofrecen directrices prácticas para seleccionar los materiales del núcleo y diseñar configuraciones de bobinado que minimicen los efectos parásitos. Adicionalmente, este trabajo aborda el problema de las asimetrías en chokes, que pueden deberse a variaciones en la fabricación o a pérdidas locales de homogeneidad en las propiedades del material del núcleo. El trabajo presenta un método novedoso para tener en cuenta estas asimetrías en el proceso de modelado, mejorando así la precisión de las predicciones y la eficacia del componente de filtro EMI. III 2Chapter 1. Introduction • Path: The path is the means by which the electromagnetic energy from the source couples with the receiver circuit. This can involve both conducted and radiated pathways. Conducted paths occur through physical conductors such as wires, cables, or PCB traces, while radiated paths involve the propagation of electromagnetic waves through free space. Understanding the propagation paths is essential for assessing the vulnerability of electronic systems to EMI and implementing effective shielding or filtering techniques. • Receiver: The receiver of EMI refers to any electronic device or system that is susceptible to interference from electromagnetic energy. This can include sensitive electronic circuits, communication systems, control systems, or any other equipment whose operation may be compromised by EMI. Identifying potential receivers and assessing their susceptibility to EMI is critical for designing robust and resilient electronic systems. Fig. 1.1 provides a schematic illustration of the aforementioned concepts. In this example, the antenna serves as a representative source of EMI, emitting signals intentionally for communication purposes. However, these emitted waves can inadvertently interfere with nearby devices that exhibit electromagnetic susceptibility. As the waves propagate through the air, they encounter the printed circuit board (PCB), establishing a coupling mechanism that induces currents within the PCB. These currents, in turn, have the potential to disrupt the normal operation of the system. Figure 1.1 Basic decomposition of an EMI problem. EMI problems can also manifest in various forms, each requiring specific mitigation approaches based on the type of emission and the receiver’s susceptibility: • Radiated Emissions: Radiated emissions occur when energy is emitted into the surrounding environment, propagating as electromagnetic waves. This can result from the operation of electronic devices or systems with rapidly changing currents or voltages. Radiated emissions can interfere with nearby electronic equipment, particularly in sensitive environments such as radio frequency (RF) communication systems or medical devices. • Conducted Emissions: Conducted emissions occur when noise currents travel along physical pathways such as power lines, signal traces, or ground connections. These emissions can result from the switching of electronic components, power supply fluctuations, or electrical noise generated within the system. Conducted emissions can propagate through interconnected systems via power lines or signal cables, potentially causing interference with other electronic devices sharing the same electrical infrastructure. Additionally, these emissions can also lead to radiated emissions, as the noise emerging from a device through its power lines or interconnects can radiate and affect nearby devices. • Susceptibility to EMI: Refers to the vulnerability of electronic devices or systems to external electromagnetic interference. This can manifest as malfunctions, data corruption, or performance degradation in the presence of electromagnetic disturbances. Susceptibility issues can arise from inadequate shielding, poor grounding, insufficient filtering, or improper design practices [ 4 ]. Addressing susceptibility to EMI requires careful design considerations, robust testing methodologies, and adherence to EMC standards. 1.2 Motivation and Purpose 3 In this study, we aim to explore effective solutions for efficiently filtering conducted emissions. To achieve this goal, it is essential to delve into a deeper understanding of the distinction between different types of conducted noise currents, namely common-mode and differential-mode currents. Consider the scenario depicted in Fig. 1.2, where two systems are interconnected by a two-wire connection, consisting of a live wire and a return wire. In ideal conditions, the current flowing through the live wire is equal in magnitude but opposite in direction to that of the return wire. This scenario represents a differential-mode (DM) current. However, as frequency increases, due to various coupling mechanisms such as capacitive or inductive coupling, unintended leakage currents may arise. These leakage currents can propagate simultaneously through both the live and return wires, maintaining the same magnitude and direction. Such currents are referred to as common-mode (CM) currents. Figure 1.2 Schematic representation of common-mode and differential-mode currents in a singlephase connection. Among these modes, common-mode currents are generally considered undesirable as they are a primary contributor to the generation of radiated emissions. However, in practical scenarios, differential-mode noise currents also occur. The attenuation mechanisms for these differential-mode currents differ from those of common-mode currents, requiring distinct filtering techniques for effective suppression. 1.2 Motivation and Purpose Electromagnetic interference remains a persistent challenge in the design and operation of electronic systems, particularly as switching frequencies continue to increase to meet the demands for higher power densities [5]. Unmitigated EMI can lead to various problems, including signal degradation, equipment malfunction, and regulatory non-compliance. Consequently, effective EMI mitigation strategies are crucial for ensuring the reliable and efficient operation of electronic devices. Inductors, including ring-core inductors and common-mode chokes, play a vital role in EMI filtering circuits. However, parasitic effects, such as parasitic capacitance and asymmetries, can significantly impact the performance of these components, compromising their ability to effectively suppress EMI. These parasitic effects can arise from various factors, including core material properties, winding configurations, and manufacturing imperfections. Addressing parasitic effects in inductors is of paramount importance for achieving optimal EMI mitigation. By reducing parasitic capacitance and mitigating asymmetries, the overall performance 4Chapter 1. Introduction of EMI filters can be enhanced, leading to improved signal integrity, increased system reliability, and better compliance with EMC regulations. The primary purpose of this work is to develop a comprehensive understanding of parasitic effects in inductors for EMI applications and to propose novel design strategies and methodologies to minimize these effects. Specifically, this work aims to: 1. Investigate the impact of core material permittivity and winding configurations on parasitic capacitance in ring-core inductors, and provide design guidelines for minimizing parasitic capacitance. 2. Explore the influence of winding strategies and core material properties on parasitic capacitance in common-mode chokes, offering practical recommendations for designing CMCs with reduced parasitic capacitance. 3. Develop a novel method to address asymmetries in common-mode chokes, which can arise from geometric imperfections or variations in core material properties, and evaluate its effectiveness in enhancing EMI suppression. By achieving these objectives, this research aims to contribute to the advancement of EMI mitigation techniques, enabling the design of more efficient and reliable electronic systems that meet stringent EMC requirements. The insights and methodologies derived from this work have the potential to impact a wide range of applications, from power electronics and telecommunications to automotive and aerospace industries, where EMI mitigation is critical. 1.3 Document Outline This work is structured into four main chapters, each focusing on a specific aspect of parasitic effect reduction in inductors for EMI applications. The chapters are organized as follows: Chapter 1 provides an overview of the research topic, highlighting the importance of EMI mitigation and the challenges posed by EMC compliance. It establishes the motivation and objectives of the research, underscoring the need for novel design strategies and methodologies to minimize parasitic effects. Chapter 2 delves into the analysis of parasitic capacitance in ring-core inductors, which are crucial components for high-frequency EMI filtering. Building upon the work presented in [ 6 ], this chapter investigates the impact of core material permittivity and winding configuration on parasitic capacitance. Through theoretical analysis and experimental validation, this chapter aims to provide practical guidelines for designing ring-core inductors with reduced parasitic capacitance, thereby enhancing their EMI filtering performance. Focusing on another essential component for EMI filtering, chapter 3 explores the influence of winding strategies and core material properties on parasitic capacitance in common-mode chokes. Drawing from the findings of [ 7 ], this chapter examines various winding configurations and core materials to identify optimal design approaches for minimizing parasitic capacitance in CMCs. Experimental results and practical design recommendations are presented to aid engineers in developing high-performance CMCs for effective EMI suppression. Asymmetries in common-mode chokes, which can arise from geometric imperfections or variations in core material properties, can significantly impact their EMI suppression capabilities. Chapter 4 introduces a novel method for mitigating the effects of asymmetries in CMCs, based on the research presented in [ 8 ]. Through theoretical analysis and experimental validation, this chapter demonstrates the effectiveness of the proposed method in enhancing EMI suppression and provides practical guidelines for its implementation. The final chapter synthesizes the key findings and contributions of the research presented in the preceding chapters. It highlights the implications and significance of the work in the field of EMI 1.3 Document Outline 5 mitigation and inductor design. Additionally, this chapter discusses the limitations of the research and outlines potential directions for future work, paving the way for further advancements in this area. The document also includes a comprehensive bibliography, providing readers with additional resources and references related to the research topic. 