Protection by Open Systems: an EMC Study

Transcription

1 Protection by Open Systems: an EMC Study

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3 Protection by Open Systems: an EMC Study PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magnificus, prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op donderdag 29 september 2005 om uur door Siarhei Kapora geboren te Minsk, Belarus

4 Dit proefschrift is goedgekeurd door de promotor: prof.dr.ir. J.H. Blom Copromotor: dr. A.P.J. van Deursen The research was performed at the faculty of Electrical Engineering of the Eindhoven University of Technology and was partially financially supported by the Interuniversity Research Institute COBRA and Viasystems Mommers B.V. Printed by Printservice Technische Universiteit Eindhoven, the Netherlands. Cover design by Paul Verspaget. CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN Kapora, Siarhei Protection by open systems: an EMC study / by Siarhei Kapora. - Eindhoven : Technische Universiteit Eindhoven, Proefschrift. - ISBN NUR 959 Trefw.: elektromagnetische interferentie / elektromagnetische koppelingen / elektrische afscherming / gedrukte bedrading / elektrische kabels. Subject headings: electromagnetic compatibility / electromagnetic interference / electromagnetic coupling / electromagnetic shielding / printed circuits / crosstalk / electric conduits.

5 To my parents

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7 Contents Summary Samenvatting iii v 1 Introduction Electromagnetic Compatibility in Modern World Definitions Objectives Methods Overview Publications Protection of Cables by Open Metal Conduits Introduction Configuration Simulations Induced Currents Induced Voltages Transmission Line Approach Different Shapes Different Orientations and Polarization Different Wire Diameters Measurements Measurements Inside Semi-anechoic Room Measurements Inside Fully Anechoic Room Effect of Conducting Floor Conduit with Cover Higher Frequencies Concluding Remarks and Outlook Three-layer PCB on Top of a Cabinet Panel Introduction Configuration Experimental Setup and Simulation Description Signal Transfer Results Resonances Non-resonant Losses Gap Variation i

8 ii Contents 3.5 Radiation Results Conclusions Reduction of Inductive Common-Mode Coupling of Printed Circuit Boards by Nearby U-Shaped Metal Cabinet Panel Introduction Configuration Inductive DM-CM Coupling Results Concluding Remarks Appendix A: Schwarz-Christoffel Transformation Appendix B: Complex Potential of a Line Current Between Two Cylinders Appendix C: Complex Potential of a Line Current Between Two Planes 56 5 Shielded Tracks on a Printed Circuit Board Introduction Characteristic Impedance Z A Single Track Two Tracks within One Shield Coupling Between Partially Shielded Tracks Conclusions Optimization of Interface Between Connectors and Tracks on Printed Circuit Boards Introduction Testboards and Measurement Setup Standard Mounting of Connectors Signal Transfer Input Impedance Modified Mounting of PTH Connectors Testboard B Simulations Configuration Effect of Pin Length Comparison Between Measurements and Simulations Additional Possibilities for Optimization Crosstalk Measurements Conclusions General Conclusions and Outlook General Conclusions Outlook Bibliography 91 Acknowledgements 97 Curriculum Vitae 99

9 Summary Electromagnetic interference (EMI) is an important factor in the design of modern electronic equipment. A fully closed structure (Faraday cage) around the electronics would prevent the coupling towards and from the environment. However, practical considerations (accessibility, thermal characteristics, production costs etc.) seldom allow the implementation of such closed shields. This thesis presents the results of experimental and numerical investigation into the electromagnetic compatibility (EMC) properties of open systems of various levels and sizes. The first study involves metal conduits, which are used for mechanical support of cables and may provide protection against electromagnetic interference. Being the most common shape, an open U-shaped conduit has been chosen as basic configuration. A number of wires inside the brass conduit represent the actual cables with their shields. This configuration is subjected to a plane wave excitation to determine induced currents in the wires. It is known that the open conduit can reduce the undesired coupling significantly. New in this study is the extended frequency range. Measurements and simulations agree up to frequencies where the wavelength is several time shorter than the conduit length, but still larger than cross-sectional dimensions. Another study concerns the coupling of printed circuit boards (PCB) with the environment, or the common-mode (CM) circuit. A nearby cabinet panel influences the signal transmission and radiation of PCB tracks. This influence has been studied for straight and meandering tracks by measurements and 3D calculations. If properly connected, a cabinet panel reduces the undesired CM coupling significantly. An improperly connected cabinet may lead to enhanced coupling. The coupling is also affected by the shape of the cabinet panel, and by the way the signals are transported, either as a balanced signal via two tracks or unbalanced signal with a single track and the groundplane. A 2D model study showed the positive effects and also many possible situations where the coupling is enhanced. A novel technology allows production of fully shielded tracks on a PCB, by which the coupling can be extremely reduced. Even with partly open shields, the differentialmode (DM) and the CM coupling of tracks is considerably smaller compared to conventional transmission lines. The influence of manufacturing tolerances on characteristic impedance has been studied as well. iii

10 iv Summary In order to correctly perform the measurements on PCB, the influence of the connectors has to be minimized. Special attention has been paid to the interface between connector and both shielded and traditional transmission lines on a PCB. The simulations were performed with Schwarz-Christoffel mapping for simply and doubly connected polygonal regions, static 2D Method of Moments, dynamic 3D Method of Moments (CONCEPT by the Technical University Hamburg-Harburg and FEKO by EMSS), and Finite Integration Technique (Microwave Studio by CST GmbH). The experimental investigations on PCBs have been carried out in the TU/e groups EPS (up to 1.8 GHz), and EM (up to 18 GHz). The radiation measurements were performed in the EMC test facility of Philips Medical Systems in Best and the Philips Electromagnetic and Cooling Competence Center in Eindhoven, the Netherlands. Various results were presented at a number of international conferences. Chapter 4 is accepted for publication in the IEEE Transactions on Electromagnetic Compatibility and Chapter 5 is published in the Journal of Electromagnetic Waves and Applications.

11 Samenvatting Elektromagnetische interferentie (EMI) is een belangrijke factor bij het ontwerp van moderne elektronische apparatuur. Een volledig gesloten structuur (Faraday kooi) rond elektronica zou de koppeling naar en van de omgeving voorkomen. Echter om praktische redenen zoals toegankelijkheid, warmteafvoer, productie kosten enz. kan men een dergelijke gesloten bescherming zelden gebruiken. Dit proefschrift geeft de resultaten weer van experimenteel en numeriek onderzoek naar de elektromagnetische compatibiliteit (EMC) van open systemen van verschillende niveaus en afmetingen. De eerste studie gaat over metalen goten die gebruikt worden voor mechanische ondersteuning van kabels. Zij kunnen tevens een bescherming bieden tegen elektromagnetische interferentie. Als basisconfiguratie hebben we het vaak gebruikte open U-vormige goot gekozen. Een aantal draden binnen een messing goot representeert de feitelijke kabels met hun afscherming. Deze configuratie hebben we bestraald met een vlakke golf; daarbij zijn de geïnduceerde stromen in de draden bepaald. Het is bekend dat zelfs een open goot de ongewenste koppeling sterk kan verminderen. Nieuw in deze studie is het uitgebreider frequentiebereik. De metingen en de berekeningen zijn nu uitgevoerd tot frequenties waarbij de golflengte enkele malen kleiner is dan de gootlengte, maar wel nog groter is dan de dwarsdoorsnede. Een verdere studie betreft de koppeling van printplaten met de omgeving oftewel de common-mode (CM) circuit. Een paneel van een kast om of nabij die printplaat beïnvloedt de signaaltransmissie en straling van printplaat sporen. Dit is bestudeerd voor rechte en meanderende sporen aan de hand van metingen en 3D berekeningen. Mits correct aangesloten, kan het kastpaneel de ongewenste CM koppeling sterk reduceren. Daarentegen kan een onjuist aangesloten kast leiden tot sterk verhoogde koppeling. De koppeling is ook te beïnvloeden door de vorm van het kastpaneel en door de wijze van signaaltransport: gebalanceerd signaal door twee sporen, of ongebalanceerde signaal door een enkel spoor en het aardvlak. Een 2D modelstudie laat de positieve effecten zien, maar ook een aantal mogelijke situaties waarin de koppeling is toegenomen. Een nieuwe, gepatenteerde technologie behelst de productie van volledig afgeschermde sporen op een printplaat. De koppeling kan dan tot in het extreme gereduceerd worden. Zelfs met een gedeeltelijk open afscherming is de differential-mode (DM) en CM koppeling van de sporen nog aanmerkelijk kleiner in vergelijking met meer gebruikelijke transmissielijnen. Tevens hebben we de invloed van de productietoleranties op de karakteristieke impedantie berekend. v

12 vi Samenvatting Voor correcte metingen aan printplaten moet de invloed van connectoren zo ver mogelijk teruggebracht worden. Bijzondere is gegeven aan de overgang tussen de connector en de sporen op de printplaat, zowel afgeschermd als de traditioneel. De simulaties zijn uitgevoerd met een aantal methodes zoals de Schwarz-Christoffel afbeelding voor enkelvoudig en meervoudig verbonden polygone gebieden, een statische 2D Method of Moments, een dynamische 3D Method of Moments (CONCEPT van de Technische Universiteit Hamburg-Harburg en FEKO van EMSS), en de Finite Integration Technique (Microwave Studio van CST GmbH). Het experimentele onderzoek was gedaan in de groepen EPS en EM van de Technische Universiteit Eindhoven. De straling metingen zijn uitgevoerd in EMC test-laboratorium van Philips Medical Systems in Best en bij het Philips Electromagnetic and Cooling Competence Center in Eindhoven, Nederland. Verschillende resultaten zijn eerder gepresenteerd op een aantal internationale conferenties, enkele op uitnodiging. Hoofdstuk 4 verschijnt in de IEEE Transactions on Electromagnetic Compatibility en Hoofdstuk 5 is gepubliceerd in het Journal of Electromagnetic Waves and Applications.

13 Chapter 1 Introduction 1.1 Electromagnetic Compatibility in Modern World Electronic equipment plays an increasingly important role in our life. Almost every household these days has one or more personal computers (PC), often connected into a wireless local area network (LAN), a fact unthinkable in the recent past. The number of mobile phones has grown enormously as well. The operating frequencies of the modern electronics lay well above 1 GHz range and continue to rise even further. A good example of this tendency is the modern PC. With the advances in semiconductor technology, the processor clock frequency approaches 4 GHz, compared with a few hundreds of megahertz just a decade ago. An extensive development of wireless communication technologies with the increased frequencies of operations due to the demands for extended bandwidths has been observed in recent years (1.8 GHz for GSM, 2.4 GHz Bluetooth and IEEE b,g wireless networks and IEEE a LANs operating in the 5 GHz range). As a result, the number of radio-frequency (RF) transmitters is constantly increasing. Together with the growth of unintentional sources, this leads to an increase of field strengths to which equipment is exposed. At the same time, lower power supply voltages of modern electronics result in decreased immunity to external disturbances. Unfortunately, the combination of these factors gives rise to all kinds of electromagnetic interference (EMI) problems. EMI can be defined as the process by which disturbing electromagnetic (EM) energy is transferred from one device to another via radiating or/and conducting paths. Another concept closely related to EMI is the electromagnetic compatibility (EMC). The International Electrotechnical Commission (IEC) defines EMC as [IEC89]: the ability of a device, equipment or system to function satisfactorily in its electromagnetic environment without introducing intolerable electromagnetic disturbances to anything in that environment. As follows from the definition, EMC can be split in two parts: EM emission (ability to operate without interfering with other systems) and EM susceptibility (ability to operate in a given environment). Both aspects have led to a development of a number of national and international rules and standards. All new equipment sold on the European market since January 1996 must comply with the EMC directive 89/336/EEC. Compatibility considerations have become a significant part in the design process of modern electronics. Early and consistent application of EMC knowledge will avoid delays and additional costs of redesign due to failures to comply with regulatory requirements. The range of EMI related problems extends from DC to microwave frequencies, from temporal effects to physical damage of equipment, from small annoyances to fatal 1

14 2 Introduction crashes. One of the common examples of harmless interference is a distorted TV reception due to electric motors of such appliances as vacuum cleaners. More serious problems can be encountered in automotive, avionic and medical domains. Infamous examples of those involve a helicopter losing control near radio towers and mobile phones which activate the car airbags or interfere with cardiac pacemakers. Due to potential hazards, the use of wireless equipment is often banned from hospitals. As a precaution, all electronic equipment onboard airplanes is required to be switched off during take-off and landing. A large, regularly updated collection of interference examples can be found on the EMC Compliance Journal website [Com05]. Electromagnetic compatibility continues to be a very important topic. A number of text books covering different aspects of EMC has been published in recent years [Kai05], [Pau92], [Goe92], [Deg93], [Wil01], [Arc01], [Mar00], [Mon99], international conferences continue to attract large audiences, new standards are constantly being developed to cope with ever-changing conditions. 1.2 Definitions Some of the terms used in the thesis are defined in this section. The distinction between common-mode (CM) and differential-mode (DM) circuits and currents/voltages is one of the main concepts in EMC. It can be illustrated by the example of the printed circuit board with the groundplane (GP) located inside the metal cabinet as shown in Figure 1.1. The track, the GP, the source and the load form the closed loop in which signal current is flowing. This intentional loop is referred to as a differential-mode circuit. The DM currents through the track and the groundplane are equal in magnitude, but opposite in direction. The PCB however is Track Source DM Load GP CM Cabinet Figure 1.1: Definition of the common-mode (CM) and the differential-mode (DM) circuits for an example of PCB inside the metal cabinet. not located in free space, in this example it also forms another current loop consisting of the groundplane and the nearby cabinet panel which closes galvanically at the left side, and via the parasitic capacitance on the right. Cables attached to the PCB can also be a part of this circuit. In the intentional signal loop, CM currents flow in

15 1.2. Definitions 3 the same direction in both conductors and can be considered as undesired currents. Even though these currents are typically smaller than DM currents, they often produce higher levels of electromagnetic radiation [Pau92]. The cables connected to the equipment normally extend over large distances and are efficient antennas for CM currents. The larger currents in DM circuits flow in opposite directions and the effect is reduced. Conversion between CM and DM signals can be described by the transfer impedance Z t and admittance Y t [Goe92]. Signals on a PCB can be transferred by one track with the return current flowing through the groundplane or by a pair of tracks above the GP. In the ideal case of basic multiconductor line when the sum of currents through all conductors is zero, two modes of propagation can be defined. These odd and even modes are illustrated in Figure 1.2 for a pair of microstrip lines. The multiconductor configuration is known +I -I +I/2 +I/2 0 -I Figure 1.2: Odd (left) and even (right) modes of signal transfer for an example of microstrip lines on a PCB. to provide the better signal integrity (SI) and EMI characteristics and is often used for high-speed interconnects. The performance of any active or passive two-port network can be characterized by the set of parameters which relate the independent excitation variables with the dependent response variables. For different applications and choices of those variables, the set of H-, Z-, Y - or S-parameters can be defined. At radio frequencies, a 1 2-port a 2 b 1 network b 2 Figure 1.3: Definition of S-parameters. the most commonly used are scattering or S-parameters. These are defined using a model shown in Figure 1.3 by the following set of equations: b 1 = S 11 a 1 + S 12 a 2 b 2 = S 21 a 1 + S 22 a 2

16 4 Introduction where S 11 = b 1 a 1 S 21 = b 2 a 1 S 12 = b 1 a 2 S 22 = b 2 a2=0 a2 =0 a1 =0 a 2 a1=0 input reflection coefficient forward transmission gain reverse transmission gain output reflection coefficient a n is the normalized incident voltage and b n is the normalized reflected voltage. As follows from this definition, S 11 and S 22 parameters describe the reflection, and S 12 and S 21 describe the transmission. More details on the S-parameters definition and derivation can be found in [Kur65]. 1.3 Objectives The best way to prevent the coupling with the environment is to put the equipment inside the fully shielded metal Faraday cage. However, due to various practical considerations (accessibility, thermal characteristics, production costs etc.) such closed shields can rarely be implemented in the real world electronic equipment and installations. In some cases, the complete shielding might not be necessary, as even the open structure can provide adequate protection. The goal of this thesis is to numerically and experimentally investigate the EMC properties of various open systems, such as cable trays and printed circuit boards inside open cabinets. 1.4 Methods The results presented in thesis rely on both numerical and experimental studies. There are many simulation techniques suitable for analysis of the EMC-related problems [Arc01], [Tes97]. The increased computational power of modern computers allows the analysis of very complex problems within reasonable time. Depending on the configuration and the requirements, different techniques were used in either simplified two-dimensional models or full-wave 3D analysis. Two-dimensional methods included the Schwarz-Christoffel mapping for simply and doubly connected polygonal regions and the static Method of Moments (MoM) with self-adaptive discretization developed at Eindhoven University of Technology. Full-wave 3D analyses were carried out with the dynamic MoM implemented in CONCEPT software by Technical University, Hamburg-Harburg, Germany and FEKO software by EM Software & Systems, Stellenbosch, South Africa, and also with the Finite Integration Technique of Microwave Studio by CST, Darmstadt, Germany. Simulation results were validated by a number of measurements. Radiation measurements were performed inside fully and semi-anechoic rooms of Philips Medical Systems in Best and Philips Electromagnetics and Cooling Competence Center in

