Method of performing electromagnetic simulations using measured magnetic permeability and electric permittivity

Abstract

The present invention relates to techniques for determining the electromagnetic response of an electrical component made of ferromagnetic material, wherein the magnetic permeability and the electric permittivity of the ferromagnetic material are derived from VNA measurements of the complex impedance and complex capacitance by means of the complex reflection coefficients- The magnetic permeability and the electric permittivity are then used in solving Maxwell's e guations using numerical simulation technigues.

Description

[0001]METHOD FOR DETERMINING THE ELECTROMAGNETIC RESPONSE OF AT LEAST ONEELECTRIC COMPONENT OF AN ELECTRICAL CIRCUIT DESCRIPTIONFIELD OF THE INVENTIONThe present invention relates to techniques for determining the electromagneticresponse in electrical devices using numerical simulation techniques. Thedetermination of radiation in a given environment allows to know for example if requirements on interference with other devices are met and if the regulations onmaximum radiation levels are complied with. Other electromagnetic response is thecharacteristic impedance of the circuit responsive to the frequency. PRIOR ARTThere are two terms related to devices or circuits that involve the flow of current, theadjective “electrical” and the adjective “electronic”. The second is mainly used toidentify those devices or components based on the use of semiconductors. However, throughout this description we will only use the adjective electrical, understanding that this term also includes electronic components and circuits. In the past, electrical equipment was designed to fulfill its function in the best way possible with the knowledge that was available, but aspects such as the degree of radiation and its influence on other devices located in the immediate vicinity of the equipment were not taken into account. Nowadays, regulations are very restrictive and a device is required to have a minimum degree of radiation precisely to avoid a negative impact both on the health of users and to avoid interfering with the correct functioning of other devices located in the vicinity. One technique for measuring the degree of radiation consists of building the circuit on which the radiation degree is to be determined and, under pre-established conditions, measuring for example under different operating conditions. For example, different operating conditions are to modify working powers or working frequencies, since at the same power an electrical component may be emitting very different values of electromagnetic radiation. Another important parameter to determine is the characteristic impedance of the circuit as a function of frequency. Another technique of major interest is the use of numerical simulators. Numerical simulation techniques establish a model that reproduces the behavior of a component or a circuit formed by a plurality of components according to the final configuration of the device to be simulated. The model must take into account, among other parameters, the spatial distribution of the components, their configuration, and the properties of each component. In particular, in a coil it will be important the number of turns, its spatial configuration and dimensions, and, if it has a ferromagnetic core, the intrinsic values of the material used in the core. Numerical models are preferably models formulated by differential equations, so the numerical problem must also define the boundary conditions and, if the equations correspond to an initial value problem to allow the simulation of devices and systems that evolve over time, for example to simulate transitory conditions, it is also necessary to define the initial conditions of the system. Once the numerical problem has been defined, solving it with a solver makes it possible to determine the value of the variables involved in the equations at any point in the domain over which the equations have been solved. The computational domain should preferably be a spatial domain that includes within it the device to be simulated as well as the environment where the measurement is to be taken.If the conditions imposed on the boundary are conditions given at infinity, then theboundary of the domain has to be far enough away to avoid its influence on the results. In the case of determining the electromagnetic field, the equations to be solved will be Maxwell's equations, either complete or according to some kind of simplification if the model knows some restriction that allows the use of a simpler model.In either case, the equations include intrinsic parameters of the materials, amongwhich are electrical permittivity ^ and magnetic permeability ^.The parameters that appear in the equations are intrinsic properties; that is, they only depend on the material and, of course, do not depend on the shape of those parts for which it is necessary to know such properties.This aspect has been a difficult problem to solve in the prior art since themeasurement of the intrinsic properties must be made on a sample of material thatmust adopt a certain shape, so the choice of the shape must be such that it isconsidered that this shape does not modify the value of the measurement.In the case of electrical permittivity ^ and magnetic permeability ^, it has been foundthat this difficulty means that the values obtained always offer a very high degree of uncertainty. To measure either of these two parameters, according to the state of theart, the material samples are as small as possible since the shape of these samples isexpected to have no influence on the measurement and the measurement result onlydepends on the sample material. Even under these conditions, results have been published, and even the frustration of those who seek accurate values of this type of measurements, where it is observed the impossibility of establishing the intrinsic values especially when the value of the frequency to which the materials are subjected exceeds certain thresholds, values ofthese thresholds well below the usual working values in electronics. An example of thiskind of publications is “On the difficulties to determine the intrinsic material parameters for MnZn Ferrites”, Richard Fischbacker et al., 2023, InternationalSymposium on Electromagnetic Compatibility – EC Europe.The present invention overcomes these difficulties by establishing a modified