2 Inductors T o understand the function and importance of an inductor in the context of EMI attenuation, one must first consider the fundamental principles of the physics behind its operation. An inductor is a passive component designed to store energy in the form of a magnetic field. It consists of a wire or conductor wound in a coil configuration. This design enables the inductor to enhance the magnetic flux passing through it when an electric current flows through its coils. At the heart of an inductor’s functionality lies the interplay between magnetic fields and electric currents, governed by Maxwell’s equations. The constitutive equation, B=µH , establishes the relationship between the magnetic flux density (B), the magnetic permeability of the medium (µ), and the magnetic field intensity ( H ). When applied in the context of a toroidal core inductor, this equation illustrates the core’s ability to concentrate magnetic flux within its structure. Ampere’s law, expressed in its integral form as HH·dl=Ienc , offers further insights into the behavior of inductors. By integrating the magnetic field intensity along a closed loop path, it corresponds to the enclosed current ( Ienc ), demonstrating how the current enclosed by the loop becomes the source of a magnetic field around the inductor. From these foundational principles, a crucial relationship emerges: Ble=µNI,(2.1) where le represents the equivalent magnetic path length, N denotes the number of turns, and I signifies the current passing through the inductor. Figure 2.1 Magnetic flux inside an inductor [9]. 7 8Chapter 2. Inductors Simultaneously, the definition of magnetic flux ( ψ ) as the surface integral of magnetic flux density over an area provides further insights: ψ=ZZS B·dS=BNAe,(2.2) where Aerepresents the effective cross-sectional area. Combining (2.1) and (2.2) yields an expression that characterizes the flux as a function of the core’s properties and the current through the inductor: ψ=µN2Ae le I(2.3) This relationship highlights the inherent self-inductance L of the inductor as the proportionality constant linking the magnetic flux traversing the core to the current through the inductor. In alternating current (AC) circuits, where the electric current through the inductor fluctuates over time, (2.3) states that the magnetic flux also undergoes proportional changes. Faraday’s Law, which asserts that any alteration in magnetic flux through a circuit induces an electromotive force (emf), completes the explanation about the interplay between current and magnetic flux in inductors. ∇×E=−∂B ∂t(2.4) In the context of an inductor, this flux variation generates an emf encircling the closed surface of the inductor. Mathematically, this is expressed as V=dψ/dt, or equivalently V=Ldi /dt. This equation reveals that the inductor acts as a kind of "resistor" to the rapidly changing current in a circuit. That is, when the current changes abruptly, the inductor generates an emf opposite to the change, which translates into an apparent resistance to current flow. This "electrical inertia" property of the inductor makes it widely used in electronic and electrical systems as filtering devices for mitigation of EMI [9, 10]. 2.1 Low-Pass Passive Filters Transient events in power converters commonly generate electrical noise, needing the implementation of effective mitigation strategies. Low-pass filters (LPFs) stand out as a well-established technique for attenuating such noise, offering tailored solutions to specific load impedances for optimal performance. • Low-Impedance Loads: In this scenario, employing a single inductor connected in series with the load path provides a high impedance to high-frequency harmonics within the DM noise spectrum. As frequency increases, the inductor’s reactance rises, effectively blocking unwanted high-frequency components while permitting the desired low-frequency signal to pass with minimal attenuation. • High-Impedance Loads: Conversely, for high-impedance loads, a capacitor connected in parallel acts as a shunt path for high-frequency noise currents. As frequency rises, the capacitor’s reactance decreases, establishing a low-impedance path for these unwanted components to be bypassed to ground. Fig. 2.2 depicts the aforementioned with a simple yet effective filter design applicable when both ZS and ZL exhibit low impedance. To analyze the circuit’s behavior, a commonly employed tool is the Insertion Loss (IL). IL is a measure of how much a filter attenuates an input signal and is defined as the ratio of the voltage at the output without the filter to the voltage at the output with the filter, expressed in decibels (dB). 2.1 Low-Pass Passive Filters 9 Figure 2.2 Schematic of a first order low-pass filter optimal for small source and load impedances, ZSand ZLrespectively. IL =20log10 Vout,without filter Vout,with filter (2.5) For the sake of convenience, the following expressions will not directly represent IL, but rather the voltage ratios expressed using Laplace transform variable s . This formulation is particularly useful for the analysis of linear time-invariant (LTI) systems, which are characterized by a consistent input-output relationship over time. For the circuit under consideration, its voltage ratio can be expressed as: Vout,without filter Vout,with filter =1+L s ZS+ZL (2.6) Note how, when both ZS and ZL dominate, the circuit’s behavior tends to nullify the filter’s impact. However, combining the aforementioned ideas, LC filters can be constructed, offering enhanced performance. An example of this is illustrated in Fig. 2.3, where a capacitor is added to improve the original filter design. With this addition, the voltage ratio takes the form: Vout,without filter Vout,with filter =1+s(L+CZSZL) ZS+ZL +s2LC ZS ZS+ZL (2.7) This transformation results in a second-order filter response, leading to an expected -40 dB/dec attenuation. Moreover, the effectiveness of the filter is heavily influenced by the impedance of ZS , with higher impedance contributing to superior performance. It’s worth noting that if the capacitor were positioned after the inductor, the resulting expression would resemble (2.7) , with ZL replacing ZSin the numerator of the second-order term. While theoretical analyses of LPFs provide valuable insights into their behavior, real-world implementations may encounter challenges due to inherent limitations of practical components, particularly inductors. Unlike ideal inductors, real-world samples exhibit parasitic effects that can degrade filter performance at higher frequencies. Careful consideration during filter design is crucial to account for these internal behaviors, especially when broad-spectrum noise suppression is critical. 10 Chapter 2. Inductors Figure 2.3 Schematic of a second order low-pass filter. 2.2 Non-ideal Behavior of Inductors At high frequencies, inductors deviate from ideal behavior due to various parasitic effects inherent in their construction and operation. This parasitic effects may greatly reduce the ability of the inductor to suppress high-frequency conducted emissions [ 11 ]. Hereafter are some common parasitic effects encountered in inductors, along with their physical mechanisms: • Resistance (DC and AC): Every real conductor has some resistance associated with it. This DC resistance (DCR) causes power loss in the form of heat when current flows through the inductor. Additionally, at higher frequencies, the tendency of alternating current to flow more towards the outer surface of a conductor results in an effective increase in resistance, which is proportional to the square root of the frequency. This effect is known as skin effect [12]. • Capacitance: Results from the inherent voltage differences between conductive elements within the inductor and between the inductor and its surroundings. This parasitic capacitance usually determines the response of the inductor at high frequencies. • Magnetic Field Coupling: In a multi-inductor or transformer configuration, magnetic flux from one inductor can induce a voltage in another nearby inductor, leading to unwanted signal interference or coupling between different parts of the circuit. • Eddy Currents: Eddy currents can be induced in the conductive materials of the inductor’s core due to alternating magnetic fields. These currents create additional losses in the form of heat and can affect the inductor’s overall performance. • Saturation: Happens when the magnetic domains within the core material become fully aligned, limiting further increase in magnetic flux. Inductor cores can saturate when subjected to high magnetic flux densities. Saturation sets a limit on the current an inductor can withstand, causing a drastic decrease in its inductance for currents exceeding this limit. This phenomenon is crucial to note, as it can lead to nonlinear behavior in the inductor, significantly affecting its performance, particularly in applications with high currents or magnetic fields. Due to its practical implications, it is of great interest to quantify parasitic capacitances and determine optimal winding strategies to minimize their effect. Fig. 2.4 depicts the impedance measured in an inductor as a function of frequency, clearly showing a resonant behavior between the inductance and the parasitic capacitance. Since these parasitic capacitances are mainly related to electric coupling between turns of the inductor, they might be influenced by the choice of core material and the specific winding technique employed during the fabrication process. 2.2 Non-ideal Behavior of Inductors 11 Figure 2.4 Measured impedance of a 1.2 µH inductor: (a) magnitude; (b) phase [9]. For instance, recent research in [ 13 ] discusses the potential for reducing the equivalent parallel capacitance (EPC) of an inductor by utilizing stacked turns on a MnZn toroidal core. Further insights are offered by [ 14 ]. That work studies the relationship between turn-to-core and turn- to-turn capacitances within the inductor. In their analysis, they model the inductor with the core considered as a material with high permittivity. Through a combination of numerical simulations and experimental validations, [ 14 ] demonstrate that physically separating the winding turns from the magnetic core can effectively mitigate the EPC of the inductor. However, it’s important to note that the conclusions drawn from this model may not be generally applicable. Specifically, when dealing with magnetic materials characterized by lower permittivity values, such as NiZn [ 15 ], the dynamics of turn-to-turn coupling become more apparent. In these scenarios, the strategies and design considerations aimed at minimizing EPC may significantly differ from those applicable to high-permittivity materials. In this context, the aim of this section is to expand the study carried out in [ 6 ]. The objective is to perform an experimental analysis to discern the effects of various winding techniques, comparing results across two distinct types of magnetic core materials commonly used in inductor fabrication. A series of inductors with differing core materials has been meticulously designed and constructed 18 Chapter 2. Inductors Loose Tight Figure 2.8 Transmission coefficient for 30-turns inductors constructed with a MnZn FAIR-RITE 5977003821 core. Measured data are compared with transmission coefficient predicted by the circuit model in Fig. 2.5 with the parameters provided by the PSO search algorithm, given in Table 2.2. in the loose winding cases. This suggests that the impact of winding geometry on the EPC of the inductors is less pronounced for MnZn cores compared to NiZn cores. The superior performance of inductors with tight windings can be attributed to the fact that the loose winding technique facilitates direct coupling to the core for high-permittivity materials [ 17 ]. By increasing the exposed magnetic core surface area while