Docteur

Nimisha Sivaraman

Thèse Dirigée Par

Professeur Fabien Ndagijimana

Thèse

Mme Daniela

Dragomirescu Professeur

Rapporteur M Eduardo Motta

Cruz Professeur

M Christian

Vollaire Professeur

M Sébastien

Serpaud Ingénieur

M Leonce

Mutel Ingénieur

Examinateur M Valence

Ndagijimana Fabien

Professeur

M Zouheir

THÈSE Pour obtenir le grade de

Keywords: 2-D cross-correlation method, Electromagnetic compatibility, near field scanning, shielded magnetic probe, source reconstruction, Transmission line matrix method

As the number of components in a confined volume is increasing, there is a strong demand for identifying the sources of radiation in PCBs and the prediction of EMC of electronic circuits. Electromagnetic near field scanning is a general method of identifying the radiating sources in a PCB. The first part of the thesis consists of the design and characterization of printed circuit magnetic probes with high sensitivity and high spatial resolution. Conventional probes based on microstrip and coplanar configuration is studied. As the length of the transmission line connected to the probe increases, the probe output contains noise due to common mode voltages which is many induced by the electric field. In order to suppress the voltage induced due to the electric field, a shielded magnetic probe is designed and fabricated using low cost printed circuit board (PCB) technology. The performance of the passive probe is calibrated and validated from 1MHz -1GHz. The shielded probe is fabricated on an FR4 substrate of thickness 0.8mm and consists of 3 layers with the signal in the middle layer and top and bottom layers dedicated to ground planes. The aperture size of the loop is 800µm x 800µm, with an expected spatial resolution of 400 µm. The high sensitivity of the probe is achieved by integrating a low noise amplifier at the output of the probe, hence making an active probe. The performance of the shielded probe with a different length of transmission lines is made to study. When the probe has to be operated above 100MHz, it is found that the transmission lines connected to the probe should be short (around 1.5cm). For frequencies below 100MH, the length of the lines can be up to 12cm. A three-axis probe which is able to measure the three components of the magnetic field is also designed and validated by near field scanning above a standard wire over the ground structure.

In The second part, the inverse transmission line matrix method (Inv-TLM) method is used reconstruct the source distribution from the near field scan (NFS) data above a single in plane on the PCB. Even though the resolution of reconstruction depends on the wavelength and the mesh parameter, the inverse propagation increases the width of the reconstructed wave. As this method is found to be ill posed and results in multiple solutions, we have developed a new method based on the two-dimensional cross-correlation, which represents the near field scan data in terms of the equivalent electric currents of the dipole. With the new method, we are able to identify and locate the current sources in the PCB and are represented by an equivalent source. The method is validated for the current sources with different orientations. The simulated near field data using CST microwave studio is used to validate both the methods. The radiated far field from these equivalent sources is compared with the simulated fields.

Introduction 1.1 Need of EMC in electronic components

The widespread use of electronic circuits for communication, computation, automation etc. makes it necessary for different electronic circuits to operate in close proximity to each other. Quite often, these circuits affect each other adversely. Electromagnetic interference (EMI) has become a major problem for circuit designers, and it is likely to become even more severe in the future. A large number of electronic devices in common use is partly responsible for this trend. In addition, the use of integrated circuits and largescale integration has reduced the size of electronic equipment. As electronic circuits have become smaller and more sophisticated, more circuits are being confined into less space, which increases the probability of interference. The products must be designed to work in the ''real world,'' with other equipment nearby, and to comply with the electromagnetic compatibility (EMC) regulations. On the other hand, the equipment should not be affected by external electromagnetic sources and should not itself be a source of electromagnetic noise that can pollute the environment. In an electronic system the most common sources of radio frequency interference (RFI) can be listed as below: (1) The electromagnetic spectrum that is used extensively by radio transmitters for communications (2) High frequency pulses trains in digital systems

(3) Intended high frequency oscillator circuits used in sub-systems (4) Circuit transients caused by simple switching operations

In digital circuit design, EMC gathers attention because of the three different technological trends.

First, in the process of achieving higher processing speeds, shorter pulse rise-times are used, contributing a significant amount of energy at high frequencies, which is capable of propagating by radiative mechanisms over long distances. Second, the modern physical design of equipment is based increasingly on the use of plastics in preference to metals. This significantly reduces the electromagnetic shielding inherent to the all-metal cabinet. The third one is due to the trend for compact design as a result of miniaturization, which in turn contributes to EMC problems.

Electromagnetic compatibility (EMC) is the ability of an electronic system to (1) function properly in its intended electromagnetic environment and ( 2) not be a source of pollution to that electromagnetic environment. The electromagnetic environment is composed of both radiated and conducted energy. EMC, therefore, has two aspects, emission, and susceptibility. Susceptibility is the capability of a device or circuit to respond to unwanted electromagnetic energy (i.e., noise). The opposite of susceptibility is radiation. The immunity level of a circuit or device is the electromagnetic environment in which the equipment can operate satisfactorily, without degradation, and with a defined margin of safety. One difficulty in determining immunity (or susceptibility) levels is defining what constitutes performance degradation. Emission pertains to the interference-causing potential of a product. The purpose of controlling emissions is to limit the electromagnetic energy emitted and thereby to control the electromagnetic environment in which other products must operate. The three aspects, which forms the basic framework of EMC design is the generation, transmission, and reception of electromagnetic energy (shown in Figure 1-1).

Whether the source or receptor is intended or unintended depends on the type of the coupling path and the source or receiver.

Figure 1-1 Universal interference model

The transfer of electromagnetic energy can be divided into four subgroups, radiated emissions, radiated susceptibility, conducted emissions and conducted susceptibility. These four aspects are shown in Figure 1-2 [1]. An electronic system normally consists of one or more subsystems that communicate each other via cables. These cables have the potential in emitting or picking up the electromagnetic energy. Longer the length of the cable, the more efficient it is in picking up or emitting the electromagnetic radiations. The factor that produces intended or unintended radiation is the currents on the cables or traces. Electromagnetic emission or susceptibility to emission not only occurs by radiation through the air, but also interference signals passes between the subsystems directly via conduction. There are also some other factors concerned with the EMC. Some of them are depicted in Figure 1-3 [2]. There is significant interest in the military in hardening the communication against the electromagnetic pulse (EMP). The electromagnetic interference from the intense current caused by lightning couples to the electronic power systems and subsequently it is conducted into the device through the ac power cord. There are instances of direct interception with the radiated emissions from which the content of the communication can be determined. This problem is called TEMPSET and is imperative for the military.

Figure 1-2 Emission and susceptibility in an electronic system [1] Figure 1

-3 Some other aspects of EMC (a) Electro Static Discharge , ESD (b) electromagnetic pulse, EMP (c) lightning (d) TEMPEST (secure communication and data processing) [2]

Controlling the emission from one product may eliminate an interference problem for many other products. Therefore, it is desirable to control emission in an attempt to produce an electromagnetically compatible environment.

There are two different approaches to predict the emission or immunity of an electronic circuit, analytical and numerical methods. However the analytical methods can be applied only to very simplified structure, they are still important as they provide insight into the significance of various parameters and also benchmarks against which numerical methods can be checked and evaluated.

For more complex configurations, numerical computer-based methods are suitable for studying the behavior of the system. The numerical methods are mainly classified into two groups:

(1) Frequency-domain methods such as the finite element method (FEM) and the method of moments (MOM).

(2) Time-domain methods such as the finite-difference-time-domain (FD-TD) method and the transmission line matrix (TLM) method.

In another classification the numerical methods are divided into following groups:

(1) Integral equation methods and

(2) Differential equation methods

Measurement methods of PCB emissions

The electromagnetic emissions from a PCB can be classified as conducted emissions and radiated emissions or common mode and differential mode emissions. The conducted emission measurements are either a voltage-capacitive-tap type of measurement or they are a current-clamp type of measurement. On the other hand, the radiated emission measurements are unique in that they must always state "the horizontal distance from the Device-under-Test (DUT) to the receiving antenna." This horizontal distance can be 1.5,5,10 or 30 meters [3].

TEM cell method:

The radiation level of a device under test can be measured using a TEM cell as shown in Figure 1-4 [4]. The DUT faces the interior of the cell while the support circuitry is maintained outside the cell. The RF voltage appearing at the input of the connected spectrum analyzer is related to the electromagnetic potential of the DUT. The measurements are repeated for at least two orientations of the DUT in order to capture all the radiations.

Figure 1-4 Setup of TEM cell method for measuring radiated emissions [4] Surface scan method: the radiated emissions from the DUT can be measured by scanning with a probe above the DUT, as shown in Figure 1-5. The measurement result of the surface scan method provides not only the electromagnetic fields from the DUT but also the relative strength of the sources. A variety of probes such as electric, magnetic and optic probes are used for surface scanning.

Figure 1-5 Surface scan method [4] Method of measurement the radiation pattern: the radiation pattern of a DUT in far field can be measured using a receiving antenna.

Figure 1-6 Radiation pattern measurement method[4]

The DUT is mounted on a turntable and rotated through 360° to find the maximum emission direction as shown in Figure 1-6. The receiving antenna is scanned in height from 1 to 4m to find the maximum level. The DUT-to-antenna azimuth and polarization are varied through 360° during the measurement to record the radiation pattern of the DUT. The standard test procedure requires that the measurements are to be done on an open area test site or semi-anechoic chamber. A balanced dipole is used as the receiving antenna below 1 GHz, and a log-periodical antenna or a horn antenna should be used for tests above 1 GHz.

Reverberation chamber measurements:

A reverberation chamber is an electrically large, highly conductive enclosed cavity equipped with one or more metallic tuners/stirrers whose dimensions are a significant fraction of the chamber dimensions. A typical measurement setup using reverberation chamber is illustrated in Figure 1234567. It is used to measure the total radiated power of a DUT. The DUT should be at least λ/4 from the chamber walls. The stirrers are rotated very slowly compared to the sweep time of the EMI receiver in order to obtain a sufficient number of samples. The mechanical tuners/stirrers can "stir" the multi-mode field in the chamber to achieve a statistically uniform and statistically isotropic electromagnetic environment. The receiving antenna measure either the maximum received power or averaged received power during a cycle of the stirrers. The recorded signals are then converted to the total radiated power and the free space field strength. The advantage of the reverberation chamber method is that it is able to measure the total field on all sides of a DUT without multiple test positions and orientations.

Figure 1-7 Reverberation chamber method [4] Direct coupling method: The simplified configuration of the 1Ω method for measuring the sum current in the common ground path is shown in Figure 1-8. The direct coupling method determines the conducted emissions from power and signal ports of a small electronic module especially an IC.

RF currents developed across a standardized load is measured to allow indirect estimation of the emission level

Figure 1-8 1𝛀 Direct coupling measurement for conducted emissions [4] Workbench Faraday Cage (WBFC) method: IEC 61967-5 defines a method of measuring the conducted electromagnetic emissions at defined common-mode points in order to estimate the emissions radiated by connected cables. The Faraday cage is typically a metallic box of 500mm x 300mm x 150 mm. A typical workbench of Faraday cage method is shown in Figure 123456789.

DUT is mounted on either an IC EMC test board or an application board if it fits inside the WBFC.

With all input, output, and power connections to the test board filtered and connected to commonmode chokes, the conducted noise is measured at PCB locations specified by the standard. [4] Magnetic probe method: IEC 61967-6 defines a method for calculating the conducted emissions from an IC pin using a magnetic field probe to measure the magnetic field associated with a connected PCB trace. The schematic of the measurement setup is shown in Figure 12345678910.

Figure 1-10 Schematic of magnetic probe method for conducted emissions [4] Standard and method

comparison of emission measurements IEC-61967

A magnetic probe is used to measure the magnetic field associated with a connected PCB trace, and the RF currents inside the circuit are then calculated. The preferred test configuration is with the DUT mounted on a standard EMC test board to maximize repeatability and minimize probe coupling to other circuits. The features of all these PCB emission measurement methods are summarized in Table 1-1 [4].

Near field measurements

Methods such as modulated scattering technique, electro-optic sampling, electron beam probing (modified scanning electron microscope), and perturbation method are already available for the identification and localization of sources. [5], [6] proposes source location estimation technique with the modulated scattering technique (MST) for indoor wireless environments. The uniform circular scatterer array (UCSA) that consist of five optically modulated stutterers as array elements and a dipole antenna at the center of the UCSA is employed for estimating a source location from the impinging signal, but these techniques require expensive components, complicated configuration and low signal to noise ratio.

Electromagnetic near field scanning is a general method for identifying the source of electromagnetic interference (EMI) in electronic circuits. Various methods have been developed by many authors for the calculation of far field pattern leading to the source identification from the near field measurements [7]- [11]. Thus, it is necessary to know the electromagnetic fields in their close environment.

Near field and far field

The space surrounding an antenna is divided into three (1) reactive near field (2) radiative near field and (3) far field. Reactive near field is that portion of the near field region immediately surrounding the antenna whereas in the reactive near field predominates. For most antennas, the outer boundary of this region is taken into exist as at a distance R<0.62D3/ λ.

Radiating near field region is defined as that region of the field of an antenna between the reactive near field region and the far field region where the radiative field predominates and the angular field distribution is dependent upon the distance from the antenna.

Far field region is defined as that region of the field of an antenna where the angular distribution is independent of the distance from the antenna. If D is the maximum overall dimension of the antenna, the far field region is at a distance greater than 2D2/λ, where λ is the wavelength [12].

Why near field measurements?

The electromagnetic emissions can be measured in either near field or far field. The near field measurements have advantages in accuracy, reliability, cost and application range compared with that of the far field measurements. The effect of some uncertain factors such as weather, scattering, electromagnetic interference has less influence on the measurement because the probe and the DUT are very close to each other and hence it gives a more accurate measurement [13][14].