simulation method which employs values of intrinsic material properties measured under specific conditions and which differ even several orders of magnitude fromthose published, but which surprisingly result in simulated values very close to thevalues measured in the laboratory on prototype circuits which correspond to the simulated circuit. DESCRIPTION OF THE INVENTIONA first aspect of the invention is a method for determining the electromagneticresponse of at least one electric component of an electrical circuit. The at least onecomponent has at least a part of ferromagnetic material.The method comprises the steps:- measuring the magnetic permeability (^^) and the electric permittivity (^^) of theferromagnetic material of the at least one electric component wherein the at least one part of ferromagnetic material under test for the measurement is a ferromagnetic piece configured with the shape and dimensions of the at least a part of ferromagnetic material of the at least one electric component of the electrical circuit;- generating in a computer system a numerical model of the at least the electriccomponent of the electric circuit, the numerical model comprising: a) the electro-magnetic equations for determining the electric and magneticfields in a predetermined domain wherein said electromagnetic equations comprise the intrinsic permeability (^) and the intrinsic permittivity (^) ofthe materials located within the domain,b) the shape of the circuit, in particular, comprising the shape of the at leastone electric component;- in any order,a) populating the numerical model with the properties of the at least oneelectric component of the circuit wherein the intrinsic permeability (^) is setto the measured magnetic permeability (^^) value and, the intrinsicpermittivity (^) is set to the measured electric permittivity (^^) value;b) imposing boundary conditions and, if the electromagnetic equationscorrespond to an initial value problem, imposing the initial conditions;- simulating in a computer system the numerical model determining the electricalfield, the magnetic field or both at least at one location of the domain. As described in the specific method of the prior art, a person skilled in the art whorequires the intrinsic value of the electrical permittivity ^ and the magneticpermeability ^ appearing in the numerical model performs a laboratory experiment inwhich these measured parameters, respectively, are desired to beindependent of the shape of the sample used in the measurements.The shape usually chosen for measuring the permittivity is that of a foil and the shapeusually chosen for measuring the permeability is that of a toroidal core.Contrary to this technical prejudice, according to the method of this first aspect of the invention, the measurement of the electrical permittivity ε^and the magneticpermeability is carried out on a sample constituted by a ferromagnetic piece havingthe same material as the component to be simulated and also having the same shape and dimensions. Under these conditions, the ferromagnetic piece is subjected tomeasurement and the measured values of the electrical permittivity ^^ and of themagnetic permeability are taken as if they were the intrinsic values of the material,^ and ^, contrary to what is taught by the state of the art. According to the preferredembodiment the experimental measurements are carried out at least at the operating frequencies of the circuit with which the simulation is to be carried out. When it is indicated that the part has the same shape and dimensions it is understood that the part has the same configuration and that it only differs in the presence ofrounding radio or not or in dimensional values according to the manufacturing errorsthemselves which will be less than 5%, and more preferably less than 4%, and more preferably less than 3%, and more preferably less than 2%, and more preferably lessthan 1%, and more preferably less than 0.5%.The next step is the generation of a numerical model in a computer system. This numerical model responds to the electrical system to be simulated where there is at least one electrical component comprising ferromagnetic material. The numerical model comprises the equations that model the behavior of the electric and magnetic fields caused by the electrical circuit where these equations incorporateas parameters the intrinsic electrical permittivity ε and the intrinsic magneticpermeability μ of the ferromagnetic material. The numerical model establishes a domain over which the equations are solved with the circuit being within the domain and therefore also the at least one electrical component with ferromagnetic material. This electrical component with ferromagnetic material, which has defined the shape and dimensions of the sample used in the measurements of the previous step, is also incorporated in the numerical model also with the same measurements and dimensions. Once included in the numerical model all those parts that are in the circuit and in the surrounding space, the values of the properties of each material, air, gas or vacuumare incorporated or populated if such parts are among the elements of the model. Inparticular, the ferromagnetic material present in the model incorporates as intrinsicproperty values the measurements on the sample from the previous step even if theydiffer from the known values as intrinsic property values of the material. These differences in value can be up to several orders of magnitude. The problem is closed by imposing the boundary conditions that establish the specific conditions of the device in operating mode and, if the equations include the time variable, the initial conditions are also imposed that allow, for example, to simulate transient periods. Finally, the simulation of the circuit behavior is carried out by solving the equationsthat provide values of the electric field, the magnetic field or both at any point in thedomain. It is understood that at least one of these values is provided, for example at apoint of interest representative of the degree of radiation of the circuit. Anotherinteresting result obtained from the solution of the numerical model is thecharacteristic impedance of the circuit. According to a specific method that can be applied to any of the previous disclosed methods, the electromagnetic equations are the Maxwell’s equations. According to this embodiment, the equations are formulated in differential form whichallows