simultaneously distancing adjacent turns, the loose winding configuration enhances the potential for direct magnetic coupling. Consequently, despite the increased distance between turns in loose windings, the tight winding strategy still outperforms it due to more efficient utilization of the core material. As a result, the conclusions drawn from the analysis of NiZn inductors cannot be straightforwardly extrapolated to inductors with MnZn cores. The prevalence of displacement currents through the core in MnZn cores also gives rise to more significant core losses, which subsequently alter the slope of the S21 curves after resonance. As previously stated, a purely capacitive response would typically appear as a 20dB/dec positive slope in this graphical representation. However, the presence of dissipative effects due to core losses results in deviations from this ideal behavior. To effectively model these dissipative effects in the circuit model, additional RC blocks have been incorporated, as illustrated in Fig. 2.5. The specific values of the capacitances and resistances of the auxiliary RC blocks required to achieve good agreement between measured and simulated curves, as depicted in Fig. 2.8 and Fig. 2.9, are detailed in Table 2.2. As detailed in Table 2.2, there exists a disparity in the inductance values regarding the two inductors constructed using the core specified as TDK B64290L0082X038, despite both being constructed with the same number of turns. This discrepancy in inductance values is attributed to the varying inductance factors of their cores, that lie within the manufacturer specifications. However, it is important to remark that while the inductance factor of an inductor’s core can significantly impact its inductance value, the conclusions regarding the effect of the winding strategy on the inductor EPC may still hold true regardless of the specific inductance values of the inductors. 2.5 Results 19 Loose Tight Figure 2.9 Transmission coefficient for 30-turns inductors constructed with a MnZn TDK B64290L0082X038 core. Measured data are compared with transmission coefficient predicted by the circuit model in Fig. 2.5 with the parameters provided by the PSO search algorithm, given in Table 2.2. The experimental evidence presented in the preceding paragraphs highlight a key disparity between NiZn and MnZn inductors: the inability to reduce the EPC in MnZn inductors through loose winding techniques. These results align with a prior investigation conducted with commonmode chokes [ 14 ]. The findings of this study, although focusing on a different type of device, provide evidence supporting that the EPC of these inductive devices can be reduced by increasing the distance between the winding turns and the MnZn core. To further validate the results presented by [ 14 ] and assess potential enhancements achievable with inductors, two additional samples were fabricated using the MnZn 5977003821 core. Unlike the previously analyzed samples, the windings of these modified inductors were intentionally separated by 2 mm from the core. This was achieved by applying multiple layers of low-permittivity insulating material, specifically paper tape, onto the core. The parameters of the circuit model that provided the best fit to the measured S21 of these modified inductors are outlined in Table 2.3. A comparison of the EPCs of these modified inductors with those of the original inductors listed in Table 2.2 reveals a reduction of over 50% in the EPC with this altered winding configuration. Table 2.3 Parameters of the inductors imposing turn-to-core separation. Manufacturer Part number Winding technique EPC (pF) CR in parallel with EPC L (mH) EPR (kΩ) NCR C1 (pF) R1(kΩ) FAIR-RITE 5977003821 Tight 1.36 1 9.74 8 2.27 ∞ Loose 3.19 1 9.10 9 2.21 ∞ The impact of this reduction on the S21 curves is illustrated in Fig. 2.10, which brings together the S21 curves generated by the circuit model of inductors utilizing the same core. It compares 20 Chapter 2. Inductors Figure 2.10 Comparison of inductor responses for different winding techniques for a MnZn 5977003821 core. scenarios where the windings are in close proximity to or separated from the core, as well as tight and loose winding strategies. While the measured data are not included in Fig. 2.10 for clarity, the results demonstrate excellent agreement with the measured data. It is noteworthy that inductors with windings separated from the core (spaced windings) demonstrate better performance at high frequencies compared to those with turns in proximity to the core. Additionally, the optimal winding strategy in this scenario, particularly with MnZn cores, involves tightly wound coils with turns kept separated from the core, which is the configuration that minimizes electric coupling between the turns and the core, as previously anticipated. Based on the findings, which support the hypothesis that different winding techniques significantly affect the high-frequency performance of ring-core inductors with the same number of turns, it is insightful to analyze the impact of material selection when designing an inductor with a specific inductance value, as is the most realistic case in the context of filter design and implementation. To explore this, two 1 mH inductors were manufactured using tight windings and different core materials: NiZn and MnZn. This involved 30 turns on a 5943003801 core and 19 turns on a 5977003821 core. The S21 transmission coefficients of these two inductors are compared in Fig. 2.11, where the measured values are exposed together with the predicted S21 curves generated by the circuit model in Fig. 2.5. These results lead to the conclusion that, for a similar winding technique and inductance value, it is generally preferable to utilize magnetic cores with lower permittivity when prioritizing improved attenuation at high frequencies in the design. In spite of the potential enhancement in the EPC achievable by separating the winding from the core in an inductor with a high-permittivity core, it’s crucial to acknowledge that opting for a lowpermittivity core may not always represent the optimal choice in inductor design. Various factors need consideration beyond just permittivity. For instance, selecting a NiZn core necessitates a higher number of turns compared to a MnZn core to achieve equivalent inductance levels. Consequently, the NiZn core-based inductor is anticipated to exhibit a lower saturation current. Based on an analysis of the core datasheets, the inductor utilizing the MnZn core is estimated to have a saturation current of approximately 1.3A, notably higher than the anticipated saturation current of 0.7A for the NiZn variant. 2.6 Conclusions 21 MnZn NiZn Figure 2.11 Measured and estimated transmission coefficient of two inductors of 1mH constructed with tight windings of different number of turns on different core materials: 30 turns on a NiZn core (5943003801) and 19 turns on a MnZn core (5977003821). 2.6 Conclusions The typical response of an inductor with respect to frequency often prompts the question of how its frequency response can be enhanced. One benefited procedure of this enhancement involves filter design. Here, selecting appropriate inductance values and employing winding strategies to broaden the bandwidth within which the inductor maintains its inductive behavior is crucial. This endeavor aims to minimize the necessity of adding multiple stages to the filter, thereby improving the overall efficiency of the filtering solution. This chapter provides insight into the impact of electromagnetic properties of core materials and winding techniques on the parasitic capacitance of single-layer ring-core inductors. By measuring the transmission coefficients of these inductors and comparing them with results obtained from a comprehensive circuit model accounting for parasitic capacitance and core losses, we gain a quantitative assessment of the effectiveness of various design strategies. Notably, the circuit models are typically valid up to frequencies on the order of tens of megahertz. Our analysis includes characterizing inductors with both tight and loose windings on both MnZn and NiZn ring cores. We find that both core material and winding technique influence the total electrical coupling between adjacent turns and between the winding and the core. In high-permittivity ferrite cores, such as MnZn materials, electrical coupling through the core dominates, whereas in cores with lower permittivity, like NiZn ferrites, coupling through air becomes more significant. These findings hold profound implications for the design and optimization of inductors, particularly in EMC applications. Specifically, our analysis reveals that increasing the distance between turns is an effective strategy for reducing the EPC of a ring-core NiZn inductor. However, for inductors with MnZn cores, this technique is ineffective and can even be counterproductive. In these cases, increasing the distance between the winding and the core may actually decrease the parasitic capacitance, as it has been proved by employing the proposed characterization technique. 3 Common-Mode Chokes A common-mode choke (CMC) is a specialized type of inductor designed to suppress EMI and radio frequency interference (RFI). These unwanted signals often appear on high-current wires, such as those in power supply lines, and can cause malfunctions in electronic equipment. A CMC operates by targeting common-mode signals, which are electrical noise signals that affect multiple wires simultaneously. The construction of a common-mode choke typically involves two parallel coil windings around a toroidal ferromagnetic core [9]. The fundamental principle behind a CMC’s operation lies in its ability to block common-mode currents while allowing low-frequency differential-mode currents to pass with minimal impedance. Differential-mode currents, flowing in opposite directions through the windings, generate magnetic fields that cancel each other out within the core. As a result, the CMC presents very little inductance to differential-mode currents, preventing core saturation. Ideally, the choke’s maximum current rating would be mainly determined by the heating effect caused by the resistance of the windings rather than core saturation. Conversely, common-mode currents, flowing in the same direction through both windings, encounter a high impedance due to the combined inductance of the windings, which reinforce each other [9, 19]. This high impedance effectively suppresses the common-mode noise. Advanced designs, such as twisted winding structures, have been developed to further improve the performance of CMCs. In these designs, the windings are twisted to reduce the near magnetic field emissions generated by differential-mode currents. This configuration helps the magnetic fields generated by these currents to cancel each other out more effectively in space. However, a small leakage inductance is typically desirable to aid in the attenuation of high-frequency DM noise. (a) Common-mode current. (b) Differential-mode current. Figure 3.1 Magnetic flux inside a CMC under different excitations [9]. 