 The near field measurement is less dependent on test conditions. It can be conducted in normal lab environments rather than an OATS or an anechoic chamber. This makes the technique highly feasible.

 Unlike the far field measurements, which give the radiation in far field, near field measurements can be used not only to obtain electromagnetic fields, but also to provide the emission tests and source diagnostics in EMC studies of PCBs and ICs. It can be used to estimate the current on the microstrip trace of a PCB or to locate the fault in the high frequency chip [15].

 Near field-far field transformation methods and equivalent source methods enhances the application and popularity of the near field measurement method.

Depending on the applications, the near field measurements can be classified into antenna near field measurements and EMC/EMI near field measurements. Antenna near field measurements are performed in the radiating near field range, typically in the range 3λ to 5λ and are focused on the determination of far field pattern from near field. EMC near field measurements are performed in the highly reactive region (typically <λ/6) and are focused on the determination of real or equivalent radiating sources in the DUT.

Objective of the thesis

The major objective of this thesis is to predict the radiated emissions from a PCB from the near field scan measurements. The steps toward this can be divided into two main tasks.

1) Design of a high resolution and high sensitivity printed circuit magnetic probe for the near field scan measurements.

2) Development of the inverse algorithm for equivalent source representation and prediction of the electromagnetic compatibility.

The state of the art about the near field probes and source reconstruction methods is described in the next chapter (chapter 2) of this thesis.

Chapter 3 of this thesis deals with the design and characterization of printed circuit magnetic field probes for near field measurements. The main goal is the design of the low cost shielded magnetic probes in the printed circuit technology towards the achievement high spatial resolution (of the order of 100µm). The thesis describes the problems encountered while miniaturization and the solutions we put forward towards the goal. The required frequency band of operation is from 1 MHz -1 GHz, which is set by the definitions of the project (LOCRAY). The thesis also focuses on the design and characterization of active probes in order to achieve high sensitivity. The effect of the position of the LNA on the probe and the effect of the gain of the LNA are also made under study. The performance of a 3 axis probe which can measure the 3 components of the magnetic field is also analyzed.

Chapter 4 describes the source reconstruction methods from near field scan data for the prediction of radiated emissions from the PCB. The inverse transmission line based on the inverse propagation of electromagnetic probes is used to find the field distribution at the plane of the source. The inverse algorithm is meant to use the near field scanned data measured by the designed probe. This chapter also describes a new method based on the 2D cross-correlation. This method represents the current sources on the PCB by an equivalent current. This chapter contains the validation for elementary current sources and simple PCBs on air. Finally, the radiated far field of the circuit is predicted using the equivalent current. In this, we use the time reversal property of the TLM matrix in order to reverse propagate the electromagnetic waves and reconstruct the radiating source.

Chapter 5 concludes the work of the thesis and also gives the directions for future developments.

State of the art

Near Field Probes

Based on the configuration of the probe, there are two near field measurement setups as shown in The near-field probes (NFPs) have been widely studied recent years because of their ability to quantify the near-field (optical, electrical or magnetic field) strength in the space close to the noise sources. Most of the studies about the NFPs focused on the improvement of spatial resolution, available bandwidth, and suppressing the coupled field in an orthogonal direction or adverse field.

Electro-optical probes

Optical magnetic field probe which has a loop antenna element and an optoelectronic crystal is presented in [4]- [7]. The study in [4] analyzes the invasiveness of the optical magnetic field probes quantitatively by experiment and finite difference time domain (FDTD) method simulation. The metallic cables in the shielded loop coils introduce disturbance to the original magnetic field, this can be eliminated by replacing the metallic cables by optical fiber cable. An optical probe for simultaneous measurements of electric and magnetic near fields as shown in Kapteos [8]. The spatial resolution of these probes are around (<=) 1mm.

Electromagnetic probes

An electromagnetic probe consists of a loop or a dipole and a transmission line which carries the signal induced at the loop terminals. An electric probe consists of a dipole and a magnetic probe consists of a loop as detecting element. Various standard antennas for measuring radio-frequency electric and magnetic fields are developed. The standard probes described are an electrically short dipole, a resistively-loaded dipole, a half-wave dipole, an electrically small loop, and a resistivelyloaded loop. A single-turn loop designed for simultaneous measurement of the electric and magnetic components of near-fields and other complex electromagnetic environments is described in [9]. Each type of antenna demonstrates a different compromise between broadband frequency response and sensitivity. A common design for an electric probe consists of an electrically-short antenna with a diode across its terminals a resistive; parallel-wire transmission line transmits the detected signal from the diode to the monitoring instrumentation (Figure 2-4 (a)). Small dipoles are desirable because they provide high spatial resolution of the field, and because they permit a frequency-independent response at higher microwave frequencies [10]. The important problem associated with the electric dipole probes is the disturbance offered to the device under test by the probe itself. The use of resistive tapering, by means of thin-film deposition and photoetching techniques, has been shown to yield significant improvements over conventional dipole elements (Figure 2-4 (b)). These include broader bandwidth, flatter frequency response, wider dynamic range, smaller size, reduced EM-field perturbation and distortion, and complete absence of in-band resonances [11]. Waveguide probes are also used for near field measurements (shown in Figure 2-5) [12]. Open-ended waveguides measure the E field component. Figure 2-6 Electric probes [14] The electric probe fabricated by [14] in an open-ended coaxial cable is shown inFigure 2-6. In the case of an electric dipole probe, the current induced can be calculated based on the capacitive model as

𝑖 = 𝑗𝝎𝜺 𝟎 𝑬 𝒛 2-1
Figure 2-7Output voltage for different diameters of probe microstrip line configuration [14] The capacitive model does not take into account coupling with external conductors. The simulated output voltage of the probe for different diameters of the inner conductor, by inserting it into a rectangular waveguide to avoid coupling with external conductors is shown in Figure 234567. The output voltage increases when the dimensions of the probe increase.

A loop operates according to Faraday's law. A voltage is induced at the terminals of the loop when the magnetic flux through the loop changes [15].

.

emf S d d V B dS dt dt       r r 2-2
As it is obvious from equation 2-2, the voltage induced on the probe depends on the size of the loop; hence the sensitivity of the loop is directly proportional to the size of the loop. The finite loop probe contains not only the usual circulating current which is proportional to the magnetic field but also certain currents which do not depend on the component of magnetic field, but rather on the average electric field in the plane of the loop. Very large errors are possible when a singly-loaded loop is used to measure magnetic fields unless its diameter is less than 0.01λ. The doubly-loaded probe may be used with comparable accuracy when its diameter is as large as 0.15λ [16].

Electromagnetic probes are fabricated using different technologies such as CMOS integration technology LTCC, thin film technology and PCB technology. The very classic magnetic probes is a circular or elliptical loop fabricated by hand and connected to the ground and signal lines of a semirigid coaxial cable as shown in Figure 2-8(a) [17]. These probes are not suitable when there is a requirement for high spatial resolution because they are difficult to fabricate manually. Different miniaturized probes are fabricated using the thin film technology. A miniaturized thin film magnetic probes for LSI measurement proposed by [18] is shown in Figure 2-8 (b). . Figure 2-8(c) shows an LTCC probe fabricated by [19]. To miniaturize further and improve the frequency band, integrated probes and probes on LTCC (Low temperature Co fired Ceramics) are used [18]- [22]. A silicon integrated RF magnetic field probe presented by [19] is shown in aperture [17] (b) thin film [18] (c)-LTCC probe [19] (d) CMOS SOI probe [20] (a) (b) probe with a bare loop and stripline loop [24] (c) loop with microstrip filter [25] There is quite a little literature on the printed circuit magnetic field probes. Since the LTCC, thin film and integrated technologies are quite expensive; this work focuses on probes based on the printed circuit technology. A rectangular loop probe with CPW fed line is proposed in [23]. The length and width of the loop are 5mm x 5mm with the conductor width of 0.5mm. A tapered transition is adapted in this paper in addition to the air bridge between the two ground planes (Figure 2-9 (a)). The probe is fabricated on a Teflon substrate with permittivity 2.5 and height 0.508mm. The authors claim that the proposed probe miniaturizes the spurious radiation and resonances by connecting the ground planes together and adapting a tapered transition. The probe works from 1 GHz-7 GHz. Two types of printed circuit magnetic probe for GHz band is proposed in [24], shown in Figure 2-9 (b). Type A is a bare loop and Type B is a strip line loop. The loop aperture has an area of 1 square millimeter and is fabricated on FR4 substrate. Later in 2009, a printed circuit magnetic probe shown in Figure 2-9(c), with a set of quasi periodic notches which acts as microstrip filters were proposed in [25]. This probe was fabricated on an FR4 substrate with a 0.8mm thickness, the aperture of the loop is 8mm (R=4mm).

(b) (c)
The sensitivity of the probe is improved by using carrier suppression technique in [26]. An array of active magnetic probes is designed by M. Yamaguchi, using CMOS integration technology [3]. An active electro-optical probe for medical MRI is proposed by [5]. These researches don't provide any information about the amplifier characteristics or the influence of the integrated amplifier on the measurement result.

The measurements in near fields and far field requires separate probes [27]. The disturbance of the probe in the far field is negligible when a probe with maximal sensitivity is used. This is not the case with the near field. The smaller the dimensions of the probe, the smaller will be the disturbances to the device under test and the higher the spatial resolution.

Synthesis of radiating sources

At present, inverse problems arise in many branches of applied sciences, such as medical diagnostics, atmospheric sounding, radar and sonar target estimation, seismology, radio astronomy, and microscopy. In a general context, an inverse problem can be broadly described as a problem of determining the internal structure or past state of a system from external measurements, which corresponds to the inverse of the usual cause-effect sequence of events. In the domain of electromagnetism, inverse problems are divided into two categories:

(1) Inverse scattering problems (inverse medium problems), which obtain the characteristics of a scattering object from its scattered wave due to external illumination, and

(2) Inverse source problems, which determine the constitution of a source from measured values of its emitted radiation.

Other common applications of inverse source problems are concealed weapon detection, nondestructive evaluation or testing, and remote sensing [28][29] [30]. The inverse source problems, in contrast, have received little attention, partially because of the severe non-unique nature in the solutions. Despite this ill-posedness, inverse source problems are still applied directly in antenna design [31]and holographic imaging [START_REF] Gaikovich | Subsurface Near-Field Microwave Holography[END_REF]. Inverse source problems have already been studied in the frequency domain [29] and in time domain [30].

The earliest works on modelling the far field emissions were direct near-field to far-field transformation based on modal expansion methods as shown in Figure 2-10(a) [33][34]. The fields radiated by a DUT are expanded in terms of planar, cylindrical, or spherical wave functions in order to obtain the far field, and the measured near-field data are used to determine the coefficients of the wave functions. An equivalent source representation composed of both magnetic and electric dipoles placed over a fictitious sphere surrounding the AUT is obtained in [START_REF] Serhir | An accurate equivalent behavioral model of antenna radiation using a mode-matching technique based on spherical near field measurements[END_REF]. A linear relation between the transmission coefficients of the AUT and the transmission coefficients of each dipole derived by a spherical wave expansion (SWE) of the NF measurements. Dipole transmission coefficients are determined using the translational and rotational addition theorems, and a least square method is employed to compute the excitation of each current source.The equivalent currents are placed in the aperture in front of the antenna so these methods do not apply to emissions in the other half space behind the antenna.

The equivalent source reconstruction from the radiated field is applied in antenna synthesis to reconstruct the equivalent source of antennas from its radiated near field as illustrated in Figure 2-10 (b). A method for computing the far field of an antenna from the near field measurements taken over an arbitrary geometry is presented in [START_REF] Sarkar | Near-field to near/far-field transformation for arbitrary near-field geometry utilizing an equivalent electric current and MoM[END_REF]. An integral equation is used to relate the near field data to the equivalent current and the MOM method is used to solve the equation by transforming it into a matrix equation. The authors in [START_REF] Las-Heras | A direct optimization approach for source reconstruction and NF-FF transformation using amplitude-only data[END_REF] present a method that reconstructs directly the sources from the knowledge of the electric field amplitude data over some region. The sources are reconstructed in terms of an equivalent magnetic current density and the equivalence principle has been used to represent the Antenna under test. With these methods, the correct far field in front of the antenna can be produced regardless of the geometry of the near-field measurement. Another way is to identify the real or equivalent sources bound to the actual DUT surface in order to locate the radiating source as shown in The approach of source reconstruction is harnessed to model the radiated emissions from PCBsand electronic devices. The equivalent source of the source distribution is obtained by numerical methods. After obtaining this equivalent source, it is quite easy to conduct source diagnostics, nearfield prediction, evaluation of the radiation performance regularized by the EMC standards like the radiated emission limitation at 3 m, 10 m even 30 m away from the DUT, and investigation of interactions between the PCBs and the shielding cavities [37][38]. The recent development in source reconstruction for EMC is done by Ping Li and Li Jun Jiang [START_REF] Li | Source reconstruction method-based radiated emission characterization for PCBs[END_REF], in which the near field TLM method has been a powerful numerical technique for solving electromagnetic structure problems including high-speed RF/microwave circuits, antennas [START_REF] Hailu | Sub-wavelength Microwave Radar Imaging for Detection of Breast Cancer Tumors[END_REF][40]The time-reversal property of the TLM method was utilized for the localization of scattering objects from external field measurement in the time domain. In [START_REF] Zhang | The solution of transient electromagnetic inverse source problems using time-domain TLM method[END_REF] non-uniqueness of the inverse source problem is addressed by additionally imposing smoothness constraints. Both the source solution and the field measurements are performed in the time domain. The inverse problem in their paper deals with the reconstruction of a transient source distribution inside a closed region in free space.

