Electromagnetic Compatibility for Device Design and System Integration

Transcription

1 Electromagnetic Compatibility for Device Design and System Integration

2 Karl-Heinz Gonschorek Ralf Vick Electromagnetic Compatibility for Device Design and System Integration 123

3 Prof. Dr.-Ing. Karl-Heinz Gonschorek EMV-Beratung - EMC-Consultant Gostritzer Straße Dresden karlheinz.gonschorek@tu-dresden.de Prof. Dr.-Ing. Ralf Vick Lehrstuhl für Elektromagnetische Verträglichkeit Otto-von-Guericke-Universität Magdeburg Institut für Grundlagen der Elektrotechnik und Elektromagnetische Verträglichkeit Postfach Magdeburg ralf.vick@ieee.org ISBN e-isbn DOI / Springer Heidelberg Dordrecht London New York Library of Congress Control Number: c Springer-Verlag Berlin Heidelberg 2009 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: estudio Calamar S.L. Printed on acid-free paper Springer is part of Springer Science+Business Media (

4 Contents 1 Motivation and Overview Availability of programs, mentioned in the book Availability of the figures, given in the book Thinking in Voltages, Currents, Fields and Impedances Electric Fields Effects of electric fields and their calculation Magnetic Fields Effects of magnetic fields Calculation of magnetic field strength of single and multicore cables Magnetic fields of Geofol transformers Magnetic stray fields of arbitrary arrangements of thin wires Magnetic field of a four conductor arrangement Magnetic fields of twisted cables Example calculation with the program STRAYF Peculiarities of magnetic fields of twisted cables Electromagnetic Fields Characterization of Electromagnetic Waves Effects of electromagnetic fields The elementary dipoles Distance conversion Field impedances Effective height, effective antenna area, radiation resistance Estimating the field strength of aperture antennas Power density and electric field strength in the far field region...76

5 VI Contents Power density and electric field strength in the near field region Description of the program APERTUR Program SAFEDIST The Interference Model Galvanic coupling Measures against a galvanic coupling interference Capacitive coupling Measures to lower the capacitive coupling Inductive coupling Magnetic decoupling Definition of an effective mutual inductance for a multicore cable Measures to reduce the inductive coupling Electromagnetic coupling Measures to reduce the electromagnetic coupling The λ/2-coupling model Some remarks regarding the estimation of the electromagnetic coupling Intrasystem Measures Some remarks regarding grounding, shielding, cabling, and filtering Grounding Shielding Cabling Filtering Shielding against electric fields - shield of bars Shielding against magnetic fields Shielding against static magnetic and very low frequency magnetic fields Shielding against medium frequency magnetic fields Two parallel plates shielding against alternating magnetic fields Hollow sphere shielding against magnetic fields Hollow cylinder within a lateral magnetic field Hollow cylinder within a longitudinal magnetic field Shielding theory according to Schelkunoff short and concise...153

6 Contents VII Source code of the program SHIELD Leakages, openings, cavity resonances Leakages, signal penetrations Low frequency resonances, cavity resonances Cable coupling and cable transfer impedance Cable coupling Coupling into untwisted and twisted two conductor cables Coupling into and between shielded cables Cable shield connection at the device input Atmospheric Noise, Electromagnetic Environment and Limit Values Atmospheric noise sources, electromagnetic environment Conversion of limit values Distance conversion Conversion E H and H E EMC Engineering and Analysis Development phases of a complex system Conceptual phase Definition phase Construction and building phase EMC- Test planning Execution of analysis Numerical Techniques for Field Calculation Selecting the appropriate technique Plausibility check Application examples of analysis Investigation of resonances on a passenger car Influence of a dielectric material on the radiation of a printed circuit board Radiation of a mobile phone Electromagnetic field on a frigate Guidelines for using numerical methods Application: Antenna coupling General remarks to the N-port theory Two port parameter Calculation of antenna coupling Source code of the program MATCH...283

7 VIII Contents 11 Model for Immunity Testing Standardised immunity test methods Statistical approach to model the immunity Malfunction probability Fault frequency function Interpretation of the results of immunity tests Time variant immunity Modelling Immunity of microcontroller based equipment A1 A2 A3 Electric Fields of Rod Arrangements A1.1 Potential coefficients and partial capacitances A1.2 Horizontal conductors above ground A1.2.1 Source code of the program HCOND A1.3 Vertical conductors above ground A1.3.1 Source code of the program VROD Magnetic Stray Fields A2.1 Stray field low installation of cables A2.1.1 The single core cable (case (a) of chapter 4.2) A2.1.2 Cable with one forward and one return conductor (case (b) of chapter 4.2) A2.1.3 Use of two forward- and two return conductors (case (c1) of chapter 4.2) A2.1.4 Installation of the forward and return conductors above a common ground plane (case (c2) of chapter 4.2) A2.1.5 Use of four forward and four return conductors (case (d) of chapter 4.2) A2.2 Computer program for predicting magnetic stray fields A2.2.1 Field of a finitely long wire A2.2.2 Field of a single layered coil A2.2.3 Considering phase relations A2.2.4 Source code of the program STRAYF Self and Mutual Inductances A3.1 Mutual inductance between a finitely long conductor on the y-axis and a trapezoidal area in the xy-plane A3.2 Decomposition of an area in the xy-plane bounded by straight lines A3.3 Treatment of arbitrary conductor loops in space...341