17 1.5. Overview 5 Eindhoven. Scattering parameters were measured with the network analyzers of the EPS group (up to 1.8 GHz) and the EM group (up to 18 GHz) of Eindhoven University of Technology. 1.5 Overview The EMC related problems as well as the measures to avoid them can occur at different levels going from the complete system down to the component level. This thesis consists of seven chapters (including this introduction) dealing with the EMC properties of open systems on various levels. The contents of each chapter are briefly described hereunder. Chapter 2 has been dedicated to the metal conduits, which are used for mechanical support of cables and may also provide protection against electromagnetic interference. Being the most common shape, an open U-shaped conduit is chosen as basic configuration. A number of wires are placed inside to represent the actual cables with their shields. This configuration is subjected to a plane wave excitation to determine the induced currents in those wires. It is known that even an open conduit significantly reduces the undesired coupling. New in this study is the extended frequency range. Measurements and simulations agree up to the frequencies where the wavelength is several times shorter than the conduit length. The influence of a nearby metal cabinet panel on the three-layer PCB has been investigated in Chapter 3. Both simulations and measurements show that an improperly connected cabinet influences the signal transmission of the microstrip line on the PCB and also leads to the enhanced coupling with the environment. The results of this chapter have been presented at two international conferences [Kap02a], [Kap02b]. A fast method for the two-dimensional analysis of coupling with the common-mode circuit has been described in Chapter 4 for the cases of balanced and unbalanced signal transmission. The significant positive effect of a properly connected open cabinet is observed. An improperly connected cabinet may lead to enhanced coupling. The coupling is also affected by the shape of the cabinet panel, and by the way the signals are transported. The possible pitfalls and guidelines to avoid them are formulated. This chapter represents the paper accepted for publication in the IEEE Transactions on Electromagnetic Compatibility [Deu05a]. Chapter 5 contains the results of cooperation with Viasystems Mommers B.V. A novel technology allows producing fully shielded tracks on a PCB, by which the undesired coupling can be reduced. Even with partly open shields the calculated differential-mode and the common-mode couplings of such tracks are considerably smaller compared to the traditional transmission lines. The influence of manufacturing tolerances on characteristic impedance has been studied as well. The materials of this chapter have been published in the Journal of Electromagnetic Waves and Applications [Deu05b] and have also been presented during a number of conferences [Kap03], [Kap04], [Deu04].

18 6 Introduction The improper mounting of connectors may significantly deteriorate the desired performance of the PCB. Special attention has to be paid to the interface between the connector and the transmission lines. For the typical SMA type of connector it is shown that the length of a central pin is a critical parameter. The numerical and experimental results are discussed in Chapter 6. Chapter 7 contains the general conclusions from the results of previous chapters and the recommendations for future research. 1.6 Publications The contents of this thesis have been published in journals and presented at a number of international conferences. These publications are listed below. A.P.J. van Deursen and S. Kapora, Reduction of Common Mode Coupling of Printed Circuit Boards by Nearby U-shaped Metal Panel (accepted for publication in IEEE Transactions on Electromagnetic Compatibility). A.P.J. van Deursen and S. Kapora, Shielded Tracks on a Printed Circuit Board, Journal of Electromagnetic Waves and Applications, volume 19, number 1, pp , S. Kapora and A.P.J. van Deursen, Schwarz-Christoffel Modelling of Shielded Tracks on a PCB, EMC Europe 2004, International Symposium on Electromagnetic Compatibility, September 2004, Eindhoven, the Netherlands. A.P.J. van Deursen and S. Kapora, Coupling of Open and Shielded Tracks on Printed Circuit Boards (invited), EMC 04/Sendai, International Symposium on Electromagnetic Compatibility, June 2004, Sendai, Japan. S. Kapora and A.P.J. van Deursen, Characteristic Impedance and Crosstalk of Shielded Tracks on a PCB, ICEAA03, International Conference on Electromagnetics in Advanced Applications, September 2003, Torino, Italy. S. Kapora and A.P.J. van Deursen, DM-CM Coupling and Radiation of a 3- layer PCB on Top of a Metal Cabinet Plane, EMC Europe 2002, International Symposium on Electromagnetic Compatibility, September 2002, Sorrento, Italy. S. Kapora and A.P.J. van Deursen, Coupling Effects and Radiation of a 3-layer PCB on Top of a Metal Cabinet Plane, URSI 2002, 27th General Assembly of the International Union of Radio Science, August 2002, Maastricht, the Netherlands.

19 Chapter 2 Protection of Cables by Open Metal Conduits The performance of metal conduits for protection of cables has been investigated. Being the most common shape, an open 1.5 m long U-shaped conduit is chosen as basic configuration. A number of wires inside represent the actual cables with their shields. This configuration is subjected to a plane wave excitation to determine the induced currents and voltages, which represent the common-mode signals in the cable shield. It is known, that even an open conduit can significantly reduce undesired coupling at low frequencies. New in this study is the extended frequency range. Measurement and simulation results presented in this chapter agree up to 1 GHz where the wavelength is five times shorter than the conduit length. 2.1 Introduction Cables interconnecting different parts of electronic equipment and systems are widely regarded as being one of the main sources of electromagnetic compatibility (EMC) problems. Inside the office buildings and large industrial installations, these cables extend over large distances, sometimes hundreds of meters, and may act as efficient antennas for external electromagnetic (EM) fields. The remarkable growth of wireless communications (GSM, WLAN, etc.) in recent years resulted in harsh electromagnetic environments to which these interconnects are exposed. Signal and power cables inside buildings are often routed in metal trays and conduits. In addition to providing the mechanical support, such structures may also provide adequate protection against electromagnetic interference, if properly designed and grounded. The research on the grounding structures performed in the earlier thesis [Hou90] led to the development of IEC guidelines [IEC97]. These have been successfully followed by many European installation builders. For example, all installations along the new Betuweroute railroad in the Netherlands have been designed and built according to these guidelines. Such grounding structures are defined in [IEC97] as parallel earthing conductors. The induced common-mode (CM) currents flow through these conductors rather than the cables, or their shields if present. As a result, lower CM currents in the cable shields lead to a lower undesired coupling with the differential-mode (DM) signals via the transfer impedance Z t of the cable. The amount of protection of open and closed conduits at the frequencies where the wavelength is much lager compared to conduit dimensions (below 1 MHz) have been studied in [Deu01a], [Deu01b]. The measurement and simulation results presented here extend the frequency range up to 1 GHz where the wavelength is several times shorter than the conduit length and the resonances occur. In one of the simulations the upper limit was shifted up to 5 GHz to 7

20 8 Protection of Cables by Open Metal Conduits estimate the behavior of the conduit at the frequencies where the wavelength becomes comparable to the cross-sectional dimensions. In order to describe the behavior of the real-life installations, ideally the full 3D electromagnetic modelling of the complete system is desired. This would allow all possible effects of different parts of the installation to be taken into account. However, the required computational effort would be high and in most cases not even necessary. As a reasonable alternative, the complete system could be split into several simple typical parts, which could be modelled by some fast computational method. The general rules then can be derived from those results. Consequently, the performance of the complete structure can be estimated or calculated in the simplified model. Such approach has been presented for example in the CM skeleton model for the printed circuit boards and interconnecting cables inside equipment housing [Ber97]. The techniques for efficient modelling of the complete systems in automotive industry with emphasis on cables are developed within the GEMCAR project [Par03]. Such full-scale modelling is outside the scope of this work. Another Ph.D. project dealing with similar issues, namely the optimized placing of cables inside buildings and large installations, is now running in the Electrical Power Systems group of Eindhoven University of Technology. This work focuses on one of the steps in the large system analysis and presents the results for a simple 1.5 m long U-shaped conduit with wires inside it illuminated by an incident plane wave. The length is chosen much larger than the cross-sectional dimensions of 0.09 m and the end effects should not play an important role. As a result, the general conclusions from this study can be extrapolated to longer conduits. In addition, such a setup also allows the comparison of the 3D results with the simplified 2D model. In the selected configuration, the actual cables are replaced by a number of solid wires. The results then represent the common-mode currents and voltages induced in the shields of real-life cables. The conduit and the wires inside it can be viewed as a number of coupled transmission lines. The coupling of incident waves and external fields to transmission lines (TL) has been extensively studied in the literature [Tes97], [Van78], [Tka01] in both time and frequency domains. Such methods normally assume a single wire on top of a perfectly conducting or lossy ground plane. In the configuration considered here, the wires are placed inside the conduit of rather complex shape and finite dimensions. It is possible to determine the per-unit-length inductances and capacitances of the wire-conduit transmission lines by a quasi-static two-dimensional analysis. However, the conduit itself is regarded as located in the free space without defined reference required for the complete TL analysis. The simulation results presented below mainly rely on the full-wave three-dimensional modelling of the coupling. These results are then compared with the simplified TL model incorporating the 3D field calculations of empty conduit and the TL parameters from the two-dimensional conformal transformations technique. This chapter is organized in the following way. Section 2.2 describes the conduit and the configurations which have been studied. The calculated results assuming a plane wave incident on the open conduit are presented in Section 2.3. These calculations are compared with measurements inside fully and semi-anechoic rooms in

21 2.2. Configuration 9 Section 2.4. Some aspects of the conducting cover at high frequencies are presented in that section as well. The additional calculations for an even higher frequency range (up to 5 GHz) where the wavelength approached the cross-sectional dimensions of the conduit are presented in Section 2.5, followed by the concluding remarks and outlook in Section Configuration Different shapes of open conduits are widely used in practical applications. These shapes include U-, H-, T- and L-shapes as schematically shown in Figure 2.1. Since Figure 2.1: Different shapes (U, H, T, L) of open conduits used in practical applications. Dots indicate possible positions of cables. the U-shaped conduit is the most common in real-life installations, it has been chosen as a basic configuration for both numerical and experimental study. An additional comparison between the U shape and other possible shapes will be performed by calculations only. h d h b h m h t w l c Figure 2.2: Cross-sectional drawing of the open U-shaped conduit with four different locations of the wires representing the cable shields. The conduit used in the measurements has been folded from a 1 mm thick brass plate to form a U shape with h = w = 90 mm (see Figure 2.2). The total length of the conduit in the dimension perpendicular to the depicted cross section is l z = 1.5 m. Four wires of d = 2 mm diameter are placed inside the conduit parallel to the conduit walls at the positions shown in Figure 2.2. Three wires on the conduit centerline will

22 10 Protection of Cables by Open Metal Conduits be referred throughout the text as bottom (h b = 5 mm), middle (h m = 45 mm), and top (h t = 85 mm) wires; the fourth as corner (h c = 5 mm, l c = 5 mm) wire. A pair of square brass plates is soldered to both ends of the conduit. All wires are directly connected (short circuit) to the plate at one end, and to BNC connectors at the other end as shown in Figure 2.3. Depending on the configuration, different terminations are used at the BNC connectors (50 Ω or short-circuit). To maintain the mechanical stability and to ensure that the wires remain at the same position along the whole conduit length, six plexiglass supports have been placed inside the conduit (see Figure 2.3). Most of the dielectric material has been removed to minimize the reflections which might cause standing waves. Figure 2.3: Photograph of the open brass conduit used in measurements. Four wires are short-circuited to the conduit at the far end and connected to BNC connectors at the near end. In both experimental and numerical studies, two parameters are employed as a measure for the protection offered by the conduit the induced voltage at the end of the wire and the induced current along the wire. Figure 2.4(a) shows the simulation 1 m 50 (a) (b) Figure 2.4: Configurations for determination of induced currents (a) and induced voltages (b) in the conduit wires. configuration to determine the currents. All wires are short-circuited at both ends and 1mΩ ideal resistors are placed exactly at the center of each wire. In the measurements, the current is determined by placing the current probe around the wire at the same center position. It is assumed that the insertion impedance of the probe is small,

23 2.2. Configuration 11 and it does not influence the results significantly. The induced voltages are studied in the configuration where one end of each wire is short-circuited to the conduit while the other is connected to the 50 Ω impedance of the test receiver (in measurements) or to the ideal 50 Ω resistor (in calculations) as indicated in Figure 2.4(b). When more than one wire is located inside the conduit, all wires that are not connected to the measurement equipment are locally terminated by 50 Ω at the connectors. Because of the relatively large difference in the induced signal it is convenient to present the results not in absolute values, but in decibels. The voltage is then expressed in dbv and defined as U in dbv = 20 log 10 U in V 1 V A similar expression applies for the current in dba. (2.1) H E k (a) H E k (b) H E k (c) Figure 2.5: Possible orientations of the conduit with respect to the incident field: front (a), side (b) and back (c). In calculations the conduit and wires are illuminated by a plane wave with an electric field of 1 V/m strength and linear polarization. The measurement results were also normalized to 1 V/m field strength. In most configurations the electric field vector is parallel to the wires, when the coupling is most effective. The comparison with the other polarization when the magnetic field is parallel to the wire is given in Section Three main possible directions of wave incidence/conduit orientations ( front, side and back ) are shown in Figure 2.5. The front orientation is studied in more details because it results in the largest coupling (worst-case scenario).

24 12 Protection of Cables by Open Metal Conduits 2.3 Simulations In order to calculate the induced currents and voltages in the conduit wires, two different calculation techniques have been employed: the Method of Moments (MoM) implemented in CONCEPT II software by Technical University of Hamburg-Harburg [Con05] and FEKO software by EMSS [Fek05], and the Finite Integration Technique (FIT) of Microwave Studio 5 by CST GmbH [Cle01], [Cst05]. One of the differences between these methods is that MoM requires the meshing of the conductor surfaces only, while the full 3D computational space with the absorbing boundary conditions has to be meshed in FIT. Another difference concerns the domain of calculations. While MoM produces results directly in the frequency domain, FIT is a time-domain method. The FIT excitation signal is a Gaussian-shaped pulse of the width corresponding to the maximum frequency of interest. The calculated response is later transformed to the frequency domain by the Discrete Fourier Transform (DFT). In all calculations the conductivity of brass is assumed to be infinite. The conduit and also the wires are modelled as perfect electric conductors (PEC). In the MoM calculations the thickness of the conduit walls is neglected. In order to reduce the computation time, symmetry planes (magnetic and electric conducting walls) have been applied to reduce the calculation domain by 50 or 75 percent depending on the configuration Induced Currents The first calculations determine the induced currents when the wires are shortcircuited to the conduit at both ends. Such a configuration resembles the typical middle section of the real-world conduit with the cable shields connected to it. The induced currents are monitored by 1 mω resistors shown in Figure 2.4(a). The front excitation indicated in Figure 2.5(a) is used. Figure 2.6 shows the results calculated by FIT for all four wires. As could be expected, the largest values are observed for the top wire, and the lowest for the wire in the corner. The resonant features around 0.2 and 0.4 GHz correspond to the situation when the multiples of the full wavelengths fit into the 1.5 m long transmission lines. The following differences in the induced currents have been calculated at the off-resonance frequency of 150 MHz: 19 db between middle and top, 42 db between bottom and top, and 54 db between corner and top wires. To estimate the level of protection offered by the conduit, the induced currents are recalculated in the similar configuration with the front excitation and all four 1.5 m long wires connected at both ends to a pair of square plates but with the conduit removed. At the frequency of 0.15 GHz the currents in all wires are about the same value of 60 dba. In the case of the top wire the current is 58 dba (compared with 68 dba of the configuration with conduit). Even for the worst case of the maximally exposed top wire, an open U-shaped conduit reduces the coupling by 10 db on the average. The results for other wires are summarized in Table 2.1. For the best protected corner wire the effect of the conduit is more than 60 db.