23 24 Chapter 3. Common-Mode Chokes Despite their effectiveness, CMCs face challenges at high frequencies, where capacitive parasitic effects —displacement currents through the air and the core— undermine their filtering capabilities. These parasitic effects can provide a path for some common-mode current to bypass the component, reducing the CMC’s performance as a filtering device. To address this issue, additional filtering components are often required, which can increase the cost and weight of the final design. 3.1 EMI Filters While ordinary LC filters can provide effective noise suppression and signal conditioning in various electronic circuits, they are not always sufficient to address the specific challenges posed by EMI. EMI filters, also known as RFI filters, are essential in ensuring the electromagnetic compatibility of electronic systems by suppressing unwanted electromagnetic noise that can interfere with the performance and reliability of electronic devices. EMI filters are designed using a specialized lowpass LC topology, which effectively attenuates high-frequency noise while allowing low-frequency signals to pass through. Fig. 3.2 illustrates a typical EMI filter configuration. This topology can be simplified to highlight its contributions to CM and DM noise suppression, as shown in the same figure. The design of an EMI filter is significantly influenced by the source and load impedances. The primary objective is to maximize the impedance mismatch between the source and the load, thereby enhancing the filter’s attenuation performance. For CM noise, the power supply is typically characterized as a high-impedance source, while the Line Impedance Stabilization Network (LISN) used during certification acts as a low-impedance load. As learned in Section 2.1, to achieve maximum attenuation, it is essential to position the high-impedance filter element, usually an inductor, adjacent to the low-impedance load (LISN). Conversely, the low-impedance filter element, typically a capacitor, should be placed next to the high-impedance source (power supply). This strategic positioning ensures that the filter effectively mitigates CM noise. For CM noise suppression, the EMI filter employs a combination of a common-mode choke and line-to-ground capacitors ( CY ). As already stated, the common-mode choke presents a high impedance to CM currents, thus impeding their flow, while the CY capacitors provide a path to ground for these currents. However, the maximum value of CY capacitors is constrained by safety Figure 3.2 Generic EMI filter topology (left). Decomposition of an EMI filter into: CM filter (top right) and DM filter (bottom right). 3.2 High-frequency Model 25 regulations to limit leakage current, thereby preventing potential shock hazards. Once the maximum permissible capacitance value is determined according to safety standards, the common-mode choke is selected to achieve the desired attenuation without exceeding the leakage current limits. This careful selection ensures effective CM noise suppression while adhering to safety constraints. DM noise poses another challenge for EMI filter design. The Y-capacitors, when connected in series, offer limited DM attenuation because their effective capacitance is halved. This reduced capacitance results in insufficient DM noise suppression, particularly at lower frequencies where stronger filtering is often required. To address this, a line-to-line capacitor ( CX ) is added to the filter. The CX capacitor, not being connected to ground, can have a higher value, thereby providing enhanced DM attenuation without violating leakage current limits. In designing the common-mode choke, it is important to consider the inductance characteristics. Ideally, the common-mode choke should not show significant differential-mode inductance. However, in practice, some leakage inductance is inevitable due to imperfect coupling between the windings [ 4 , 19 ]. This leakage inductance can contribute to differential-mode attenuation, but must be managed to prevent the choke from saturating under high AC power currents. Excessive leakage inductance can cause the common-mode choke to saturate at low AC power levels, compromising its effectiveness. Therefore, the design must balance these inductances to ensure effective noise suppression while preventing saturation. Lastly, it’s important to acknowledge that parasitic effects in both the capacitors and CMC can limit the bandwidth in which an EMI filter is effective. These parasitic capacitances and inductances can impact the filter’s performance, particularly at higher frequencies. Therefore, the rest of the chapter will focus on how to optimize the construction and design of CMCs to reduce parasitic capacitances, thus improving the filter’s bandwidth and overall reliability. 3.2 High-frequency Model Fig. 3.3 schematically depicts the various mechanisms contributing to the high-frequency electrical coupling between two adjacent turns of a CMC winding. • Direct capacitive coupling Ctt : This component represents the parasitic capacitance arising directly between the two turns due to their physical proximity and the surrounding air as the dielectric medium. • Indirect capacitive coupling through core ( Ctc and Ccc ): This combined capacitance reflects an alternative coupling path via the core material. It can be further decomposed into: – Turn-to-core capacitance Ctc : This capacitance represents the coupling between each turn and the core through the air gap between them. – Core capacitance Ccc : This component models the parasitic capacitance arising from the core material itself. It can be visualized as a capacitor filled with a dielectric characterized by permittivity ε. For cores with high permittivity ( ε≫ε0 , where ε0 is the permittivity of free space), Ccc becomes significantly larger compared to Ctc due to the enhanced electric field concentration within the core. In this case, the overall coupling through the core is primarily determined by Ctc . This simplification is commonly adopted in existing literature [ 11 , 21 , 22 , 23 , 14 ] when treating the core as a conductive material for parasitic capacitance calculations in inductors and CMCs. The results presented in Chapter 2 confirm that when considering windings placed on materials with high permittivity, such as certain ferrites, the parameter Ctc often emerges as the dominant factor influencing the electrical coupling between windings. This phenomenon has been extensively studied and confirmed by recent research [24, 14]. 26 Chapter 3. Common-Mode Chokes Ctt Ctc Ctc Ccc ε Figure 3.3 Schematic representation of the electric coupling mechanisms between two adjacent turns of a winding on a magnetic ring-core. Interestingly, looser winding geometries (i.e., increased spacing between turns) can lead to an increase in Ctc . This can be attributed to the presence of a larger effective overlap area between the turn and the core, allowing for enhanced electric field penetration and a stronger capacitive coupling effect [ 17 ]. Consequently, designers employing loose windings on high-permittivity cores may inadvertently increase the EPC of the inductor [ 14 ]. The EPC represents the effective capacitance introduced by the winding configuration in parallel with the inductor’s inherent inductance, thereby influencing its overall electrical behavior at high frequencies. The scenario changes considerably when the core material exhibits a lower permittivity, as is typical with NiZn ferrites [ 24 ]. In such cases, the total capacitive coupling through the core ( Ctc +Ccc ) is expected to be significantly lower. As a result, the overall EPC of a CMC might be primarily determined by the direct air gap capacitance, Ctt . Under these circumstances, employing a loose winding strategy might lead to a different outcome. Since the capacitive coupling through the core material is expected to be weaker, a loose winding might not result in a significant enhancement of the overall electrical coupling between windings. Therefore, for CMCs constructed with low-permittivity cores, it’s reasonable to expect that a loose winding technique could potentially lead to a decrease in the coupling between adjacent turns within the same coil, as confirmed by the results in the previous chapter. This decrease would primarily be due to the reduced influence of Ctc on the overall coupling. To validate the hypotheses regarding the influence of core permittivity and winding geometry on CMC performance, a systematic modeling and measurement approach is proposed here. The initial step involves the development of precise high-frequency circuit models for CMCs employing various core materials. These models incorporate the electrical characteristics of the core material, the winding configuration (tight or loose), and parasitic capacitances. The specific circuit model elements and their corresponding values are carefully chosen to accurately represent the behavior of the CMC across the desired frequency range. Subsequently, these models were used to investigate the impact of different winding configurations on the overall electrical behavior of the CMC, with a particular focus on parasitic capacitances. By analyzing the model under various winding scenarios, the changes in the values of key parasitic capacitances are quantified. This provides valuable insights into how winding geometry influences the overall capacitive coupling within the CMC. To further validate the model predictions and quantify the actual performance improvements achievable through optimized winding configurations, experimental measurements were conducted. These measurements involved characterizing the transmission coefficients (S-parameters) or insertion loss of the CMCs within a suitable test setup. To facilitate this analysis, an accurate high-frequency model of the CMC has been utilized. 