8 Contents IX A3.4 Mutual inductance between 2 circular loops with lateral displacement A3.5 Source code of the program MUTUAL A4 Elementary Dipoles A4.1 Hertzian dipole A4.1.1 Prediction of the field strength components for the general case A4.1.2 Solution for time harmonic excitation A4.2 Current loop (loop antenna) A4.3 Comparison of the wave impedances A5 The Polarization Ellipsis A5.1 Two dimensional case (E z =0) A5.2 Three dimensional case solution in the time domain A5.2.1 Some consideration regarding the plane of the polarization ellipse A5.3 Three dimensional case solution in the frequency range A6 Skin Effect and Shielding Theory of Schelkunoff A6.1 Skin effect of a conducting half space A6.1.1 Strong skin effect within a cylindrical conductor A6.1.2 Weak skin effect within a cylindrical conductor A6.2 Shielding theory according to Schelkunoff A6.2.1 Introduction A6.2.2 Necessary equations A6.2.3 Shielding mechanism A6.2.4 Shielding efficiency A6.2.5 Simple application of Schelkunoff s theory A6.2.6 Procedure for a graphical determination of the shielding efficiency A6.2.7 Error estimations A6.2.8 Summary A7 Example of an EMC-Design Guide for Systems A7.1 Grounding A7.2 System filtering A7.3 Shielding A7.4 Cabling...396

9 X A8 A9 Contents 25 EMC-Rules for the PCB-Layout and the Device Construction Easy-to-use Procedure for Predicting the Cable Transfer Impedance A9.1 Predicting the voltage ratio with help of an oscilloscope A9.2 Predicting the voltage ratio by a network analyzer A10 Capacitances and Inductances of Common Interest A11 Reports of Electromagnetic Incompatibilities A12 Solutions to the Exercises A13 Physical Constants and Conversion Relations A13.1 Physical Units and Constants A13.2 Conversion table for pressure A13.3 Conversion table for energy A13.4 Conversion relations for electric and magnetic quantities A13.5 Conversion of logarithmic quantities A13.6 Abbreviations A14 Bibliography Index...467

10 1 Motivation and Overview After working for more than 30 years in the field of EMC; having published numerous papers on the subject of interference, counter measures and numerical field calculation; the idea emerged to collate all experiences, successful analysis techniques and solutions into one comprehensive book. This was done in 2003/04 and the book was published in 2005 in the German language. Discussions with colleagues and with the publisher revealed that an English version of the book is desirable. Moreover, the discussions suggested, as expected, some areas for improvement. The two main areas of criticism were firstly, the inclusion of extensive program lists and secondly, the chapter regarding filtering. Regarding the program lists, it was the original wish of the authors to have them printed. These have now been removed but remain available on the web-pages of the authors and in there place more application examples of the programs have been included. Only very small program lists have been left in. It has been recognized that the chapter concerning filtering is more a concise theoretical treatment of Butterworth filters than a chapter describing the necessary EMC-features. Therefore, this chapter has been extended, showing more elements from the EMC-point of view and giving suggestions for an EMC-justified installation. Considering the aforementioned arguments, this English version of the German EMC-book EMV für Geräteentwickler und Systemintegratoren is not a simple translation, hopefully it is a further development. Nevertheless more than 90% consists of translated German text. Which young scientist has not experienced, that he published a paper or gave a presentation at a symposium, all the time being proud of his work. Then afterwards, seeking praise or criticism, learns that feedback is the exception rather than the rule? But nevertheless, the next paper, the next investigation or the next presentation is still prepared with great care and enthusiasm. So the idea to write this book rose from the idea to summarize the results of the different publications and presentations; to compile and to show, as far as possible, the inner relations and dependences of the experi- K.-H. Gonschorek, R. Vick, Electromagnetic Compatibility for Device Design and System Integration, DOI / _1, Springer-Verlag Berlin Heidelberg 2009