Conclusion

The near field scanning probes in the literature is for frequencies above 1 GHz. The higher resolution probes is said to operate in the frequencies above 3 GHz. The probes with high spatial resolution in the range of micrometers (µm) were always achieved with expensive CMOS, LTCC or thin film technologies. There was no information in the literature about the near field probes which operates in the frequencies below 1 GHz with spatial resolution below 1 mmusing the printed circuit technology. The influence of the amplifier factors such as gain, noise figure and position on the probe on the performance of the active probe has to analyze.

The source reconstruction incorporates the electric or magnetic field integral equations with the numerical methods such as MoM. Most of these methods needs to have information about the device under test in order to predict the radiated field and requires large computational time and memory. Use of the near field data from two planes above and below the device under test requires large scanning time. So, it is required to have a method for the reconstruction of sources with near field scan data from single plane to reduce the scanning time and the memory of computation.

3. Design and characterization of printed circuit magnetic probes

Introduction

Near field scanning is a general method for the measurement of radiated emissions from PCBs. The accuracy of this measurement depends on the probes used for the near field scan. As seen in the literature, the sensitivity and selectivity of the probe are inversely proportional. Therefore, the objective of this chapter is to design a magnetic probe with high sensitivity and high spatial resolution. The design and characterization of high-resolution magnetic probes using printed circuit technology are discussed in this chapter. The sensitivity of the probe is enhanced by integrating a

Low noise amplifier at the probe output. The active probe discussed here is the first active probe in the literature, which is fabricated using printed circuit technology. The validation of active probes and three axis probes are also contained in the following sections.

Parameters of the probe

The important parameters of the probe are listed in Figure 3-1. Selectivity: It is the ability of the probe to distinguish between the normal component and the tangential component of the electric or magnetic field.

Spatial resolution:

The Rayleigh criterion defined the spatial resolution as the ability to discriminate two RF sources in close proximity. That amounts to determining a distance δ from which the system will be unable to distinguish these two sources. The spatial resolution in the case of the dipole is estimated to be equal to half of the length of the dipole probe.

Antenna factor:The antenna factor of a dipole is defined by the ratio between the incident field and the voltage induced at the input of a receiver. The antenna factor is defined as the ratio between the electric or the magnetic field of the circuit under test and the voltage induced at the probe when placed on the device under test.

𝐴𝐹 𝑖𝑛 𝑆/𝑚 = 𝐻 𝑖𝑛 𝐴/𝑚 𝑉 𝑖𝑛 𝑉 3-1
And the antenna factor in dB is expressed as

𝐴𝐹 𝑖𝑛 𝑑𝐵𝑆/𝑚 = 𝐻 ( 𝑑𝐵𝐴 𝑚 ) -𝑉 (𝑑𝐵𝑉) 3-2
For calculating this parameter the theoretical or the simulated magnetic field of the DUT is divided with the measured voltage or the simulated voltage at the probe.

The antenna factor (AF) can be derived theoretically from Ampere's law as

𝐴𝐹 = 1 𝑗𝜔𝜇𝑛𝑆 3-3
Where, n is the number of turns, S is the area of the loop and 𝝎 is the angular frequency

The AF is important to know the level of the field above the DUT when using the probe in the nearfield measurement system.

The near field test bench

The characterization of the probe is performed with the near field test bench. A near field test bench has been developed by IRSEEM (Research Institute for Electronic Embedded Systems, the laboratory at Rouen, France) to collect the electromagnetic field close to devices of various sizes.

The system is based on a direct measurement method and its schematic is shown in

Figure 3-2 Schematic of the near field characterization setup

The 3D positioning system can be made to operate in 2 scanning modes,

1.

A constant height mode and

2.

A constant distance between the probe and a device under test mode.

The distance between the probe and the DUT is kept constant by using the relief model of the object to regulate probe position. The method used to acquire the relief model of objects is based on laser triangulation. The object is illuminated from one direction with a laser lime projector and viewed with the camera from another one. Laser and camera are fixed on the robot. The relief model of the device under test is acquired by translating the positioning system along the x-axis of the robot. Zdata provided by the camera are recorded on a computer and converted into probe coordinates.

Finally, these data are used to position the probe over the device under test during electromagnetic measurement. The low noise amplifier having a gain of 37dB is associated with the arm of the robot.

𝐸 𝑦,𝑇ℎ𝑒𝑜𝑟𝑦 = 8𝐾 𝑦𝑧𝑛 (𝑦 2 + (𝑧 + 𝑛) 2 )(𝑦 2 + (𝑧 -𝑛) 2 ) 3-4 𝐸 𝑧,𝑇ℎ𝑒𝑜𝑟𝑦 = 4𝐾 𝑛(𝑦 2 -𝑧 2 + 𝑛 2 ) (𝑦 2 + (𝑧 + 𝑛) 2 )(𝑦 2 + (𝑧 -𝑛) 2 )
3-5

𝐻 𝑦,𝑇ℎ𝑒𝑜𝑟𝑦 = - 1 𝜂 𝐸 𝑧 3-6 𝐻 𝑧,𝑇ℎ𝑒𝑜𝑟𝑦 = 1 𝜂 𝐸 𝑦 3-7
Where,

𝜂 = 𝜇 0 ℇ 0 , 𝐾 = √2𝑃𝑍 𝑐 𝑙𝑛( ℎ+𝑛 ℎ-𝑛 )
and 𝑛 = √ℎ 2 -𝑎 2

Printed magnetic field probes

An ideal magnetic probe is only a loop. But, in reality, this configuration is not possible, because it requires an interface to carry the voltage induced at the probe to the receiver system. A printed circuit magnetic probe consists of a loop and a transmission line followed by the loop as shown in the schematic in Figure 34567.

Figure 3-9 Simulation model of the probe above the reference circuit (view from HFSS)

The probe is moved along the y-axis as shown in dotted lines in the figure, keeping the reference circuit fixed. The Port 2 is assigned a power of 10 dBm. The scattering parameter S12 gives the ratio of the voltage at port 1 to the voltage at port 2, that is, the ratio between the voltages at the probe and the input voltage. Knowing the input power at port 2, the voltage induced at the probe can be calculated.

𝑉 𝑝 = 𝑆 12 𝑉 𝑖𝑛 3-8
Where, 𝑉 𝑝 is the output voltage of the probe, and 𝑉 𝑖𝑛 is the input voltage at the port 2 of reference circuit.

Simulated results

Figure 3-10 Simulations results of the magnetic field measured by the probe MP-1 at different frequencies

The simulation results of the probe in Figure 3-8are plotted in Figure 3-10 along with the original magnetic fields present at the same position of measurement, which is obtained using the analytical equation (3)(4)(5)(6). The measured H field of the probe is calculated by multiplying Antenna Factor (AF)

or Calibration Factor (CF) with the output voltage of the probe. The comparison is made at different frequencies from 10 kHz -1 GHz. From the figure, it is seen that the probe detected the profile of the magnetic field in all the frequencies from 10 kHz-1 GHz. The received magnetic field is in very good agreement with the theoretical magnetic field from 10 kHz -200 MHz. All the peaks are detected perfectly in this frequency band. At frequencies above 200 MHz, we can see that the detected magnetic field has the shape of the original magnetic field, but the two minima at the side lobes couldn't reach up to the level of the original field. It is also being observed that as the frequency increases, the level of the detected minima reduces. At 300 MHz, the detected minimum level of the magnetic field was 30dBA/m, at the same time, the detected minimum decays to -22 dBA/m at 1 GHz. The reason for this behavior is investigated in the following sections. As the probe consists of a loop and transmission line, the parameters considered for analysis are the effect of the structure of loop and the effect of the transmission line. However, with the addition of the line, the minimum of the magnetic field is not detected correctly from 100 MHz with MP-4 and MP-5. The profile of MP-5 at frequencies above 500 MHz is very much affected by noise than MP-4. This shows that the probe output contains the voltage induced in the loop and the voltage induced on the transmission line, which can be called as noise. These noise voltages corrupted the frequencies above 100 MHz. When the length of the transmission line increases, the highest operating frequency of the probe is reduced.

Figure 3-14 Simulations results of the magnetic field measured by the probe MP-1, MP-4, and MP-5 at different frequencies

The features of all the microstrip probes are tabulated in Table 3-1 along with its simulated operating frequency bandwidth. It is obvious from the table that when the number of layers of the loop increases, the frequency bandwidth reduces. Also, the number of turns of the loop is inversely proportional to the frequency bandwidth. It is also noted that the frequency bandwidth reduced with the increase in the length of the transmission line connected to the probe. 3-4 is used for the characterization. The fields are plotted from 100 KHz, as the probe is not able to detect signals below 100 kHz. The probe has a good profile up to few MHz, and when it reaches around 50 MHz, the shape of the detected profile is lost. The probe is not able to detect the magnetic field minimum positions above 50 MHz, even though the profile of the probe is good up to 100 MHz in the simulation. So, in the measurement, there are some factors other than the electric field which cause the deviation from the ideal response. The reasons for this behaviour is investigated in the following sections.

Printed circuit probes type 2 (with CPW line)

The designed and characterization of probes based on coplanar waveguide (CPW) configuration is presented in this section. A new probe with Grounded CPW (GCPW) transmission line is proposed and compared with the conventional probe with CPW transmission line

Coplanar waveguide (CPW) design

Coplanar waveguide (CPW) is an alternative to microstrip and stripline that places the signal and ground currents on the same layer. It is a printed circuit analogous to three-wire transmission line (Figure 3 -16). A center strip which acts as the signal line is separated by a narrow gap from the ground plane on each side. The gap in the waveguide is usually very small and supports electric fields primarily concentrated in the dielectric. With the little fringing field in the air, the coplanar waveguide exhibits low dispersion. In order to concentrate the fields in the substrate area and to minimize radiation, the dielectric substrate thickness is usually set equal to about twice the gap width. A CPW has a zero cut-off frequency, but its low order propagation mode is quasi TEM. Some electric and magnetic field lines for the Quasi-TEM mode in CPW are indicated in Figure 3-17 in a defined cross-section and a defined time [2]. At higher frequencies, dispersion arises and the field becomes less TEM and more TE in nature. The two ground planes of the CPW must be maintained the same potential to prevent the unwanted modes from propagating. If the grounds are at different potentials, the CPW mode will become uneven, with a higher field in one gap than the other. In the CPW two fundamental modes in CPW are coplanar mode and the parasitic slotline mode. Air bridges between the ground planes have to be applied to suppress the undesired slotline mode. If wire bonds are used to connect the ground planes, the wires should be spaced one-quarter wavelength apart or less. The use of substrates with high dielectric constant, with recommended values greater than 10, the electromagnetic field is mainly concentrated inside the dielectric and avoids the field radiation in air. Spurious modes (mainly microstrip mode) can easily be generated if the separation between the CPW structure and the backing metallization is too close. The characteristic impedance is determined by the ratio of the centre strip width a to the gap width b, so the size reduction is possible without limit at the expense of higher losses.

Design of coplanar probes

Based on the CPW and GCPW configuration two types of probes are fabricated. The probe with the CPW transmission line is a conventional probe, which is said to operate in the frequency band of 2 GHz -7 GHz [3][4]. We have designed and fabricated the conventional CPW probe and a new GCPW probe, which has the same dimensions of the loop as in [4]. Both the probes are fabricated on Roger RO 3210, which has a dielectric constant 10.2 and thickness of the substrate h is 0.635mm. The structure of both the probes is shown in Figure 3-21.The width of the conductor of the loop is 0.5mm, and hence the aperture of each loop is 4mm x 4mm in dimension. Metallic wire bonding is provided between the grounds of the CPW probe. As the wire bond is a bridge in the air, it is easy to break and handled carefully. In order to have an equipotential ground and avoid the air bridge of the conventional CPW probe, a new configuration of probe employing a grounded coplanar waveguide is fabricated. In the GCPW probe, metallic vias having a diameter of 0.2mm are used to connect the grounds from the top to the bottom. proposed GCPW probe, l=5mm, w=5mm, h=0.635mm Both the probes have a very bad profile at frequencies below 2 GHz. Even though, the detected profiles of GCPW probe at frequencies above 600MHz is found to be better than the CPW probe these profiles prove that the probes are not a suitable candidate for near field scan below 1 GHz. So, we can write,

𝑉 𝑝𝐼 = 𝐶 𝐼 𝐼 𝑡𝑟 3-9
Where,𝐶 𝐼 is the proportionality constant.

In addition, the loop is also exposed to a vertical electric field which leads to charge redistributions on the loop and on the transmission line connected to the loop. As the field alternates, the current will flow on the loop causing a magnetic flux coupling into the loop and which in turn induces a secondary voltage 𝑉 𝑝𝑉 at the probe output. At any given frequency, the induced voltage is proportional to the trace voltage𝑉 𝑡𝑟 . With a proportionality constant, the induced voltage 𝑉 𝑝𝑉 𝑉 𝑝𝑉 = 𝐶 𝑉 𝑉 𝑡𝑟 3-10 For an ideal prove 𝐶 𝑉 would be zero. In practical, it has a non-zero value. This effect can be associated with the common mode currents on the ground of the receiver or the outer shield of the coaxial cable. So, the total voltage 𝑉 𝑝 can be expressed as follows 𝑉 𝑝 = 𝑉 𝑝𝐼 + 𝑉 𝑝𝑉 = 𝐶 𝐼 𝐼 𝑡𝑟 + 𝐶 𝑉 𝑉 𝑡𝑟 3-11 𝐶 𝐼 and 𝐶 𝑉 are frequency dependent complex values , which can be derived from the measurement and simulation using two different values of load impedances 𝑍 𝐿 to the trace [5].