25 2.3. Simulations Current in dba Top wire Middle wire Bottom wire Corner wire Frequency in GHz Figure 2.6: Induced currents in the wires calculated by FIT. Front excitation. Table 2.1: Effect of the conduit on the induced currents in wires. Wire I without conduit, dba I with conduit, dba Difference, db Top Middle Bottom Corner The analysis of the current configuration requires quite a long calculation time. The excitation in FIT method is a Gaussian-shaped pulse of 0.8 ns width for 1 GHz and 0.16 ns for 5 GHz. The resulting currents and voltages in the lumped elements (1 mω and 50 Ω resistors respectively) are calculated in the time domain and later transformed into the frequency domain by the Discrete Fourier Transform. For an accurate DFT, the time-domain signals should ideally decay completely to zero. The lower those signals are, the more accurate the resulting frequency domain values will be. The total energy in the calculation domain is used as a criterion; it has been set at 60 db with respect to the initial value. If the calculation is stopped before that condition is achieved, large numerical artefacts appear in the results. Some minor representation of them is still visible in Figures 2.6 and 2.7 in form of ripples near the resonant frequencies. As a result of higher total losses in the voltage configuration the energy criterion is met earlier and the calculation time is reduced considerably. For example, the calculation with the 1 GHz Pentium III PC with 60 thousand mesh cells, 0 1 GHz frequency range and 60 db accuracy settings requires only 1 hour for the induced voltages. The induced currents calculations with the same settings would require more than 24 hours. This makes the voltage setup more suitable for the quick evaluation of the conduit properties when the configuration (for example, conduit dimensions, wire locations or the incident wave parameters) changes.

26 14 Protection of Cables by Open Metal Conduits 60 Current in dba Top wire (FIT) Top wire (MoM) Middle wire (FIT) Middle wire (MoM) Frequency in GHz Figure 2.7: Comparison between FIT and MoM calculations of induced currents in the top and middle wires. Front excitation. The same configuration for the induced currents was also modelled in the frequency domain by a different approach. The CONCEPT II software utilizing the Method of Moments was used for benchmarking. Figure 2.7 shows the results for the top and middle wires, calculated by both methods. Good agreement along the whole frequency range is apparent. Special attention was paid to the meshing of the conduit surfaces. The mesh had to be refined near the bottom and corner wires because the standard λ/10 rule was not sufficient for an accurate determination of very low currents in these wires. Still, the large values of the top two wires are quite accurately predicted even with a coarse mesh. In addition to the frequency dependence of current in the center of the wire, the current distribution along the wire has been also determined. The origin of this z- coordinate is set at the wire center. The end plates of the conduit are then located at z = 0.75 m and z = 0.75 m. The mesh on these end plates has been refined near the wire connection points to ensure the accurate modelling of end effects. The FEKO software (another realization of 3D Method of Moments) has been used for these calculations. Figure 2.8 shows the distribution for the top wire at a number of frequencies outside the sharp resonances. After the exact frequencies of the minimum and the maximum of the resonance around 200 MHz (shown in Figure 2.6 for the wire center) were determined, the calculations have been repeated at those frequencies for all positions along the wire. The results are shown in Figure 2.9. The character of the current distribution changes dramatically when the frequency changes from MHz (minimum at z = 0) to MHz (maximum at z = 0). For the center wire position, the difference in currents is of the order of 40 db. At this resonant frequency, the current is also reaches its maximum of 42 dba at the ends of the wires (points of connection to the conduit).

27 2.3. Simulations Current in dba MHz 150 MHz 250 MHz 300 MHz z coordinate in m Figure 2.8: excitation. Current distribution in the top wire at non-resonant frequencies. Front MHz MHz MHz 205 MHz 50 Current in dba z coordinate in m Figure 2.9: Current distribution near 200 MHz resonance. Top wire, front excitation.

28 16 Protection of Cables by Open Metal Conduits Induced Voltages As mentioned earlier, the voltage configuration can be calculated much faster in FIT because of the higher total losses in the 50 Ω resistors. Again, the front excitation is considered. The results are presented in Figure The differences in signals with Voltage in dbv Top wire Middle wire Bottom wire Corner wire Frequency in GHz Figure 2.10: Induced voltages calculated by FIT in configuration with all 4 wires present. Front excitation. respect to the top wire at off-resonance frequencies remains the same as in the previous current configuration: 19, 42 and 54 db. The resonant dips at the multiples of 0.1 GHz correspond to the half-wavelength resonances in the 1.5 m long transmission line. In most practical applications, as well as in the conduit used for measurements there will be more than one cable (wire) present. To investigate how these additional conductors influence the coupling, the calculations were repeated four times with only one of the four wires present at each time; results are shown in Figure While the voltage at the top position remains the same, the voltages at other positions reduce quite significantly. The results are summarized in Table 2.2. For example, Table 2.2: Comparison between configurations with four wires and single wire. Wire U(4 wires), dbv U(1 wire), dbv Top Middle Bottom Corner for the corner position, the voltage now is approximately 14 db (a factor of 5) larger with the respect to the situation when all four wires are considered. Due to

29 2.3. Simulations Voltage in dbv Top wire Middle wire Bottom wire Corner wire Frequency in GHz Figure 2.11: Induced voltages calculated by FIT in configurations when only one wire is present. Front excitation. the coupling between the wires (or cable shields in practical situations), the wires located at the top of the conduit act as an additional protection for the wires placed deeply inside the conduit. Together with already lower coupling for the wires placed closely to the walls/corners this leads to a simple rule of cable placement inside the real-life conduits. The bad cables (with higher transfer impedance Z t ) or the cables carrying the critical signals should be placed as close to the metal as possible. Then the good or less critical cables will provide the additional protection for the bad cables Transmission Line Approach The transmission line (TL) approach can also be applied to calculate the induced signals in the conduit wires. This method has an advantage over the full 3D approaches presented above. If the position of the wire changes, both FIT and MoM require the whole configuration to be recalculated completely, which takes a few hours of computer time. While using TL approach the field distribution inside the conduit has to be calculated only once per given conduit geometry. Such a method then allows a quick evaluation of the level of protection offered by the conduit as a function of the cable position. The field inside the empty conduit is regarded as an excitation source for the transmission line formed by the conduit and the wire. The transmission line parameters can be accurately and quickly calculated by a 2D method, for example by MoM or Schwarz-Christoffel (SC) transformation. More details on the SC and its application in 2D problems will be presented in the next chapters for different types of problems. The inductance and impedance values for the discussed four wires are shown in Table 2.3. In case of MoM, the round wires were approximated by 16-sided polygons. Good agreement between both methods is apparent, the deviation is less than 0.5%.

30 18 Protection of Cables by Open Metal Conduits Table 2.3: Transmission line parameters Wire L(SC), nh/m L(MoM), nh/m Z 0 (SC), Ω Z 0 (MoM), Ω Top Middle Bottom Corner The required field distribution inside the empty conduit as a function of both frequency and position can be calculated by either MoM or FIT. The Vance s approach for the coupling of the external field to the transmission lines is used for the TL formulation. The details are presented in Chapter 3 of [Van78]. As follows from that formulation, only the component of the electric field parallel to the wires (zcomponent in the original formulation) is used as an excitation source. A 3D field calculation shows that the required field component does not vary much along the conduit length, except near the ends. In the first approximation these variations can be neglected and ideal terminations can be assumed at the ends of conduit. In this case the field needs to be determined only in the central cross section of the conduit, and ultimately a purely 2D method should suffice for a first impression of the induced signals Top wire (TL) Bottom wire (TL) Top wire (FIT) Bottom wire (FIT) Voltage in dbv Frequency in GHz Figure 2.12: Induced voltages calculated by TL (dashed lines) and FIT (solid lines). Top and bottom wires, front excitation. Figure 2.12 presents the voltages calculated by the transmission-line approach (dashed lines) plotted against the full 3D results (solid). Both methods assume only one wire inside the conduit. Good agreement over the most of the frequency range is observed. Above 0.1 GHz and at off-resonance frequencies, the difference in the signal level between both methods remains within a few decibels. The largest deviation of 6 db is observed for the bottom wire. For the sake of clarity, only the results for top and

31 2.3. Simulations 19 bottom wires are presented in the figure. A similar agreement has been obtained for the middle wire as well. The corner wire was not considered because of the difficulties with correct determination of the electric field close to the corner of the conduit. In addition to the calculations of TL parameters, the Schwarz-Christoffel approach can also be used to quickly estimate the induced signals in the 2D approximation. The conduit is mapped onto a unit disc by a numerical SC method [Dri02]. The corresponding positions of the wires are mapped to the outside of this disk. Two different approaches can be considered. Firstly, such a configuration is placed inside the uniform 1 A/m magnetic field. The induced currents are driven by the flux between the images of the wires and the unit disk. Secondly, a 1 A common-mode current is assumed through the conduit. Again, the flux between the images of the respective wires and the image of the conduit characterizes the induced currents. The calculated ratio between the current in top wire and the total current through conduit and wires is or db. The results for the various calculation methods are summarized in the Table 2.4. As can be seen, even the simple and therefore fast 2D approaches are able to quite accurately predict the ratios of the induced currents. The disagreements from the full 3D calculations are within 2 4 db. Table 2.4: Induced signals with the respect to the top wire calculated by different approaches. The FIT results are determined at the off-resonance frequency of 150 MHz. Wire U(FIT), db I(FIT), db I(field, SC), db I(current, SC), db Middle Bottom Corner Different Shapes To investigate the influence of the conduit shape on the level of protection, the voltage calculations have been repeated for two additional configurations with only one or both sidewalls removed to form an L-shape or flat plate respectively. T and H shapes shown in Figure 2.1 were not analyzed. The results for the middle wire calculated in presence of all four wires are shown in Figure As anticipated, more open conduit results in larger induced voltages for the fixed wire position. The same dependence is valid for the other 3 wires as well. For example, in case of the bottom wire, the difference between the U shape and a flat plate is more than factor 35 (31 db) at 0.15 GHz.

32 20 Protection of Cables by Open Metal Conduits Voltage in dbv Figure 2.13: Flat plate L shaped U shaped Frequency in GHz Effect of the conduit shape on the induced voltage. Middle wires Different Orientations and Polarization It is expected that the front orientation with the electric field polarization parallel to the wires and the conduit results in the largest coupling. For the U-shaped conduit other possible situations were also modelled by FIT. In case of the front orientation but now with the H-field component of the incident wave parallel to the wires and the E-field component normal to them, the voltages in all wires lay below the -100 dbv (10µV) level; for the middle wire the reduction is of the order of 60 db. Another brief comparison was made for all three orientations shown in Figure 2.5. The results for the middle wire are shown in Figure The largest difference between the front and the side orientations for this wire is about 10 db. The same relation is valid for other three wires as well Different Wire Diameters In practice, the outer diameter of the cable shield can vary in wide ranges from approximately 2 mm (the value used in this study) of RG-316/RG-174 to 4 mm of RG-223/RG-58U and 11 mm of RG-217. Naturally, the coupling will also change with the diameter. To investigate this effect, the calculations were repeated for the top and middle wires while varying their diameter from 2 to 20 mm. The calculations show that the general transmission-line behavior with resonant peaks does not change significantly. On the other hand, the overal signal level increases logarithmically with the diameter as shown in Figure 2.15 for the off-resonance frequency of 150 MHz. This behavior corresponds to the logarithmic decrease of the wire inductance with its diameter. However, the signal level difference between these two wires remains the same at 10 db for the whole diameter range investigated. The thin-wire results are still suitable for describing the general system behavior with thicker cables. Only a few db variations in configurations with all 4 wires were observed when the wire diameters varied from 2 mm to 8 mm. At d = 10 mm, the bottom and the corner wires are in contact with conduit and the results are below -100 dbv at low frequencies.

33 2.3. Simulations Voltage in dbv Front Side Back Frequency in GHz Figure 2.14: Different conduit orientations with respect to incident wave. Middle wire Voltage in dbv Top wire Middle wire Wire diameter in mm Figure 2.15: Influence of the wire diameter on the induced voltages. Front excitation.

34 22 Protection of Cables by Open Metal Conduits 2.4 Measurements In order to experimentally evaluate the performance of conduit and to validate the simulation results of the previous section, a number of measurements have been carried out. The reproduction of the exact simulation configuration is somewhat limited, because it is difficult to produce a plane-wave excitation within the limited space of an anechoic room. Moreover, due to the presence of conducting floor in the semianechoic room measurements, both direct and ground-reflected waves arrive at the conduit and at some frequencies this will change the resulting field at the observation point. However, since the most important point is the ratio of induced signals as a function of wire position inside the conduit, these limitations (mainly at lower frequencies) are not considered to be critical Measurements Inside Semi-anechoic Room The first measurements were performed inside the semi-anechoic room of Philips Medical Systems in Best, the Netherlands. The measurement setup consists of the aforementioned brass conduit which is vertically placed on the floor at 6 m distance from the log-periodic antenna Schaffner CBL The vertically polarized antenna is located at the lowest possible 0.88 m distance from the floor and connected to the 0 dbm output of the tracking generator of Rohde & Schwarz ESI 7 EMI test receiver. This receiver is also used to measure the induced voltages at the ends of wires. The frequency range is MHz. To minimize the effect of induced common-mode currents in the measuring cables, a number of ferrite beads are placed around them. The absolute values of the measured voltages for all wires are shown in Figure The results show the same relative dependance of signal on wire position as in simulations (about a factor of 10 reduction when going from top to middle to bottom wires). The small signal of the corner wire is apparently close to or below the noise level of the measuring system. Similar to the simulation results, resonances at frequencies, that are multiples of 100 MHz, are also present in the measurements. There is also an additional resonant dip around 130 MHz and a dip around 250 MHz, which are caused by the environment of the semi-anechoic room. To confirm this, an additional experiment inside the fully anechoic room without the reflecting floor has been performed. The details and results are presented in the next subsection. The antenna used in the setup does not provide a 1 V/m plane wave excitation as used in simulations and the measured values have to be corrected. In contrast to the measurement conditions with the reflecting floor, the simulations implicitly assume the conduit to be located in free space. Only a typical free-space antenna factor (AF) for this model of antenna has been available. As a very rough estimate, it has been used to correct the measurement values, corresponding to an electric field strength of 1 V/m at the conduit location. The resulting voltage for the top wire is compared with FIT calculations in Figure Overal, a reasonable agreement is observed. The deviation at frequencies below 70 MHz is caused by the the antenna mismatch and reflection of the power back to the generator (large S 11 parameter) in this frequency range. As a result, the produced field for a given output of the generator is small. In this case, the differences in real (not typical) antenna factors between different antennas of the same model would also play an important role. In

35 2.4. Measurements Top wire Middle wire Bottom wire Corner wire Voltage in dbv Frequency in GHz Figure 2.16: Uncorrected measured voltages for all four wires. 20 Measurements FIT calculations 40 Voltage in dbv Frequency in GHz Figure 2.17: Measurement and simulation results for the top wire. The measurement data has been corrected by the typical antenna factor.

36 24 Protection of Cables by Open Metal Conduits addition, the environment with the reflecting floor at less than 1 m distance from the vertically polarized antenna by no means represents the free-space conditions under which the typical AF was provided. This leads to a reduced accuracy of both the correction factor and the absolute values of the induces voltages. More information on the antenna measurement issues can be found in [Dij05]. Still, from comparing Figures 2.16 and 2.10 it is clear that the ratio of the signals in different wires, as well as the general frequency dependence, are about the same in both measurements and calculations Measurements Inside Fully Anechoic Room A better approximation of the free-space conditions assumed in the calculations can be achieved in a fully anechoic room. The second measurement session was performed inside the 3 meter room of Philips Electromagnetics and Cooling Competence Center in Eindhoven, the Netherlands. In contrast to the semi-anechoic room of previous measurements, the reflective floor is now covered by the same absorbing ferrite tiles as the walls and the ceiling of the room. This provides a reflection-free environment up to 1 GHz. Figure 2.18: The measurement setup inside the fully anechoic room. In the measurement setup shown in Figure 2.18, a significant length of the measuring cable from the conduit wires to the test receiver is exposed to the field generated by the antenna. This may lead to large induced common-mode currents in the cable shield and, as a result, inaccurate measurements. To minimize this effect, the cable was loaded with ferrite rings along the whole length inside the fully anechoic room. Two different orientations of the conduit have been considered. They are referred to as vertical and horizontal and schematically shown in Figure It is clear that under other circumstances equal, the horizontal orientation is preferable since in that case the incident electric field is perpendicular to the the cable and the coupling is minimal.