11 2 1 Motivation and Overview ences gained in EMC-analysis, EMC-system planning, and defining countermeasures to overcome interference. Shortly after starting it became clear that the degree of experience of a single human being is always limited. Therefore, in order to produce a comprehensive publication of EMC, a lot of problem solutions have to be taken from other papers and books and revised to fit into the foreseen concept. Moreover, the expert assessment of others has to be considered. For that reason at this point we must thank the experts of WATRI, Perth (Western Australian Telecommunication Research Institute), especially Dr. Schlagenhaufer, as well as Prof. Singer from the Hamburg University of Technology, who have generously contributed pictures, ideas and solutions without requesting acknowledgement or their source. Starting with the idea to make the author s own experiences the main topic of the book, it became immediately clear that the offered solutions have to be revised in order to make them accessible to engineers who are attempting to solve similar problems or who are searching for explanations to apparently unexplainable phenomena. It is intended that this book is not an addition to the vast array of generally excellent introductions to EMC. Rather it is envisaged that this book will give help and hints to the experienced engineer in the development and construction of electric and electronic products and systems. Moreover it will provide help in planning new projects, help in solving actual interference cases, support in analysing apparent incompatibilities, but predominantly to find a way to assess the problem. With this in mind, this book is intended to be an EMC-assistant for engineers, in which strategies, ways and methods, diagrams, rules of thumb, background theory and computer tools are brought together, which are helpful in solving problems of electromagnetic incompatibilities. Solving an interference problem by a means other than trial and error requires a deeper understanding of the physical background of the problem. Therefore, this book tries, in annex chapters, to deliver the physical basis together with the necessary mathematics in order to provide a compromise between completeness, necessity and precision. Reading the book you will find a lot of material familiar from your study of electromagnetic technique. An attentive observer will identify that the elementary dipoles play a special role in the physical picture presented by the authors. It may also be evident that the experiences of the authors are given predominantly at the system level, while for EMC-problems at the device and circuit board level valuable experience from other experts has been taken into account.

12 1 Motivation and Overview 3 It is normally expected that EMC-books deliver solutions and if possible tailor-made solutions to specific problems the reader may have. This demand cannot be fulfilled by any book because the variety of incompatibilities is as vast as the electromagnetic technique and its applications. In contrast an EMC-textbook is able to fulfil two requirements; firstly it may state and explain a certain number of basic measures, which are the basis for an interference free construction of a device or a system, regarding both susceptibility and emission. As an example we refer to grounding (measures to provide low potential differences also for high frequencies) where approximately 98% of all interference cases are related to bad or non problem-matched grounding. Secondly an EMC-textbook may explain the physical interrelations and background in order to teach an understanding of electromagnetic coupling phenomena. For instance, the way each voltage is associated with an electric field strength, each current with a magnetic one. For EMC, more than for other physical disciplines the saying is valid: A known enemy is not a real enemy! Converting this proverb to EMC, it could be said with great conviction: If the source for the interference is known, better the reason for incompatibility has been detected, then the suppression and elimination of the interference is not the real big problem! Some available EMC-books suggest that knowing and using only a handful of equations and rules is sufficient for handling interference questions, such installing an electromagnetic shield to eliminate radiation problems or using a filter for conducted problems. Books which are easy to read and bring about the feeling of being an EMC-expert are generally of little value. They only serve as a first step to provide problem awareness and solutions, or better a solution methodology, may not be possible. This EMC-textbook starts with the phenomenon: Currents, voltages and fields with their impedances are the electromagnetic quantities which carry wanted signals; these phenomenon as secondary effects may produce electromagnetic incompatibilities. Whether a wanted signal of one circuit becomes an interference signal for a second circuit is always a question of the power needed in both circuits for transporting the information. For that reason after the second chapter, which is at the same time also an introduction into the EMC-thinking, the different field types will be highlighted. The usual classification of the electromagnetic technique into electric fields (chapter 3), magnetic fields (chapter 4) and electromagnetic fields is very suitable for treating the EMC. The propagation, the ability to produce (unwanted) signals, as well as the measures against interference depend strongly on the field type and its characteristics. Chapter 6 discusses the interference model, in which the field couplings will be ex-

13 4 1 Motivation and Overview plored. Countermeasures, measures to lower the coupling will be described in chapter 7 (intrasystem measures). A chapter about the actual situation in standardisation has been omitted consciously. However, standards and legal requirements are mentioned at their respective places as far as is necessary for explanation. Dramatic accidents and damage caused by electromagnetic incompatibilities are often used in justifying the necessity of EMC-measures. It is no exaggeration, that 90 % of all EMC-work is associated with the fulfilment of legal requirements in terms of emission limits. The aim of chapter 8 is to introduce the philosophy of defining limit values. Starting with the natural noise sources, taking the requirements of licensed radio services into account, the limit values for radiated emissions are discussed in more detail. In this area however, it seems only natural, that great differences exist between civilian and military considerations. In chapter 9 the sequence of steps is stated, which, especially for planning the EMC of complex systems with antennas, has proven to be reasonable and economical. Converting this system planning methodology into a methodology to handle the development of new devices should prove a trivial task. A special chapter (chapter 10) is dedicated to the simulation software for numerical analysis of electromagnetic fields and couplings. In this chapter the available programs with their mathematical background are briefly presented. This chapter is not meant to be an introduction to numerical field calculation in general; it is intended to provide help for the beginner in using modern simulation software and choosing the correct simulation method for analysis of their specific problem. The main focus of the chapter lays in the application. The chapter aims to show that the available programs are powerful tools, if they are used in the correct way. Hints are given for the economical implementation. In order that the reader may become familiar with numerical field analysis some sample arrangements with reference solutions are given. These sample arrangements are chosen to have a certain practical relevance. A potential user of the described software can request the names and sources of commercial software packages from the authors. The user should take time to become familiar with the software by varying the parameters, but more than this, based on the given examples, he should gain confidence into the program he is going to use. A very powerful demo-version of the program package CONCEPT is kindly made available by Prof. Singer and Dr. Brüns. It can be downloaded from the web-site of the authors. The discussion and significance of susceptibility tests and the expertise of one of the authors lead to the integration of a special chapter (chapter 11) handling such questions. The discussed items and related equations,