to provide values at any location in the domain and not only at locations of theboundary of predetermined control volume. Specific solving techniques suitable for this type of equations are the finite element method, finite difference techniques, finite volume techniques or spectral techniques to name a few.The resolution using these techniques can be embodiment with generic or specificsolvers that allow the incorporation of electric and non-electric components definedby their shape, interconnection and also their materials where among the parametersto be incorporated is the power supply operating conditions, for example at a certainfrequency. According to a specific method that can be applied to any of the previous disclosedmethods, the at least one electric component having at least a part of ferromagneticmaterial is a coil having a ferromagnetic core. The use of coils with a ferromagnetic core is a commonly used component in devices operating at certain frequencies. Examples of devices with ferromagnetic coils and cores are transformers, chokes, filters, or simply inductances that are part of more complex devices. According to a specific method that can be applied to any of the previous disclosedmethods, the measurement of the magnetic permeability (^^) of the ferromagnetic According to this specific embodiment, the coil used for the measurements may bedifferent from the coil of the final device being simulated. This coil is used only to carryout the measurement of the magnetic permeability ^^ of the sample piece.The measurement of the magnetic permeability ^^ according to this embodimentrequires the prior measurement of the complex impedance ^^ measured in theexcited coil at a given frequency ^. By varying the frequency ^, complex impedance ^^measurements are also obtained in the frequency range in which the measurementvalue of the magnetic permeability ^^ is to be taken. That is, the measured magneticpermeability ^^ will therefore also be a frequency-dependent function ^^(^).The real part and the imaginary part of the complex impedance ^^are used in theformulas identified above to separately determine the real and imaginary part of thecomplex magnetic permeability, ^’ and ^” respectively.The formulas depend on the number of turns of the measuring coil and its dimensional features as well as the dimensions of the sample piece.That is, magnetic permeability ^^ is a complex and frequency-dependent property.According to a specific method that can be applied to the previous disclosed method, the number of turns of the coil is less than 10 turns, more preferably between 2 and 8, more preferably between 3 and 6. In order to carry out a magnetic permeability ^^measurement, a plurality of coils witha different number of turns ^ have been used. Contrary to what is considered in thestate of the art, the most accurate measurements are not obtained with any numberof turns but with a small number of turns, the optimum number of turns ^ beingbetween 3 and 6. According to a specific more accurate method that can be applied to the previous One of the specific ways to measure the complex reflection coefficient is by means of aVNA (Vector Network Analyzer) however the measurement can be carried out with anyother specific reflection coefficient measurement circuit. The complex reflectioncoefficient, as the term indicates, is a complex variable, hence by means of the generalformula it is possible to obtain the complex impedance indirectly and such compleximpedance is frequency dependent, depending on the frequency of the sinusoidal signal used when exciting the coil winding. According to a specific method that can be applied to any of the previous disclosedmethods, the measurement of the electric permittivity (^^) of the ferromagnetic piece According to this embodiment, the ferromagnetic core also maintaining the specific shape that is subsequently used in the simulation, is used to configure a capacitor. This capacitor makes use of two electrodes of flat configuration, distanced from each other and being the piece of ferromagnetic material interposed between both electrodes. Since the ferromagnetic material is conductive, between the piece of ferromagnetic material and each of the electrodes is interposed an electrically insulating sheet to prevent the passage of electric charge between the electrode and the ferromagneticmaterial. This foil or sheet should interfere as little as possible in the measurement ofthe electrical permittivity ^^. Suitable materials are paper, cellulosic foil or plasticsheets. These foils or sheets should be thin to reduce the spacing between theelectrode and the ferromagnetic material and at the same time ensure that there is no electric charge transfer. With this configuration, a complex capacitance measurement is carried out where suitable laboratory devices are available in the state of the art to provide the measurement directly. According to a specific method that can be applied to the previous disclosed method,the complex capacitance ^(^) is determined according to a real model wherein thecapacitance ^(^) comprises the capacitance of the core ^^^^^(^) configured by twoelectrodes and the ferromagnetic piece and the capacitance of the electrical insulationmaterial ^^^^^(^) in series and, a further parasitic capacitance ^^^^^^^^^^(^) in parallelwith the previous combination is series; the ^^^^^^^^^^(^) being determined byremoving the ferromagnetic core and the electrical insulation located between two electrodes from the arrangement wherein the capacitance of the electrodes without the two removed elements is the theoretical capacitance of a capacitor using air as dielectric material. In this embodiment the parasitic capacitance is modeled since the capacitor formed to carry out the measurements does not have ideal conditions. Insulators always allowsome electric charge transfer and the core is not a perfect insulator either.In this embodiment what is done is to get to calculate the parasitic capacitance bycarrying out two separated measurements so that, once determined, it is possible toeliminate the value of the contribution of the parasitic capacitance to themeasurement of the capacitor including the number of ferromagnetic material. A first measurement is an actual measurement of the capacitor formed by the plate-shaped electrodes, the piece of ferromagnetic material configured as the core used inthe simulation and, the insulating sheets which in a preferred