3.2 High-frequency Model 27 Figure 3.4 High-frequency modal-parameters circuit (MPC) model of a CMC used in this work. The CM and DM blocks determine the response of the component to asymmetrical and symmetrical test setups defined in CISPR-17 standard, respectively [25]. This model, depicted in Fig. 3.4, provides a comprehensive representation of the CMC’s electrical behavior, enabling a detailed examination of the effects of winding configurations on its performance. The modal-parameters circuit (MPC) model was first introduced in [ 25 ]. The paper also introduced an efficient characterization technique that facilitates the fast and straightforward estimation of the MPC model’s parameters. The foundation of the MPC model lies in the inherent symmetry of a CMC. As demonstrated in [ 25 ], this symmetry translates to a well-defined equivalent four-port circuit characterized by four predetermined natural modes, also known as the eigenvectors of the admittance matrix. These natural modes, designated as G, C, D, and W, represent distinct excitation scenarios within the CMC. To ensure clarity and establish a consistent reference, the normalized voltage excitations corresponding to each natural mode are provided here in matrix form. In this matrix, each column represents the specific voltage excitation required at each terminal of the CMC to excite one of its natural modes. Specifically, the first element of each column corresponds to the excitation at terminal 1 as depicted in Fig. 3.4, the second element corresponds to terminal 2, and so forth. M M Mm=1 2    1 1 1 1 1−1−1 1 1 1 −1−1 1−1 1 −1     (3.1) The response of the CMC to each of the four natural modes is characterized by modal admittances, denoted as YG , YC , YD , and YW . These modal admittances correspond to the eigenvalues of the CMC’s admittance matrix and provide crucial information about its high-frequency behavior under different excitation scenarios. Each modal admittance in the MPC model is a composite quantity formed from various MPC parameters. While these parameters are primarily modal in nature, they can still offer valuable 34 Chapter 3. Common-Mode Chokes 3.3 Characterization Technique This section details the characterization technique for CMCs as proposed in [ 25 ]. The technique focuses on two key measurement setups and a decision-making algorithm to obtain accurate and simplified CMC parameters. The characterization method employs two specific setups: the open-circuit (OC) setup and a winding-to-winding (WD) setup. These setups are critical for measuring the transmission coefficients, which are subsequently used to determine the natural admittances of the CMC. Fig. 3.10 illustrates the setups utilized for the characterization of CMCs. The OC setup involves connecting the CMC in a configuration that simultaneously excites both the C and D natural modes. This setup is essential in revealing the resonance characteristics of these modes, which are key to understanding the CMC’s behavior. Measuring the transmission coefficient SOC 21 , this setup provides information about the corresponding modal admittances. The transmission coefficient in the OC setup is mathematically expressed as: SOC 21 =2RYCYD YC+YD+2RYCYD (3.7) This setup enables the identification of two distinct resonance peaks corresponding to the CM and DM blocks, which are modeled as parallel RLC resonators. The peaks in the transmission coefficient provide essential data for characterizing the admittances YCand YD. The WD setup, on the other hand, is designed to measure the transmission coefficient associated with the winding-to-winding (W) mode of the CMC. This setup is particularly important for capturing the capacitive coupling effects between the windings, which dominate at lower frequencies for this configuration. In the WD setup, the measurement ports are connected across the windings of the CMC, allowing for the excitation of the W mode. The focus once again is on measuring the L L TG VTG RR 12 34 SA (a) OC setup. L L 13 4 R VTG R TG SA 2 (b) DW setup. Figure 3.10 Setups for characterizing a CMC according to the MPC method [25]. 3.4 Results 35 transmission coefficient SDW 21 , which is expressed as: SDW 21 =2RYDYW YD+YW+2RYDYW (3.8) After the measurements have been taken, a decision-making algorithm ensures that the modal parameters derived from the measurement setups accurately represent the CMC’s behavior across a wide frequency range. The first step involves obtaining an initial set of parameters. The self-inductance of a coil when the other coil is either open-circuited or short-circuited can be used to estimate both LC and LD . Then, the resonant frequencies in the OC curve can be used to estimate CC and CD , and the value of |SOC 21 | at those frequencies is used to estimate RC and RD . Finally, a value of the DW curve at low frequency is used to determine CW. Once the initial parameters are extracted, a particle swarm optimization (PSO) algorithm refines the modal parameters to improve the match between the measured and predicted transmission coefficients using (3.7) and (3.8) . If metrics for the final model such as its mean squared error (MSE) or its root mean squared error (RMSE) are not satisfactory, additional RC branches can be added to the CM block to further improve the fit. The final step is to validate the accuracy of the refined MPC model. This process involves comparing the model’s predictions for the symmetrical and asymmetrical connections with measured data, which were not used in the initial parameter extraction. This step is done as a consistency check to ensure the final set of parameters accurately represents the CMC’s behavior across the frequency range of interest. The characterization technique followed in this work offers several advantages in the characterization of CMCs, such as a structured and systematic approach to parameter extraction, model refinement, and validation, ensuring accuracy at each step. Additionally, the validation process ensures that the model is not only accurate for the initial measurements but also generalizable across different conditions and frequency ranges. 3.4 Results As previously outlined, this study aims to optimize winding techniques to minimize the EPC of CMCs, thereby improving their performance at high frequencies. To achieve this objective, this section undertakes a quantitative analysis of the influence of pivotal design parameters such as turn- to-turn spacing and the dielectric constant of the core on the parasitic capacitances of single-layer CMCs. To conduct this analysis, various CMC samples were fabricated employing three distinct cores composed of two ferrite materials: NiZn and MnZn. These cores, detailed in Table 3.2, were selected due to their comparable dimensions yet diverse permeabilities and permittivities. Each core serves as the basis for the construction of CMCs with 30 turns per winding, although the winding geometries may vary. Subsequently, a high-frequency equivalent circuit was derived for each CMC utilizing the methodology delineated in [ 25 ], as laid out in Section 3.2. This methodology facilitates a comparative analysis of the parasitic capacitances across the CMC samples. To assess the impact of these varying parasitic capacitances on the performance of the CMCs, transmission coefficient measurements were conducted using both asymmetric and symmetric test setups as defined in CISPR17. These setups are designed to evaluate the attenuation of CM and DM noise, respectively, provided by a filtering device. The measurements were carried out employing an R&S ZND VNA. 36 Chapter 3. Common-Mode Chokes Table 3.2 Ring cores employed in this work to construct the chokes. Core # Manufacturer Part number µr @10kHz Material 1 FAIR-RITE 5977003821 2000 MnZn 2 TDK B64290L0082X038 8500 MnZn 3 FAIR-RITE 5943003801 800 NiZn Table 3.3 Parameters of the MPC model of the CMCs characterized in this section. Key capacitive parameters are highlighted. Manufacturer Part number Winding technique C C CC (pF) CR in parallel with CCLC (mH) RC (kΩ) C C CD (pF) LD (µH) RD (kΩ) C C CW (pF) Csym (pF) LCRWnetwork NCR C1 (pF) R1 (kΩ) L (µH) C (pF) R (kΩ) FAIR-RITE 5977003821 Tight 4.79 1 3.79 26 4.37 ∞4.11 82.95 ∞21.11 -12.89 2.65 6.92 4 Loose 5.81 1 3.88 19 4.23 6510 7.67 40.18 100 33.84 -18.50 1.62 17.25 1 TDK B64290L0082X038 Tight 4.28 1 8.39 60 35.78 129 2.98 103.13 ∞16.00 -10.04 3.10 5.57 5 Loose 5.03 1 9.09 54 33.06 147 4.90 67.72 132 23.78 -13.98 2.62 9.02 3 Spaced 2.29 1 10.69 50 32.88 162 1.52 81.56 29123 4.69 -1.65 9.78 0.21 5 FAIR-RITE 5943003801 Tight 1.08 0 1.69 79 0.85 109.94 311 1.14 0.56 Loose 0.52 0 1.58 84 0.30 60.27 524 2.03 -1.43 22.26 0.10 125 Optimal 0.91 0 1.63 79 0.63 83.85 327 1.30 -0.04 2.78 2.73 23 3.4.1 Analysis of the parameters of the high-frequency circuits Table 3.3 shows the parameters derived for the MPC model of the analyzed CMC samples. For each core, we investigated two winding techniques: tight and loose windings. In the tight configuration, the distance between turns is minimized, whereas loose windings are designed to achieve an angular coverage of approximately 120o per coil. Additionally, for one of the MnZn cores (core 2), an additional sample with spaced turns was constructed. For the NiZn core (core 3), an additional winding technique labeled as optimal was examined, with details provided in Section 3.4.3. A thorough examination of the parameters in Table 3.3 for both tight and loose winding cases yields intriguing insights. Firstly, the CM inductance ( LC ) of the CMCs exhibits a high dependency on permeability, whereas the winding strategy exerts minimal influence on this CM inductance. This outcome aligns with expectations for a ring-core (non-gapped) inductor [ 12 ]. In contrast, the DM or leakage inductance ( LD ) is contingent upon winding geometries and remains relatively unaffected by core permeability. In this regard, the behavior of LD inductance mirrors that of a gapped or rod-core inductor. This observation can be elucidated by the fact that the leakage inductance is associated with magnetic field lines closing their paths outside the ring core [19]. Researching into the subtleties of the capacitive elements encapsulated within the MPC model, as delineated in Table 3.3, offers an interesting insight into the behavior of CMCs across different core materials. Notably, the parasitic capacitances CC , CD , and CW manifest a noteworthy contrast between CMCs employing MnZn cores and those outfitted with NiZn cores, despite maintaining an equivalent number of turns. This divergence finds its roots in the divergent electric permittivity exhibited by MnZn and NiZn cores. The substantial contrast in permittivity between these core materials underscores a fundamental difference in the dominant mechanisms governing parasitic electric coupling. Specifically, the higher electric permittivity inherent to MnZn cores accentuates the role of displacement currents that flow through the core in facilitating parasitic electric coupling mechanisms. Conversely, NiZn cores predominantly experience direct electric coupling through the surrounding air. 3.4 Results 37 Zooming in on CMCs outfitted with MnZn cores, an intriguing observation emerges upon varying the turn-to-turn spacing—a manipulation achievable through loose winding configurations. Herein lies a pivotal insight: widening the spatial separation between turns gives rise to a simultaneous increase in both CC and CD . As already stated in Section 2.5, the underlying mechanism for this phenomenon lies in the enhanced electric coupling facilitated by the expanded gap between turns. This augmentation further strengthens the predominant coupling mechanism within highpermittivity MnZn cores, thus leading to the observed increase in parasitic capacitances. This observation draws parallels with analogous findings reported for inductors in the literature [ 14 ], reinforcing the coherence and validity of the observed trends. When examining CMCs with NiZn cores, a noteworthy deviation from the trends observed in MnZn cores emerges from the parameters detailed in Table 3.3. Notably, both CC and CD for these CMCs not only exhibit a marked decrease compared to their MnZn counterparts but also display lower values in loose winding configurations as opposed to tight windings. This unexpected trend prompts a closer examination of the underlying mechanisms at play. The observed decrease in electric coupling as the distance between turns increases aligns with the notion that, in low-permittivity cores such as NiZn, coupling through the surrounding air may constitute the dominant mode of electrical coupling between turns. This phenomenon underscores the intricate interplay between core material properties and winding configurations, wherein the effectiveness of electric coupling is influenced by the relative permittivity of the core material and the spatial arrangement of the windings. Moreover, it’s noteworthy that the impact of winding geometry on the parasitic capacitances of CMCs is less pronounced for MnZn cores compared to NiZn cores. Specifically, in the case of CMCs with NiZn cores, the transition from tight to loose winding configurations results in a significant 50% decrease in CC , which accounts for the EPC of the CMC excited in CM. In contrast, the corresponding increases experienced by CC in MnZn cores are of a more modest magnitude, on the order of 20%. A critical consideration lies in the analysis of the parasitic capacitance CW , which refers to the electrical coupling between the two coils within the CMC. Examining the data presented in Table 3.3, a consistent pattern emerges: across all core types, CMCs manufactured with loose winding configurations consistently exhibit higher values of CW compared to their counterparts wound tightly. This trend can be intuitively understood: when the turns within each coil are spaced out, it effectively brings the coils closer together electrically. Consequently, this proximity intensifies the electrical communication between the coils, resulting in increased CWvalues. 