14 1 Motivation and Overview 5 based on the probability theory make it possible to state confidence intervals for the immunity of modern electronic circuits and devices against pulse shaped interference signals. In addition, the phenomenon of the time dependent susceptibilities is discussed. Extensive derivations and diagrams are shifted into annex chapters. The annex furthermore contains an EMC-design guide for systems, which could be the basis for a project specific guideline of the reader. Naturally a book is a self-presentation of the author(s) as given here. On the other hand this book should help to better analyse or solve one or another interference case whether artificial or real. In this case the goal of the book is achieved. Starting with this English version of the book Prof. Vick is also stated as one of the main authors, hence he takes over the full responsibility for the contents, too. Dresden, spring 2009 Karl H. Gonschorek Ralf Vick Remarks: In this text book the numbers are written as far as possible in American notation; this means a decimal point is used instead of the usual German comma. Keep in mind in certain places it may not have been possible to change. Furthermore the frequency, the impedance, and also the electric quantities abbreviations are often used in the German manner, for instance 1 GHz instead of 1 Gc. Acknowledgement: A special thank has to be given to Mr. Mark Panitz from the University of Nottingham, Great Britain, who did a great job in polishing the English of this text.

15 6 1 Motivation and Overview 1.1 Availability of programs, mentioned in the book From the outset of German version of the book, it was planned to add a CD with the software mentioned within the text. This has been disregarded for a number of reasons, not at least for the short shelf life and the different operation systems of computers. The program CONCEPT is, as stated earlier, made available as a very powerful demo-version by Prof. Singer und Dr. Brüns from the Hamburg University of Technology. The other programs, which were produced by one of the authors during his professional life, are written in POWER-BASIC and in no way optimized. The information within the single chapters should be sufficiently comprehensive that an experienced user of modern computer resources should be able to create a respective program fully to his requirements and taste. In most cases he will quickly produce adequate results with demonstrative graphics via MATHEMATICA or a comparable program. It is also recognised that a hands-on engineer may wish to use a finished and reliable program, without the need to learn programming or the use of mathematic packages. In order to satisfy this demand the programs mentioned are available at the web-sites of the authors. Three options are offered: 1. source codes in POWER-BASIC, except for CONCEPT, or 2. executable elements of the programs, running under WINDOWS, downloadable from the home page 3. it is also possible to obtain source codes and the executables complete on a CD. In this case expenses of Euro has to be paid in advance. 1.2 Availability of the figures, given in the book Due to printing limitations all figures (diagrams, sketches, and pictures) in the book are reproduced in black and white. Should the reader desire colour versions of diagrams and pictures these are available from the authors. Thanks to the permission of the Springer publisher all figures of the book may be downloaded in TIF-format from the internet address It is therefore possible for the reader of the book to obtain figures ready for education purposes or otherwise. The authors request that this book is cited as the source of the figure.

16 2 Thinking in Voltages, Currents, Fields and Impedances In order to achieve the EMC of a device or system, several measures must be taken. These measures start by thinking about the layout of the circuit and the design of the printed circuit board. They comprise the support of the inner arrangement of components and the wiring of equipment and extend up to the formulation of guidelines for the construction of the system. The measures include the application of grounding, filtering and shielding guidelines as well as the implementation of problem-matched wiring and cabling. Furthermore, they may comprise the planning of device placement and installation within a system. This variety of isolated and sometimes seemingly unrelated single measures can be brought together if one remembers some basic knowledge of electromagnetics: Electric charges produce electric fields. Electric fields on the other hand produce forces on other charges and these forces cause an unbound charge to move. Moving electric charges (currents) produce a magnetic field. Magnetic fields on the other hand produce forces on other moving electric charges (currents). Time varying fields, which are produced by time varying currents, produce forces on electric charges at rest. This effect is called induction, producing an induction voltage. Temporal and spatial variations of electric and magnetic fields are related to each other. Time varying fields propagate as electromagnetic waves. These properties of electric charges have to be accepted as given. In order to eliminate some common interference there are, in general, only the following possibilities: Currents must be suppressed (providing the currents are not needed as signal currents). Currents must be damped in such way, that the effects on other systems are negligible. K.-H. Gonschorek, R. Vick, Electromagnetic Compatibility for Device Design and System Integration, DOI / _2, Springer-Verlag Berlin Heidelberg 2009