37 2.4. Measurements 25 Figure 2.19: Vertical (left) and horizontal (right) orientations of the conduit and the antenna with respect to the room. Side view. The conduit is placed at 3 m distance from the the antenna. The signals are measured with the HP 8546A EMI Receiver. The 0 dbm output of the tracking generator is connected to the CBL6112B antenna, which is used as an excitation source. The frequency range of 30 MHz 1 GHz is split into several sub-ranges to obtain a higher resolution. To accurately determine the electric field at the location of conduit, a similar log-periodic antenna with known antenna factor is used. Figure 2.20 shows the results for the top and the middle wires and their comparison with FIT calculations. The voltage is corrected to account for the difference between the measured field at the location of conduit and the 1 V/m electric field of calculations. Very good agreement for the whole frequency range is observed without any additional resonances seen in semi-anechoic room measurements. The low frequency ripples in the measured results are caused by reflections in the signal cable. In the second configuration, the FCC F-2000 current probe has been used to measure the induced currents at the center position of the middle and the top wires, which were short-circuited to the conduit at both ends as in simulations. Once again, the results presented in Figure 2.20 show good general agreement with the calculated signal levels Effect of Conducting Floor In order to confirm the initial assumption that the additional resonant peaks in the semi-anechoic room results are caused by the reflection from the conducting floor, a new set of measurements has been performed. The ferrite tiles were again removed from the floor to convert the room back to semi-anechoic configuration. The conduit is then vertically placed with a good contact to the conducting floor. In contrast to the first semi-anechoic room measurements, the antenna was not fixed at a certain height, but swept in vertical direction. The measured voltages for top wire under front excitation now contain additional peaks with their frequency and intensity depending on the antenna position (varied from 0.95 to 4.0 m height from the floor).

38 26 Protection of Cables by Open Metal Conduits Voltage in dbv Top wire Middle wire Frequency in GHz Current in dba Top wire (measurements) Top wire (calculations) Middle wire (measurements) Middle wire (calculations) Frequency in GHz Figure 2.20: Voltages at the end of the wires (top) and currents along the wires (bottom). Measurements and FIT calculations.

39 2.4. Measurements Conduit with Cover It has been shown in [Deu01a] for the lower frequencies (below 1 MHz), that even a non-connected brass cover with 1 mm slit reduces the coupling from the outside world by factor of six in comparison with an open U-shaped conduit. This coupling can be reduced by another order of magnitude when the cover is connected to the conduit by four screws at the corners. However, at higher frequencies where conduit becomes electrically large, such a solution may not provide the desired effect and could lead to opposite results and enhanced coupling. The general rule of thumb states that, in order to provide efficient shielding, the bolts connecting two metal panels should be placed not further than λ s /10 apart, where λ s is the smallest wavelength of interest. For the 1.5 m long conduit that condition corresponds to the maximum frequency of the order of 20 MHz, which is below 30 MHz minimum limit of the antenna. To extend this frequency range, additional screws have been put along the whole length at distances 24.5 cm apart. This should make the cover effective at least up to 100 MHz. Measurements show that a configuration with a floating (not galvanically connected to the conduit) cover provides only a slight reduction of the voltage and leads to additional resonance peaks distributed over the whole frequency range Voltage in dbv Open Connected with screws Connected with tape Frequency in GHz Figure 2.21: Effect of the conduit cover and the type of connection. Measured voltage at the end of top wire. Figure 2.21 compares the induced voltage at the end of the top wire when all screws are put in place (dashed line) with an open U-shaped conduit (thick solid line). The cover indeed reduces the coupling by up to 30 db, but only in the lower frequency range (below 300 MHz). These effects should be taken into considerations when choosing the practical conduits which may have holes for the weight saving. The only way to make it effective within the whole frequency range is to make the contact along the full length. The results obtained with the copper tape glued over the slit are shown by the thin solid line in Figure The signal level is reduced by 30 db on average. Some residual coupling is still present due to the fact that the tape makes random contact with the conduit.

40 28 Protection of Cables by Open Metal Conduits 2.5 Higher Frequencies In view of the agreement between simulations and measurements, the calculations are extended to even higher frequencies. The results of the previous sections for the induced currents and voltages as a position of the wire are valid up to GHz. At higher frequencies, where the wavelength approaches the cross-sectional dimensions of the conduit (0.09 m), other than TEM modes will also be excited by the incident wave. The results of preliminary simulations showing the related additional effects are indicated in Figure 2.22 for the frequencies up to 5 GHz. 20 Voltage in dbv Top wire Middle wire Bottom wire Corner wire Frequency in GHz Figure 2.22: Induced voltages. Front orientation. 2.6 Concluding Remarks and Outlook The analysis of the protection offered by an open cable conduit has been carried out. Previous studies of similar configurations were performed mainly at the low frequencies (below 1 MHz). The frequency range was extended up to a few gigahertz in this study. The induced currents over the cables inside an open U-shaped cable conduit have been investigated assuming the plane-wave excitation. A good agreement between measurements and simulations was observed. Both showed a significant reduction of external coupling to the wires inside, especially when the wires are located near the conduit walls. This is valid for the whole frequency range investigated. Some practical aspects of the measurement setups have been discussed as well. Ideally, the variations in electric field along the conduit length should be incorporated into the TL model of Section to account for the effects near the end plates. Also, when several wires are present, the mutual coupling between them should be also included in the model. The off-diagonal elements (mutual inductances) of L-matrix can be calculated by a SC approach. The corresponding capacitance matrix is then obtained by the inversion of this inductance matrix. The analysis of systems containing

41 2.6. Concluding Remarks and Outlook 29 multiple cables have been earlier reported in the literature [Sal00], [Pau94], [Fra77]. The development of such an elaborated coupled transmission-line model for the conduit can be included in future research. In order to investigate the influence of the semi-anechoic room environment (Section 2.4.1) the calculations of the conduit can be extended to include both the reflecting floor and the real antenna in the model. In addition to the information about the conduit properties, these simulations would also help to determine the behaviour of the measurement site and take the curved wavefront of the antenna into account. The conduit considered in this chapter contains only four sparsely placed parallel wires. The real-world conduits are normally more densely filled with cables in randomly interweaved bundles. This issue can be addressed in future research along with the incorporation of current results for a free-space conduit into more complex installation structures. The sharp resonances in the currents of Figure 2.6 may cause an increased coupling to the cables in the conduit. For calculations, the actual wave velocities outside and inside the cable, as well as the amplitude and the phase of transfer parameters Z t and Y t have to be known. The theory has been already formulated by Vance [Van78, page 147]. The measurements with actual cables could also be included in further research.

42 30 Protection of Cables by Open Metal Conduits

43 Chapter 3 Three-layer PCB on Top of a Cabinet Panel A nearby metal cabinet panel influences the transmission of signals on a printed circuit board and also leads to an increased radiated emissions. A three-layer board with a continuous ground plane has been mounted above a cabinet panel. In the frequency range GHz several resonances occur in the common-mode circuit formed by the ground plane and the cabinet. At the resonance, this circuit couples strongly with differential-mode circuits on the board. The measurements for different track geometries are compared with the calculations based upon the Finite Integration Technique Introduction Metal cabinets are often used to protect electronic equipment against electromagnetic interference. The cabinet and the printed circuit boards (PCB) inside it form common-mode (CM) circuits, whereas the circuits on the PCB are regarded as the differential-mode (DM) circuits. These DM circuits induce a CM current through a first-order DM-CM coupling. It is well known [Pau92], that the radiation due to the CM currents often dominates the direct radiation by the DM circuits, in particular if cables are attached to the board. At the CM resonance frequencies, a second-order DM-CM-DM coupling also becomes important, which affects the DM signal transmission on the board. This DM-CM-DM coupling is strongly influenced by the track geometry and the parameters of the CM circuit. A three-layer PCB with a ground plane (GP) has been selected as a basic test board. It should be mentioned that in real-life applications most PCBs normally have an even number of layers (2, 4, 6...) with the power plane in addition to the ground plane. However, the main item presented in this chapter is the dependence of the coupling on the geometry of the track located on top and bottom of the PCB and the influence by a cabinet panel under the PCB. This relative coupling is not likely to be influenced by the number of the additional planes inside. Three-layer PCB design also allows a better connection between GP and the cabinet, which turns out to be a relevant factor. Moreover, using such a setup allows the comparison with the results discussed in an earlier thesis [Hor01]. Firstly, we investigate the signal transfer characteristics of the microstrip lines on a PCB and their dependence on the setup parameters. Secondly, we consider the electromagnetic radiation from the PCB. Conclusions derived in this chapter rely mainly on the measurements, which are checked by the Finite Integration Technique (FIT) simulations. 1 Results discussed in this chapter have been earlier presented at XXVIIth URSI General Assembly [Kap02a] and EMC Europe 2002 Symposium [Kap02b]. 31

44 32 Three-layer PCB on Top of a Cabinet Panel 3.2 Configuration Figure 3.1 shows the configuration and the parameters of the three-layer PCB mounted in a so-called precompliance setup, similar to the one proposed in [Hor01]. The continuous copper ground plane has length l = 200 mm, width 2w = 100 mm and thickness d = 0.03 mm. Two tracks of width b = 1.5 mm and different geometries are placed at a distance h = 1.5 mm above and below the GP. Track 1 meanders over the surface as shown in Figure 3.1(c), while straight track 2 runs parallel to the longer edge of the PCB. Both tracks are interconnected through a via in the GP at the far end, near side B. The relative dielectric constant of the typical glass epoxy FR-4 board material is ε r = 4.7, the loss tangent is tan δ = The cabinet panel (CP) is a folded brass plate of 200 mm width and 2 mm thickness. The PCB can be placed at different distances h CP from this panel, with the typical value of h CP = 10 mm. The board can also be turned upside-down, so either track can face the cabinet. A pair of SMA connectors are placed at the end of each track at side A to allow the measurements of signal transfer. The vertical part of the cabinet at side B can be moved along the CP to adjust the gap width g, which varies between 1 and 20 mm. The differential-mode circuit is formed by track 1 which continues through the via in track 2 with both tracks having the GP as a return, whereas the common-mode circuit consists of the GP and the CP. This setup is chosen for two reasons: it allows a direct measurement of the DM-CM and DM-CM-DM coupling, and it also bears the resemblance to a PCB mounted on a backplane inside metal cabinet. 3.3 Experimental Setup and Simulation Description The transfer characteristics of the tracks on a PCB can be described in the frequency domain by means of the S-parameters. These scattering parameters have been measured with the network/spectrum analyzer HP 4396A in combination with the S-parameters set HP 85046A. A pair of high quality SMA cables, selected for their low transfer impedance, connected ports 1 and 2 of the PCB to the measuring equipment as shown in Figure 3.2. As in previous chapter, CST Microwave Studio employing the Finite Integration Technique (FIT) [Cle01], [Cst05] is used for numerical analysis. Some details of the method are presented below. The calculations are performed in the time domain, the signals of ports 1 and 2 are subsequently converted into the frequency-domain S-parameters by using the Discrete Fourier Transform (DFT). The excitation signal is a Gaussian-shaped pulse of the width corresponding to the frequency of range of interest ( 0.4 ns). The actual SMA connectors were not modelled, they were replaced by 50Ω discrete ports through which the power was injected into the system. In the first simulations, the tracks, the ground plane and the cabinet were modelled as perfect electric conductors (PEC). The dielectric loss of the PCB material was also not taken into account. The open boundary conditions were applied at some distance from the setup. The meshing settings had to be modified to more accurately discretize the tracks and PCB itself. This resulted in about 40 thousand mesh cells for the whole structure and in about 8 hours of calculation on a 1 GHz Pentium III PC with 1 GB of memory for the typical configuration with the frequency range 0 2 GHz

45 3.3. Experimental Setup and Simulation Description 33 side A port 1 l track DM GP g side B Y port 2 CM CP hcp Z X (a) h 2w b GP d Y r CP hcp Z X 2p (b) Y Z X (c) Figure 3.1: Side view (a), cross section (b) and 3D view (c) of the three-layer PCB on top of a cabinet panel (not to scale).

46 34 Three-layer PCB on Top of a Cabinet Panel Figure 3.2: Photograph of the S-parameters measurement setup. and the energy criteria set at 60 db. The nature of the method requires the timedomain signals to be sufficiently reduced to zero. If the calculation is stopped earlier, numerical artifacts of DFT will appear in the frequency-domain results. Because of the resonances, the total energy in the system decreases very slowly, leading to long computational times. The latest version of Microwave Studio 5.0 also allows to include the dielectric losses in calculations. For these calculations, the metals (brass and copper) have been modelled as the surface impedances with the conductivity of σ copper = S/m for the tracks and the GP and σ brass = S/m for the cabinet. The relative permeability of both materials is µ r = 1. The dielectric losses of FR-4 PCB substrate were characterized by the typical loss tangent tan δ F R 4 = Signal Transfer Results Resonances The DM transmission characteristics of the combined tracks 1 and 2 have been studied in a number of configurations. As mentioned earlier, the signal transfer from port 1 to port 2 depends on the presence of the nearby cabinet panel. The visibility of the common-mode circuit resonances in the DM transfer and their intensity also strongly depends on the orientation of the PCB or on the shape of the track located between GP the CP. The most common way to express the transfer of 2-port system is with forward transmission gain or S 21 parameter. However, due to the impedance mismatch between the 50 Ω measuring equipment and the tracks, the results might be obscured by the additional reflections. This can be avoided by using the available power gain parameter G A, defined as the ratio of the power available from the system at port 2 to the power available from the excitation source. G A is related to the S-parameters by [And96]:

47 3.4. Signal Transfer Results 35 G A = S 21 2 (1 Γ S 2 ) (1 S 22 2 ) + Γ S 2 ( S 11 2 D 2 ) 2Re(Γ S M) (3.1) where Γ S = (Z S Z 0 )/(Z S + Z 0 ), D = S 11 S 22 S 21 S 12, and M = S 11 DS 22. Here Z S = 50 Ω is the input and output impedances of the network analyzer, and Z 0 = 68 Ω is the characteristic impedance of the microstrip lines formed by the tracks and the GP, calculated in [Hor01]. As is clear from the numerator, G A is mainly determined by S 21. However, the use of G A eliminates the effect of impedance mismatch and results in smoother curves, while retaining the resonance effects. Figure 3.3 presents the numerical and experimental results when the straight track 2 faces the cabinet panel. The gap width is g = 10 mm and the distance between GP and CP is h CP = 10 mm. The structure shows its resonant behavior at about 0.30, G A FIT calculations (without losses) FIT calculations (with losses) Measurements Frequency in GHz Figure 3.3: GP and CP. Measured and calculated signal transfer characteristics. Straight track between 0.95 and 1.6 GHz. These frequencies correspond to the odd multiples of the first quarter-wavelength resonance in the 0.21 m long CM circuit, which is short-circuited at side A and capacitively terminated at side B. As expected, the calculations also show the corresponding increase of the electric field inside the gap at side B and of the magnetic field between GP and CP at side A. To show the importance of the material properties, especially the dielectric losses, on the signal transfer, the calculations with lossless materials are compared with the calculations with all losses included. As can be seen clearly in Figure 3.3, the model with lossy dielectric and metals represents the general behavior of measurements more accurately. More details on these losses will be presented in the next subsection. The additional small peak around 0.85 GHz is also seen in the measurements curve. It is attributed to the resonance in another non-terminated track running parallel to the straight one. This resonance is damped by a 50 Ω termination at least at one end of the track.