example are made of paper. This measurement corresponds to a capacitance which is modeled by two capacitors inparallel, a first capacitor which in turn is formed by a model of two capacitors in series,the capacitor formed by the electrodes and the core and, another capacitor whichincludes as dielectric material between the electrodes the insulating sheets, in thepreferred case of paper. In the other branch arranged in parallel the model capacitor isthe one corresponding to the parasitic capacitance and which is at this stage unknown.Hence a second measurement is carried out where now between the electrodes there is neither the piece of ferromagnetic material nor the insulating sheets. That is, a capacitor is formed where the dielectric is air with known values of electrical permittivity of the air. With this measurement the model to be used also has two capacitors in parallel, one with the capacitor using air as dielectric and the other capacitor corresponding to the parasitic capacitance. It is assumed by hypothesis that the parasitic capacitance is the same in the first model and in the second model. As in this case the capacitance of the capacitor having air as dielectric material can be calculated theoretically, the measurement of the capacitance of the model allows to calculate the parasitic capacitance.Once the parasitic capacitance is calculated by means of the second model, it is usedas known data in the first model and therefore, from the first measurement it ispossible to know the capacitance of a capacitor that has the core, the first model, sincethe capacitance of the insulating sheets are theoretically calculable from their relative electrical permittivity. Finally, from the capacitance of the core formed by the piece of ferromagnetic material, it is possible to calculate the electric permittivity of the ferromagnetic material.According to a specific method that can be applied to any of the previous disclosed response, wherein- ^(^) is the resistance,- ^^ is the predetermined characteristic impedance,- ^ is the angular velocity relative to frequency ^,- ^^^ parameter being the complex reflection coefficient measured at the output portin respect to the input port, being the two electrodes excited with a sinusoidal signal; and,- ^^^^^(^) is the capacitance to be solved in the ^(^) equation for determining theelectric permittivity (^^) as ^^ = ^(^) · ^ / ^.Once the impedance ^(^) is known by determining a measurement of the complexreflection coefficient ^^^, the above identified formula comprises the capacitance ofthe core. Then it is the only undetermined variable that can be solved. This is analternative measurement of ^^^^^(^) allowing to calculate the electric permittivity ^^by means of the equation ^^ = ^(^) · ^ / ^ where the rest of the variables are known.According to a specific method that can be applied to any of the previous disclosed methods,VNA ^-parameters are commonly used in VNA devices and are a ratio of the incident power at one port to the output / reflected power at another port. An parameter is thus defined through the ratio where ^^ is the reflected / output power at port ^ and is the incident power at port ^.In the case that the impedance of port ^ and port ^ are the same (usually 50 ohms), itcan be considered to be a ratio between the incident voltage at port ^ and thereflected / output voltage at port ^. In this case the impedance of the ports is 50 ohmswhich is usual in radio-frequency (RF) so in principle it could be considered a voltageratio also in these circumstances. However, disclosed cases use the definition ofcomplex reflection coefficient so it is not necessary to use voltages.DESCRIPTION OF THE DRAWINGS These and other features and advantages of the invention will be seen more clearly from the following detailed description of a preferred embodiment provided only by way of illustrative and non-limiting example in reference to the attached drawings.Figure 1 This figure schematically shows an embodiment of the inventionformed by a board containing a circuit and the circuit has at least one component containing both a coil and a ferromagnetic core. The circuit board is within a region delimited by a dashed linerepresenting a numerical domain in which it is desired to determine,by a numerical simulation, the radiation level caused by the circuit.Figure 2 This figure schematically shows a model of a real impedancecomprising an ideal inductance and a resistor.Figure 3 This figure schematically shows a measuring process directlymeasuring the response on a coil comprising a piece of ferromagnetic material.Figure 4A, 4B,5A, 5B,6A, 6B Figures 4A, 5A and 6A show the real part of the magneticpermeability measured on an specific piece of three different ferromagnetic materials with the shape and dimensions of an specific core according to an embodiment, the three materials are: MnZn,NiZn and a nanocrystalline. Figures 4B, 5B and 6B show the imaginary part of the same measurements.Figure 7 This figure schematically shows an experiment designed to measureelectric permittivity of a piece of ferromagnetic material.Figure 8a, 8b These two figures schematically show a first capacitor model and asecond capacitor model for calculating the electric permittivity of a piece of ferromagnetic material according to a more accurate method. Figures 9A, 9B, 9C These figures show the measurements of the relative electric permittivity of three pieces, being the material MnZn, NiZn, and nanocrystalline material.Figure 10 This figure shows the permeability (left scale) and the permittivity(right scale) used for the simulation and some results disclosed in the literature.Figure 11 This figure shows the impedance response of the core in thesimulation according to an embodiment and also the impedance response when the permittivity used in the simulation of the same circuit is according to the values disclosed in the literature.Figure 12 This figure shows the simulation results of the previous experimentwherein the permittivity has been multiplied by factor 5. When referring to nanocrystalline material, the embodiments refer specifically to VITROPERM 500F material manufactured by VACUUMSCHMELZE comprising Fe, Si, B, Nb, Cu. The nanocrystalline structure is disclosed by reference in DETAILED DESCRIPTION OF THE INVENTION As it will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a method that, according to a preferred embodiment, is at least partially implemented in