17 8 2 Thinking in Voltages, Currents, Fields and Impedances Additional currents have to be driven, producing fields which compensate the initial fields. The last point has a special meaning within the set of EMC-measures because shielding efficiency, the influence of ground planes, as well as the effectiveness of cabling with low stray fields can be related back to this principle. Voltage: The starting point of every electromagnetic consideration is the elementary charge. It has a measured value of e = C. A single elementary charge is so small (radius of an electron = m) that an accumulation of charges, let s say 10 6 elementary charges, can still be considered as a point charge Q. The mass of the elementary charge, or electron is kg. Between two point charges there exists a force given by the vector: Q Q 1 2 F = e 2 r (2.1) 4πε r If the charges have alternate polarities the force between them is attractive. On the other hand, the force between charges of equal polarity is repulsive. If one charge, for instance Q 2, is defined as a test charge and the force given by Eq. (2.1) is divided by the magnitude of the test charge, a new quantity is derived, termed the electric field strength: F Q 1 E = = e 2 r (2.2) Q 4πε r 2 Electric field strength: The electric field strength is the force per unit charge on a stationary charge. If electric field strength is present forces act upon charges, which can lead to their displacement. Separating two charges (unequal polarity) over a certain distance requires a force to be applied over that distance. In other words, a defined amount of energy is required. Upon releasing the charges, they will move to collide and the energy will be gained back again. Therefore, a displacement of a charge in the direction of the electric field vector leads to gain in energy. By relating the energy gain to the test charge one can obtain the potential. A potential difference (movement from position 1 to position 2) between two points in space is called voltage. Hence, the voltage is a measure of the working potential of a given field. This means with relation to the ElectroMagnetic Compatibility: If a voltage source is connected between 2 electrodes, charges on these electrodes and also on uninvolved metallic structures are displaced until

18 2 Thinking in Voltages, Currents, Fields and Impedances 9 on each electrode and on each metallic part an equal potential is obtained (equipotential). This statement equates to asserting that The tangential electric field strength on a metallic surface is equal to zero!. If the voltage varies (for this consideration we assume a sinusoidal variation) from positive to negative the charges have also to follow this change in polarity. On all electrodes and metallic structures in which a movement of charges occurs it is prescribed that a current is flowing. If the voltage alteration is very fast it is possible that the charges are not able to follow this variation (transition from static considerations for a slowly alternating field to a high frequency field variation). In the area of EMC a limit for the transition from static or stationary considerations to high frequency behaviour has been defined: l = λ/10 (structure extension = 1/10 of the wave length). (2.3) If the structure to be investigated is smaller than 1/10 of the smallest wavelength to be considered (wavelength of the highest frequency in question) it is satisfactory to use static or stationary approaches and considerations. We take here a main board of a computer with dimensions 30 cm by 20 cm as an example, if we assume a clock frequency of 400 MHz then high frequency investigations have to be carried out. Current: Each movement of a charge is called an electric current. If in one second electrons (charge carriers) are flowing through a wire (the cross section of the wire), then it is defined that the current will be 1 A. The single charge carriers take their polarity with them to attract or to push away other charge carriers. Additionally, there appears a second force effect acting on moving charges: F = q ( v x B), (2.4) q = charge, which moves with the velocity v, B = magnetic flux density, for instance produced by another current. The electric current in the first approach produces a magnetic field strength, which can easily be converted for non-magnetic materials to a magnetic flux density using the B = μh relation. Furthermore, for simple arrangements the magnetic field strength may be calculated by the Ampére s Law: H ds = I. (2.5) Here the critical feature is the fact that every current produces a magnetic field, which in turn leads to a force on other moving charges. Only