When referenced to the local common or ground, a common-mode signal appears on both lines of a 2-wire cable, in-phase and with equal amplitudes [6]. Such signals can arise from one or more of the following sources:

 Radiated signals coupled equally to both lines,  An offset from signal common created in the driver circuit, or  A ground differential between the transmitting and receiving locations.

The fundamental deviations from ideal response of the probe are related to the excitation of higherorder current modes in the loop, i.e., current distributions other than the ideal uniform current around the loop periphery. The first higher-order mode corresponds to a short electric dipole response giving rise to electric-field coupling. Any electric field present at the probe location causes a receiver response in addition to the desired pure magnetic field response. Further higher-order terms in the loop current give rise to additional unwanted responses. All these higher-order terms are related to the loop dimensions (loop radius, for a circular loop) measured in wavelengths. In the case of an ideal loop, which is isolated from ground, the worst-case plane-wave E-field to H-field coupling ratio equals twice the ratio between probe perimeter and wavelength [7]. There are quite a few literatures which treated the common mode response of the probe. because of the length of the robot arm used to hold the probe and the width is W1=10mm. The grounds at layer 1 and layer 2 are connected by cylindrical vias of 300µm diameter at consecutive intervals in order to avoid the parallel plate mode of operation of the stripline and increase the isolation from the electric field. A rectangular metallic pad of 500µm x 500µm is provided at the end of the loop in order for the connection of via during fabrication.

Design of the transmission line

The transmission line used is a stripline structure having a strip conductor sandwiched between two ground layers [8]. A stripline is essentially a printed circuit version of a coaxial transmission line.

Stripline has three layers of conductors (as seen in Figure 3-26). The internal conductor is commonly called "hot conductor". The other two conductors which are always connected to the signal ground are called the "cold conductors" or "ground conductors". The hot conductor is embedded in a homogeneous isotropic dielectric of dielectric constant ε r. Its dominant mode is pure TEM, assuming perfect conductors. The stripline is more suitable for use at low microwave frequencies because of the possibility of exciting parallel plate mode at higher frequencies.

Figure 3-26 Cross section of astripline Figure 3-27 Electric E and magnetic H field lines of stripline

The electric and magnetic field lines of the strip line are indicated in Figure 3-27in defined crosssection and a defined time. As the region between the two conductor plates of stripline contains only a single medium, the phase velocity and the characteristic impedance of the dominant TEM mode do not vary with frequency. In the fundamental mode, the hot conductor is equipotential ie., every point in it is at the same potential. If the top and bottom ground plates are not at the same potential, a parallel-plate mode can propagate between them. If excited, this mode will not remain confined to the region near the strip but will be able to propagate wherever the two ground planes exist.

Choice of the via and the via spacing

Striplines are less sensitive to lateral ground planes of a metallic enclosure because the electromagnetic field is strongly contained near the center conductor and the top-bottom ground planes. The return current path for a high frequency signal trace is located directly above and below the signal trace on the ground planes. The high frequency signal is thus contained entirely inside the PCB, minimizing emissions and providing natural shielding against incoming spurious signals. The metallized via holes connecting the two ground planes suppresses the parallel plate mode of the stripline. The via should be placed closely; a spacing "s" of one-eighth of a wavelength in the dielectric is recommended to prevent a potential difference from forming between the ground planes. Such vias form a cage around the strip and makes it like a basic coaxial line. When the vias are placed too close to the edge of the strip, they can perturb the characteristic impedance. The via separation 'w' should be a minimum of three-strip widths, and 5 is preferable. If the via separation is too large, a pseudo-rectangular waveguide mode can be excited. This mode has a cut off frequency given by

𝑤 < 𝑐 2𝑓 𝑚𝑎𝑥 3-12
Where, c is the speed of light in the dielectric. Thus, at the highest frequency of operationf max , the via separation should be less than the ratio of the velocity of light and twice the maximum frequency.

Considerations for thickness of the shield

The thickness of the shield t s is chosen to be greater than the skin depth δ of the metallic shield over the frequency range of interest.

𝑡 𝑠 > 𝛿 3-13
The skin depth δ is calculated as [9] 𝛿 = √ 2𝜌 𝜔𝜇 3-14

Where, 𝜌 -resistivity of the conductor 𝜔the angular frequency of the current 𝜇 = 𝜇 𝑟 𝜇 0 𝜇 𝑟the relative permeability of the conductor 𝜇 0the permeability of free space For copper resistivity is 𝜌 = 1.98 × 10 -8 Ohm meter. At 50MHz, copper has a skin depth of 9.2 µm and at 1 GHz, 𝛿 is 2 µm.

Equivalent circuit model

A simple circular loop isolated from the ground is used to explain the reception of the electric and magnetic field by the loop [10]. Assume that a plane wave impinges on the loop with magnetic field perpendicular to the plane of the loop and the electric field along the plane of the loop. This configuration maximizes the interaction between the loop, the H field, and E field. The radiation resistance in series with L and C is neglected in this case. Ideally pure magnetic response and first order e field response are considered.

V E = πbE 3-17 V H = -jwµπb 2 H, 2пb<<λ0 3-18
The ratio of the H field response to the E field response is 𝑍 𝐿 is the impedance of the receiving device, 𝐶 𝑒 represents the effect of the E field coupling. C is the capacitance of the loop; 𝐿 𝑠 is the self-inductance of the loop.𝐿 𝑔 is the self-inductance of the ground.

V 0H V 0E = c 4πbf 3-19
M is the mutual inductance [11].

Characterization

The results of the simulation and measurement of the probe are discussed in this section. The design of the probe is done using HFSS. The photograph of the fabricated probe is shown in Figure 3-30

Simulated near field scan results

The probe in Figure 3-29 is simulated above the reference circuit in order to get the magnetic field received by the probe along the y-axis. The simulated tangential magnetic field received by the probe is plotted in up to 100 MHz.The levels of the minimum don't coincide with the minimum level of the theoretical magnetic field for frequencies above 100 MHz, even though the profile has a similar shape of the original magnetic field. This is because, as the dimensions of the probe are very small, the proposed probe has very less sensitivity in the entire frequency band from 1 MHz to 1 GHz and the noise floor of the vector network analyzer is very high in order to be not able to receive the signals in all positions. Even at frequencies above 1 GHz (profile at 2 GHz is shown in Figure 3-36), the detected voltage is below the noise floor of the receiver.

Near field scanning with external amplifier

In order to increase the sensitivity of the probe, an amplifier with a gain curve as shown Figure 3 close to the minimum level. This indicates that the 37 dB gain of the amplifier is not enough to detect the frequencies below 1 MHz. The fields are measured only up to 1 GHz because the amplifier is usable up to 1 GHz. The profile of the measured tangential field is in good agreement with the theoretical magnetic field from 10 MHz to 400 MHz. In the frequency band of 400 MHz-900 MHz, even though the maximum and minimum are correctly detected, there is a small deviation from theoretical values at the positions of the side lobes. This is expected due to the 10 cm long length of the transmission in the probe, which is not calibrated. This length of the line was unavoidable due to the length of the arm of the robot in the near field test bench.

Effect of the length of the probe and arm of the measurement system

In order to measure the probes with length less than 10cm, we used another scanning system because of the mechanical limitations of the length of the arm holding the probe.

3.8.4.1

An alternate near field scanning system A scanning system has been developed at Pheline lab ( at CSTB Grenoble), which consists of a robot, Teledyne LeCroy Wave Runner 640Zi oscilloscope, PC and the designed 3D H-field probes.

The robot is able to move in 3-axis with a step size of 1mm. As the step size is very high, the precision of this scanning system is less compared to the one presented in the section 3.3. The scanning robot is connected to the oscilloscope to the PC. The PC is programmed to control the movement of the robot and the data collection from the spectrum analyzer. The plastic arm of the robot holds the probe above the DUT. The movement of the robot arm can be precisely adjusted to 0.1mm/step by a 3D movable controller system. The output of probe can be connected to any of the channels of the oscilloscope. The amplified output of the probe is connected to spectrum analyzer inside the oscilloscope. Near field scanning is performed at every desired frequency. The input power from the signal generator is 10dBm. The tangential field measured by this configuration is plotted in Figure 3-41.

Unlike the probe SP1-A with a long line, the scanned profile of the probe SP1-B at frequencies above 400 MHz are in very good agreement with the theoretical field. So, it is the length of the line in SP-A which caused the small deviations from the theoretical field at some frequency band as suspected. But it is not well understood that the frequencies below 400 MHz, has deviated more from the theoretical fields in the side lobe levels, even though it preserves the shape of the profile.

Design and characterization of3 axis magnetic field probes

It is necessary to have all the 3 components of magnetic or electric fields for accurate prediction of radiated emissions [13]. But it requires a large scanning time in order to complete one surface of a PCB during the near field measurements. In [14] a 3D near field scanner for IC chip level measurements is proposed. It consists of 3D near field scanner with a magnetic probe head. Two separate magnetic fields probe (to measure the normal and tangential component of the magnetic field) for measuring three-dimensional fields in high frequency planar circuits is proposed in [15].

Still, these methods don't reduce the scanning time because each component has to be measured separately. In order to minimize the scanning time, we propose a three dimensional (3D) scanning system consisting of a near field scanner and a three-axis probe which measures the three components of the magnetic field at the same time. Jomaa has already realized a scanning system with a 3-axis probe consisting of conventional circular loops [16]. These probes suffer from having a poor spatial resolution because of its larger size and are also difficult to fabricate manually. The proposed 3-axis probe is a printed circuit magnetic probe which has 3 loops printed inside a substrate in order to measure the three components of the magnetic field simultaneously. Each loop having a dimension of 3.2mm x 3.2mm is fabricated on both sides of an FR4 substrate with a thickness of 3.2mm. The probe has an overall dimension of 0.9mm x 0.9mm x 3.2mm. In order to form loops on the X and Y directions, top and bottom conductors are connected through a cylindrical via having a radius of 500 µm. The connecting pads for all individual loops are provided at the top surface in order to be able to connect it to the coaxial cable.

Calibration

The calibration setup used in this work is shown in Figure 3-43 FCC-TEM-JM1 cell was used to produce calculable electric and magnetic field strengths. It operates in the transverse electromagnetic mode so that both the E and H-field components generated between the septum and outer conductor have the characteristics of a wave propagating in free space. The field strength can be calculated from the dimensions of the cell, its impedance at the measurement plane and the input power as shown in the equations below [17]:

E z [V/m] = √2Z c P in [watt] h tem [m] 3-20 H[A/m] = E[V/m] η[Ω] 3-21
Where Z c is the input impedance of the measuring instrument in Ohm P in is the input power in watts h tem is the distance in meters between the septum and the outer conductor of the TEM cell ηis the intrinsic impedance of the free space in ohms.

The antenna factor then can be calculated by placing the probe inside the TEM cell and measuring the induced voltageV ind across the loop terminals, according to the following equation:

AF [dB A/m V ] = 20log ( H[A/m] V ind [V] ) 3-22
Where V ind is the induced voltage in the loop (in volts) and it is given by: to the coupling between the individual probes in the 3D probe.

V ind = √2Z c

Near field scanning

The near field scanning setup of this 3 axis probe is shown in Figure 3 shows that the field measurements are in good agreement with the theoretical calculations for the 3D probe. Also, a good spatial resolution is obtained for the probes in measuring the magnetic field components. The volume of the proposed probe is only 15 % of the previous 3D probe [16].

Compared to the conventional circular loop probes printed circuit probes are easy to miniaturize and less susceptible to damage. Also, the proposed probes have the advantage of being low cost, compact and easy to handle.

The electrical connection between the loop and the coaxial cables is found to be very critical in the near fields scanning. The long connecting lines printed in the probe are found to distort the scanned profile of the probe. So the connecting pad to connect the loop to the coaxial cable is made very small in order reduce the coupling effects.

Active magnetic probes

There is always a trade-off between the sensitivity and the spatial resolution of the probe. The sensitivity of the probe is reduced when the probe is reduced, especially at low frequencies. Figure 3-48 shows the relation between the size of the probe, spatial resolution, and sensitivity of the probe at different frequencies. The spatial resolution of the probe is directly related to the size of the probe in such a way that the spatial resolution is half of the size of the probe. At the low frequencies, there is a gradual reduction in the sensitivity of the probe with the reduction in the size of the probe. The active probe AP1-A is characterized using a vector network analyzer from 1 MHz to 10 GHz.

The near field map of the tangential magnetic field received by the active probe AP1-Ais plotted in At frequencies up to 10 MHz, the detected signal is completely below the noise floor as it was the case with AP1-A. But, unlike AP1-A, the profile at all frequencies are distorted. So, it can be concluded that there is an interaction between the magnetic field of the microstrip and the amplifier circuit. When the amplifier is away from the loop, it is away from the device under test also, so, there is less disturbance offered to the device under test by the amplifier. So, it is not wise to keep the amplifier circuit close to the loop, At the same time it is not possible to keep the amplifier very far, because it increases the length of the line between the loop and hence the total length of the probe increases, which in turn reduces the highest operating frequency of the probe. The choice of the position of the amplifier has to be made subject to the frequency band in which the probe is required to operate. The reason for the deviation of the performance of the active probes from the passive probes can be explained from the measurement of the scattering parameter of all these probes above the device under test. The S-parameter S21 is a measure of the output voltage of the probe. When the probe is placed at the center of the cylindrical conductor, as in Figure 3-53, the detected output voltage has maximum value. The S21 as a function of frequency is plotted for both the active probes and the passive probe in Figure 3-55. The curve of the passive probe plotted here belongs to SP1-A, by using the external amplifier (ZPUL-30).  Due to the interaction between the fields of the microstrip line and the probe.