a computer system.Figure 1 schematically shows an embodiment of the invention formed by a board (likea PCB or “Printed Circuit Board”) containing a circuit (Cr), typically an electronic circuit,wherein the circuit (Cr) has at least one component (1) containing both a coil (1.1) anda ferromagnetic core (1.2).In a first example, it is of interest to know the degree of radiation caused by thecircuit (Cr), either in this configuration or by including a shielding that can protect theenvironment of a device containing this circuit (Cr) from radiation. In a secondexample, it is of interest to know the characteristic impedance of the same circuit (Cr).In either case, the technique to be used will be the simulation of a numerical modelthat represents the circuit (Cr) in such a way that, numerically solving the modeldefined by the components (1) and configuration of the circuit (Cr) under realoperating conditions, it is possible to determine the degree of radiation. In particular, the resolution of Maxwell's equations allows to determine the electricand magnetic fields depending on the operating frequency of the circuit (Cr).The circuit (Cr) board is within a region delimited by a dashed line representing anumerical domain (Ω) in which it is desired to determine, by a numerical simulation,the radiation level caused by the circuit (Cr).According to another numerical experiment, the electromagnetic response is used todetermine the characteristic impedance of the circuit (Cr).If, for example, the circuit (Cr) is shielded, the physical components that give rise tothe shielding will be part of the components (1) that make up the model and will bewithin the computational domain (Ω) in which the numerical problem is solved, as willall the other components (1) of the circuit (Cr). The computational domain (Ω) is themathematical domain (Ω) where the equations for simulating the circuit (Cr) aresolved. In either case, the equations to be solved during the simulation of the numerical model that establishes the behavior of the circuit in operational mode require the propertiesof the materials, in particular the electrical permittivity ^ and magnetic permeability ^.These parameters are especially necessary in components that provide the circuit withan inductance (L) and that consist of a coil (1.1) and a core (1.2) formed by a piece (P)of ferromagnetic material.The way to introduce these two material properties (^, ^) in the numerical model isthrough the equations that must be solved in the numerical model and that establishthe physical behavior of the circuit (Cr). The properties are parameters that appear inthe equations as in Maxwell's equations.The properties that appear in the equations are the intrinsic properties (^, ^) of thematerial where these values are published in the literature and obtained mainly by means of laboratory experiments.The obtaining of these properties, according to literature, is performed on the materialin which the property is to be measured but, adopting a form and size such that it isconsidered that it will not affect the measurement, that is, the resulting measurement must only depend on the intrinsic material properties. This is especially difficult whenmeasuring both, electric permittivity (^) and permeability (^). According to literaturesamples are obtained by mechanizing thin sheets or tiny elements that are considered suitable for measuring properties that do not depend on its shape and size. Contrary to the state of the art, according to this preferred example, the measurementof both the electrical permittivity (^) and the magnetic permeability (^) of thecore (1.2) of the component (1) having a coil (1.1) and a core (1.2) are to be carried outon a physical piece (P) of ferromagnetic material, not being necessary to bemechanized, having the shape of the element to be simulated within the circuit (Cr)and also its same dimensions. Measurement of the magnetic permeability In order to estimate the value of the magnetic permeability of the ferromagneticmaterial, a piece (P) of such ferromagnetic material with the same shape anddimensions as the core (1.2) is made and placed inside a winding (W). The winding (W)is not the coil (1.1) of the component (1), but a new winding (W) for carrying out themeasurement of the magnetic permeability (^^).In this embodiment, measurements are performed with a VNA through the setup usedfor the measurement and shown schematically in Figure 3, and the circuit model (Cr) isthe one shown in Figure 2, where the coil (1.1) is modeled as a real inductancecomprising an ideal inductance (L) formed by a winding formed with a conductorhaving a resistance (R).It is important to emphasize that this equivalent model does not take into account the influence of the electric field on the measurement, which may lead to a large source of error, especially if the Maxwell equations are used in the numerical model. However, it has been found that an optimal solution to reduce this influence of the electric field on the measurement is to use a reduced number of turns in thewinding (W), preferably between 3 and 6 turns.Figure 3 shows a VNA device connected to a winding (W) around the piece (P) havingthe shape and dimensions of the core (1.2) and, the ferromagnetic material also as thecore (1.2). The shape, dimensions and properties of the ferromagnetic material are atleast part of the parameters of the numerical model under simulation that allow todetermine the radiation of the circuit (Cr) among other response measurements.Once the response measurement of the complex ^^^ parameter is carried out using theVNA, that is, the ratio between the reflected output power and the incident powersupplied by means of a sinusoidal signal at a given frequency, and taking into accountthat the value of the impedance ^^ is 50Ω, the value of the complex impedance iscalculated by means of the equation: wherein ^^ uses ^ as index since such index, along the description, indicates that thecomplex impedance is the result of a measurement. The same applies to othervariables using index ^, such index denotes that the variable is the result of ameasurement unless otherwise stated.