19 10 2 Thinking in Voltages, Currents, Fields and Impedances full metal screens with a completely symmetrical construction do not have an electric or magnetic field in the surrounding space. In order to transfer electric energy or information from one place to another by electromagnetic means, electric voltages or currents are required. Therefore, it would seem impossible (except in special cases like the fully symmetrical fully shielded coaxial cable) to avoid electric and magnetic fields. For that reason, the task of EMC can not be to eliminate the required currents or voltages, but to provide defined places and paths for them so that the effects on other circuits can be kept sufficiently low. For completeness at this point it should be mentioned that there are also convection currents that exist, which are detached from metallic conductors. These are not normally a concern for the subject of EMC. Furthermore, current loops may also be closed via displacement currents, where a displacement current is always produced when a time varying electric field occurs in a dielectric material. Impedance: If the voltage of a circuit or a loop is divided by the produced current the input impedance at that point is obtained. The impedance consists of a real and an imaginary part. The real part describes the losses in the circuit; the imaginary part is a measure of the fields related to the voltage and current in the circuit or loop. The imaginary part may be capacitive and becomes smaller with increasing frequency; or inductive and becomes larger with increasing frequency. The current will always use the path of lowest resistance. If we also consider complex impedances we can extend this theorem: The current always uses the path of lowest impedance. This simple theorem has a very special meaning in the area of EMC. If interference occurs and the interference source is known then the coupling path, or the route of the current, has to be found. Remembering that the current is using the path of lowest impedance reduces the task to finding this transfer route. In this analysis it has to be considered that, not only do discrete elements have to be taken into account, but that current loops can also close via electric or magnetic stray fields. Furthermore, these stray fields have effective impedances which have to be included in the analysis. The following first example may serve as a demonstration of the behaviour of the current: 10 cm above a conducting plane (with losses) a cylindrical conductor (made from copper) of a total length of 1.2 m and a radius of 1 mm is installed. The conductor is arranged in such a way that it is bent at its half length by an angle of 90 degrees. It is required to calculate the surface current and equivalently the return current within the plane. The arrangement is given in Fig The driving voltage is located at the left end of the wire between the wire and ground plane, the generator has a

20 2 Thinking in Voltages, Currents, Fields and Impedances 11 source impedance of 50 Ω. The right end of the wire is directly connected to the conducting plane. Fig. 2.2 shows the surface current on the plane for the following frequencies: 1 khz, 10 khz, 100 khz, and 1 MHz. It is very demonstrative to see that for a frequency of 1 khz the direct path from the short circuited right end to the feeding point is taken. At this frequency this path has the lowest impedance. At 10 khz it can be seen that the current is drawn slightly to the conductor and at 100 khz the current is nearly completely following the path of the wire. It can be presumed, taking the self inductance into account, that every other path has a higher impedance. -0,5, 1,0, 0,0-0,05, 0,55, 0,1 1,0, 1,0, 0,0-0,5, -0,5, 0,0-0,05, -0,05, 0,1 0,55, -0,05, 0,1 1,0, -0,5, 0,0 Fig. 2.1 Arrangement of a bent conductor above a conducting plane a) b) c) d) Fig. 2.2 Currents in the plane for a) 1 khz, b) 10 khz, c) 100 khz, d) 1 MHz

21 12 2 Thinking in Voltages, Currents, Fields and Impedances 240 2r MS= 3.74 mm 2r = 2r = ZL ZL 1mm 1mm d ZL = 3.7 mm d MS = 0.2 m lr, l ZL, l MS = 1m I I R I M ground loop U0 =1V Fig. 2.3 Two conductor arrangement, in which the return conductor is connected to ground forming a ground loop With the second example, which can also be treated analytically, it is intended to clearly show the effect of field concentration. The arrangement (Fig. 2.3) consists of a 240 Ω two conductor arrangement, in which the return wire is connected directly to ground at both ends, effectively forming a ground loop. The relative arrangement parameters have been chosen in such a way that the ground loop resistance is only 1/10 of the return wire resistance. By feeding the arrangement with a DC-voltage it is found that 91 % of the total current is flowing via the ground; only 9 % of the total current is to be found in the dedicated return conductor. From the data stated above and a conductivity of κ = S/m the following network parameters can be calculated: Resistance of the return wire: l R = R R 2 = 22.3 κπ r R mω (2.6)

22 2 Thinking in Voltages, Currents, Fields and Impedances 13 Resistance of the ground loop: l R = M M mω 2 = 2.23 κπ r M Inductance per m of the two conductor line: ' μ d L ln ZL ZL = 0.8 μh/m π rzl Capacitance per m of the two conductor line: ' επ CZL = 13.9 d ln ZL rzl Self inductance of the ground loop: pf/m (2.7) (2.8) (2.9) μ l MS d L ln MS MS = 2.13 μh π (2.10) rzl rms Mutual inductance between the two conductor circuit and ground loop: μ l M ZW 2π d ln ZL rzl ' L ZL lzw 2 = 0.4 μh (2.11) Remark: For L MS and M the simplified formulas of parallel conductors have been used. In Fig. 2.4 the currents I 0, I R und I M as function of frequency are plotted, as they have been obtained using the program CONCEPT. Subfigures a), c) and e) show the frequency range 100 Hz to 20 khz and the remaining subfigures b), d), f) show the range 100 Hz to 5 khz. Examining the behaviour of the currents I M and I R of Fig. 2.4 as function of frequency the following results can be recognized: 1. At the frequency 0 Hz (here for the calculation at 100 Hz) the return current is divided in accordance with the associated resistances. 91 % of the return current is flowing in the ground loop and only 9 % is flowing in the dedicated return conductor. 2. With increasing frequency the inductive part of ground loop impedance becomes greater and greater. At a frequency of f 3dB = 1.7 khz it reaches a value equal to the return wire resistance ωl MS = R R (The skin effect does not need to be considered at this frequency). A sig-