3.4.2 Comparison of performances of CMC samples MnZn cores (cores 1 and 2) The analysis conducted on the parameters of the MPC model of CMCs, as detailed in the preceding section, lends credence to the primary hypothesis posited in this study. Namely, it asserts that the impact of a specific winding strategy on the parasitic capacitances of a CMC is heavily contingent upon the permittivity of the core material. The practical implications of the disparities observed in the parasitic capacitances across the assembled CMC samples were experimentally clarified to examine the attenuation provided by these CMCs for both common-mode and differential-mode signals. Illustrated in Fig. 3.11, are the magnitude and phase plots of the measured S21 curves for both the asymmetrical and symmetrical test setups. These measurements were conducted on two CMCs—one wound tightly and the other loosely—fabricated using core 1 detailed in Table 3.2 (MnZN core with lower permittivity). Notably, the precision of the MPC model is verified through the inclusion of calculated S21 curves in the aforementioned graphs. 38 Chapter 3. Common-Mode Chokes (a) Asymmetrical mode (CM). Magnitude. MSE×10−6: Tight: 9.2; Loose: 18. (b) Asymmetrical mode (CM). Phase. (c) Symmetrical mode (DM). Magnitude. MSE×10−3: Tight: 3.5; Loose: 4.2. (d) Symmetrical mode (DM). Phase. Figure 3.11 Transmission coefficients for asymmetrical (CM) and symmetrical (DM) mode connections measured for two samples of 30-turns-per-winding CMCs with tight and loose winding configurations on a MnZn FAIR-RITE 5977003821 core. Measurements are compared with transmission coefficient predicted by the circuit model in Fig. 3.4 with the parameters given in Table 3.3. Concordances of each pair of experimental and circuit-model curves are quantified by the mean squared errors (MSE) provided below each graph. In Fig. 3.11(a), a discernible trend emerges: the tight winding configuration yields a marginal improvement in CM noise attenuation at higher frequencies compared to the loose configuration. This enhancement can be attributed to the fact that the tight winding setup effectively mitigates the electrical coupling between turns within a CMC equipped with a high-permittivity core. Conversely, Fig. 3.11(c) highlights how the tight winding configuration also amplifies the DM attenuation of the CMC. In this instance, the enhancement extends to the low-frequency region due to the reduction in turn-to-turn distances, resulting in an increase in the leakage inductance ( LD ) of the CMC, as discussed earlier. Additionally, Fig. 3.11(c) unveils a second high-frequency resonance in the symmetrical transmission coefficient, attributed to the resonant behavior of YW , as detailed in Section 3.2. Figs. 3.11(b) and 3.11(d) provide insights into the phase characteristics of the measured transmission coefficients. It’s noteworthy to observe that these phases exhibit sharp transitions around the resonance frequencies of each coefficient, accurately captured by the CMC circuit model. These 3.4 Results 39 (a) Asymmetrical mode (CM). Magnitude. MSE×10−6: Tight: 6.1; Loose: 9.0; Spaced: 7.1. (b) Asymmetrical mode. Phase. (c) Symmetrical mode (DM). Magnitude. MSE×10−3: Tight: 1.0; Loose: 3.6; Spaced: 2.9. (d) Symmetrical mode. Phase. Figure 3.12 Transmission coefficients for asymmetrical and symmetrical mode (CM and DM) connections measured for two samples of 30-turns-per-winding CMCs with tight and loose winding configurations on a MnZn TDK B64290L0082X038 core. Measurements are compared with transmission coefficient predicted by the circuit model in Fig. 3.4 with the parameters given in Table 3.3. Concordances of each pair of experimental and circuit-model curves are quantified by the mean squared errors (MSE) provided below each graph. phase transitions are intricately linked to changes in the behavior of the modal admittances YC and YD . As delineated in Table 3.1, these admittances correspond to parallel LCR resonators; thus, they undergo a transition at resonance from an inductive to a capacitive response. The findings with respect to the CMCs crafted with the MnZn core of higher permeability, denoted as core 2 in Table 3.2, are delineated in Fig. 3.12. In this scenario, the high permeability of the core gives rise to a higher value of LC , thereby resulting in a lower resonance frequency for Sasym 21 . Nonetheless, akin to the observations made for the other MnZn core-based CMC, the tight winding configuration yields marginally superior performance compared to the loose configuration for both CM and DM signals. This improvement can be attributed to the slightly lower parasitic capacitances and higher LDcharacteristic of the tight winding setup. This analysis suggests that significantly enhancing the performance of CMCs with high-permittivity cores through alterations in turn-to-turn winding distance is unlikely to be feasible. Insights derived from prior studies on inductors [ 14 ] indicate that a cost-effective strategy to mitigate these parasitic 40 Chapter 3. Common-Mode Chokes (a) Asymmetrical mode (CM). Magnitude. MSE×10−6: Tight: 4.3; Loose: 5.5. (b) Asymmetrical mode. Phase. (c) Symmetrical mode (DM). Magnitude. MSE×10−3: Tight: 1.5; Loose: 3.4. (d) Symmetrical mode. Phase. Figure 3.13 Transmission coefficients for asymmetrical and symmetrical mode (CM and DM) connections measured for two samples of 30-turns-per-winding CMCs with tight and loose winding configurations on a NiZn FAIR-RITE 5943003801 core. Measurements are compared with transmission coefficient predicted by the circuit model in Fig. 3.4 with the parameters given in Table 3.3. Concordances of each pair of experimental and circuit-model curves are quantified by the mean squared errors (MSE) provided below each graph. capacitances involves increasing the distance between the turns and the core. To investigate the beneficial effect of this strategy on the attenuation and equivalent circuit parameters of practical CMCs, an additional CMC sample was fabricated. This sample features tight coils wound on the same MnZn core 2; however, the turns of the coils have been deliberately separated from the core by 2 mm using multiple layers of low-permittivity insulating material (paper tape). This winding technique, labeled as “Spaced" in Table 3.3, yields notable reductions of approximately 50% in CC and CD parasitic capacitances compared to the tight version of the CMC. Consequently, this modification results in substantially improved attenuation provided by the CMC at high frequencies for both symmetrical and asymmetrical mode connections, as depicted in Fig. 3.12. Notably, a noteworthy reduction of 5 dB in CM transmission above resonance is observed. Similar outcomes have been verified for the CMC constructed with MnZn core 1. An alternative strategy that could be explored to enhance the attenuation of CMCs manufactured with highpermittivity cores involves stacking the turns of the windings to separate some of them from the 3.4 Results 41 core. However, our investigations reveal that this strategy leads to significant increases in parasitic capacitances CCand CD, resulting in markedly inferior CMC performance at high frequencies. NiZn core (core 3) Fig. 3.13 presents the results obtained for the CMCs constructed with the NiZn core identified as core 3 in Table 3.2. Several intriguing differences emerge when compared to the results obtained for MnZn cores. Firstly, NiZn CMC samples exhibit a significantly lower LC inductance for the same number of turns, in line with expectations. Consequently, this leads to a higher resonance frequency in Sasym 21 , as depicted in Fig. 3.13(a). Additionally, owing to the substantially lower parasitic capacitances associated with this low-permittivity core, the attenuation provided at high frequencies surpasses that provided by the CMCs with MnZn cores. However, the most notable distinction lies in the optimal winding configuration for achieving better attenuation of CM noise at high frequencies. Surprisingly, for the CMC with a NiZn core, the loose winding configuration outperforms the tight winding configuration. This observation concurs with the analysis presented in Section 3.4.1, which suggested that for low-permittivity cores, increasing the distance between turns should reduce the parasitic capacitance CC. Regarding DM attenuation, the results depicted in Fig. 3.13(c) unveil a noteworthy trend: related to high-permittivity cores, a higher attenuation is achieved by employing the tight winding configuration. This enhancement primarily stems from its impact on LD . Additionally, Fig. 3.13(c) highlights a distinct difference in the high-frequency behaviors of the transmission coefficient Ssym 21 between the loose and tight winding configurations. Specifically, the tight configuration exhibits a sharp resonance, contrasting with the noticeably smoother resonance of the loose configuration. This disparity arises from the fulfillment of the condition CW>2CD in the case of loose windings. Consequently, the difference YD−YW in the numerator of Ssym 21 in (3.3) yields a negative virtual capacitance, preventing the cancellation of susceptances necessary for a pronounced resonance. Conversely, for the tight winding configuration, where CW<2CD , the opposite scenario unfolds. This assertion is corroborated by examining the parameters in Table 3.3. What’s intriguing about this situation is the existence of an intermediate winding arrangement that satisfies the cancellation condition CW≈2CD. The performance of a CMC that meets this condition is worthy of investigation in the subsequent section, as it holds the promise of exhibiting unique electrical characteristics distinct from those observed for either extreme winding configuration. 