^^ depends on the frequency ^ and can be explicitly expressed with the real andimaginary part:^^(^) = ^^(^) + ^^^(^) allowing to calculate the real part (μ’) andthe imaginary part (μ’’) of the magnetic permeability respectively: where ^ is the number of turns of the coil, ^^ and ^^ are the external and internaldiameters of the core (1.1) respectively and ℎ is the height of the core (1.1), ^ is theangular velocity relative to frequency ^, ^^is the magnetic permeability in the vacuummedium, and ^ is the ratio between the length of a circle and its diameter. Thecomplex permeability is μ(^) = where the minus sign is an adoption byconvention.According to different experiments, complex permeability ^ is extracted fromimpedance measurements with various turn numbers (^ = 1, 3, 6, 8, 12 and 18) forthree different cores having three ferromagnetic materials: MnZn, NiZn and ananocrystalline core material. Figures 4A, 5A, and 6A present the real part ^’ of theextracted for each material, while Figures 4B, 5B and 6B show the imaginary part^”. It has been proven that the behavior of the real part ^’ and of the extracted issimilar in the plurality of materials with a high value at low-frequency and a value closeto zero at higher frequencies.The best measurement values are between 3 and 6 turns of the winding (W) used forthe measurements by means of the VNA. As a result, once the real and imaginary parts have been defined, the complex functionthat establishes the value of the measured complex magnetic permeability isdefined. It is noteworthy that comparing the measured values with values established in theliterature as intrinsic values of the magnetic permeability μ, both values are differentso that a skilled person in the field would not use these values as intrinsic values of thematerial. On the contrary it is these values which are used by the method according to the invention and in particular in this embodiment. Measurement of the permittivityRelative permittivity ^^ = ^ / ^^, being ε the permittivity of the material and ^^ thepermittivity of the vacuum, is also a complex value that is represented as: wherein ^ is the frequency and where the minus sign is an adoption by convention.In this case, the method for determining the permittivity is based on an experimentbuilding a plate capacitor with the interposition of the ferromagnetic material, in thisembodiment the ferromagnetic material in the form of a piece (Cr) having the shapeand dimensions of the core (1.2) that will be under the numerical simulation.The use of a plate capacitor is used in the prior art only with dielectric thin materials, no with thick magnetic toroidal cores.A modification of the plate capacitor method is used, in which not only a piece (P) withthe shape and dimensions of the core (1.2) is incorporated, but also such piece (P)does not need to be machined to improve the fit with the plates of the electrodes.Figure 7 shows the experiment used in this embodiment formed by two walls (W1,W2) of conductive material between which is included the capacitor with which themeasurements are carried out. Each of the walls (W1, W2) has a perforation throughwhich passes an electrically insulated conductor (l). This insulation is also maintainedwith respect to the wall (W1, W2) it passes through. These walls allow shielding theinner region between the two walls (W1, W2) from various fields.On the inside, Figure 7 shows the two electrodes (2) in the form of a plate betweenwhich is interposed the piece (P) corresponding to the core (1.2) in shape anddimensions. The orientation of the piece (P) is such that its orientation with respect tothe winding axis (1.1) when the core (1.2) is forming the component (1), establishesthat said axis is perpendicular to the electrodes (2).That is, if for example the core (1.2) has a toroidal configuration with its axis ofsymmetry coincident with the axis of symmetry of the coil (1.1), then in themeasurement of the electrical permittivity the part (P) with the shape of the core (1.2)will have its axis of symmetry perpendicular to the electrodes (2). The method calculates the relative electrical permittivity ^^as a function of capacitance using the equation: where ^ is the thickness of the capacitor, ^ is the area of the electrodes (2) and ^^ isthe electrical permittivity in vacuum. The two electrodes, according to this embodiment, are made of copper. It is possiblethat current may flow through the piece of ferromagnetic material since it is not aperfect insulating material. To avoid this problem, two sheets of paper (sh) have beenincluded between the piece (P) and each of the electrodes (2) acting as electricalinsulators. Additionally, nylon screws and nuts have been used to ensure theparallelism of the electrodes (2).As shown in Figure 7, in this embodiment a VNA is used to carry out the measurementof the ratio between reflected output power and incident input power by providing the parameter ^^^where the measurement is done by connecting port 1 and 2 to eachelectrode (2) respectively. From ^^^ the following relation is used: where ^^ is the characteristic impedance (50Ω), ω is the angular velocitycorresponding to the frequency ^, ^ is the resistance and ^ is the variable to be solvedfor, the capacitance. A VNA is a readily available device on the market, however, thissame measurement of reflected power relative to the incident input power can beobtained using other types of devices or specific circuits.Figures 8A and 8B show two electrical models, the equivalent circuit of themeasurements, figure 8A showing the model having the core and the sheets (sh) ofpaper and figure 8B without the core and without the sheets (sh) of paper.Only two measurements for each magnetic toroidal core are needed to calculate its ^^according to the following steps:- A first measurement is performed with the piece (P) and the paper sheet (sh)located between the electrodes. Then, the capacitance ^ of this measurement,identified as ^^^^^^^, is calculated using former equation based on the knowledge of ^^^(^) parameter. The equivalent circuit is shown in figure 8A.- Then, the piece (P) and the paper is removed from the inner part of the capacitorand the capacitance is measured again. Then, the capacitance ^ of thismeasurement, identified as ^^^^^^, is calculated with the same equation. Now the equivalent circuit is shown in figure 8B.