For the probe AP1-B, there are more oscillations which are expected due to the reflection between the output of the amplifier and the semi-rigid coaxial cable, because the LNA has poor output reflection coefficient

Conclusion

In this chapter, we have designed and characterized probes based on microstrip line, CPW line,and shielded probes. The probes with single turn loop have the highest frequency band of operation. The output voltage at the probe is not only due to the voltage is a sum of the voltage due to the magnetic field and the voltage due to the electric field. The highest frequency of operation of the probes decreases with the increase in the length of the transmission line. E field coupling into the probe has very undesired effects. The common mode voltages are a big problem, which causes a large error in the measurement of the probes. The electric (E) field coupling into the probe is the major cause of common mode voltages at the probe output. The probes with microstrip and CPW configurations suffer from common mode response and the probe fails to detect the minimum magnetic field in the frequency band of 100 MHz-1GHz.

The shielded probe suppresses the voltage due to the electric field. Rejection of the electric field in the shielded probe has also reduced the common mode response. It is observed that, for a single turn loop,it is not necessary to use the shielding for frequencies below 100 MHz, as they are not susceptible to electric field response.

The introductions of the shielded probe could resolve this problem up to some extent and increase the operating frequency range of the probe. Even with the shielded probe, the total length of the probe (loop + transmission line) plays an important role in the measured results.

As the size of the probe decreases, the sensitivity of the probe reduces, which requires the receiver with high sensitivity or the use of the amplifier in the measurement. The frequency operation of the probe then depends on the characteristics of the amplifier.

For a loop with 800µmx 800 µm dimensions, all the frequencies below 1GHz require the use of an amplifier. With an external amplifier connected to the probe, the sensitivity of the probe is increased and the profile of the magnetic field is detected correctly. But the active probe introduces more errors in the measurement, depending on the characteristics of the amplifier and the position of placement of amplifier. It may be not required to use an active probe to increase the sensitivity of the probe, as it introduces other problems and causes a spurious error in the measurement.

Source reconstruction methods for the prediction of EMC 4.1 Introduction

It is required to predict the far field radiated from PCBs for the prediction of electromagnetic interference. The prediction of far field needs to have the knowledge of the radiating sources. The electromagnetic inverse problem can be defined as the reconstruction of the electromagnetic source from its radiated field. This source distribution can be used to calculate the far field which is more cost efficient than the direct far field measurement, which requires a large anechoic chamber.

This chapter deals with the methods for reconstruction of the sources from the near field scan data.

Two methods based on the inverse transmission line matrix and 2D cross-correlation method is presented in the following sections.

EM source reconstruction using inverse-TLM method

Time reversal-an overview

A device that produces an outgoing wave, equal to the time symmetric of an incoming wave is defined as a time reversal mirror. It is an array of transceivers and dedicated electronics. The time dependence of an electric field is recorded on each transceiver in the first step. Each transceiver plays back the signal in reverse order during the second step. In the case of a tile symmetric propagation medium, the wave propagates back and finally focuses on the initial source location.

The time reversal mirror is experimentally realized by D. Cassereau and M.Fink in their laboratory for the 3 D time reversal of ultrasonic fields [1][2]. A theoretical model for time reversal cavities to optimize homogeneous and inhomogeneous media is described. It used impulse diffraction theory to obtain the impulse response of the cavity in any inhomogeneous medium. After that TRM has been developed for acoustic applications such as sound focusing, ultrasonic non-destructive testing, ultrasonic hyperthermia for medical therapy and seismology [2][3]. The acoustic wave equation in a non-dissipative heterogeneous medium is invariant under a time reversal operation. Indeed, it only contains a second-order time-derivative operator. Therefore, for every burst of sound ϕ(r, t)

diverging from a source-and possibly reflected, refracted or scattered by any heterogeneous mediathere exists in theory a set of waves ϕ(r,-t) that precisely retraces all of these complex paths and converges in synchrony, at the original source, as if time was going backwards. This is the basic idea behind the time reversal in acoustics. It requires both the time-reversal invariant and spatial reciprocity to reconstruct the time-reversed wave in a whole volume. In acoustics, a closed time-reversal mirror (TRM) consists of a two-dimensional piezoelectric transducer array that samples the wavefield over a closed surface as shown inFigure 4-1 [4]. An array pitch of the order of λ/2, where λ is the smallest wavelength of the pressure field needed to ensure the recording of all the information on the wavefield. Electronic circuitry connected to each transducer consists of a receiving amplifier, an A/D converter, a storage memory and a programmable transmitter able to synthesize a time-reversed version of the stored signal. The time reversal technique is applied more recently in electromagnetics [5][6].

The first experimental demonstration on time reversal focusing of electromagnetic waves is done by G. Lerosey et.al [7]. Theory of monochromatic time reversal for electromagnetic waves was developed by [8]. Figure 4-2 shows the simplified sketch of time reversal with dipolar sources. The applications of time reversal mirrors include radio communications, terahertz imaging and medical imaging [9][10] [11]. The decomposition of time reversal mirrors (DORT) method is used to detect the scatterers in the electromagnetic field [12]. The converging wave is followed by a diverging one [7].

A numerical synthesis technique based on inverse transmission line matrix was first proposed by [13]to reconstruct the scattering sources. Later it is used in the synthesis of microwave filters and antennas and deals with the problem of resolution [14]

Transmission line matrix (TLM) method

The transmission line method is an approach to the simulation of wave motion and other physical phenomenon. It is a physical model with an exact computer solution. It is a modelling process rather than a numerical method for solving differential or integral equations. TLM method sets up a spatial

𝑉 𝑟 = 𝑆𝑉 𝑖 4-1
Where S is a 12x12 matrix with elements 𝑆 𝑚𝑛 in the m th row and n th column.

Figure 4-3 TLM symmetrical condensed node (SCN)

For a condensed node without stub, the scattering matrix is given as follows

𝑆 = [ 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 -1 0 0 0 0 -1 0 1 0 1 0 0 0 -1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 -1 0 1 0 -1 0 0 0 -1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 -1 0 0 -1 0 1 0 0 0 -1 -1 0 1 0 -1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 1 1 0 1 0 ] 4-2
In order to excite the separate components of E and H, a possible set of incident pulses are given by the following equations. The output E and H fields are calculated as follows,

𝑉 1 𝑖 = (𝑢𝐸 𝑥 + 𝑤𝑍 0 𝐻 𝑧 ) 2 ⁄ 4-3 𝑉 2 𝑖 = (𝑢𝐸 𝑥 -𝑣𝑍 0 𝐻 𝑦 ) 2 ⁄ 4-4 𝑉 3 𝑖 = (𝑣𝐸 𝑦 -𝑤𝑍 0 𝐻 𝑧 ) 2 ⁄ 4-
The pulses at port 1, 2, 9 and 12 contribute to Ex field. The pulses at port 3, 4, 8, and 11 contribute to Ey field. And the pulses contributing to Ez field are at ports 5, 6, 7 and 10. Similarly, the Hx field is contributed by pulses at ports 4, 5, 7 and 8. Hy is contributed by pulses at ports 2, 6,9,10 and Hz is due to the pulses at ports 1, 3, 11, 12.

Inverse TLM method

The 1-D scalar wave equations aregiven by

∇ 2 - 1 𝑐 2 𝜕 2 𝜕𝑡 2 𝛹(𝑟 ̅, 𝑟 0 ̅̅̅̅, 𝑡) = 0 4-22
Theory of wave propagation TR is based on the invariance property of the scalar wave equation 4-22 under TR transformation, in a lossless space. Where, 𝛹(𝑟 ̅, 𝑟 0 ̅̅̅̅, 𝑡) is the scalar radiated field, r is the distance-vector between the source and the observation point, 𝑟 0 is the source position, t is the time and c is the speed of light. This is a differential equation, containing only a second order derivative with respect to time. Therefore, if 𝛹(𝑟 ̅, 𝑟 0 ̅̅̅̅, 𝑡) is a solution of this equation, then 𝛹(𝑟 ̅, 𝑟 0 ̅̅̅̅, -𝑡) is also a solution [23], [24]. It can be said in other words that, scalar wave equation remains invariant under TR transformation in a non-absorbing medium.

Maxwell's equations are also symmetrical under time reversal. Where 𝐺(𝑟 ̅, 𝑟 0 ̅̅̅̅, 𝑡) is the greens function, 𝑓(𝑡) initial time domain excitation, * is the convolution operator in time domain. So, changes in the initial condition generates the dual solution 𝛹(𝑟 ̅, 𝑟 0 ̅̅̅̅, -𝑡).

The impulse scattering matrix of the two-dimensional TLM shunt node which relates the reflected voltage impulses at the time (k + 1)At to the incident voltage impulses at the previous time step kAt is identical to its inverse. So we can write

[ 𝑉 1 𝑉 2 𝑉 3 𝑉 4 ] 𝑘+1 𝑟 = 1 2 [ -1 1 1 1 1 -1 1 1 1 1 1 1 -1 1 1 -1 ] [ 𝑉 1 𝑉 2 𝑉 3 𝑉 4 ] 𝑘 𝑖

4-24

The scattering matrix is equal to its inverse

𝑆 -1 = 𝑆 4-25
Where

𝑆 = 1 2 [ -1 1 1 1 1 -1 1 1 1 1 1 1 -1 1 1 -1 ] 4-26
This property of the scattering matrix implies that the TLM process can be reversed without any change in the scattering algorithm. Practically speaking, if a TLM network has been excited by a single voltage impulse at time t = 0, and if after k computational steps the impulses on all branches of the mesh have been computed and stored, one can return to the initial state at t = 0 by reversing the direction of all impulses at t = k and iterating k-times. By virtue of the unique property of the scattering matrix, this reverse simulation is identical to a forward simulation in which the initial excitation has been obtained by re-injecting the result of a previous simulation. So, one can reconstruct a source distribution from a field distribution by reversing the TLM process in time. This is true for three dimensional distributed and condensed node algorithms. Thus, an EM radiation process can be theoretically time-reversed without any change. The unique difference is that the initial conditions change. The reconstruction of the source is affected only by the round-off error which is typically less than 10 -5 for several thousand computation steps in single precision [13]. They have reconstructed the induced sources from the scattered field using inverse TLM method. Figure 4-5 shows two identical sections of parallel plate waveguide which are terminated with absorbing boundaries at its ends.

The upper one is empty and the lower one contains a thin perfectly conducting septum. Figure 456shows different steps in the reconstruction process from the scattered field. A Gaussian pulse is used as the excitation signal. This procedure differs from the previous one in that the forward response is not simply reversed at all nodes in the network, but it has first picked up the response at a limited number of output points, and then re-injected after subtracting the incident filed. The resolution of reconstruction was directly proportional to the mesh parameter Δl.

(d)-(e) the perspective, side and front views

of the maximum field after re-injection [13] Another synthesis procedure for conducting scatterers is proposed by [27]. They have also demonstrated the source reconstruction in a simple discontinuity inside a parallel plate waveguide as shown in Figure 4-7, which consists of a thin conducting obstacle at the center. Their synthesis method consists of the following stages (1) a time sampled Gaussian pulse is injected into the empty waveguide and the incident pulses on both the absorbing boundaries are stored using forward analysis; (2) the same pulses are stored with the discontinuity in place using forward analysis; (3) as a final step, both the impulse responses are subtracted from each other yielding a particular solution and this output function is then time reversed and applied to both ends of the waveguide. The number of computational steps in all stages was kept the same. The different aspects of the contour of the obstacle were determined from different field components. The highest value of the normal electric field occurs at the surface of the obstacle. The position of the sharp edges of the scatterer was determined from the longitudinal magnetic field components. The shape of the reconstructed obstacle extracted from the Poynting vector distribution [27].

A.Ungureanu has used the Time reversed TLM method to reconstruct the unknown source reconstruction from the far field radiation [18]. An additional resolution improvement step is performed in order to overcome the spatial resolution limit of half wavelength. In order to validate the source reconstruction using inverse TLM algorithm, the developed method is applied to ideal sources with different polarization. The sources are considered to be above a ground plane as the real PCB will have a large ground plane.

Ey polarization

Excitation by an electric field corresponds to a voltage source. A distributed voltage source Vy is excited at the center of the XZ plane. The metallic ground is provided at 1. It has a positive and negative maximum along the x-axis with the same magnitude. Along z-axis, the field has only one peak, and there are no alternating maxima and minima.

Ez polarization

Similarly, a voltage source is excited with z polarization as in Figure 4-16. The length of the source is 2mm, which is same as before. Now, we can conclude that for a tangential voltage source, the distribution of the normal component can be used to determine the orientation of the source. If the source is oriented along the xdirection, the normal component of E field will have alternating maximum and minimum along the axis and if the source is oriented along the z-axis, the alternating maxima and minima of the normal electric field component are found along the z-axis.