3.4.3 Customizing DM attenuation of a CMC with NiZn core To construct a CMC whose parasitic capacitances adhere closely to the cancellation condition CW≃2CD , we undertook the fabrication of an additional single-layer CMC sample utilizing a NiZn core (core 3). Starting with a tight configuration, we progressively separated the turns of the two coils until a discernible alteration was observed in the measured transmission coefficient for the symmetrical connection of the CMC. We designate this configuration as the "optimal configuration". The parameters of the MPC model corresponding to this optimal case are detailed in Table 3.3. Notably, Csym ≃0for the optimal case, indicative of its proximity to the cancellation condition. In Fig. 3.14, the measured curve |Ssym 21 | for this optimal configuration is juxtaposed with both the tight and loose winding cases. Due to the emergence of additional resonances at high frequencies, achieving ideal attenuation becomes unachievable. This observation underscores the inherent complexities associated with engineering CMCs to precisely meet cancellation conditions while accommodating real-world constraints and imperfections. These findings align seamlessly with the analysis delineated in Section 3.2.1, thereby enabling us to draw conclusive insights. For single-layer CMCs outfitted with low-permittivity cores, the 42 Chapter 3. Common-Mode Chokes               Figure 3.14 Measured transmission coefficient in symmetrical connection (DM) for 30-turns per winding CMCs constructed with NiZn FAIR-RITE 5943003801 core. Previous samples with the same core are compared with an additional CMC designed to optimize the gap between neighboring turns. manipulation of turn-to-turn distances emerges as a viable strategy to attain a compromise solution. This solution entails significantly enhancing attenuation against DM noise compared to the loose configuration, while concurrently achieving superior attenuation against CM noise compared to the tight configuration. 3.5 Conclusions This chapter analyzes the influence of core electrical permittivity and winding arrangement on the high-frequency performance of single-layer ring-core CMCs. Various CMC samples were fabricated utilizing different core materials and winding techniques, conducting thorough examinations to assess their impact on the parasitic capacitances governing their high-frequency behavior. Employing an accurate high-frequency circuit model tailored to these CMCs, the effect of diverse winding strategies on their efficacy against CM and DM noise has been meticulously quantified. The investigations corroborate the validity of the central hypothesis: the electrical coupling mechanism in CMCs exhibits notable variations depending on whether the core comprises MnZn or NiZn material, attributable to their distinct electrical permittivities. Specifically, it has been observed that the coupling mechanism is primarily determined by the effect of displacement currents through the air or the core. CMCs featuring high-permittivity MnZn cores primarily manifest displacement currents through the core, while those with low-permittivity NiZn cores predominantly exhibit displacement currents through the air. Consequently, the optimal winding strategy for enhancing high-frequency response differs between these core types. Tight coil winding configurations prove advantageous for CMCs with high-permittivity cores, while for substantial CM attenuation improvements, a single-layer configuration with windings separated from the core is preferable. Conversely, NiZn cores benefit from increased spacing between turns to enhance CM attenuation, albeit at the expense of DM attenuation. These insights, constituting the primary contribution of the study, find support in experimental measurements and the coherence observed between these measurements and the precise circuit models developed for the analyzed CMCs. 3.5 Conclusions 43 In addition, an intermediate optimal configuration for NiZn cores has been identified, marked by the cancellation of parasitic capacitors. However, it has been demonstrated that the noticeable improvements in DM attenuation achieved with this configuration are primarily constrained to the proximity of the CMC’s resonance frequency. This analysis finds support in a novel multi-stage model of the CMC, facilitating the explanation and quantification of the bandwidth limitations inherent in this optimization technique. This multi-stage model offers insights into the frequency of high-frequency resonances observed in real CMCs and elucidates their physical significance, serving as a tool for precise frequency calculations and explanation of observed phenomena. 50 Chapter 4. Addressing Asymmetries in Common-Mode Chokes discrepancy in the measured responses depending on the terminal connection is clearly shown in the figure, thus highlighting the asymmetry of the CMC. Importantly, the asymmetric behavior is effectively captured by the model. It is worth noting that the frequency range in the figure was extended to 30 MHz, aligning with the range where many EMC standards regulate conducted emissions. Following characterization of the CMC, an evaluation was conducted to determine the accuracy of the obtained asymmetric model in predicting the attenuation provided by the CMC within the designated frequency range. The transmission coefficient of the CMC was measured under both symmetrical and asymmetrical configurations as outlined in CISPR17 to characterize the DM and CM attenuation of filtering devices, respectively. These measured results were then compared with the predictions of both a symmetric and asymmetric MPC model of the CMC. Notably, for the asymmetrical setup, no significant improvement was observed when employing the asymmetric model compared to the symmetric model. This aligns with the findings presented earlier in Fig. 4.2, where no discrepancies were identified in the first resonance of the OC curve –a characteristic associated with the CM response of the CMC– when utilizing different terminal pairs for the measurement. Despite the absence of significant enhancements for the asymmetrical configuration (CM attenuation), the asymmetric model demonstrated significant enhancements in the prediction of the transmission coefficient across the entire frequency range for the symmetrical configuration (DM attenuation). This is further illustrated in Fig. 4.3, where the asymmetric model exhibits a more accurate fit, particularly in the inductive region of the curve. These findings suggest that incorporating asymmetries is crucial for accurately modeling the effect on the CMC’s leakage inductance, which is primarily responsible for DM behavior. This observed disparity in the impact of asymmetries on differential and common mode inductance can be explained by considering the fundamental concept of inductance in each winding. The total inductance witnessed in each winding is the sum of its self-inductance and the mutual inductance between windings, with the latter being nearly equal to the self-inductance as referenced in [ 9 ]. In such a scenario, a minor difference between self-inductances has minimal relative impact on the overall CM inductance. Conversely, leakage inductance is directly proportional to the difference between the selfinductance of each winding and the mutual inductance. Consequently, the same discrepancy between the two self-inductances has a considerably larger effect on the leakage inductance. An Figure 4.3 Transmission coefficient for the EMIKON FHE-05-1055 CMC under symmetrical connection. Both models with and without perturbations are jointly presented. 4.4 Conclusions 51                Figure 4.4 Comparison of differential mode transmission and differential-to-common mode conversion for the EMIKON FHE-05-1055 CMC under symmetrical connection. alternative explanation can be framed by considering that CM inductance is associated with the total magnetic flux within each winding, generated by the combined field lines of both windings. Slight asymmetries in the windings are unlikely to significantly alter this total flux. In contrast, the DM inductance of each winding is related exclusively to the magnetic field lines not linking both windings. Any deviations from perfect symmetry in the windings are expected to have a more pronounced effect on this specific magnetic field and, consequently, the DM inductance. The preceding results have demonstrated that incorporating potential CMC asymmetries into the MPC model enhances its accuracy, particularly regarding the DM response of the CMC. However, another crucial benefit of considering asymmetry during CMC modeling lies in the ability to estimate mode conversion induced by the device. Upon determining the parameters of the asymmetric MPC model, mode conversion can be estimated by calculating the SCD21 term within the mixed-mode S-parameter matrix, as shown in (4.7) . Fig. 4.4 presents the SCD21 parameter for the CMC characterized in this section. It is compared alongside the SDD21 parameter, representing the transmission of the DM signal and equivalent to Ssym 21 in (3.3) . The figure reveals that around 40 MHz, the magnitudes of SCD21 and SDD21 become comparable. This indicates that, for this specific CMC, the amount of output CM noise generated by a given DM excitation at these high frequencies can be of the same order of magnitude as the transmitted DM noise. Fig. 4.5 presents a similar comparison between the SCC21 and SDC21 parameters. It is noteworthy that the high-frequency behavior of the SCC21 representing CM-to-CM transmission, is likely influenced by the capacitive parasitics of the CMC. This is evident from the similar increase in transmission at high frequencies for both mode conversion (SDC21) and CM transmission (SCC21). In fact, the SCC21 curve for the asymmetrical connection consistently remains above the SDC21 parameter by a margin of approximately 20 dB across the entire frequency range. This observation suggests that mode conversion is not a significant concern for this particular CMC when subjected to CM excitation. 4.4 Conclusions The study presented in this chapter highlights the importance of accounting for inherent asymmetries in common-mode chokes when modeling their high-frequency behavior. Often overlooked, these 52 Chapter 4. Addressing Asymmetries in Common-Mode Chokes Figure 4.5 Comparison of common mode transmission and common-to-differential mode conversion for the EMIKON FHE-05-1055 CMC under asymmetrical connection. asymmetries can significantly impact the accuracy of CMC models, particularly in their response to differential mode excitations. To address this issue, the research proposes a modified physically-based model of the CMC and a characterization method that incorporates asymmetry effects. Results for a specific CMC demonstrate that considering asymmetries enhances the model’s accuracy, improving its ability to predict the CMC’s response to differential-mode excitations. Furthermore, a preliminary investigation confirms the proposed model’s sensitivity to mode conversion caused by CMC asymmetries. This work serves as a foundation for more comprehensive studies that can analyze additional CMC samples, integrate other components within EMI filters, and estimate mode conversion to optimize filtering solutions. Future research could also explore the impact of asymmetries on multiphase CMCs, contributing to the understanding and design of effective EMI suppression solutions for electronic systems. 