- The theoretical ^^^^^^ and ^^^^ capacities are calculated using the equation ^^^^ is the theoretical capacitance of the air that occupies the space of the core,the piece (P) in this stage, plus the sheets (sh) of paper. For ^^^^ calculation, ^ isthe area occupied by the piece (P) according to the projection perpendicular to theelectrodes (2), ^ is the height of the piece (P) measured in the perpendiculardirection of the electrodes (2) plus the thickness of the paper sheets, in thisexample 0.15mm, and ^^is air’s relative electric permittivity which is 1.00059. At the same time, ^^^^^^ is the equivalent capacitance of the paper sheets (sh), andits value is calculated considering the area of the core, in this case formed by the paper sheets (sh), the thickness of the paper sheets, 0.15mm, and 1.5 as therelative electrical permittivity of the paper.- The different error sources have been taken into account when applying themethod as a parallel parasitic capacitance named ^^^^. This capacitance is obtained by removing ^^^^from ^^^^^^capacitance using the next equation: Once ^^^^^^ and ^^^^ are known, then ^^^^^^ is obtained for each piece (P) of anyof the three materials being tested according to the circuit depicted in figure 8A bymeans of the following equation The relative electric permittivity of all the pieces used when measuring the magnetic permeability has been tested and shown in figures 9A, 9B and 9C. The measurements exhibit two issues. Firstly, S-parameters measured by the VNA at low frequencies are exceptionally low, resulting in a very noisy signal. Attempts have been made to mitigate this problem, including averaging and slightly increasing the output power of the VNA, but they did not lead to significant improvements. Secondly, the setupresonance appears at higher frequencies (around tens of MHz). Therefore, theequation ^^ = is no longer valid over this frequency since the setupmodel is not that of an ideal capacitor. Two assumptions were made to overcome these issues. First one was that the low- frequency noise was white Gaussian; hence, the true relative electric permittivity value is approximately the mean value of the measurements. Second assumption was that the relative electric permittivity value remains constant at high-frequency, effectively avoiding the resonance frequency problem. Following these assumptions, relative electric permittivity value curves shown in figures 9A, 9B and 9C are used to model delelectric permittivity properties of the pieces and, therefore, of the cores (1.2) duringthe simulation process. In the case of MnZn, values of several tens of thousands ofrelative permittivity are obtained in the literature. While using this method the values obtained are a few hundred.Some examples of papers disclosing high values, higher than 10^ for MnZn are:- Li, Y., & Wang, S. (2021). Modeling and increasing the high-frequency impedance ofsingle-layer mn-zn ferrite toroidal inductors with electromagnetic analysis. IEEE Transactions on Power Electronics, 36(6), 6943–6953. https: / / doi.org / 10.1109 / TPEL.2020.3039809- Kacki, M., Rylko, M. S., Hayes, J. G., & Sullivan, C. R. (2022). Measurement Methodsfor High-Frequency Characterizations of Permeability, Permittivity, and Core Loss of Mn-Zn Ferrite Cores. IEEE Transactions on Power Electronics, 37(12), 15152– 15162. https: / / doi.org / 10.1109 / TPEL.2022.3189671- Salomez, F., Videt, A., & Idir, N. (2022). Modeling and Minimization of the ParasiticCapacitances of Single-Layer Toroidal Inductors. IEEE Transactions on PowerElectronics, 37(10), 12426–12436. https: / / doi.org / 10.1109 / TPEL.2022.3177642 Finally, the measured values of both magnetic permeability and electrical permittivity,with the described assumptions, are those that have been used as intrinsic values ofthe material in the simulation of the circuit (C). As a result, it has been assessed thatthe radiation estimated by simulation and the radiation measured experimentally with a circuit comprising the element with a core formed by the part used in the experiments have resulted to be very similar while the use of the intrinsic properties from the literature give rise to simulated values that do not correspond to the measured radiation values. Specifically, figure 10 shows the real part and the imaginary part of the magnetic permeability measured according to an embodiment of measurements, that is, using a piece having the shape and dimensions of the core of an inductance of the circuit. The scale used for the complex magnetic permeability is shown at the left side of the plot. The same applies to the permittivity wherein the same piece used for measuring the magnetic permeability is the piece used for measuring the permittivity. The results arerepresented in the same plot wherein the scale of the permittivity is at the right side.In this case, the permittivity (the real part) is shown using a continuous line and, the values disclosed in the literature is represented using a dashed line. In this case it is shown that the disclosed in literature is in the range[10^, 10^] andis a positive value. In contrast, the relative electrical permittivity ^^value measuredusing the piece has a difference of up to four orders of magnitude. This so differentvalue of the permittivity would never be used by a skilled person in the prior art as the intrinsic relative permittivity value appearing in equations of a numerical model for the simulation of a circuit comprising a ferromagnetic core.Surprisingly, as shown in Figure 11, the characteristic impedance ^ of a coil comprisinga core like the one used for the measurements and the simulation of the same fits the response very accurately. The characteristic impedance shows a peak response around 1MHz. On the other hand, the simulation using the literature values almost does not predict the peak and the maximum value is predicted at a frequency one order of magnitude lower.In addition, to see the margin of the permittivity that can be used in simulation, thepermittivity used for MnZn core simulation has been multiplied by 5. That is, apermittivity value of 250 for the MnZn core simulation has been used that is too faraway from the [10^, 10^] values that are provided by the literature. As it can be seenin figure 12, applying this permittivity variation the resonance frequency shifts, and thesimulation no longer matches the measurement. Thus, it is concluded that the method according to any of the embodiments uses the permittivity value that allows the simulation of the circuit to provide reliable results according to the measurements made on the circuit.. That is, even if the correct measurement of the intrinsic properties of magnetic materials remains unsolved, the proposed method allows to provide simulations where the response matches the measurements made over thephysical circuits being simulated.