Current source Jy

A circulating magnetic field produces a current at the center and vice versa. A current source Jy is excited at the center of the TLM mesh as shown in Figure 4-18. The length of the current source is 3mm and is oriented along the y-direction. The current source is simulated using the direct TLM method. The E and H fields at 1mm above the current source are recorded in the XZ plane. These fields are time reversed and inverse propagated towards the direction of the source. The number of time steps in both the forward and reverse computation is kept the same. As it is a vertical current source, the tangential component of the magnetic field will give the information about the current source. The reconstructed tangential magnetic fields Hx and Hz are plotted at 2.5mm above the ground plane (shown in Figure 45678910111213141516171819). We can see that the Hx component alternates along the xdirection and the Hz component alternates along the z-direction, forming a circulating magnetic field. From this, we can determine the current source is a vertical current Jy and is at the center of the alternating magnetic field Hx and Hz. The time reversal mirror is located at 1 mm above the current source. The electric and magnetic fields recorded at 1mm are applied in the TRM.We know that the plane at which the source is reconstructed is tangential to the source. As the source is a tangential current source, the circulating magnetic field cannot be found in the tangential plane. The maximum amplitude of magnetic field is found for the reconstructed normal component of the magnetic field Hy, at the plane containing the source. The reconstructed normal component of the magnetic field is shown in Figure 4-21. From the cross-sectional view through the X and Z axis along the dotted lines (Figure 4-21 (b)), it is clear that the magnetic field has a positive and negative maximum along the x-axis. This implies that there is an alternating magnetic field along the x-direction, which in turn indicates the current along the z-direction. These results show that the normal component of the current can be identified from the two tangential magnetic field components and the tangential current can be identified from the normal component of magnetic field depending on the direction in which the magnetic field alternates. For a current along the x-direction, the normal component alternates along z-direction and vice versa.

Effect of near field scanning height on source reconstruction

In order to investigate the effect of the height between the source and the near field scanning plane, the simple example of the voltage source Vy, which is discussed before is considered here. The electromagnetic fields are recorded at different heights (d=1mm, 2mm, 3mm, 4mm) using the forward simulation. The source is reconstructed by using data from each height separately using the inverse propagation. The reconstructed E field at the plane containing the source is plotted in Figure 4-24 (a)-(d). The original field distribution at the position of the source, which obtained with the forward simulation, is compared with the reconstructed field at the same position. It is obviously seen from the figures that the width of the reconstructed pulse has increased when the height d increased from 1mm-4mm. Also, the increase in width of the reconstructed field is proportional to the height d.

Spatial resolution

The spatial resolution is the distance between two sources that can be reconstructed by the inverse method. Two voltage sourcesEy, separated by a distance 's' as shown in Figure 4-25 are simulated using forward using propagation. Inverse propagations are made using the fields recorded at 1mm above the source for each value of 's' in the forward propagation. The time steps in both the forward and inverse propagations are the same for all cases. normalized with respect to its maximum value in order for the comparison. When the separation between the sources is 2u which is equal to 2cm, the reconstructed E field is not able to distinguish between the two sources. It is seen that there only one peak, which is in the middle of the two sources, this indicates that the source is a single voltage located source at the middle of the two sources. When the distance between them has increased to 3cm (3u), the two peaks are found in the reconstructed field at the same position of the source. When the distance between the sources is increased, the sources are reconstructed more accurately. The factor which limits the resolution of the reconstruction is the mesh parameter (u and v in this example).

In order to reconstruct the sources more accurately, the mesh parameter has to be reduced, that means the number of spatial sampling points in the near field recording has to be increased. that there is a one to one correspondence between the two [28].

EMC measurements are carried out in the frequency domain.The near field scan (NFS) data contains the magnitude and phase of the magnetic field components at different frequencies. As the inverse transmission line matrix method is based on time reversal of electromagnetic waves it is not possible to apply the scanned data directly on its mesh. The discrete Fourier transform (DFT) of the time domain signal gives the corresponding frequency domain signal, and it is applicable in the case of TLM method as well [28], [29]. As per the properties of the Fourier transform, a delayed signal

4-29

Where, the bar over H denotes complex conjugation.

For example, consider the following 2-D cross-correlation:

𝑋 = 1 1 1 1 1 1 𝐻 = 1 4 2 5 3 6
The cross-correlation between X and H gives the matric C as follows with all other terms in the double sum equal to zero.

Formulation of the equations

The cross-correlation of the measured magnetic field with a magnetic field produced by a known current element will give the presence of that current element in the measured magnetic field. So, in equation 4-29 the function X can be referred to as the measured magnetic field and the function H can be referred to as a standard function.

As per equivalence theorem, any source of current can be determined from its tangential magnetic field components [30].

𝐽 = 𝑛 ̂× 𝐻 4- 30
Where, H is the tangential magnetic field.

Then, the equation 4-29 can be modified as

C(k, l) = ∑ ∑ 𝑋 𝑝𝑡 (𝑚, 𝑛)𝐻 ̅ 𝑝𝑡 (𝑚 -𝑘, 𝑛 -𝑙) N-1 n 𝑀-1 𝑚=0

4-31

Xpt is the tangential magnetic field radiated from the DUT. 𝐻 ̅ 𝑝𝑡 is the complex conjugate of the standard function.

In a 3-D space, a current element has two tangential magnetic field components as the magnetic monopoles don't exist. The above equation can then be written as,

C(k, l) = ∑ ∑ 𝑋 𝑝𝑡1 (𝑚, 𝑛)𝐻 ̅ 𝑝𝑡1 (𝑚 -𝑘, 𝑛 -𝑙) N-1 n 𝑀-1 𝑚=0 × ∑ ∑ 𝑋 𝑝𝑡2 (𝑚, 𝑛)𝐻 ̅ 𝑝𝑡2 (𝑚 -𝑘, 𝑛 -𝑙) N-1 n 𝑀-1 𝑚=0 4- 32
Where,𝐻 ̅ 𝑝𝑡1 and𝐻 ̅ 𝑝𝑡2 is the standard function for the two tangential magnetic field components. It is the complex conjugate of the tangential magnetic field calculated using 4-29. The suffix p indicates the orientation of the dipole (x y or z). The parameters t1 and t2stands for two tangential magnetic field components for each configuration of dipole. So, for a dipole oriented along z axis, the suffix As the current is oriented along the z-axis, the above equation can be written in spherical coordinates as

𝐴 𝑝 ⃗⃗⃗⃗⃗⃗ = (𝑟̂ 𝑐𝑜𝑠(𝜃) -𝜃 ̂𝑠𝑖𝑛(θ)) 𝜇 0 𝑑 4𝜋𝑟 𝐼𝑒 -𝑗𝑘𝑟 4-34
Magnetic field is then calculated by applying the curl of the vector potential

𝐻 = 𝛻 × 𝐴 𝑝 ⃗⃗⃗⃗ 𝜇 0 = (𝜇 0 𝑟 2 𝑠𝑖𝑛 𝜃) -1 𝑑𝑒𝑡 | | 𝑟̂𝜃 ̂𝜑 ∂ 𝜕𝑟 𝜕 𝜕𝜃 𝜕 𝜕𝜑 𝐴 𝑟 𝐴 𝜃 𝐴 𝜑 | | 4-35 𝐻 ⃗ ⃗ = 𝑗(𝑘𝐼𝑑𝜂 0 /4π𝑟) 𝑒 -𝑗𝑘𝑟 [1 + 1 𝑗𝑘𝑟 ] sin θ 4-36
The E field is then obtained by applying Faraday's law

𝐸 ⃗ = 𝑗(𝑘𝐼𝑑𝜂 0 /4π𝑟) 𝑒 -𝑗𝑘𝑟 {𝑟̂[ 1 𝑗𝑘𝑟 + 1 (𝑗𝑘𝑟) 2 ] 2 cos 𝜃 + 𝜃 ̂[1 + 1 𝑗𝑘𝑟 + 1 (𝑗𝑘𝑟) 2 ] sin θ}

4-37

The standard function in rectangular coordinates can be calculated by applying spherical to Cartesian conversion. The standard function at this same plan is then calculated using the equation 4-36. The standard function used here is only one dimensional (1-D) that is the magnetic fields are calculated either along the x-direction or along the y-direction depending on the current source to be found. The position of the source used for the standard function is shown in Figure 4-42. The source is assumed to be at (5,5). The window size of the standard function is chosen as 9mm along each direction.

The fields at 14mm due to the current element are plotted in Figure 4-43 for all the three orientations, i.e., for a current source along x-direction (Jx), a current source along y-direction (Jy) and a current source along z-direction (Jz). The developed algorithm is able to identify and localize the elementary current sources. As the method uses scalar multiplication, the phase of the detected current may not be the same as the original current. But the polarization and the position of the elementary current sources are found accurately. In order to validate the feasibility of thee developed source reconstruction method, a bend in a monopole on an air substrate is taken as a PCB and is simulated using CST microwave studio. The structure is excited by 1 V through a coaxial cable below the PCB (Figure 4 To validate the procedure, the current source above a ground, discussed before is again considered here to be the device under test. The equivalent source is calculated by using the 2D crosscorrelation method.

Two Current source

Conclusions

The inverse TLM method can be used to reconstruct the fields at any plane above the source and below the near field scanning plane. In the case of the known distribution of sources, this method can be used to identify the sources. In the case of the voltage sources, the source can be found from the maximum value of tee the normal component of the electric field. Ann alternating normal component of electric field is found only for a tangential voltage source. The orientation of the The inverse TLM method can be used to reconstruct the fields at any plane above the source and below the near field scanning plane. With this method, the equivalent current could only be found accurately for a vertical current source in an arbitrary PCB, where there is no knowledge about the sources. The newly developed cross-correlation method could overcome this limitation of the inverse propagation method. The cross-correlation method is applied directly to the near field scan data. The method is not applied to the inverse propagated fields because the electric and magnetic fields become wider than the original filed after inverse propagation. The spatial resolution of the reconstruction depends on the mesh size and the wavelength. So, when a number of spatial points in the near field scan data increases, the more accurately we reconstruct the sources. This illustrates the need of having a probe with high spatial resolution.

The developed cross-correlation method is validated for ideal current sources. It is found that the procedure could accurately determine the position and orientation of the source. The method is also validated for multiple current sources. The window size of the standard function is optimized to a one-dimensional window of size 9mm. The accuracy of the equivalent source decreases when the window size of the standard function increases.

The final objective of the developed source reconstruction methods is to apply to real PCBs. In order to validate the procedure experimentally, we have designed few demonstrators. Two of them are shown in Figure 5-2. The demonstrator in Figure 5-2 (a) is a loop above a metallic ground plane and is fed by a coaxial cable at one end and terminated by 50 Ohm impedance at the other end. The 2D cross-correlation will not be able to distinguish between the positive and negative currents. So, the equivalent current source for this PCB may appear as two vertical dipoles with same phase (Jz) as one horizontal dipole. As the phases of the sources are the same, the current due to the vertical dipoles (+Jz and -Jz) will not be able to cancel in the calculation of the far field, which will lead to some errors in the predicted radiated field.

B. Grounded CPW transmission line

The effective dielectric constant and characteristic impedance for the conductor-backed CPW is calculated as follows, for zero strip thickness (t=0) For a finite strip thickness t, the characteristic impedance is calculated as follows [5]

𝜀

Résumé

Au fur et à mesure que le nombre de composants augmente, il existe une forte demande pour identifier les sources de rayonnement pour la prédiction de la compatibilité électromagnétique des

Figure 1 - 9

 19 Figure 1-9 Setup of Faraday cage measurement for conducted emissions[4]

Figure 2 - 1 [ 1 ]

 211 Figure2-1[1]. In the first configuration, the measurements done with a single probe controlled by a precise positioning system. The second one uses a planar array of probes terminated with 50 Ohm impedance. With this probe array, the DUT can be scanned in a single measurement or in a few numbers of measurements depending on the area of the DUT and the probe array. In this setup, the presence of a large number of probes induces first order disturbances to the measured field. The former one, which uses single probe is the widely used method for near field scanning[2][3].

Figure 2 - 1

 21 Figure 2-1 Probe setup in near field measurement[1]

Figure 2 - 2 Figure 2 - 3 A

 2223 Figure 2-2 Schematic layout of active electro-optical dipole antenna[6]

Figure 2 -

 2 Figure 2-2 is presented in [6]. The probe consists of a loop antenna element doubly loaded with LiNbO EO crystals. One of the LiNbO has two domains where -axes (optical axes) in each domain are directly opposite to each other. Using optical technology, the probe can work as a conventional double-loaded loop probe without metallic cables and electrical hybrid junctions. An electro-optical probe which uses an electro-optical crystal (shown in Figure 2-3) is available commercially from

Figure 2 - 4

 24 Figure 2-4 Model for dipole receiving probe[10][11]

Figure 2 - 5

 25 Figure 2-5 Waveguide probe[13]

Figure 2 -Figure 2 - 8

 228 Figure 2-8 Magnetic probes fabricated on different technologies (a) coaxial probe with elliptical

Figure 2 - 9

 29 Figure 2-9 Different printed circuit probes: (a) loop with a tapered CPW transmission line[23]

Figure 2 -Figure 2 -

 22 Figure 2-10 Different ways of modelling emissions from near field measurement[1]

Figure 2 -

 2 Figure 2-11 Equivalent source reconstruction problem (a) measurement schematic (b) the equivalent current source domain is the whole surface of the original PCB and it is solved by matching the measured tangential magnetic fields over two planes S1 and S2.[START_REF] Li | Source reconstruction method-based radiated emission characterization for PCBs[END_REF]

Figure 3 - 1

 31 Figure 3-1 Parameters of the probe

Figure 3 - 2 .

 32 The probe is connected to the spectrum analyzer through the arm of the robot, which is mounted on a 5 axis robot at the same time. The 5 axis robot is shown in the photograph of the near field test bench in Figure3-3. A computer monitors the probe displacement over the device under test and acquires data provided by the spectrum analyzer. The maximum scanning area is of size 200cm (x) x 100cm (y) x 60cm (z) with a mechanical resolution of 10µm in the three directions (x, y and z) and 0.009° for two rotations. To ensure high resolution the probe must be close to the surface of the device under test due to the coupling with evanescent waves.