5 Conclusions I n this final chapter, we draw broad conclusions from the research presented in this document. The insights gained from the preceding chapters have significant implications for the design and optimization of inductors and common-mode chokes for electromagnetic interference applications. One of the primary insights from this study is the significant impact of parasitic capacitance on EMI filtering performance. Throughout the chapters, it has been demonstrated that by addressing parasitic capacitance through careful design considerations, engineers can substantially improve the effectiveness of inductors and CMCs in real-world applications. The findings emphasize that optimizing the design to minimize these parasitics is crucial for maintaining the efficiency, reliability, and regulatory compliance of electronic devices. The research presented practical design guidelines for minimizing parasitic effects, particularly focusing on ring-core inductors and CMCs. For instance, the investigation into ring-core inductors revealed that loose winding strategies can effectively reduce parasitic capacitance for low-permittivity core materials, thus enhancing the resonance frequency and lowering the transmission coefficient above resonance. This insight is invaluable for engineers seeking to improve EMI mitigation in high-frequency applications. In the case of CMCs, the study highlighted the influence of winding strategies on parasitic capacitance, showing how core material properties play a crucial role. Practical guidelines were developed to aid in designing CMCs with reduced parasitic capacitance, thereby improving their performance in suppressing EMI. Additionally, the research addressed the challenge of asymmetries in CMCs, which can arise from manufacturing imperfections or variations in core material properties. A novel method was introduced to account for these asymmetries, significantly enhancing the accuracy of models and the effectiveness of EMI suppression strategies. While significant progress has been made in understanding and mitigating parasitic effects, there remain avenues for further research. Future studies could explore synthetic materials such as nanocrystalline cores and sophisticated modeling approaches based on finite element simulations to continue advancing the state-of-the-art in EMI mitigation. Additionally, incorporating other EMI filter components will refine mode conversion estimations and optimize filter design. In summary, this document has synthesized key findings and practical insights from extensive experimentation and analysis, providing a robust foundation for future endeavors in the field of EMI mitigation. The conclusions drawn from this research not only advance the understanding of parasitic effects in inductors and CMCs, but also offer practical solutions to enhance the performance and reliability of electronic systems in increasingly complex electromagnetic environments. 53 List of Figures 1.1 Basic decomposition of an EMI problem 2 1.2 Schematic representation of common-mode and differential-mode currents in a singlephase connection 3 2.1 Magnetic flux inside an inductor [9] 7 2.2 Schematic of a first order low-pass filter optimal for small source and load impedances, ZS and ZLrespectively 9 2.3 Schematic of a second order low-pass filter 10 2.4 Measured impedance of a 1.2 µH inductor: (a) magnitude; (b) phase [9] 11 2.5 Lumped elements circuit for inductors 12 2.6 Experimental setup for measuring the transmission coefficient of an inductor with a spectrum analyzer (SA) with tracking generator (TG) 14 2.7 Transmission coefficient for 30-turns inductors constructed with a NiZn FAIR-RITE 5943003801 core. Measured data are compared with transmission coefficient predicted by the circuit model in Fig. 2.5 with the parameters provided by the PSO search algorithm, given in Table 2.2 17 2.8 Transmission coefficient for 30-turns inductors constructed with a MnZn FAIR-RITE 5977003821 core. Measured data are compared with transmission coefficient predicted by the circuit model in Fig. 2.5 with the parameters provided by the PSO search algorithm, given in Table 2.2 18 2.9 Transmission coefficient for 30-turns inductors constructed with a MnZn TDK B64290L0082X038 core. Measured data are compared with transmission coefficient predicted by the circuit model in Fig. 2.5 with the parameters provided by the PSO search algorithm, given in Table 2.2 19 2.10 Comparison of inductor responses for different winding techniques for a MnZn 5977003821 core 20 2.11 Measured and estimated transmission coefficient of two inductors of 1mH constructed with tight windings of different number of turns on different core materials: 30 turns on a NiZn core (5943003801) and 19 turns on a MnZn core (5977003821) 21 3.1 Magnetic flux inside a CMC under different excitations [9] 23 3.2 Generic EMI filter topology (left). Decomposition of an EMI filter into: CM filter (top right) and DM filter (bottom right) 24 3.3 Schematic representation of the electric coupling mechanisms between two adjacent turns of a winding on a magnetic ring-core 26 3.4 High-frequency modal-parameters circuit (MPC) model of a CMC used in this work. The CM and DM blocks determine the response of the component to asymmetrical and symmetrical test setups defined in CISPR-17 standard, respectively [25] 27 55 56 List of Figures 3.5 Setups for characterizing a CMC according to CISPR-17 standard [ 1 ] with a spectrum analyzer (SA) featuring a tracking generation (TG) 29 3.6 Setup for insertion loss measurement in symmetrical (DM) connection according to CISPR- 17 standard. Commercially available 1:1 transformers (Coilcraft WB2010-1) have been utilized as 180◦dividers 30 3.7 Equivalent circuit of a CMC connected in symmetrical test setup (left). Decomposition of the circuit into the natural modes excited by the connection. The arrows indicate the direction of the current (right) 31 3.8 High-frequency circuit in stages to include distributed effects of CMCs. Each stage is connected in series 32 3.9 Ratio between the frequencies of resonance of modes W and D as function of close and distant coupling coefficients. Cancellation of D and W modal capacitances has been assumed 33 3.10 Setups for characterizing a CMC according to the MPC method [25] 34 3.11 Transmission coefficients for asymmetrical (CM) and symmetrical (DM) mode connections measured for two samples of 30-turns-per-winding CMCs with tight and loose winding configurations on a MnZn FAIR-RITE 5977003821 core. Measurements are compared with transmission coefficient predicted by the circuit model in Fig. 3.4 with the parameters given in Table 3.3. Concordances of each pair of experimental and circuit-model curves are quantified by the mean squared errors (MSE) provided below each graph 38 3.12 Transmission coefficients for asymmetrical and symmetrical mode (CM and DM) connections measured for two samples of 30-turns-per-winding CMCs with tight and loose winding configurations on a MnZn TDK B64290L0082X038 core. Measurements are compared with transmission coefficient predicted by the circuit model in Fig. 3.4 with the parameters given in Table 3.3. Concordances of each pair of experimental and circuit-model curves are quantified by the mean squared errors (MSE) provided below each graph 39 3.13 Transmission coefficients for asymmetrical and symmetrical mode (CM and DM) connections measured for two samples of 30-turns-per-winding CMCs with tight and loose winding configurations on a NiZn FAIR-RITE 5943003801 core. Measurements are compared with transmission coefficient predicted by the circuit model in Fig. 3.4 with the parameters given in Table 3.3. Concordances of each pair of experimental and circuit-model curves are quantified by the mean squared errors (MSE) provided below each graph 40 3.14 Measured transmission coefficient in symmetrical connection (DM) for 30-turns per winding CMCs constructed with NiZn FAIR-RITE 5943003801 core. Previous samples with the same core are compared with an additional CMC designed to optimize the gap between neighboring turns 42 4.1 Modified high-frequency modal-parameters circuit (MPC) model of a CMC used in this chapter [ 25 ]. Asymmetries are modeled as perturbations in specific values within the differential block 46 4.2 Transmission coefficient for the EMIKON FHE-05-1055 CMC for the OC connections. Measurements are compared with transmission coefficient predicted by the circuit model in Fig. 4.1 with the parameters given in Table 4.3 49 4.3 Transmission coefficient for the EMIKON FHE-05-1055 CMC under symmetrical connection. Both models with and without perturbations are jointly presented 50 4.4 Comparison of differential mode transmission and differential-to-common mode conversion for the EMIKON FHE-05-1055 CMC under symmetrical connection 51 4.5 Comparison of common mode transmission and common-to-differential mode conversion for the EMIKON FHE-05-1055 CMC under asymmetrical connection 52 List of Tables 2.1 Ring cores employed in this work to construct the inductors 16 2.2 Parameters of the inductors characterized in this section 16 2.3 Parameters of the inductors imposing turn-to-core separation 19 3.1 Modal admittances of the MPC model of a CMC 28 3.2 Ring cores employed in this work to construct the chokes 36 3.3 Parameters of the MPC model of the CMCs characterized in this section. Key capacitive parameters are highlighted 36 4.1 Eigenvectors of a symmetrical four-port network. Ports are numbered according to Fig. 4.1 46 4.2 Modal admittances of the asymmetrical model of a CMC shown in Fig. 4.1 47 4.3 Parameters of the proposed model of the CMC characterized in this section 49 57 Bibliography [1] CISPR-17:2011, “Methods of measurement of the suppression characteristics of passive EMC filtering devices,” 2011. [2] MIL-STD-461F, “Requirements for the control of electromagnetic interference characteristics of subsystems and equipment,” 2007. [3] RTCA/DO-160G, “Environmental conditions and test procedures for airborne equipment,” 2010. [4] H. Ott, Electromagnetic Compatibility Engineering, 1st ed. Wiley Publishing, 2009. [5] B. Zhang and S. Wang, “A survey of emi research in power electronics systems with widebandgap semiconductor devices,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 8, no. 1, pp. 626–643, 2020. [6] P. Ruiz-Morales, Ojeda-Rodríguez, J. Bernal-Méndez, and M. A. Martín-Prats, “Reducing parasitic capacitances of ring-core inductors,” in 2023 International Symposium on Electromagnetic Compatibility – EMC Europe, 2023, pp. 1–6. [7] ——, “Winding optimization for reducing parasitic capacitances of common-mode chokes,” IEEE Transactions on Electromagnetic Compatibility, 2024, in press. [8] P. Ruiz-Morales, J. Bernal-Méndez, and M. A. Martín-Prats, “Modelling asymmetry and mode conversion in common-mode chokes,” in 2024 International Symposium on Electromagnetic Compatibility – EMC Europe, 2024, forthcoming. [9] C. R. Paul, Introduction to Electromagnetic Compatibility, 2nd ed. Hoboken, New Jersey: John Wiley and Sons, 2006. [10] E. Bogatin, Signal and Power Integrity - Simplified, 2nd ed. USA: Prentice Hall PTR, 2009. [11] A. Massarini and M. Kazimierczuk, “Self-capacitance of inductors,” IEEE Transactions on Power Electronics, vol. 12, no. 4, pp. 671–676, 1997. [12] W. Hurley and W. Wölfle, Transformers and Inductors for Power Electronics: Theory, Design and Applications, ser. Ingenieria electrica. Wiley, 2013. [Online]. Available: https://books.google.es/books?id=MtGRBQAAQBAJ [13] Y. Li and S. Wang, “Modeling and increasing the high-frequency impedance of single-layer mn-zn ferrite toroidal inductors with electromagnetic analysis,” IEEE Trans. Power Electron., vol. 36, no. 6, pp. 6943–6953, jun 2021. 59