23 14 2 Thinking in Voltages, Currents, Fields and Impedances nificant proportion of the return current is now flowing via the dedicated return conductor. 3. With further increasing frequency the inductive reactance of the ground loop becomes higher and higher. The result is that the total return current is now flowing via the dedicated return conductor. However, due to the mutual inductance M between the two conductor circuit and the ground loop, a current in the ground loop will occur. The effect of this is that the measurable return current will be reduced to M I R I 1 LMS 0. (2.12) M In the ground loop a current of I MS I 0 is flowing. LMS Taking I 0 = 1 V/240 Ω = 4.2 ma and M/L MS = 0.19 results in a measurable current in the dedicated return wire of I R = 3.4 ma; this result is in very good agreement with the simulation results. In the ground loop a current of 0.8 ma (for this particular arrangement) is still flowing; it is this current which is the main contributor to the radiation. It is proposed that a reduction in the ground loop current is required. To do this the mutual inductance M between the two conductor arrangement and the ground loop has to be reduced; in the ideal case it should reduced to zero. This can be achieved by twisting the two conductor line or by using a coaxial cable for the information channel. With respect to the self inductance of the ground loop the degree of freedom is very limited. To increase the self inductance of the ground loop would mean making the loop size greater, a solution which is contradictory to the requirement of minimizing the loop to limit coupling and radiation.

24 2 Thinking in Voltages, Currents, Fields and Impedances 15 Fig. 2.4 Behaviour of the currents within the two conductor arrangement, a) and b) forward current I 0, c) and d) return current I R, e) and f) ground loop current I M, b), d), f) currents with a zoomed frequency range Exercises Exercise 2.1: What is the force (in Newton) that is occurring between the two plates of a capacitor where the plate separation distance is d = 1 mm, the capacitance is C = 1 nf and the capacitor is loaded to a voltage of U = 1000 V? Exercise 2.2: a) The shielding of a room against electric fields is realized by the use of wire grids in the ceiling and floor. Between both grids there exists a conducting connection. The diagonal measurement of the grid planes

25 16 2 Thinking in Voltages, Currents, Fields and Impedances in the ceiling and floor is D = 10 m, the distance between ceiling and floor is measured to d = 3 m. Up to what frequency is it acceptable to use static field considerations to approximate the shielding efficiency? b) The main board of modern personal computers have dimensions of 30 cm 20 cm. Up to what frequency might it be acceptable to accurately calculate the internal couplings and unwanted interactions on the board by static and stationary field assumptions? Exercise 2.3: A very long metal plate of a width of b = 10 cm is guiding a current of I = 10 A. How big is the magnetic field strength at a distance of d = 1 cm: a) away from the edge of the plate, b) above the middle of the metal plate? Exercise 2.4: An electron is moving with a speed of v x = km/s through a magnetic field of H z = 2 A/m. How large is the deflection d, perpendicular to the electron s initial trajectory, after moving a distance of s = 30 cm? Exercise 2.5: At a frequency of f = 50 Hz a twisted three conductor cable is producing, at a distance of r M = 10 cm from the cable axis, a magnetic flux density, which can be described by B ϕ = B 0 cos (2 π x/sl); where SL = turn width = 0.8 m, B 0 = 10 µt. The magnetic flux density is directed perpendicularly into an interference area. The interference area has a radial extension (with respect of the cable axis) of d = 1 cm (starting at r = 9.5 cm) and an axial extension of Δx, starting at x = 0. a) After what length Δx of the area does the coupling (open circuit voltage) reach its maximum? b) How large is the maximum open circuit voltage? c) After what length Δx of the area does the coupling reach its minimum? Remark: The radial dependence of the field is neglected! d) The area in which the induction may take place is surrounded by a closed copper wire of a thickness of 2R = 0.4 mm. How large is the current flowing in the influenced wire loop? e) At what frequency is the resistance of the wire loop equal to the inductive reactance (R W = ωl)?

26 2 Thinking in Voltages, Currents, Fields and Impedances 17 Remark: The self inductance of the influenced loop may be calculated using the relations of a two conductor arrangement.