Figure 3 -Figure 3 - 4

 334 Figure 3-3Near field test bench

Figure 3 -

 3 Figure 3-5The tangential component of magnetic field (Hy) at 10 MHz

Figure 3 -Figure 3 -

 33 Figure 3-6The normal component of magnetic field (Hz) at 10MHz

Figure 3 -shielded magnetic probes 3 . 5

 335 Figure 3-7Schematic of a probe

Figure 3 - 8 4 3. 5 . 1

 38451 Figure 3-8 Structure and geometrical dimensions of the probeMP-1: l=3mm, w=3mm, g=0.2mm, h=0.8mm, ε r =4.4

3. 5 . 3 2 (b) MP- 3 Figure 3 -MP- 2 :

 532332 Figure 3-11 Structure of the probes (a) single layer double loop probe: MP-2 (b) single layer single loop probe: MP-3 l=3mm, w=3mm, g=0.2mm, h=0.8mm, εr=4.4

Figure 3 -

 3 Figure 3-13Effect of transmission lines of the probes MP-4 and MP-5

  3.5.5 Characterization of microstrip probesThe probe MP4 is characterized in the frequency range of 30 KHz-1GHz. The measured tangential magnetic field Hy of the probe is plotted in Figure3-15 by applying the antenna factor.

Figure 3 -

 3 Figure 3-15 Measured tangential field components of the microstrip probe at different frequencies

Figure 3 -

 3 Figure 3-16 Cross section of a CPW transmission line

Figure 3 -

 3 Figure 3-18 Air bridge connection between the grounds

Figure 3 -

 3 22 shows the fabricated prototype of the CPW probe and GCPW probe.

Figure 3 -

 3 Figure 3-21 Structure of the coplanar probes-simulated view (a) conventional CPW probe (b)

Figure 3 -

 3 Figure 3-22 Fabricated probes with CPW and GCPW transmission lines

Figure 3 -

 3 Figure 3-23 Measured tangential magnetic field components of the CPW and GCPW probes at different frequencies

Figure 3 -

 3 Figure 3-24 Schematic of the loop above the reference circuit

Figure 3 - 16 L

 316 Figure 3-28 (a) EM field reception; (b) simplified equivalent circuit model of the receiving loop

Figure 3 -

 3 Figure 3-29 Equivalent circuit representation of the shielded magnetic probe (a) shielded probe above the microstrip trace (b) equivalent circuit (c) alternative representation

Figure 3 -

 3 29 (a) shows the simulated view of the probe above the reference circuit.

Figure 3 -

 3 29 (b) shows the equivalent circuit representation of this configuration. 𝑅 𝑠 is the source impedance. 𝑅 𝐿 is the load impedance connected to the microstrip line.

Figure 3 -

 3 Figure 3-30 Photograph of the fabricated probe SP1-A

Figure 3 -

 3  Gain curve of the amplifier ZPUL-30[12]

Figure 3 -Figure 3 -

 33 Figure 3-32 Measured and simulated Antenna factor of the probe SP1

Figure 3 -

 3 34 by applying the simulated antenna factor. The detected profile of the tangential magnetic field is in good agreement with the theoretical fields of the microstrip in all the frequencies from 10 MHz to 3 GHz. The simulated fields below 10 MHz are not plotted because the antenna facto below 1 MHz is very high and the probe is expected to have very less sensitivity.

Figure 3 -

 3 Figure 3-34 Simulated tangential magnetic field of probe SP1 at 1.7mm

Figure 3 -

 3 Figure 3-36 Measured tangential field received by the probe at different frequencies without any amplifier

- 31 is

 31 connected immediately at the terminals of the probe as shown in Figure3-37.The near field scanning is again performed at the same height (at d=1.7mm).

Figure 3 -

 3 Figure 3-37Near field scanning setup with an external amplifier.

Figure 3 -

 3 Figure 3-38 Measured tangential component of magnetic field (Hy) with amplifier

Figure 3 - 40 (Figure 3 -Figure 3 -

 34033 Figure 3-39 Alternate near field scanning system

3. 9 . 1

 91 Design and characterization 3.9.1.1 Structure of the probe The 3 axis printed circuit probe consists of 3 rectangular loops oriented in 3 different directions X, Y and Z. Every single loop is designed to measure one component of magnetic field.Figure 3-42 shows the fabricated 3-axis probe along with the 3D view. The 3-axis printed circuit probe consists of 3 loops oriented in 3 different directions X, Y and Z. The loop oriented in the y-direction measures the x component of the magnetic field and the loop oriented along the x-direction measures the y component of magnetic field. The loop in the XY plane measures the normal component of magnetic field.

Figure 3 -

 3 Figure 3-42Structure of the 3 axis probe, l = w = z1= 3.2 mm

23 Figure 3 -Figure 3 -

 2333 Figure 3-43 Calibration setup with TEM cell

  -45. During the near field scan, the z-axis is normal to the scanned plane. Measurements were done at different heights and frequencies. The scanning is done along the y-axis with a step width of 1 mm. The computed theoretical field values are compared with the measured ones at 13 MHz and 400 MHz and they are presented in Figure 3-46 and Figure 3-47 respectively. The normal and tangential component of the magnetic field is plotted atd= 0.5mm and 2.5mm, where d is the distance from the top of the cylindrical conductor to the bottom side of the probe when placed as shown in Figure 3-45.

Figure 3 -Figure 3 -Figure 3 -Figure 3 -

 3333 Figure 3-45 Configuration of near field scanning

Figure 3 -Figure 3 -

 33 Figure 3-48 Graph showing the relation between the size of the probe and the sensitivity at various frequencies

Figure 3 -Figure 3 -

 33 Figure 3-50 Measured gain and reflection coefficient of the amplifier

Figure 3 -

 3 Figure 3-52 at different frequencies. The detected profile up to 100 MHz is under the noise of the network analyzer. The 27 dB gain of the amplifier is not enough to detect the signals below 100MHz. The distorted profile at 10 MHz is completely below the noise floor of the receiver. From 100 MHz-500 MHz, even though the profile is detected, the points near minimum are close to the noise floor. But the profiles of the magnetic field from 800 MHz-1 GHz are lost. This is due to the bad input and output reflection coefficient of the amplifier from 500 MHz to 1GHz.

Figure 3 -

 3 Figure 3-52 Measured tangential magnetic field of active probe AP1-A

Figure 3 -

 3 Figure 3-53 Active probe (AP1-B) and measurement configuration

Figure 3 -

 3 Figure 3-55 Comparison of the measured s parameter of the active and passive probes at the centre of the microstrip line

Figure 4 - 1

 41 Figure 4-1 Time reversal in acoustics (a) Recording step: A closed surface is filled with transducer elements. A point-like source generates a wavefront which is distorted by heterogeneities. The distorted pressure field is recorded on the cavity elements. (b) Time-reversed or reconstruction step: The recorded signals are time-reversed and reemitted by the cavity elements. The timereversed pressure field propagates back and refocuses exactly on the initial source.[4]

Figure 4 - 2

 42 Figure 4-2 Schematic illustration of the far field time reversal by dipolar sources: (a) A source generates a wave. The electric components are recorded on a closed surface. (b) This electric field is time reversed and re-emitted by dipolar sources and the back propagated wave is generated. (c)The converging wave is followed by a diverging one[7].

  [15][16][17][18][19].

  and time discretization scheme. It substitutes the original medium by an analogous transmission line mesh in which voltage and current pulses propagate in the same way as the electromagnetic waves would propagate in the original medium.The expanded node network has been used for a variety of applications until the 1990s. It is a network of transmission lines developed by interconnecting two-dimensional series and shunt nodes. As these nodes have a time delay of half a time step, these nodes are called as expanded node network. The topology of the expanded node network and finite difference method is quite complicated. The nodes to calculate different field component are spatially separated. Due to this, the data preparation for the modelling of boundaries is difficult and liable to error, and the problem is acute in the implementation of automatic data preparation schemes. The inconvenience of an expanded node structure has led to the development of a condensed node structure by P. Saguet and E. Pic in 1982[20]. Depending on the direction of view, the first connection in the node is either shunt or series. Hence, the node is said to be an asymmetrical condensed node. Even though the effect of these asymmetries is insignificant, the boundaries viewed in one direction have slightly different properties when viewed in another direction. Although it involves quite lengthy arithmetic, the asymmetrical condensed node technique uses less resource than expanded node technique. The symmetrical condensed node (SCN) developed by P.B. Johns eliminates the disadvantages of asymmetric and lengthy arithmetic while preserving the advantages of condensed node working. He has developed the scattering matrix for the SCN with and without the stubs. The absence of stubs means that the node represents only a cubic block of Cartesian mesh. The extra inductance and capacitance cannot be added locally to the node. The node with stubs can be used in inhomogeneous problems[21][22].The symmetrical condensed node without stubs is shown in Figure4-3. The two polarizations in any direction of propagation are carried out on two pairs of non-coupling transmission lines. There are 12 transmission lines and each of them has characteristic impedance 𝑍 0 same as that of free space. Since these lines link the Cartesian mesh of nodes together, they are called as link transmission lines. The incident and reflected pulses appear on the terminals of the transmission line. The 12 incident pulses on the link transmission lines produces scattering into 12 reflected pulses. The scattering is defined by

4. 2 . 4

 24 EM source synthesis with reverse TLM method-state of the art The EM point source reconstruction using the radiated fields outside the region containing the sources has been studied in[25][26]Different phases of forwarding and backward simulation of an impulsive point sources using inverse TLM is shown in Figure4-4.

Figure 4 - 4

 44 Figure 4-4 Four phases of a forward/backward simulation involving (a) the excitation of a lossless structure by a single impulse after the first iteration, (b) the field in the structure after 20 iterations, (c) the field in the structure after 100 iterations, and (d) the reconstructed source after 100 inverse computation steps[13].

Figure 4 -Figure 4 -

 44 Figure 4-5Top views of two parallel plate waveguide sections matched at both ends. The uppersection is empty and the lower section contains a conducting septum[13]

Figure 4 -

 4 8 (a) shows the image from which the conducting septum is reconstructed.

Figure 4 -Figure 4 -

 44 Figure 4-7Parallel plate waveguide: (a) Empty waveguide yielding the homogeneous field solution.(b) Waveguide with an obstacle[27]

Figure 4 -

 4 9 shows the result of the reconstruction of two point sources. The first figure (a) is obtained after the first reconstruction process and the second figure (b) is obtained after the resolution improvement step. With the resolution improvement procedure, they have overcome the spatial resolution limit of half wavelength. They have also applied inverse TLM method to reconstruct the monopole antenna from its far field radiation pattern. The reconstructed normal magnetic field component of monopole is shown in Figure 4-10. The position and orientation of the current distribution are determined from the reconstructed field.

Figure 4 - 9 Figure 4 - 4 . 3

 49443 Figure 4-9 Reconstructed sources (a) after coarse reconstruction step (b) after resolution improvement step[18]

Figure 4 -

 4 Figure 4-11 Excitation signal used in the TLM mesh

  5mm below the source (Figure 4-12).

Figure 4 -

 4 Figure 4-12 TLM cell with an ideal voltage source Ey

Figure 4 -

 4 17 shows the reconstructed electric fields at the plane of the source.

Figure 4 -Figure 4 -

 44 Figure 4-16 TLM cell with ideal voltage source Ez

Figure 4 -Figure 4 -

 44 Figure 4-18The vertical current source in the TLM mesh, d=1mm

Figure 4 -Figure 4 -

 44 Figure 4-20 Horizontal current source Jz in the TLM mesh, d=1mm

Figure 4 -Figure 4 -

 44 Figure 4-22 Horizontal current source Jx in the TLM mesh, d=1mm

Figure 4 -

 4 Figure 4-24 Results of the reconstruction of the voltage source Vy using fields from a different height of the near field plane, d.

Figure 4 -

 4 Figure 4-25 Two voltage sources separated by a distance s

Figure 4 -

 4 Figure 4-26 (a) to (c) shows the real component of the reconstructed E fields for S=2mm, 3mm, and 4mm respectively. The reconstructed fields are compared with the original field present at the source position, which is obtained using direct propagation. The E field values at the position containing the position of the source, which is obtained after direct and inverse propagation are

Figure 4 -

 4 Figure 4-26 Reconstructed normal component of E field of two voltage source Vy with a distance of separation's' between them. (a) S=2cm (b) S=3cm (c) S=4cm

  in the time domain corresponds to a phase shifted signal frequency domain. 𝐹[𝑥(𝑡 ± 𝑡 0 )] = 𝑋(𝑗𝜔)𝑒 𝑗𝜔𝑡 0

Figure 4 -Figure 4 -

 44 Figure 4-27 (a) Sinusoidal Gaussian pulse used for superposition (b) Frequency spectrum

Figure 4 -Figure 4 -

 44 Figure 4-27shows sinusoidal Gaussian pulse used as the reference signal. The time period of this

Figure 4 -

 4 Figure 4-30 Monopole above a ground plane

Figure 4 -Figure 4 - 28 Figure 4 -Figure 4 -

 442844 Figure 4-31 Simulated magnetic fields at 2mm above the monopole

Figure 4 - 4 . 4

 444 Figure 4-37 Circulation of magnetic field in the XZ and YZ plane (a) XZ plane (b) YZ plane

]

  The C(1,1) element in the output corresponds to C(1-3,1-2) = C(-2,-1) in the defining equation, which uses zero-based indexing. The C(1,1) element is computed by shifting H two rows upward and one column to the left. Accordingly, the only product in the cross-correlation sum is X(1,1)*H(3,2) = 6. Using the defining equation, we obtain C(-2, -1) = ∑ ∑ 𝑋(𝑚, 𝑛)𝐻 ̅ (𝑚 + 2, 𝑛 + 1) 0,0)H ̅ (2,1) = 1 × 6 = 6

  pt1 and pt2 corresponds to x and y components. The individual summations terms in 4-32 are the 2-D cross correlation. The position of the equivalent source is the position at which the product of the cross correlation has a peak value.