48 36 Three-layer PCB on Top of a Cabinet Panel When the board is turned upside down such that meandering track 1 faces the CP, the intensity of the first resonance (dip in G A ) becomes less, while the intensity of the third one becomes much larger as shown in Figure 3.4. Numerical results also show this behavior, even though not to the extent observed in the measurements G A FIT calculations (without losses) Measurements Frequency in GHz Figure 3.4: Measured and calculated signal transfer characteristics. Meandering track between GP and CP. In order to determine the relative coupling strength of both tracks, the straight track 2 between the GP and CP has been replaced by a semi-rigid coaxial cable. The comparison between the shielded track and the microstrip is presented in Figure 3.5. The resonances in G A are absent over the entire GHz frequency range in the case of shielded track. A similar effect is observed when the cabinet panel is placed at a large distances h CP > 30 mm which results in decreased DM-CM coupling, or when it is completely absent. The results of this configuration are shown by the dashed line in Figure 3.5 which is almost identical to the results with CP present, except for the frequencies of the CM resonances. From both experimental and numerical results it can be concluded that at lower frequencies the DM circuit with the straight track between CP and GP couples stronger with the CM circuit (see Figure 3.3) in comparison to the meandering track between CP and GP (Figure 3.4). On the other hand, the coupling of the meandering track is larger at higher frequencies. This difference can be attributed to two causes. Assuming the example of the straight track, it has been shown in [Hor01] by the transmission-line model that the ratio of the DM-CM coupling for the straight track between the GP and CP or on top of the GP is about a factor πw/2h CP, or 8 in the presented case (see Eq. 4 and 8 in [Hor01]). The same dependence on the track location is also seen in the FIT calculations if only the single-sided PCB is considered. The resonant coupling is much stronger when the track is located between GP and CP, meaning that in the analysis

49 3.4. Signal Transfer Results G A Shielded track between GP and CP Straight track between GP and CP Without CP Frequency in GHz Figure 3.5: Measured signal transfer characteristics. Shielded track between GP and CP compared with the straight track between GP and CP, and with the configuration without cabinet. we can neglect the coupling from the track located above the ground plane. The straight track couples stronger in the lower frequency range because its length lies closer to the corresponding wavelength of the first resonance around 0.3 GHz. On the other hand, the meandering track couples stronger at the frequency of third resonance ( 1.6 GHz) due to the better match of its 0.05 m long parts with the wavelength of the resonance. This has been checked by the FIT calculations where the length of the straight track between GP and CP varied from 0.2 m (as in real PCB straight track) down to 0.05 m (the length of the meandering part parallel to the straight track). Summarizing, the longer tracks couple more effectively at lower frequencies, while the shorter tracks (or shorter parts of the track in current case) do so at the higher frequencies. By the introduction of losses into the CM circuit, the resonances can be sufficiently damped so that they are no longer visible in the DM transfer in any of the possible configurations. For example, this can be done by the addition of the 150 Ω CM load over the gap as in the original precompliance setup [Hor01] where such a resistance was used to represent the cable attached to a PCB. Another, less practical way is similar to the reduction of the common-mode currents in cables by ferrite beads. When the mm ferrite tile used in fully anechoic rooms is placed between GP and CP, then the resonances also disappear from the DM signal curve. As expected, if the gap is bridged by a short piece of wire, the resonances are shifted to higher frequencies. Lower overall decrease of G A on the PCB with shielded track (Figure 3.5) is attributed to the lower dielectric absorbtion due to the fact that only one side of the board is used. Another effect was observed during the measurements. The results presented above consider a configuration with the ground plane soldered to the side A of the cabinet

50 38 Three-layer PCB on Top of a Cabinet Panel over the whole width. In one of the earlier board designs the GP was connected to the cabinet by the means of a small strip at the top layer of the PCB with a number of vias connecting this strip to the GP at the middle layer. While the same resonances are still present in the DM transfer, additional effects show up at higher frequencies. A detailed analysis of this type of connection has not been performed Non-resonant Losses The overall non-resonant reduction in S 21 and G A with frequency in measurement results is mainly caused by the dielectric losses in the board substrate. The FR-4 used for this PCB has relatively high losses and has an acceptable performance only at lower frequencies. High-speed interconnects require different materials, which have not only lower losses, but also better frequency stability of the dielectric constant. Lossy dielectrics can be characterized by a complex permittivity ε = ε iε where ε is the real (or lossless) part and ε is the imaginary part related to the losses. This imaginary part appears in Ampère s law as frequency-dependent term ωε with dimensions of conductance. A more commonly used parameter is the loss tangent, which is defined as tan δ = ε ε (3.2) To investigate the effect of dielectric losses, a second PCB with the same track geometries has been made from Taconic RF-35 organic ceramic substrate. This low-loss material has dielectric constant ε r = 3.5 and its loss tangent is tan δ RF 35 = 0.002, ten times lower than the typical value of tan δ F R 4 = 0.02 for FR-4. Figure 3.6 shows the comparison between these 2 boards when the straight track is located between GP and CP, hence the strong resonances at 0.3 GHz. The better overall performance of RF-35 board is apparent, at 1.8 GHz the losses are 3 times smaller compared to FR-4 board. This non-resonant behavior can be predicted using G A RF 35 PCB (measurements) RF 35 PCB (TL model) FR 4 PCB (measurements) FR 4 PCB (TL model) Frequency in GHz Figure 3.6: Comparison between FR-4 and RF-35 boards.

51 3.4. Signal Transfer Results 39 the simple transmission-line (TL) model. Results are also shown in Figure 3.6. The total length of the tracks of l total = 0.8 m and the respective loss tangents and the microstrip dimensions are used in this model. Somewhat higher values of G A for RF-35 board are related to the fact that the skin effect, which is also responsible for the frequency-dependent losses, has not been taken into account in TL calculations Gap Variation The resonance frequencies depend on the gap width g. Figure 3.7 shows the measured results for the first resonance near 0.3 GHz for Taconic RF-35 board. The board is located at h CP = 10 mm from the cabinet. The vertical part of the cabinet on side B was fixed at 3 different positions (g = 3, 10, 20 mm) or was removed completely (g = ). A larger gap leads to a higher resonance frequency due to a smaller capacitance C g between the far edge of the PCB and vertical part B of the cabinet [Hor98]. The same gap dependence is also observed in FIT simulations g = 3 mm g = 10 mm g = 20 mm g = 0.93 G A Frequency in GHz Figure 3.7: Measured effect of the gap width g on the frequency of first resonance.

52 40 Three-layer PCB on Top of a Cabinet Panel 3.5 Radiation Results To evaluate the influence of cabinet panel on the radiated emissions, a new set of measurements on low-loss RF-35 board was performed inside the semi-anechoic room of Philips Medical Systems in Best, the Netherlands. The PCB is positioned at 80 cm height over the floor of a semi-anechoic room, at 3 m distance from the CBL 6143 antenna. One port of the PCB (always the top track of the setup) was connected to the tracking generator of the Rohde&Schwarz EMI test receiver; the other track was terminated into 50 Ω. The generator output was set at 0 dbm. The radiation was determined in the direction perpendicular to the board surface, the y-axis in Figure 3.8. The antenna polarization was parallel to the z- axis, in agreement with the radiation originating from the gap between PCB and CP. Y Z X Figure 3.8: Electric field measurement setup. Figure 3.9 shows a 40 db increase in the measured field at the 0.30 GHz CM resonance due to the presence of the cabinet panel, when the straight track is between the CP and GP. A slightly smaller (30 db) increase is observed for the meandering track between ground plane and the cabinet. For the 0.9 GHz resonance the situation is less clear. At 1.6 GHz, the measured radiation is now stronger for the meandering track between GP and CP than for the straight track; a corresponding increase was also found in the DM-CM-DM coupling results of previous section. Even far off-resonance, the presence of the CP tends to increase the radiation. A similar configuration has been modelled using the FIT method. However, in order to reduce the calculation space and as a result to minimize the memory requirements and computer time, the electric field probe for the given z-polarization was placed at 0.5 m distance from the board. By necessity we also neglected the ground plane that was present in the semi-anechoic room measurements. Still, as can be seen from Figure 3.10, the resonances in calculations show the same behavior as in measurements at 3 m distance.

53 3.5. Radiation Results Without CP Straight track 2 between GP and CP Meandering track 1 between GP and CP 80 E z in dbµv/m Frequency in GHz Figure 3.9: Electric field in the z-polarization measured at 3 m distance from the PCB. The markers at the horizontal axis indicate CM resonance frequencies. 150 Without CP Straight track 2 between GP and CP Meandering track 1 between GP and CP 130 E z in dbµv/m Frequency in GHz Figure 3.10: calculations. Electric field in the z-polarization at 0.5 m distance from the PCB. FIT

54 42 Three-layer PCB on Top of a Cabinet Panel 3.6 Conclusions The experimental and numerical results of the DM-CM-DM coupling of the threelayer PCB on top of the metal cabinet panel have been presented. The DM circuit with the straight track between the CP and the GP couples strongly with the CM circuit at lower frequencies, whereas the meandering track between the CP and GP couples more at higher frequencies in the investigated range of GHz. This coupling not only affects the signal transmission on the PCB, but also leads to an increased radiation from the PCB at the resonance frequencies. This effect has been observed both in measurements and in calculations. The shielding around the track reduces the coupling and can be used as a preventive measure against the possible interference problems. Shielded tracks will be discussed later in Chapters 5 and 6.

55 Chapter 4 Reduction of Inductive Common-Mode Coupling of Printed Circuit Boards by Nearby U-Shaped Metal Cabinet Panel The effect of a nearby U-shaped metal cabinet panel on the inductive common-mode coupling of a printed circuit board (PCB) is calculated in a two-dimensional (2D) model by Schwarz-Christoffel (SC) transformations for doubly connected regions. Such an open metal cabinet can significantly reduce the mutual inductance between the microstrip lines on the PCB and the common-mode circuit if the cabinet is properly connected. But it may also increase the coupling for balanced pairs of tracks, in particular where the coupling for a single track varies strongly with position. Details of the SC approach are presented. The SC results agree with those of a static Method of Moments approach, but also clearly indicate the accuracy limits of the latter method Introduction Common-mode currents flowing through cables connected to printed circuit boards (PCB) are known to be major sources of electromagnetic interference. These currents are often driven by the inductive coupling between the differential-mode (DM) circuits on the PCB and the common-mode (CM) circuit. In recent paper M. Leone and V. Navratil [Leo04] presented a detailed analysis of the inductive coupling towards CM circuit for PCB with a ground plane (GP) and a single track or a balanced pair of tracks. They considered a GP with a slit, and derived engineering equations. However, in many applications the PCB will be mounted inside some open or closed cabinet and the metal cabinet panels (CP) will change the coupling. The first goal of this paper is to calculate in a two-dimensional (2D) model the influence of an open CP, which is either electrically floating or connected to the GP. As a typical setup we selected a PCB inside the U-shaped metal CP shown in Fig The additional panel often reduces the inductive coupling, certainly for a single track. However, at the end of Section 4.4, it will be shown that the CP may also increase the coupling for a balanced pair. A 2D analysis for a thin GP and a wire as track has been published earlier by several authors [Leo04], [Hoc96]. Analytical results for the inductive coupling have also been obtained [Leo04], [Hoc97]. Exact expressions have been derived from the Schwarz- 1 This chapter is an adapted version of the paper accepted for publication [Deu05a]. c 2005 IEEE. Reprinted, with permission, from IEEE Transactions on Electromagnetic Compatibility. 43

56 44 Reduction of Inductive Common-Mode Coupling h c p 0 w s s h g h s w w c p Figure 4.1: Cross section of a PCB inside the U-shaped cabinet which defines the positions s, s and h for a balanced pair of tracks, and the parameters for the ground plane and the cabinet plane. Christoffel (SC) transformation in which the thin GP is mapped onto the unit circle by a Joukowski transformation ([Hor01], Section II). The second goal of this paper is to show the advantages of the SC transformation for an unbounded doubly connected region. This transformation allows to include the cabinet panel, and simultaneously maps both polygons which describe the GP and the CP, onto two concentric circles. The parameters of the transformation are obtained numerically by a fitting procedure. As far as the authors are aware, this application has not been presented in earlier EMC literature. We also compare the SC results with those obtained by a static 2D Method of Moments (MoM) approach. For the sake of simplicity the thickness of conductors is neglected, although this is strictly speaking not a requirement for either method. For the purposes of this paper 1000 MoM elements sufficed, distributed over all conductors. The self-adaptive discretization maximized the accuracy for small couplings. This approach has been discussed and compared with exact calculations in [Deu01c]. Due to its near-to-exact nature [Däp88], [Hu98], the numerical SC software is well suited to determine the limits of the MoM approach for very small couplings. An example will be presented in Section 4.4. The paper is organized as follows. The basic configuration is presented in Section 4.2, the inductive coupling model and the limits of its applicability in Section 4.3. The calculation results for various configurations are discussed in Section 4.4. Concluding remarks are stated in Section 4.5. All mathematical details are collected in three appendices. Appendix A describes the Schwarz-Christoffel integral for an unbounded doubly connected region, together with the computation method to obtain the necessary parameters. Appendix B discusses the 2D complex potential for the magnetic field of a wire carrying an alternating current, which is placed between two perfectly conducting cylinders. The similar potential for a wire between two flat plates provides insight into the asymptotic behavior; it is briefly presented in Appendix C. 4.2 Configuration Figure 4.1 shows the cross section of a typical configuration. For convenience, we kept the same designations and, whenever applicable, the same values as in [Leo04]. The PCB consists of a continuous ground plane of width w = 100 mm. A single

57 4.3. Inductive DM-CM Coupling 45 infinitely-thin wire represents the track, which is at the distance of h = 1 mm above or below the GP. The distance from the middle of the GP to the wire is s. In case of a differential pair, two wires are placed at the mutual distance s = 1 mm and s is measured with respect to the mid-position between the wires, as shown in Fig Such a PCB is symmetrically placed inside the U-shaped metal cabinet panel of width w cp = w + 2g with sidewalls of height h sw = 20 mm. The GP is at the height h cp = 10 mm above the CP. In the MoM simulations tracks of finite width w t = 0.6 mm replace the wires, and the positions s or s are reckoned with respect to the track center. 4.3 Inductive DM-CM Coupling In a practical PCB, cables are commonly attached to the ground plane. We assume the connection at both ends in the third dimension perpendicular to the cross section of Fig Figure 1 of [Leo04] similarly proposes one cable at each end. Up to frequencies where the PCB length becomes comparable to the free-space wavelength λ, a simple model correctly represents the inductive DM-CM coupling. The DM circuits on the PCB induce a CM voltage V CM : V CM = jωm l t I DM (4.1) which drives the CM current through the cables. Here, ω is the angular frequency, and I DM is the current through a single straight track of length l t which extends in the third dimension. The voltage source V CM may be localized on the PCB. The mutual inductance M describes the magnetic flux per unit length (p.u.l.) of track, induced in the CM loop between the ground plane and infinity, due to a track current of 1 A; see [Hoc97] and [Hor01]. The current I DM returns through the GP and in part also through the CP if connected. The SC calculation of M and the employed MoM assume that the frequency is sufficiently high that the magnetic field does not penetrate the conductors. For a typical PCB of 100 mm width and a 35 µm thick copper GP, this starts at several hundred kilohertz ([Hor01], Fig. 3). The usable upper frequency limit may be extended to l t λ by modelling the PCB and CP in their environment as a transmission line (TL). The precompliance setup in ([Hor01], Fig. 1) has been analyzed this way. The inductive coupling parameters then have to be completed by the capacitive parameters p.u.l. which could also be derived by MoM or approximated by SC. However, such a TL approach is outside the scope of this paper. In case of a differential pair of tracks as in Fig. 4.1, the currents through both wires 1 and 2 are assumed to be of equal magnitude and to flow in opposite directions: I 1,2 = ±I DM. The difference in coupling of the individual wires M then replaces M in (4.1). If both wires are at identical vertical distance from the GP, or h 1 = h 2, M is a function of s only, and one has M (s) = M (s + s 2 ) M (s s 2 ) (4.2)

58 46 Reduction of Inductive Common-Mode Coupling Retaining only the first-order term in a Taylor expansion of M (s), one may rewrite (4.2) as M = M s (4.3) s In practice, some current imbalance may occur, and then the term jωm l t I e should be added to (4.1); see Equation 5 of [Leo04]. Here, M is the average of M for both wires, and I e = I 1 + I 2 is the even-mode current [Leo04]. Possible sources of current imbalance are different characteristics of the drivers and receivers, or different characteristic impedances of the tracks, which depend on height, width and position. Some of these items have already been discussed by others [Leo04], [Boc95], [Xia03]. In this paper, I e = 0 is assumed, since the focus is on the effects on M and M by the CP. Connectors mounted at the GP ends of a practical PCB will contribute their M- coupling, which depends on their design and mounting. Also, the connection between the cabinet and the ground plane is important. A continuous contact over the full cross section is implicitly assumed. Still, the calculated M s are of direct use when looking for the weakest spot, or to decide for the first item to improve when EMC quality is at stake. Many guidelines derived from a 2D picture can be carried over to the 3D case. 4.4 Results First, we consider the track(s) on top of the GP as indicated in Fig The gap between the GP and the sidewall of cabinet is fixed at g = 5 mm. The parameters for the SC transformation are given in Table 4.2 in Appendix A, and the corresponding prevertices are shown by markers on the circles in Fig in Appendix B. Figure 4.2 shows the M -results for three cases: a) no cabinet present as in [Leo04] (dashed lines), Without CP (SC) Disconnected CP (SC) Connected CP (SC) Connected CP (MoM) 10 0 M nh/m M s/w Figure 4.2: DM-CM mutual inductance M for a single track and M for a differential pair. The tracks are on top of the GP, as shown by the inset.