27 3 Electric Fields Electromagnetic fields are described mathematically by the four Maxwell s equations. Expressed in integral form they are: Ampère s circuital law H ds = J da+ D da = IL + IV, t (3.1) Gauss law s A A D da= ρ dv = Q, (3.2) A V Faraday s law of induction = = φ E ds B da, (3.3) t t s A B da= 0, (3.4) A H = magnetic field strength, J = current density, D = displacement current density, I L = conductor current, I V = displacement current, ρ = charge density, Q = electric charge, E = electric field strength, B = magnetic flux density, φ = magnetic flux, ds = infinitesimally small element of the contour of area A, Eqs. (3.1) and (3.3). K.-H. Gonschorek, R. Vick, Electromagnetic Compatibility for Device Design and System Integration, DOI / _3, Springer-Verlag Berlin Heidelberg 2009

28 20 3 Electric Fields These 4 Maxwell s equations in their integral form can be explained in the following way: Eq. (3.1): The closed loop integral of the magnetic field strength is equal to the current enclosed by that loop, which is given by the sum of the conductor and the displacement current through the area enclosed by the loop. Eq. (3.2): The integral of the displacement current density over a closed area is equal to the electric charge enclosed by this area. Eq. (3.3): The closed loop integral of the electric field strength is equal to the negative time derivative of the magnetic flux flowing through the area enclosed by the loop. Eq. (3.4): The integral of the magnetic flux density over a closed area is always zero. (i.e. magnetic charges or magnetic monopoles do not exist) Eq. (3.3), the induction law, is more commonly known in the following form: u i φ =, (3.5) t u i = induced voltage. When assessing electromagnetic incompatibilities it should be noted that the induction voltage given by Eq. (3.5) is only a valid simplification of Eq. (3.3) for the case in which the loop enclosing an area is open at a signal point. At this position in the loop all collected parts of the product E ds are measurable. If the loop has two openings then the external circuitry determines the voltages appearing at the openings. If the loop is closed (short circuited) it must form an induction current which, neglecting the resistance of the loop, produces a magnetic flux equal to the initial flux. It seems important at this point to mention the fact that Maxwell s equations, which are the theoretical basis of the electromagnetics, do not explicitly use voltages and potentials. It has turned out to be very meaningful to divide the electromagnetic fields into:

29 3 Electric Fields 21 a) Static fields (no time dependence, no current), Maxwell s equations reduce to H ds = 0, E ds = 0, D da = ρ dv and B da = 0. A A (3.6) Applications: high voltage technology, the effect of voltages and charges, prediction of capacitances, shielding of static electric and magnetic fields b) Stationary fields (no time dependence, but currents), H ds = J da = I (3.7) A (Ampère s law in the simplest form), other expressions are the same as in a). Applications: Prediction of magnetic fields, calculation of self and mutual inductances c) Quasi stationary fields (time dependence with the B -field, currents), φ E ds = B da = (3.8) t A t (induction law), other expressions are the same as in b). Applications: Theory of the skin effect, eddy current attenuation d) High frequency fields (complete set of Maxwell s equations) Applications: Electromagnetic wave radiation, electromagnetic coupling, antenna theory, shielding theory Electric fields in the sense of EMC are fields produced by stationary electric charges. If the charges are moving with a low enough speed that the magnetic effects can still be neglected or only a few charged particles are moving (due to circuits with high impedance), then the fields of these charges are still, in the sense of EMC, to be understood and treated as electric fields. In the frequency domain, the boundary between static (stationary) and non-static is taken at a system extension of l = λ/10; where l is the largest dimension of the arrangement under investigation and λ the wavelength. Electromagnetic incompatibilities at 16 2/3 Hz, 50 Hz or 400 Hz occur either as a result of electric incompatibilities (capacitive interferences) or magnetic incompatibilities (inductive interferences, direct or indirect effects of magnetic fields).

30 22 3 Electric Fields 3.1 Effects of electric fields and their calculation In chapter 2 it was explained that all electromagnetic phenomena originate from electric charges. Between electric charges force effects occur. Charges with the same polarity repel each other and charges with different polarity attract. This observation leads to the electric field strength E and the electric displacement density D. The electric field strength (as a vector) at a point in space describes the force acting on a charge. An electric field strength of 1 V/m, for instance, applies a force of 1 N on a charge of 1 C. The direction of the vector determines the direction of the force effect. An unbound charge will move as long as the force effect will become zero or a mechanical boundary condition does not allow any further displacement. No electric field strength is possible inside a perfect conductor nor tangentially on its surface. Therefore, the condition E tan = 0 (E tan = tangential component) must be fulfilled. This description has been noticeably repeated here because this association is very helpful in assessing the effects of electric fields. On the body of a car, which is parked under a high voltage line, 50 Hz currents occur due solely to the electric field. This is due to the restriction that at each point of the surface, at every moment in time, the tangential component of the electric field is zero. Considering the unchangeable law where E = E (3.9) tan1 tan 2 E tan = 0 (3.10) on an ideal conducting metallic surface, many couplings and electric phenomena become apparent. A lot of practical problems involving the treatment of electric fields do not require predicting the potential distribution (or the distribution of the electric field) when the charge distribution is given. In most cases the inverse problem has to be solved, where it is necessary to find the charge distribution which leads to a given potential distribution. Subsequently, from this charge distribution the complete field may be predicted. In this manner the problem of predicting the field from given charges is implicitly not a simple task as evaluation of the involved integrals can be difficult. For more details regarding this see annex chapter A1 - solving the problem of finitely long line charges.