4. 4 . 2 . 1

 421 Derivation of the standard function Consider a short current filament illustrated in Figure4-38. A current with amplitude I, angular frequency ω extends from -dl/2 to dl/2. Of course, a real current element couldn't start and stop abruptly like this, however realistic current distributions can be modeled by a superposition of current elements like this. The potential due to this current element at a point p can be expressed as[31].

Figure 4 -

 4 Figure 4-38 A current element oriented along the z axis

4. 4 . 3 Figure 4 - 41 For a current source Jy 4 . 4 . 4 . 1

 434414441 Figure 4-39 Parameters of the source in the standard function

Figure 4 -

 4 Figure 4-40 Simulated structure of the current source (Jz) from CST

Figure 4 -

 4 Figure 4-42 Position of the source used for standard function

Figure 4 -Figure 4 -Figure 4 -

 444 Figure 4-45 Calculated equivalent source

Figure 4 -Figure 4 -

 44 Figure 4-50 Two current sources separated by a distance of 3cm

4. 4 . 4 . 5

 445 Effect of the window size of the standard functionIn order to understand the influence of the window size of the standard function of the developed algorithm, the example of two current sources discussed in the previous section is made under study. At First, a 2-D window of size 9mm x 9mm as shown in Figure4-52 is taken for the standard function. It shows the normalized value of magnetic fields at 14mm above the ideal currents. In this case, the source is assumed to be at the center of the window(5, 5). The equivalent source obtained with this window is shown in Figure4-53. It is able to detect the equivalent sources correctly, in the same position as that of the original sources. The amplitude of the equivalent source is very high compared to that of Figure4-51, which is obviously due to the more number of cells taken for cross-correlation. Another important fact to be noted is that the width of the calculated equivalent source has increased..

Figure 4 -Figure 4 -Figure 4 -Figure 4 -

 4444 Figure 4-52 standard functions for a window size of 9mm x 9mm

Figure 4 -

 4 Figure4-57. The equivalent source is identified as a Jx and Jy, i.e. a current along x axis and a current along y axis. The amplitude of the reconstructed current is not the same as the original source current, but the position and orientation of the source is identified correctly. The two major peaks appear as equivalent current Jx and Jz. But there is also two small peaks found for the equivalent current Jy which don't correspond to the original source. In this case, it is required to incorporate the knowledge about the device under test in order to determine the equivalent sources correctly. The electric field radiated by this equivalent source at 1m is calculated in the next section.

Figure 4 -

 4 Figure 4-56 Simulated magnetic field at 2mm above the PCB

Figure 4 -

 4 Figure 4-58 Equivalent sources on PCBThe equivalent source represents the source distribution which gives the same far field radiated by the original source. The equivalent sources are identified as either as current Jx, Jy, Jz or the combination of these currents as in Figure4-58. Knowing the equivalent currents it is possible to calculate the fields radiated from the sources at any distance away from the source. In order to validate the reconstruct equivalent source, it is necessary to predict the radiated fields which involve the calculation of the far field radiated by the equivalent source. The radiated field is calculated from the current density using the far field integrals discussed in the following session.

Figure 4 -

 4 Figure 4-59 Coordinate system for far field calculationThe radiated far filed can be found using the far field approximations.

Figure 4 -Figure 4 -

 44 Figure 4-61 Calculated E field of the monopole at 1mThe radiated E field at 1m is plotted in Figure4-61. The E field is normalized in each plane. The maximum radiation is in the XY plane. The radiation pattern is same as that of a dipole oriented

Figure 4 -

 4 Figure 4-62 Comparison of the calculated magnetic field with the simulated magnetic field of a bent monopole

Figure 5 - 1

 51 Figure 5-1 Layout of some passive probes under fabrication (view from ADS momentum)

Figure 5 - 2

 52 Figure 5-2 Validation circuits under fabrication 3D view (a) loop above a ground plane (b) PCB with an OscillatorIn reality, the PCBs are assumed to have more current loops. In order to have an accurate equivalent model of these loops, it is necessary to represent them in terms of the magnetic dipole current. So, modifying the developed method to represent the sources in terms of magnetic dipole current can accurately predict the behavior of these demonstrators. After validating the method for the demonstrator in Figure5-2(a), we plan to apply to more complex PCBs containing oscillator circuits as shown in Figure5-2 (b).

,

  Its characteristic impedance for a zero thickness strip is determined by the following conformal mapping formulas[4] 𝑘 ′ = √1 -𝑘2

  circuits électroniques. Le balayage d'une sonde à proximité du circuit est une méthode générale d'identification des sources rayonnantes dans une PCB. La première partie de la thèse consiste à concevoir et à caractériser des sondes magnétiques à haute sensibilité et à haute résolution spatiale.Les sondes conventionnelles basées sur la ligne micro ruban et la configuration coplanaire sont étudiées. À mesure que la longueur de la ligne de transmission connectée à la sonde augmente, le bruit sur le signal de sortie augmente en raison de tensions de mode commun induites par le champ électrique. Afin de supprimer cette tension induite par le champ électrique, une sonde magnétique blindée est conçue et fabriquée à l'aide d'une technologie de circuit imprimé à faible coût (PCB). La performance de la sonde passive est validée dans la bande 1MHz -1GHz. La sonde blindée est fabriquée sur un substrat FR4 d'une épaisseur de 0,8 mm et se compose de 3 couches avec le signal dans la couche intermédiaire et les couches supérieure et inférieure dédiées aux plans de masse. La taille d'ouverture de la boucle est de 800 μm x 800 μm, avec une résolution spatiale attendue de 400 μm. La haute sensibilité de la sonde est obtenue en intégrant un amplificateur à faible bruit à la sortie de la sonde, ce qui en fait une sonde active. La performance de la sonde blindée avec différentes longueurs de lignes de transmission est faite pour étudier. Une sonde à trois axes capable de mesurer les trois composantes du champ magnétique est également conçue et validée par un balayage en champs proches au-dessus d'une structure standard plan de masse.Dans la deuxième partie, la méthode de la matrice de la ligne de transmission inverse (Inv-TLM) est utilisée, pour reconstruire la distribution source à partir des champs proches (NFS) mesurés audessus d'un plan sur la carte PCB. Même si, la résolution de la reconstruction dépend de la longueur d'onde et des paramètres du maillage, la propagation inverse augmente la largeur de l'onde reconstruite. Comme cette méthode corresponde à un problème « mal posé» et entraîne des solutions multiples, nous avons développé une nouvelle méthode basée sur la corrélation croisée bidimensionnelle, qui représente les données de balayage en champ proche sous forme de de dipôles équivalents. Avec cette nouvelle méthode, nous avions pu identifier et de localiser les sources actuelles dans le PCB et est représenté avec des sources équivalentes. La méthode est validée pour les sources avec des orientations différentes. Les données simulées des champs proches utilisant le logiciel commercial CST sont utilisées pour valider les deux méthodes. Le champ lointain prédit à partir de ces sources équivalentes est comparé aux champs simulés.

Table 1 - 1

 11

			Frequency	Speed	Accuracy	complexity
	IEC-61967-2	Radiated	150kHz-1GHz	Fast	Medium	Low
	TEM cell	emissions
	IEC-61967-3	Radiated	10 MHz-1GHz	Slow	High	High
	Surface scan	emissions
	IEC-61967-4	Conducted	150kHz-1GHz Medium	Medium	Medium
	Direct	CM and DM
	coupling	emissions
	IEC-61967-5	Conducted	150kHz-1GHz Medium	Medium	Medium
	Faraday cage	CM emissions
	IEC-61967-6	Conducted	150kHz-1GHz Medium	Medium	Low
	Magnetic	CM and DM
	probe	emissions
	EN-55022	Radiated	>30M	Medium	Low	High
	Radiation	emissions	Hz
	pattern
	EN-61000-4-	Radiated	>LUF	Medium	Medium	High
	21	emissions
	Reverberation
	chamber

Table 3 -

 3

	Name of the	Loop size	Number of	Number of	Line length	Simulated operating
	probe		layers	turns in a		frequency bandwidth
			In the loop	layer
	MP-1	3mm x 3mm	2	2	1mm	<800MHz
	MP-2	3mm x 3mm	1	2	1mm	>2GHz
	MP-3	3mm x 3mm	1	1	1mm	>2GHz
	MP-4	3mm x 3mm	2	2	6.7cm	<100MHz
	MP-5	3mm x 3mm	2	2	14cm	<100MHz

1 Comparison of different microstrip probes

List of abbreviations

Ex polarization

A voltage source with x polarization Vx is placed above the ground plane (as shown in Figure 4-14). The length of the source is 2mm. The ground plane is situated 1.5mm below the source. The electric and magnetic fields in the XZ plane at 1mm above the source are recorded using the direct TLM process and time reversed for inverse propagation. This is because we took the fields for reconstruction from the plane which is tangential to the source

For a current source Jx

The resultant matrix after cross-correlation will be of size (M+K-1) (N+L-1).

The results of the cross-correlation will have a maximum value when the analytical function matches with the simulated field.

4. Fit the results of correlation to the scanning plane of the PCB.

The size of the matrix after performing will be larger than the dimensions of the PCB. To locate the sources on the DUT, the size of the resultant matrix should be identical to that of the DUT.

As the source is assumed to be at K+1/2, L+1/2 and the size of the standard function is (K, L), the first (K-1)/2 points and last (K-1)/2 points don't represent any sources. So, this part has to be eliminated from the matrix and the resultant matrix will have (M, N) points and each point corresponds to that of the device under test.

so, the number of points in the matrix after subtraction is

Validation by application to elementary currents

In order to validate the proposed method, the algorithm is applied to 3 current sources oriented in 3 different directions. As it is a theoretical problem, the near field scanned data is simulated magnetic fields, instead of the measured magnetic field. The simulations here are carried out using the simulation software CST microwave studio. The procedure is explained in detail for a current source oriented along z-direction in the following section. And later, the results of the current sources along x and y directions after following the same procedure are given. In order to validate the algorithm for tangential currents, the same structure has simulated in CST, with the direction of the current element along the x-axis as shown in Figure 4-46. The three magnetic field components have recorded at 14mm above the structure from the centre of the coaxial connector. The magnetic fields have recorded in the same XY plane as before. The coaxial connector is excited with a current of magnitude 1A. As the current carrying conductor is oriented along the x-direction, the expected equivalent current is Jx. After applying the recorded magnetic field to the developed algorithm, the equivalent currents obtained has plotted in Figure 4-47. The voltage source is determined from the direction of alternation of the normal E field. In the case of the normal voltage source, the normal component of E will have a peak at the position of the source.

The current source is determined from the magnetic field components.

In the case of the normal current, the equivalent current can be calculated by calculating the circulation of the magnetic field. But, in the case of the tangential current sources, the circulating current is not found in the reconstructed plane, because of the fact that the plane is tangential to the current source. Even though we will be able to identify the source positions from the near field scan data and the reconstructed fields, we need an algorithm which represents the radiations from devise under test with an equivalent source. In order to calculate the equivalent current in complex PCBs, it needs to have both the tangential components of the magnetic field.

So, the equivalent current can only be found accurately for a vertical current source in an arbitrary PCB, where there is no knowledge about the sources. The newly developed cross-correlation method could overcome this limitation of the inverse propagation method. The cross-correlation method is applied directly to the near field scan data. The method is not applied to the inverse propagated fields because the electric and magnetic fields become wider than the original filed after inverse propagation. The spatial resolution of the reconstruction depends on the mesh size and the wavelength. So, when a number of spatial points in the near field scan data increases, the more accurately we reconstruct the sources.

The developed cross-correlation method is validated for ideal current sources. It is found that the procedure could accurately determine the position and orientation of the source. The method is also validated for multiple current sources. The window size of the standard function is optimized to a one-dimensional window of size 9mm. The accuracy of the equivalent source decreases when the window size of the standard function increases.

The prediction of the far field requires both the magnitude and phase of the equivalent current. Even though the source position and orientation are correctly identified, it needs to have the accurate information about the exact amplitude and phase of the source in order to calculate the radiated far field.

Conclusions and perspectives

In this thesis, we have designed and validated magnetic probes based on microstrip line, CPW line, and printed shielded probes. The single loop probe is found to have higher selectivity than multiple loop probes and hence it has the highest frequency band of operation. The transmission connected to the loop has a significant influence on the performance of the probe. The voltage at the output of the probe contains not only the voltage due to the magnetic field but also, the common mode voltages induced by the electric field. As the length of the transmission line increases, the common mode voltages increases and the highest frequency of operation of the probe decreases. The shielded magnetic probes reduce the voltage due to the electric field and increase the frequency band of operation. For the frequency range between 1MHz-1GHz, the shielded magnetic probes with the stripline configuration are found to be the better choice than the conventional probes. It is necessary to use the shielded probes for frequencies above 100 MHz. As the aperture size of the loop is 800 µm x 800 µm the sensitivity of the probe is very poor and is not able to detect the magnetic field at all positions without an amplifier. The use of an external amplifier has increased the sensitivity of the probe. With an external amplifier of 37 dB, the probe could measure the magnetic field at all frequencies from 10 MHz-1GHz. It is found that the amplifier should not be placed very close to the probe because it causes noise at the output due to the probe.

APPENDIX

Design equations of the transmission lines used in this thesis are provided below

A. CPW transmission line

Closed form expressions of effective dielectric constant and characteristic impedancefor zero strip thickness (t=0) are given below according to [1] thickness (t=0) are given below according to [1] 𝜀 The effective dielectric constant and the characteristic impedance of the CPW considering the thickness t of the strip (t>0) is calculated as follows [3].

List of publications

International conferences