Claims

CLAIMS1.- Method for determining the electromagnetic response of at least one electriccomponent of an electrical circuit, the at least one component having at least a part offerromagnetic material, the method comprising the steps:- measuring the magnetic permeability (^^) and the electric permittivity (^^) of theferromagnetic material of the at least one electric component wherein the at leastone part of ferromagnetic material under test for the measurement is aferromagnetic piece configured with the shape and dimensions of the at least a partof ferromagnetic material of the at least one electric component of the electricalcircuit;- generating in a computer system a numerical model of the at least the electriccomponent of the electric circuit, the numerical model comprising:a) the electro-magnetic equations for determining the electric and magneticfields in a predetermined domain wherein said electromagnetic equationscomprise the intrinsic permeability (^) and the intrinsic permittivity (^) of thematerials located within the domain,b) the shape of the circuit, in particular, comprising the shape of the at leastone electric component;- in any order,c) populating the numerical model with the properties of the at least oneelectric component of the circuit wherein the intrinsic permeability (μ) is setto the measured magnetic permeability (^^) value and, the intrinsicpermittivity (^) is set to the measured electric permittivity (^^) value;d) imposing boundary conditions and, if the electromagnetic equationscorrespond to an initial value problem, imposing the initial conditions;- simulating in a computer system the numerical model determining the electricalfield, the magnetic field or both at least at one location of the domain.2.- A method according to claim 1, wherein the electromagnetic equations are theMaxwell’s equations.3.- A method according to any of the previous claims, wherein the at least one electriccomponent having at least a part of ferromagnetic material is a coil having a ferromagnetic core.4.- A method according to any of the previous claims, wherein the measurement of themagnetic permeability (^^) of the ferromagnetic piece is as follows:- placing the ferromagnetic core in a coil winding, the coil winding being theimpedance load connected to line having an input port and an output port for testing the coil winding response;- measuring the complex impedance ^^ = ^^(^) +wherein ^^ is the realpart, ^^ is the imaginary part, ^ is the imaginary unit and ^ is the frequency betweenthe input port and the output port;- determining the real (μ’) part and the complex part (μ”) of the measured magneticpermeabilitywhere ^ is the number of turns of the coil, ^^ and ^^ are the external and internaldiameters of the core respectively and ℎ is the height of the core, ω is the angularvelocity relative to frequency ^, ^^is the magnetic permeability in the vacuum medium, and ^ is the ratio between the length of a circle and its diameter.5.- A method according to the previous claim, wherein the number of turns of the coil isless than 10 turns, more preferably between 2 and 8, more preferably between 3 and 6.6.- A method according to claim 4 or claim 5, wherein the measure of the compleximpedance ^^ = ^^(^) + ^^^(^) is as follows:- measuring the complex reflection coefficient at the input port, anparameter,being the coil winding excited with a sinusoidal signal; and- determining the measured complex impedance ^^ = ^^(^) + ^^^(^) as:being the characteristic impedance of the line a predetermined value ^^.7.- A method according to any of the previous claims, wherein the measurement of theelectric permittivity (^^) of the ferromagnetic piece is as follows:- placing the ferromagnetic core between two electrodes in the form of flat plates,with the two electrodes arranged in parallel, and wherein the ferromagnetic core is electrically insulated with two sheets of electrical insulation material from the twoelectrodes;- determining the complex capacitance ^(^) of the arrangement and determining theelectric permittivity (^^) as ^^wherein ^ is the thickness of the effective capacitor, ^ is the area of the electrodesin the form of flat plates and ^0 is the electric permittivity in the vacuum medium.8.- A method according to the previous claim, wherein the complex capacitance ^(^) isdetermined according to a real model wherein the capacitance ^(^) comprises thecapacitance of the core ^^^^^(^) configured by two electrodes and the ferromagneticpiece and the capacitance of the electrical insulation material ^^^^^(^) in series and, afurther parasitic capacitance ^^^^^^^^^^(^) in parallel with the previous combination isseries; the ^^^^^^^^^^(^) being determined by removing the ferromagnetic core and theelectrical insulation located between two electrodes from the arrangement wherein thecapacitance of the electrodes without the two removed elements is the theoretical capacitance of a capacitor using air as dielectric material.9.- A method according to any of the previous claims, wherein the impedance of theelectrodes comprising the ferromagnetic core between two electrodes and the electricalinsulation is ^(^) wherein:and measured in the arrangement of the two electrodes, the two electrodes being connected to a line having an input port and an output port for testing the electrodes response, wherein- ^(^) is the resistance,- ^^ is the predetermined characteristic impedance,- ω is the angular velocity relative to frequency ^,- ^^^ parameter being the complex reflection coefficient measured at the output portin respect to the input port, being the two electrodes excited with a sinusoidal signal; and,- ^^^^^(^) is the capacitance to be solved in the ^(^) equation for determining theelectric permittivity (^^) as ^^ = ^(^) · ^ / ^.10.- A method according to any of claims 5 to 8, wherein the complex reflectioncoefficient ^^^, ^^^ or both are measured using an VNA (Vector Network Analyzer).11.- A method according to any of the previous claims, wherein the electromagneticresponse is the characteristic impedance of the circuit, the electromagnetic radiationor both.12.- A method according to any of previous claims, wherein the ferromagnetic materialis at least one of the following:- MnZn;- NiZn;- Vitroperm 500F nanocristaline;- a combination of any of them.

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