59 4.4. Results 47 b) with cabinet which is not connected to the GP (thin solid line), and c) with interconnected GP and CP (thick solid line). Even an electrically floating CP (case b) decreases the coupling, be it by about a factor of 2 at most. When the CP and GP are properly connected at both ends in the third dimension (case c), the net magnetic flux passing between the GP and the CP should be zero, and the return current is shared by the GP and the CP. To simulate this in MoM, both conductors are put at the same potential. Appendix B gives the complex potential function used in the SC approach for cases b) and c). For a track approaching the PCB edge, M now decreases compared to cases a) and b); at the GP edge (s/w = 0.5) the reduction is a factor of 10. The reduction is mainly caused by the sidewalls. M is also strongly reduced by the CP; the deep minima at s/w = 0, s/w = 0.35 and near s/w = 0.5 stem from a zero derivative of M (s). The circles in Fig. 4.2 show a selection of the MoM data for the connected CP case, which agree very well with the SC values. Table 4.1 shows the actual values for the position s/w = 0.2 of Fig In case of the single Table 4.1: Comparison of SC and MoM M -values in nh/m at s/w = 0.2 SC MoM MoM w t = 0.6 mm w t = 10 3 mm M M track the difference between SC and MoM results is less than 0.6%. The finite width of the track influences the M, and even better agreement to within 0.16% is found if the track width is reduced to w t = 10 3 mm in the MoM calculation. For the balanced pair the reduction of the track width decreases the deviation from 1.12% to 0.3%. Figure 4.3 shows the results for the three cases mentioned, but now for the track(s) below the GP. For a single track and disconnected CP (case b) the changes with respect to case a) are minor: a reduction of about a factor of 2 for a track near the edge, and remarkably enough an increase by the same factor when the track is near the GP center. On the other hand, M decreases substantially in accordance with the leveling-off of M for s/w < 0.4. In fact, M varies proportionally to e πs/h cp for small s. This exponential dependence is the expected large-distance behavior of the flux function belonging to a dipole formed by two line currents embedded between two floating parallel plates at h cp distance; see Appendix C. When the GP and CP are connected (case c), the wires are positioned between two plates at the same potential. Both M and M now follow the same exponential decrease down to very small s. By virtue of (4.3), the exponential behavior also ensures that the ratio M /M becomes constant, equal to π s/h cp 0.3, independent of the track height for equal h 1,2. Given the already small M-values and the small benefit of balanced signal transport, other reasons should justify its application, for instance tracks crossing a GP slit [Leo04]. Although not shown in Fig. 4.3 in order to limit the vertical range, the SC calculated M for the interconnected CP and GP decreases down to the minimum of about 10 8 nh/m at s = 0, in agreement with the exponential behavior. Because of the symmetry M is zero at s = 0. Due to the inherent finite numerical accuracy,

60 48 Reduction of Inductive Common-Mode Coupling Without CP (SC) Disconnected CP (SC) Connected CP (SC) Connected CP (MoM) 10 0 M nh/m M 10 3 M M s/w Figure 4.3: Mutual inductance M for a single track and M for a differential pair. All tracks are below the GP, as indicated by the inset. the MoM data start to deviate from the SC values for very small M. For instance, a doubling of the number of elements to 2000 reduces the difference between MoM and SC from about a factor of 4.5 to 1.3 for the lowest MoM value shown at s/w = Figure 4.4 shows M when the gap g between the PCB edge and the sidewall of the cabinet is varied. The single track is on top of or below the GP and near the edge 10 2 Disconnected CP 10 1 M in nh/m Connected CP Track below GP (MoM) Track below GP (SC) Track above GP (MoM) Track above GP (SC) Track below GP (MoM) Track below GP (SC) g in mm Figure 4.4: Mutual inductance M as a function of gap width g, for a track placed near the edge of the GP (s/w = 0.497). at s/w = In case of the disconnected CP, the variation in M with g is small, and the difference in M between tracks on both sides of GP is only about 5%; the dashed line shows the data for the track below the GP only. In case of the connected CP, the reduction of coupling with closure of the gap is clear. For the track on top

61 4.4. Results 49 M becomes very small because of the corner formed by the GP and the CP sidewall. Obviously, M is zero for the track below the GP if g = 0. The reduction of M with smaller g is not accompanied by a similar reduction of M because of the increased M / s near the GP edge. Figure 4.5 shows results for g = 1, 4, 7, and 10 mm, with the track on top of the GP. In particular near the GP edge M is still quite smooth, but M varies over several orders of magnitude with either s or g. Assuming somewhat arbitrarily an M-value of 10 2 nh/m as criterion, the best gap of the set would be g = 10 mm, since M remains below this limit except for a narrow range of s between 45 and 50 mm g = 1 mm g = 4 mm g = 7 mm g = 10 mm M 10 0 nh/m M s/w Figure 4.5: Mutual inductance M and M as a function of track position s/w for gap widths g = 1, 4, 7, and 10 mm. The track is on top of the GP. The inductive coupling strongly depends on the shape of the cabinet. We started from the 110 mm wide cabinet base, and extended the CP by adding metal of length l at each side to a total of l mm. We then compared three situations: a) simple flat horizontal extensions of the base, b) vertical sidewalls of height l, and c) the same sidewalls up to h sw = 20 mm, but now folded inwards starting at the height h sw so that fins of length l h sw are formed; see the thick lines of the insets in Fig The single track is again near the edge at s/w = and either on top of or below the GP. Because the disconnected CP has nearly no effect, only the results for the connected CP are shown. In situation a) the added metal is least effective, as M decreases only slowly with l. In situation b) about an order of magnitude reduction is obtained at l = 20 mm, equal to h sw of the typical setup. At larger l, the sidewalls form two parallel plates and the exponential decrease proportional to e πl/wcp sets in. Situation c) confirms the intuitive guess that it is better to fold the sidewalls and bend them inwards over the PCB. The steeper descent is proportional to e πl/(hsw hcp), because the track is now in a slit formed by the GP and one of the fins, acting as parallel plates at the distance of h sw h cp = 10 mm; see Appendix C. Again, this does not necessarily imply that M is also improved, because of the increased derivative M / s. As an example, in Fig. 4.7 we show M and M as

62 50 Reduction of Inductive Common-Mode Coupling M in nh/m Track above GP (Flat) Track below GP (Flat) Track above GP (Sidewall) Track below GP (Sidewall) Track above GP (Fins) Track below GP (Fins) l in mm Figure 4.6: M versus l for: a) horizontal extensions, b) vertical sidewalls, and c) sidewalls of h sw = 20 mm with fins of length l h sw bent inwards, as indicated by the thick lines of the insets. Solid lines represent the SC results, the markers a subset of the MoM data. a function of s/w for l = 40 mm, or a sidewall of h sw = 20 mm, with fins of the same length extending over the GP. For comparison, the dashed lines correspond to the data of Fig. 4.2 with only the sidewall of h sw = 20 mm. Near the GP edge the fins indeed reduce M. Because of the exponential variation of M (s) between the GP and fin, M is about M π s/(h sw h cp ) as follows from (4.3). However, M increases by more than an order of magnitude near the fin edge (s/w = 0.35). One observes that the range of positions where M is over 10 2 nh/m is extended and shifted. As a result, tracks that were not critical without the fins, may become so with them Sidewall only (SC) Sidewall and fin (SC) Sidewall and fin (MoM) M nh/m M s/w Figure 4.7: Mutual inductance M and M as a function of s/w for a sidewall and fins of combined length l = 40 mm. The track is on top of the GP. The dashed lines are the data of Fig. 4.2 for the connected CP.

63 4.5. Concluding Remarks Concluding Remarks An open U-shaped cabinet panel can strongly reduce the inductive common-mode coupling of circuits on a printed circuit board, in particular when the cabinet is connected to the PCB ground plane. The reduction of M for a single track can be accompanied by a reduction in M for a balanced pair. However, it is shown that M may even increase by an order of magnitude when the cabinet panel causes large variations in M as a function of position. A cabinet panel extended by fins over the PCB served as an example. The Fortran-coded numerical implementation of the Schwarz-Christoffel transformation for an open doubly connected region is able to calculate very small M-couplings accurately and fast. A common present day laptop computer with 1.4 GHz processor delivers the necessary SC parameters for the GP and CP in less than a second; these have to be determined only once. The inversion of the real-space points and the evaluation of the complex potentials take about the same time per track position. For those reasons a search for engineering equations was not felt necessary. In addition, as Fig. 4.1 shows, there are many parameters to be varied, which does not help to establish compact equations. The MoM approach used here aims at maximum accuracy, rather than speed [Deu01c]; it has been programmed in Matlab. On the same computer about 90 s is required for the calculation of one track position. In an actual PCB design, the 10 2 nh/m criterion should be replaced by a value corresponding to the time derivative of the signals to be transported and to the proper EMC limits. The SC method then allows a fast optimization of the CP parameters g, h sw and l. 4.6 Appendix A: Schwarz-Christoffel Transformation A brief outline of the Schwarz-Cristoffel transformation for an unbounded doubly connected region is described for the sake of completeness. The references cited provide detailed information about the analytical formulation and the numerical approaches for the improper integrals and for the efficient evaluation of the θ-functions. The required Schwarz-Cristoffel integral reads: f(w) = C w m k=1 [ ( θ )] α0k 1 n w µw 0k [ w θ ( w w k=1 ) θ ( w w [ ( )] θ µw α1k 1 w 1k )] 2 dw (4.4) See ([Däp88], Section 3.2), ([Kop59], ) and [DeL03]. The function z = f(w) maps the annulus µ < w < 1 in the complex w-plane onto the exterior of two disjoint polygons described by sets of vertices z 0k with k = 1,, m and z 1k with k = 1,, n in the complex z-plane. The subscripts indicate whether the prevertices w {0,1}k are on the outer (0) or the inner (1) circle. The exponents in (4.4) are related to the outer angles α {0,1}k π of the polygons (see Fig. 4.8), and obey the relations α0k = m + 2 and α1k = n + 2

64 52 Reduction of Inductive Common-Mode Coupling Figure 4.8: Typical setup with the vertices and the angles indicated. The dot above the GP indicates a possible track position. The denominator of the integrand in (4.4) ensures that w is mapped onto infinity in the z-plane ; w is the image of w with respect to the inner circle, and equals µ 2 /w with w the complex conjugate of w. The prevertices w {0,1}k, and the parameters µ, w and C can be determined in a nonlinear fitting procedure as described by [Däp88] and [Hu98]. Because of the rotational degree of freedom of both circles, it is convenient to chose w on the real axis µ < w < 1, which uniquely determines the arguments φ {0,1}k of w {0,1}k apart from a trivial factor of 2π. This leaves as m+n+4 fitting object functions the three complex (or six real) values of z 11 z 1n, z 01 z 0m and z 1n z 0m, plus the m+n 2 absolute values of the remaining polygon side lengths. We let the inner circle correspond to the ground plane (n = 2), and the outer circle to the cabinet panel (m = 6). For the nonlinear fit procedure we relied on the Fortrancoded numerical implementation given in [Hu05], and adapted it to also accommodate exterior regions by the addition of the denominator of the integrand in (4.4). On a present-day laptop computer the fit required about 1 s to converge with the desired maximum deviation of the object functions set at The values given in Table 4.2 have been obtained for the typical example discussed in the main text, with z {0,1}k in units of 100 mm. The full double-precision results are presented, accurate at least to the first 6 digits. For a current I through the GP which returns through the CP, four magnetic field lines are shown in Fig. 4.9 with a constant flux between the lines. The corresponding complex potential is W 1 of (4.9) given in Appendix B. The fins discussed in the main text required four additional prevertices w 0k Axes in mm Figure 4.9: Magnetic field lines for a current through the GP which returns through the U-shaped CP.

65 4.7. Appendix B: Complex Potential of a Line Current Between Two Cylinders 53 Table 4.2: 100 mm Parameters of the typical GP-CP example of Fig. 4.1, with z {0,1}k in units of µ = w = C = i k z 0 (k) α 0 (k) φ 0 (k) i i k z 1 (k) α 1 (k) φ 1 (k) i i Appendix B: Complex Potential of a Line Current Between Two Cylinders A line current I flows perpendicular to the complex w = u + iv plane, and passes through that plane at the point r located on the real axis between two circles of radii µ and 1; see Fig The circles represent the perpendicular cross section of cylindrical conductors. The line generates a series of mirror images in the inner and outer circles ([Hen86], Section 15.6 IV). The first image in the inner circle is located at µ 2 /r on the real axis, the first image in the outer at 1/r. These images are reflected again, and the position of the subsequent images can be obtained from the scheme shown hereunder o i r o i µ 2 /r 1/r r/µ 2 + rµ 2 µ 4 /r 1/rµ 2 r/µ 4 + rµ where the o and i on the top row indicate whether the reflection occurs in the inner or outer circle, and the alternating signs indicate whether the image current runs in the same (+) or opposite ( ) direction with respect to the line current at r. The total complex logarithmic potential W at the point w is the one due to the wire plus

66 54 Reduction of Inductive Common-Mode Coupling µ r Figure 4.10: Circles with radius w = 1 and w = µ = 0.5, and several magnetic field lines due to a line current I at r = 0.71 (+). The return current I flows through the inner circle. The markers on the outer circle indicate the points where the current density is zero. There is no net current through the outer circle. the sum of those of the images [Kad59]: W (w) = ii log [(w r) 2π (w r/µ2 )(w r/µ 4 ) (w µ 2 /r)(w µ 4 /r) (w rµ2 )(w rµ 4 ) (w 1/r)(w 1/rµ 2 ) ] (4.5) The first fraction corresponds to the left part of the scheme, the second to the one at the right. The argument of the logarithm can be converted into θ-functions; combine for example all terms with µ 2, and becomes (w rµ 2 )(w r/µ 2 ) (w 1/rµ 2 )(w µ 2 /r) µ2 /wr µ 2 /wr (1 µ 2 r/w)(1 µ 2 w/r) (1 µ 2 wr)(1 µ 2 /wr). By virtue of Equations and of [Hen86], which read θ(w) = (1 µ d w)(1 µ d /w) (4.6) and we arrive at d=1,3,5, θ(µw) = (1 w 1 ) v=2,4,6, W (w) = ii θ(µw/r) log 2π θ(µwr) (1 µ v w)(1 µ v /w) (4.7) (4.8)

67 4.7. Appendix B: Complex Potential of a Line Current Between Two Cylinders 55 The magnetic field follows from {H u, H v } = { U/ u, U/ v} with U the real part of W, or equivalently H u ih v = dw/dw. The imaginary part V of W is the flux function. The expansions (4.6) and (4.7) show that θ(µ 2 w) = 1 µw θ(w) and θ(µ 2 w) = w µ θ(w) which may be used to prove that the difference in flux function between the outer and inner circle is V (1) V (µ) = I 2π log(r). By inspection of the real part of W one observes that the return I of the line current flows through the outer circle. If the potential W 1 (w) = ii log(w) (4.9) 2π is added to (4.8), the return current flows through the inner circle instead. For this case several magnetic field lines are shown in Fig The markers on the outer circle indicate the positions where the H-field and consequently the current density are zero. Between the markers and near r, the current density on the outer cylinder is in the direction opposite to I; it is in the same direction on the remainder of the cylinder. If W 1 is multiplied by log(r)/ log(µ), the return current distributes over both circles such that the magnetic flux between them is zero. This occurs when the cylinders or the physical conductors they represent are interconnected at the ends. The M-values of the main text result from the following steps ([Deu01b], Appendix A): numerical inversion of the mapping (4.4) to obtain the w t -image of the track position z t (see Fig. 4.11), w t = f 1 (z t ) (4.10) rotation of the track image to the real axis to result in r t, rotation of w to w,r over the same angle, w t,r = w t e i arg(w t) ; r t = R(w t,r ) (4.11) w,r = w e i arg(wt) (4.12) determination of the imaginary part of the potential W plus W 1 multiplied by the appropriate factor β, which is either 1 for the non-connected CP or log(r)/ log(µ) for the connected CP, V (w) = I [W (w) + βw 1 (w)] (4.13) determination of the difference of the total V at the inner circle and at the rotated image of infinity. M = µ 0 I [V (µ) V (w,r)] (4.14) µ 0 is the magnetic permeability of vacuum. In the reciprocal approach, M follows from the flux between the track and GP due to a current through the GP and the CP which returns at infinity. This is equivalent to a current I at w.

68 56 Reduction of Inductive Common-Mode Coupling w Figure 4.11: The path of the track position image w t for the typical example of Fig. 4.1 in the main text with the track on top of the GP (x), or below the GP (o). The position of w (+) and the prevertices w {0,1}k are indicated. 2 The paper focuses on the DM-CM coupling. The differential mode coupling between tracks can be obtained by calculating in the last step the difference of V between the w-image of the victim wire position and the inner circle. In [Deu01a] two numerical SC transformations for simply connected regions [Dri02] were applied to a -shaped cable conduit and a symmetrically placed overlapping cover. The first transformation approximately described the overall outside; the equivalent approach for Fig. 4.8 would be to map the contour z 11 z 12 z 06 z 05 z 04 z 03 z 11 onto a circle and to use the potential (4.9). The second transformation described one half of the separated conductors and one slit by mapping them onto a rectangular region; here the symmetry was necessary. This transformation gives the same field lines as in Fig The symmetrical GP-CP system could have been approximated in a similar way. On the other hand, the SC transformation for a doubly connected region deals in a natural and exact way with larger openings between GP and CP and also with asymmetrical configurations. 4.8 Appendix C: Complex Potential of a Line Current Between Two Planes The line current I of Appendix B is now located at (u, v) = (a, 0) on the real axis of the complex w = u + iv plane. The lines u = 0 and u = π/2 represent two conducting plates perpendicular to the w-plane. The complex potential follows again from a series of images. It has been derived in [Wal51], as cited in Section of [Bin92]: W (w) = ii 2π log sin(w + a) sin(w a) (4.15)

69 4.8. Appendix C: Complex Potential of a Line Current Between Two Planes 57 Both plates share the return current I, and it can be shown that I u=0 = I(1 2a/π) and I u=π/2 = I2a/π. From (4.15) one finds that the flux function or imaginary part of the potential varies as V (w) = I π [ sin 2 (u + a) sin 2 (u a) ] e 2v (4.16) for large distance from the line, or v π/2. The potential could also be written as series in functions V n (w) V n (w) = sin(2nu)e 2nv, n = 1, 2,... (4.17) The set of V n form a complete set of basis functions, which satisfy Laplace s equation with boundary conditions V n = 0 at u = 0 and u = π/2. V (w) has the same asymptotic behavior for large v as V 1 (w). The higher-n terms decay faster. If the emanation of field lines from a single slit in the typical setup of Fig. 4.1 determines M, the n = 1 term dominates for wires deeply buried between two planes, or GP and CP. This leads to the observed exponential decrease of M with distance from the slit. At the middle position between GP and CP (s = 0 in the main text) both slits contribute equally, and M assumes a minimum. In the main text the exponent is converted to take the actual distance between the plates into account, rather than π/2. In case of a balanced pair, both lines are at a small separation v. Then M can obtained from a first-order Taylor expansion of V with respect to the position. With (4.16) we have V 2 v e 2v and the ratio of M and M becomes constant. This relation is mentioned in the main text, adapted again to the relevant dimensions. The figures are based on the actual difference of M between both wires, given by (4.2) in the main text. The plates carry no net current with a balanced pair of lines at identical distance a from the plates. Still, the exponential behavior of V for large v is retained in Fig. 4.3 for the non-connected CP. The asymptotic flux function (4.16) varies linearly with a near a = 0. An unbalance in height between both tracks a causes an additional unbalance in M, according to M /M = a/a. A similar proportionality holds near a = π/2.

70 58 Reduction of Inductive Common-Mode Coupling

71 Chapter 5 Shielded Tracks on a Printed Circuit Board Fully shielded tracks can be embedded in multilayer printed circuit boards by a novel manufacturing technique. The paper presents a numerical analysis of the influence of dimension tolerances on the characteristic impedance. For partly shielded tracks the coupling between tracks and the environment is studied as well. The analysis relies on a two-dimensional approach, using Conformal Transformations and a static Method of Moments Introduction When compared to the commonly used microstrip and strip lines, fully shielded track structures on a printed circuit board (PCB) reduce undesired couplings to neighboring tracks and environment. In the recently developed E-Coax (or embedded coax) [Via05], such a shield is manufactured by creating and subsequently metalizing trench walls in three outer layers of a multilayer PCB. The middle layer contains the tracks, and the upper and lower layers are interconnected by the metalization; see Fig. 5.1 for the photograph of the cross section. A single shield may also contain several tracks. We first calculate the dependence of the characteristic impedance Z 0 of the E-Coax on manufacturing tolerances for a single signal track and for a differential pair consisting of two symmetrically placed tracks. Secondly, we consider the mixing of odd and even modes for two tracks at asymmetrical positions. Thirdly, we evaluate the coupling between tracks, when the metalized sidewall has a small opening near the bottom of the trench. Applications of such partial shields may be filters and directional couplers; again the sensitivity on manufacturing tolerances should be accurately known. The cross section of the E-Coax is of the order of 1 mm, and the dielectric is close to being homogeneous. The quasi-tem approximation is then valid up to a frequency of many GHz, which allows Z 0 to be evaluated from the static inductance and capacitance. The paper mainly deals with the magnetic field and the inductances, which are readily converted into the capacitances and into Z 0 for a homogeneous dielectric. The high-frequency signal damping is caused by the dielectric absorption and conductor resistance, which will be enhanced by the skin effect at high frequencies. The dielectric losses in the E-Coax are comparable to those in a stripline with the same insulating material. The skin-effect damping could in principle be obtained from a sheet current density approach in combination with the equivalent surface impedance; 1 This chapter is an adapted manuscript of the paper published in Journal of Electromagnetic Waves and Applications [Deu05b] 59

72 60 Shielded Tracks on a Printed Circuit Board w t h t b Figure 5.1: Cross section and parameters for an E-Coax with single track. see e.g. [Kad59, Goa01]. However, the current distribution in the E-Coax inner conductor differs slightly from the one in e.g. a stripline. As a result, the signal attenuation in the E-Coax can be expected to be similar to non-shielded tracks. Therefore, we do not consider the attenuation in detail in this contribution. Conformal mapping is an elegant and accurate method to solve a number of twodimensional static potential problems, in particular if the medium is isotropic and homogeneous. For the sake of completeness, an outline of the procedure is given here; for details please consult [Dri02, Hen86, Hu98]. Most calculations have been performed with Schwarz-Christoffel (SC) transformation, which maps the unit disk E in the w = u+iv plane onto a polygon P with a boundary Γ in the physical z = x+iy plane (Fig. 5.2). The SC mapping expression is: z = f(w) = A + C w n k=1 (1 w w k ) αk 1 dw (5.1) where A and C are complex constants, z k = f(w k ) and the starting point of the integral can be conveniently chosen to coincide with one of the prevertices w k. The exponents α k are related to the internal angles as shown in Fig The MATLAB Toolbox [Dri02] determines A and C and the prevertices w k numerically in a close to exact way. The sides of the polygon are calculated within a relative accuracy of or better. The SC approach is then well adapted to study the effect of small variations in the polygon dimensions. In the procedure, the mapping parameters can be adjusted to locate the current I at the center of the circle. Assuming a homogeneous non-magnetic dielectric, the complex potential for the magnetic field due to a filamentary current I at the origin in the w-plane is Z(w) = i I log(w). (5.2) 2π The magnetic field follows from {H x, H y } = { X/ x, X/ y} with X the real part of Z, or equivalently H x + ih y = dz(f(w)) /dz. The imaginary part Y of Z is the flux function.

73 5.1. Introduction 61 z 03 z 02 f(w) w 01 z 13 z 12 z 14 z 11 z 04 z 01 w 02 w 12 w 11 w 13 w 03 w 14 w 04 1 Figure 5.2: Schwarz-Christoffel transformation, shown for doubly connected regions. In the case of a simply connected region the inner conductor is replaced by a filament at the inner conductor center; then also all z 0k z k and all w 0k w k. A single track of finite size can be described by the SC transformation for doubly connected regions [Hen86, Sect. 17.5]: f(w) = A + C which involves a θ-function w m k=1 θ(w) = [ ( )] w α0k 1 n [ θ θ µw 0k k=1 d=1,3,5,... ( µw w 1k )] α1k 1 dw, (5.3) (1 µ d w)(1 µ d w 1 ) (5.4) The function f(w) maps the annulus µ < w < 1 to a doubly connected polygonal region, which is in our case the area between the inner conductor and the shield. We used the Fortran coded numerical implementation given in [Hu98]. Please note that the designation of z and w to the physical and the canonical domain as used here is the same as in [Hen86], but that it is inverted with respect to [Dri02]. To our knowledge, no code is available for multiply connected regions. Therefore, we calculated the field for two tracks inside a shield by a Method of Moments (MoM) approach in which an iterative procedure adapts the discretization to increase the accuracy [Deu01c]. In several configurations we compared the SC results with those by MoM. The paper borrows some terminology from the field of electromagnetic compatibility (EMC). A signal track forms a closed current loop with the shield; this loop is called a differential-mode (DM) circuit. The shields and ground planes on the PCB form the common-mode (CM) circuit together with the PCB environment, such as a metal cabinet or other neighboring conductors. The term common indicates that both DM conductors on the PCB carry a net current off the PCB. A DM circuit can induce a CM current through a first-order DM-CM coupling, and vice versa. It is well known [Ber83] that the radiation due to the large CM circuit often dominates the direct radiation by the small DM circuits, in particular if cables are attached to the board.

74 62 Shielded Tracks on a Printed Circuit Board 5.2 Characteristic Impedance Z A Single Track Consider a single signal track in its shield, with parameters shown in Fig In the example chosen, their designations and the values are: base width b = 700 µm, height h = 468 µm, width of the track w t = 205 µm, thickness t = 18 µm, slope angle between base and sidewall α = 80 degrees. The relative dielectric constant ε r of the insulation is assumed to be homogeneous. The track and shield are regarded as perfect electrical conductors. Such configuration can be analyzed by SC mapping (5.3). The inner radius of the annulus is related to the characteristic impedance in a straightforward manner: Z 0 = 1 µ0 ln(1/µ). (5.5) 2π ε r ε 0 The parameters mentioned above and ε r = 3.5 result in a largest Z 0 of Ω when the track is located near the center, i.e. (x, y) = (0, h/2). For comparison, the stripline formed by the track of the same size between two ground planes at the same distance h, has Z 0 = Ω. In the manufacturing process a variation in the insulator thickness or the y-position is possible, as well as a position deviation in the x-direction. As an example, Fig. 5.3 shows the contours for deviations of 1, 2, 5 and 10 percent from the maximum Z 0 -value when the position of the center of the signal track is varied in both x and y-directions while keeping the other parameters, notably the total height h, constant. Because of the symmetry of the E-Coax, only the right % y in µm % 2% 5% x in µm Figure 5.3: Contours for the position of the track center, at which Z 0 deviates by 1, 2, 5 and 10 percent from the maximum value. Thick markers at the left axis indicate the corresponding positions for a stripline. Please note that the x and y scales differ. half needs to be shown. The contours have a slight vertical asymmetry due to the slant side walls. Thick markers on the left axis indicate the equivalent variations in y-direction for a stripline track, which nearly coincide with the contours at x = 0

75 5.2. Characteristic Impedance Z 0 63 for the E-Coax track. For comparison the right half of the track is indicated by the dashes. The angle α turns out not to be critical when pivoting the side wall at mid height: at α = 66 degrees Z 0 is reduced by 1 percent. In order to keep Z 0 within 5 percent, the total width of the shield b should remain within ( 100, +70) µm of the value b = 700 µm mentioned above. These bounds are well within the tolerances of the manufacturing process. For the four points indicated by the circles in Fig. 5.3, we compared the SC results with Z 0 obtained by MoM. Both methods produced results equal to at least the fourth significant digit or to within percent Two Tracks within One Shield High-speed interconnects for telecommunication applications often require that differential signals are sent via a pair of balanced transmission lines. Two identical tracks within one shield are shown as inset in Fig The shield parameters are again b = 700 µm, h = 468 µm, and α = 80 degrees. First both tracks are symmetrically placed inside with their centers at ( d/2, h/2) and (d/2, h/2) and the distance d is varied. Two propagation modes occur, the even mode with equal currents through both tracks, and the odd mode with opposite currents through the tracks and no net current through the shield. These modes have been investigated by the MoM. Figure 5.4 shows the resulting Z 0,e [Gup96, Eq. 8.29] and Z 0,o [Gup96, Eq. 8.30] for several track widths w t. d Figure 5.4: Z 0,e and Z 0,o as functions of distance d between tracks. The symmetry is broken when the tracks shift in x direction (as indicated in Fig. 5.5 by offset o). The resulting even-odd mode mixing can conveniently be represented as follows. For = 0 the inductance matrix ( ) L + M (5.6) M L

76 64 Shielded Tracks on a Printed Circuit Board has the even and odd mode eigenvectors (1, 1) T and (1, 1) T. For 0 the new eigenvectors are those for = 0, to which the fraction F = ±{ 1 + M 2 / 2 M/ } of the other is added. Fig. 5.5 shows F as a function of the offset o for two values of the track width w t and the fixed value d = 200 µm. o o Figure 5.5: F as function of offset o. 5.3 Coupling Between Partially Shielded Tracks In order to evaluate the importance of fully shielded tracks we calculated configurations where the metalized sidewall of the shield did not reach the bottom of the trench. Two E-Coax tracks are located next to each other on top of a ground plane. The shield dimensions are identical to those of Section The distance between centers of the tracks is 800 µm. The sidewall closest to the adjacent track has a gap g near the bottom of the trench, which indicates the open fraction of the E-Coax height; i.e. g = 1 when the sidewall is absent and g = 0 when shield extends to the bottom. The thickness of the shield wall is neglected in the calculations. As before we concentrate on the magnetic inductance. Table 5.1 lists five configurations: traditional microstrip (a) and striplines (b), an E-Coax with open (c, g = 1) and half-open (d, g = 1/2) sidewalls and an E-Coax with a tunnel in-between (e). The mutual inductance between the tracks is calculated by SC mapping with the current carrying track replaced by a single wire at the center, by SC mapping combined with the method of wires (SCw) and by MoM. Infinitely wide groundplanes at the base of E-Coax are assumed for (a), (b) and (c). For the small M of (d) and (e) the SC mapping might lose its accuracy due to the phenomenon known as crowding : the prevertices get very close to each other, in particular those that correspond to vertices farthest from the current carrying

77 5.3. Coupling Between Partially Shielded Tracks 65 wire (see Fig. 5.6). The resulting loss of numerical accuracy can be remedied by the introduction of additional prevertices, optimized by considering the cross ratio in a Delaunay triangulation (CRDT) procedure; see [Dri02, p. 30]. The existing CRDT software does this automatically. Since it can only be applied to closed regions, a large box has been placed around the E-Coax. The size of this box was chosen at least 5 times the size of the E-Coax. Resulting M-values did not depend on the size of this external box to an accuracy of better than z 17 z 18 z 1 z 7 z 2 z 3 z 12 z 13 z 6 z 5 z 10 z 9 z z 4 z 11 k z 8 z 16 z 14 z 15 f(w) w 6 w 7 w 5 w 4 w k w..w 1 3 w..w 8 18 Figure 5.6: Vertices z 1 z 18 for the shield of case (d) in Table 5.1, and for the box required for the CRDT method. Prevertices show the crowding on the unit circle. In the SCw approach a number N of thin wires are positioned along the perimeter of both tracks. In an N-times repeated procedure, each wire k (e.g. the black one in Fig. 5.6) is regarded as a magnetic field source and mapped to the center of disk E. The mutual inductance M with respect to any other white wire l follows from M lk = µ 0 2π ln( w l ) (5.7) where w l is the image of wire l in the disk. In order to complete the inductance matrix, the self inductance of the source wire is approximated by the average of the magnetic flux over four points evenly distributed over the wire surface. The equation to be solved becomes ( ) ( ) ( ) L1 M I1 1 0 = (5.8) M L 2 I Table 5.1: Mutual inductance M in nh/m calculated by three different methods for five different configurations Configuration SC SCw MoM a) b) c) d) e)

78 66 Shielded Tracks on a Printed Circuit Board where L 1,2 are the block matrices corresponding to the wires of track 1 or 2, M is the block describing the coupling between the wires of differing tracks and I 1,2 are the column vectors of wire currents for both tracks. The two resulting current vectors are combined to a total current of 1 A through track 1 and zero through track 2. The corresponding flux between track 2 and the shield is the M-value sought. This procedure is repeated for different numbers of wires N. The M-values in Table 5.1 are obtained by a linear extrapolation of 1/N 0 taking data obtained over the range 100 N 800. Table 5.1 shows that the mutual inductance M decreases significantly even when the sidewall is still partly open. The good agreement between MoM and SCw mapping with wires is apparent; both methods take the current distribution over the track surface into account. The SC mapping with the track replaced by a single wire at the track center underestimates M by 20 percent at most M in nh/m M 1 M simp M 2 M tunnel M CM g Figure 5.7: M as function of gap parameter g. For several configurations we varied the gap size g from 1 down to , where we assumed a single wire at the track center, as for the column SC in Table 5.1. The results are given in Fig First, the curve M 1 represents one track inside an E-Coax, which couples to another track without a shield (microstrip). The slit causes M 1 to vary as g 4 for smaller g. This behavior can also be shown using a simpler mathematical approach; see Fig The function sin(w) maps the strip 0 < u < π/2 in the complex w = u + iv plane onto the right half of the z = x + iy plane with a cut along the real axis x > 1, which leaves an open slit 0 < x < 1. Moving both wires at z 1 and z 2 simultaneously to larger distances is equivalent to narrowing the slit. The complex potential due to a current through a wire at (a, 0) on the real u-axis between the planes is : sin(w + a) Z(w) = log sin(w a). (5.9) See [Wal51] as referred in [Bin92, Sect ]. The coupling then results from the mapping w = arcsin(z), followed by a shift of w 1,2 over the imaginary part of the

79 5.3. Coupling Between Partially Shielded Tracks 67 source wire. For Iz 1,2 > 1 the g 4 behavior becomes apparent, as shown by the dashed line M simp in Fig z 1 sin(w) a w 1 z 2 w 2 Figure 5.8: Sine function mapping. Secondly, two equal E-Coax lines couple through equal gaps in the neighboring walls as in row (d) in Table 5.1. The corresponding M 2 has been calculated by the CRDT approach and appears to be proportional to g 7 for small g. Thirdly, the coupling through the tunnel (M tunnel in Fig. 5.7 and case e) in Table 5.1) initially shows a similar g 7 behavior, which changes into an exponential decay below g = 0.2 due to the additional field attenuation in the tunnel. As a last example, the coupling towards the outside of the PCB can be expressed as the mutual inductance M CM between the track DM circuit and the common-mode circuit formed by the ground plane (GP), now of finite width, and the environment. The M CM describes the flux between the GP and infinity due to a current through the track, which returns through the GP as in previous configurations. The GP including the E-Coax has been mapped onto the unit circle. A line dipole is formed by the transform w 1 of the current carrying track at z 1 and its mirror image with respect to the circle at 1/w 1. The value of M CM is then [Deu01b]: M CM = µ 0 2π ln( w 1 ) (5.10) In the example, the width of the GP is chosen as 4 mm, and the E-Coax is placed in the middle. As could be expected, M CM also varies as g 4 like M 1. In [Deu01b] it is also shown that M CM is inversely proportional to width of the GP. The accuracy of the M-values has been estimated from the accuracy α of the transformations; the MATLAB Toolbox [Dri02] and the Fortran code [Hu98] return α as the maximum error in the computed lengths of the lines between vertices excluding infinity in the z-plane. All M-values are proportional to ln( w ). The error in M is then proportional to α/(w dz/dw), where the derivative dz/dw is easily retrieved as integrand of the SC transformation. The relative numerical error for M CM varied between at g = 1 up to at g = For the smallest value of M tunnel at g = in Fig. 5.7, the relative accuracy is still

80 68 Shielded Tracks on a Printed Circuit Board 5.4 Conclusions Novel fully-shielded tracks on PCBs have been studied numerically. Characteristic impedances of such structures have been modelled by means of numerical Schwarz- Christoffel conformal transformation and the Method of Moments; both methods produced accurate results. The effect of the opening in a shield on coupling to the environment and adjacent tracks has been analyzed. Acknowledgements This work was supported by the Interuniversity Research Institute COBRA (the Netherlands) [Cob05] and was performed in cooperation with Viasystems Mommers.

81 Chapter 6 Optimization of Interface Between Connectors and Tracks on Printed Circuit Boards Connectors have a significant influence on the transmission characteristics of tracks on printed circuit boards (PCB). Experimental results for different types of standard and modified SMA connectors are presented in this chapter. Connection details such as the length of the central pin of the connector play an important role in the overal system performance. Simulations in a 3D model show a good agreement between the calculated reflection parameters and measurement results. The crosstalk measurements on the specially designed boards confirm the advantage of the shielded track over the traditional transmission lines Introduction The numerical investigation of shielded tracks performed in the previous chapter has shown a significant reduction of coupling with respect to the traditional microstrip and striplines. In order to experimentally compare the performance of such shielded tracks (referred to as E-Coax or embedded coax) with traditional lines, a number of testboards described in Section 6.2 were manufactured by Viasystems. The measurement results on those boards are presented in Sections 6.3 and 6.4 for standard and modified SMA connectors. It turned out that the type of the connector and the way it is mounted strongly influence the signal transfer. Section 6.5 describes the full three-dimensional simulations for a PCB of reduced size. These simulation results are compared with the measurements in Section 6.6. A number of possible ways for further optimization of the connector-track interface are presented in Section 6.7. The crosstalk measurements on the final test PCB with modified connectors in Section 6.8 confirm the significant advantage of the new shielded tracks over the traditional ones. With the similar distances between two parallel tracks, the measured coupling is at least 20 db lower in case of E-Coax. 1 A part of the results presented in this chapter have been published in the project report for Viasystems Mommers B.V. 69

82 70 Optimization of Connector-Track Interface 6.2 Testboards and Measurement Setup For the experimental investigations presented in this chapter we used several types of printed circuit boards. The first board (referred to as the testboard A) has been manufactured for signal transfer characterization measurements and is mainly used to investigate the connector properties. This PCB has a number of E-Coax and microstrip tracks of various lengths and geometries. The lines are designed to result in 50 Ω characteristic impedance. Time-domain reflectometry (TDR) measurements performed by Viasystems confirm this value with deviations less than 10%. The dielectric material is FR-4, and as a result of its high dielectric losses the high-frequency measurements are possible on short tracks only. Commercially available vertically mounted pin-through-hole (PTH) SMA connectors have been soldered to both ends of each track. In order to compare different connector-track interfaces, another smaller PCB has been made. This board is referred to throughout the text as the credit card board because of its typical dimensions. This PCB is produced from Isola IS410 laminate (also a FR-4 type of material) with ε r = 3.9 and tan δ = specified at 2 GHz. The same type of SMA connector is now mounted horizontally at the edge of the board, as shown on Figure 6.1, and the central pin of the connector is soldered to the small pad on the top layer of the PCB. This pad is connected to the 13 cm long E-Coax track on layer 2 by a via. Figure 6.1: Edge-mounted SMA connectors on the credit card PCB. Based on the preliminary results obtained with these two boards, the final test PCB (testboard B) has been designed and manufactured in several versions for the crosstalk and high-frequency characterization measurements. This PCB has a 6-layer design with layers 1, 3, 4 and 6 being the ground planes and layers 2 and 5 the signal layers. All four ground planes are interconnected by a number of vias distributed over the PCB. The board consists of two logical sides: layers 1, 2 and 3 have transmission lines connected to PTH SMA connectors (designated as P11,...,P22); similarly layers 4, 5 and 6 have transmission lines with edge-mounted connectors (E11,...,E22). Such a design allows the comparison between two connector types on the same board. The

83 6.2. Testboards and Measurement Setup 71 pair of tracks on each side has the geometry shown schematically in Figure 6.2. These tracks are running parallel to each other for 140 mm. The total length of the tracks varies between 260 and 270 mm. The SMA connectors are placed as far as possible from each other in the corners of the mm 2 PCB in order to minimize the direct coupling between them. P11 P12 E11 E12 d 140mm E21 E22 P21 P22 Figure 6.2: Schematic drawing of the testboard B. Rogers RO4350B (core) and Rogers RO4450B (prepreg) materials have been used to build up the testboard B. These materials have five times lower dielectric losses (tan δ = 0.004) than FR-4 used in the testboard A, and as a result allow measurements at higher frequencies. The parameters (track width, dielectric thickness etc.) of E-Coax and stripline are chosen to result in 50 Ω impedances of the respective transmission lines when taking into account the average dielectric constant of Rogers material (ε r = 3.5). These values are again confirmed by the TDR measurements on the manufactured boards. Six boards of similar design, but with different distances between parallel parts of the tracks were made: 4 with microstrip lines and 2 with E-Coax. The board designations and the distances between centerlines of the tracks are presented in Table 6.1. Table 6.1: Different versions of the testboard B used in measurements. Version Track type Distance between centerlines 06A stripline 2300 µm 06B stripline 920 µm 06C stripline 690 µm 06D stripline 460 µm 06E E-Coax 1 trench 06F E-Coax 2 trenches The measurements were performed with the HP 8530A microwave receiver in combination with the HP 8517A S-parameter test set at the Electromagnetics group of Eindhoven University of Technology. The frequency range is up to 18 GHz.

84 72 Optimization of Connector-Track Interface 6.3 Standard Mounting of Connectors Firstly, we present the experimental results for the testboard A and the credit card boards. In these measurements, we consider a single track on the PCB with its ends connected to the ports of the network analyzer. All four S-parameters are recorded, but due to the symmetry and reciprocity, only S 11 and S 21 suffice to characterize the reflection and transmission of the network consisting of the track and two connectors. The effect of the connector-track interface can be observed in both parameters Signal Transfer Figure 6.3 shows the measured S 21 parameter for a number of tracks of different lengths on the testboard A with PTH connectors and for the credit card board with the egde-mounted connectors. As can be clearly seen, the S 21 parameter decreases 0 20 S 21 in db cm (PTH) 13 cm (Edge mounted) 30 cm (PTH) 90 cm (PTH) Frequency in GHz Figure 6.3: connectors. Signal transfer for various E-Coax tracks with PTH and edge-mounted SMA quite rapidly for the 90 cm long track. The high dielectric losses of FR-4 material cause a 40 db signal loss through this track already at 5 GHz. The lower losses of shorter tracks (with the same PTH type of connectors) allow the other phenomenon to be observed. The S 21 parameter of both 10 and 30 cm tracks has a large resonance dip (more than 40 db) in the frequency range between 7 and 8 GHz. On the other hand, the edge-mounted connectors on the 13 cm track of the credit card PCB do not show any resonant behavior in the signal transfer, only an overall decrease due to the dielectric and to minor extent the skin-effect losses. This indicates that the cause of such behavior lies not in the connector or the track separately, but rather in the interface between them Input Impedance The dip in the signal transfer is accompanied by an increase in the reflection from the ports of the network. At the higher end of the frequency range, the measured

85 6.3. Standard Mounting of Connectors 73 S 11 parameter is close to 0 db. These reflection results can be also interpreted in terms of the input impedance. The following formula to calculate the Z in of the network (combination of the connectors and track in this case) from the measured S-parameters can be applied: Z in = Z S 11 1 S 11 (6.1) where S 11 (or S 22, depending on the port) is the reflection coefficient and Z 50 is the characteristic impedance of the measuring system (network analyzer and cables). The results for two E-Coax tracks of similar lengths, but with different types of connector mountings, are shown in Figure 6.4. It is clearly seen that in case of PTH SMA con cm (PTH) 13 cm (Edge mounted) 1000 Z in in Ω Frequency in GHz Figure 6.4: connectors. Input impedance for similar E-Coax tracks with PTH and edge-mounted SMA nector, the input impedance is close to 50 Ω only at very low frequencies. The system shows capacitive behavior until 2 GHz, followed by an increase of inductance and resonance around 7 GHz. Again, the performance of the PCB with edge-mounted connectors is significantly better (smaller deviations of the input impedance from 50 Ω). The analysis of the comparable via-hole structures interconnecting microstrip and striplines on different layers of PCB has earlier been performed by different methods in both the time and frequency domains [Mae91], [Pil94], [Lae02]. A similar behavior of the S-parameters associated with the open via-hole stubs has been observed for example in [Lae02], [Den04] and [Kus03]. Such a stub represents an open transmission line causing the additional reflection of the excitation signal. The solution to the reported problems is known in the PCB industry as a backdrilling [Cam04]. In such an approach the unused part of the via plating is removed; a significant improvement of the overall system performance has been reported. The configuration of the PTH SMA connector is similar to the via (central pin) surrounded by four ground pins.

86 74 Optimization of Connector-Track Interface The same backdrilling method is then applicable to connector configuration as has been shown by calculations in [Vog04]. 6.4 Modified Mounting of PTH Connectors In order to suppress the peak in the input impedance and the dip in the signal transfer, the length of the central pin of the standard SMA connector was backdrilled. Its length is reduced from 4.5 mm (standard value) to approximately mm (necessary to make a connection to the E-Coax track on top layer of PCB). Both types of PTH connector mountings are schematically presented in Fig. 6.5; the photographs are shown in Fig Figure 6.5: Schematic drawing of the SMA PTH connector mounting: standard (left) and backdrilled (right). Not to scale. Figure 6.6: Photographs of the SMA PTH connector mounting: standard (left) and backdrilled (right) Testboard B The new testboards B utilize low-loss (tan δ = 0.004) Rogers material, which allows to extend the frequency range of the measurements up to 18 GHz. This is the maximum specified frequency of the SMA connectors. First we performed the measurements with the standard mounting of PTH connectors (with a long central pin). After that, the central pin was backdrilled, and the measurements were repeated for the modified connectors and the edge-mounted connectors (see Figure 6.7). This procedure was repeated for all six testboards B. The results for signal transfer and input impedance of one E-Coax PCB and one stripline PCB are presented on the next pages.

87 6.4. Modified Mounting of PTH Connectors 75 Figure 6.7: testboard B Backdrilled PTH (left) and edge-mounted (right) SMA connectors on the Figure 6.8 shows the S 21 parameter for both stripline and E-Coax lines and 3 possible types of the connector-track interface. The track lengths in all cases are 27 cm which is comparable with the 30 cm long track on testboard A. The figures show only minor differences between E-Coax and stripline in terms of the signal transfer. The results for the input impedance calculated from the S 11 parameter are presented in Figure 6.9. These results also show the significant improvement of the PTH connector after backdrilling. The resonance is less visible in both S 21 and Z in results, similar to the edge-mounted design. This modified version of the connector will be used in the final crosstalk measurements. Even though the lines are designed for 50 Ω characteristic impedance (the same as in measurement equipment), the discontinuity in the impedance at the track-connector interface results in the ripples in the measurement curves. The 0.3 GHz separation between the ripples corresponds to a half-wavelength fit on the 27 cm long transmission line with ε r = 3.5.

88 76 Optimization of Connector-Track Interface 0 20 S 21 in db Normal PTH Edge mounted Backdrilled PTH Frequency in GHz 0 20 S 21 in db Normal PTH Edge mounted Backdrilled PTH Frequency in GHz Figure 6.8: Signal transfer for microstrip (top) and E-Coax (bottom) lines with different types of SMA connector mounting.

89 6.4. Modified Mounting of PTH Connectors Z 0 in Ω Normal PTH Edge mounted Backdrilled PTH Frequency in GHz 1000 Z 0 in Ω Normal PTH Edge mounted Backdrilled PTH Frequency in GHz Figure 6.9: Input impedance for microstrip (top) and E-Coax (bottom) lines with different types of SMA connector mounting.

90 78 Optimization of Connector-Track Interface 6.5 Simulations In this section we present the simulation results for the track-connector interface and the effect of backdrilling. Even though the measurements in the previous sections do not show any significant difference between the microstrip line and the E-Coax in terms of the connector performance, we still consider both types of tracks. The calculations presented here are performed by the Finite Integration Technique (FIT) of CST Microwave Studio [Cst05]. Since the method requires the complete discretization of the calculation space, the full 3D modelling of the entire PCB would be computationally intensive. In order to perform the numerical analysis within reasonable computer time and memory requirements, we kept the layers stack-up and the vertical dimensions along the pins of the connector the same as in the real PCB, while reducing the total dimensions of the board and the track length Configuration The stack-up of both real and simulation boards and the coordinates of the layers is shown in Figure The metallization thickness of track(s) and the groundplanes GP GP GP track GP Figure 6.10: Stack-up of the PCB. The coordinates of layers are in micrometers. (GP) is 18 µm. The width of the track is 200 µm for E-Coax and 230 µm for stripline. Because the main focus here is on the connector performance, we discard both dielectric and skin-effect losses and model all metal parts of the system (outer shield of the connector, pins, groundplanes and tracks) as PEC, and PCB material as lossless (tan δ = 0) dielectric with a relative permittivity ε r = 3.5. Figure 6.11 shows the three-dimensional cross section of the simplified PCB we used in the numerical analysis. The board is 35 mm long and 20 mm wide. The SMA connector is placed at the near side, with its center at 10 mm distance from the board edges. The waveguide port 1 is defined at the end of this connector. The 25 mm long track (stripline or E-coax, depending on the configuration) runs along the PCB. At the near side it is attached to the central pin of the SMA connector, at the far side it terminates into another waveguide port 2. Such definition of the excitation sources, with only one connector present, still allows calculations of both S 11 and S 21 parameters. On the other hand, the simpler structure requires less meshing cells and as a result leads to faster calculations. It also avoids the problem of the direct cou-

91 6.5. Simulations 79 Figure 6.11: A 3D view of the configuration used in FIT simulations. Cut over the middle line where the symmetry plane is applied. pling between two connectors that otherwise would have been located close to each other in the model. Open boundary conditions are applied directly at the edges of PCB, while the extra space is added between the open boundaries and the ends of connector. A magnetic symmetry plane (H t = 0) is set along the middle line of the PCB to reduce the computational domain by a factor of two. The standard meshing parameters are adjusted to account for the small thicknesses of the groundplanes and the track. All four groundplanes are interconnected by four ground pins of the SMA connector. In case of the E-Coax line, the top two GPs are also connected by the sidewalls of E-Coax shield. The two parameters we varied in the calculations are the length p and the diameter d of the central pin, as shown schematically in Figure The effect of the p d Figure 6.12: Side view (left) and bottom view (right) of the connector with variable parameters: length and diameter of the central pin. length p is of main interest. The value of this parameter is counted downwards from the top of the PCB (see Figure 6.10). In the present configuration it can be varied from 286 µm to 4500 µm.