DE102021208276A1 - Procedure for modal analysis and identification of resonant circuits in an electrical network model - Google Patents

Abstract

The invention relates to a method for analyzing an electrical network model (10) for simulating the behavior of an electronic or electrical system (1) and for identifying the resonant circuit of the system (1) that is decisive for a resonance, with the following steps:
- selecting (S4) a natural mode corresponding to a resonance of the system (1) to be analyzed;
- Approximate the resonance properties according to the selected eigenmode;
- Calculating (S5) the energy stored in the components of the network model (10) acting as capacitances and inductances as a function of the resonance properties of the selected natural mode;
- Selection (S7) of the components (11, 12, 14) acting as capacitance or inductance with the/the highest stored energies;
- Determination (S8) of the relevant resonant circuit based on the selected components.

Description

technical field

The invention relates to the analysis of electrical networks resulting from electronic systems with electronic circuits. The invention also relates to the analysis of a corresponding network model for the identification of components and resonant circuits responsible for a resonance in the network model.

Technical background

The EMC behavior of an electrical or electronic system with an electronic circuit is generally determined by its geometric design, its environmental properties and the functional components used in the electronic circuit, such as resistors, capacitors and inductances. The design features of the structure of such a system can be described in terms of their interaction with the functional components by one or more parasitic components, which can specify the electrical interaction of the geometric design features with the functional components.

In the construction phase of such electronic or electrical systems, a network model is created from functional components and parasitic components and simulated in order to determine their probable behavior.

Disclosure of Invention

According to the invention, a method for analyzing a system and for identifying components of the system that cause a certain resonance are solved according to claim 1 and by the device according to the independent claim.

Further developments are specified in the dependent claims.

• - Auswählen einer Eigenmode entsprechend einer zu analysierenden Resonanz des Systems;
• - Approximieren der Resonanzeigenschaften entsprechend der ausgewählten Eigenmode;
• - Berechnen der gespeicherten Energie in den als Kapazitäten und Induktivitäten wirkenden Bauteilen des Netzwerkmodells abhängig von den Resonanzeigenschaften der ausgewählten Eigenmode;
• - Auswählen der durch eines oder mehrerer der als Kapazität oder Induktivität wirkenden Bauteile mit der/den höchsten gespeicherten Energien;
• - Ermitteln des maßgeblichen Resonanzkreises basierend auf den ausgewählten Bauteilen.

According to a first aspect, a method is provided for analyzing an electrical network model for simulating the behavior of an electronic or electrical system and for identifying the resonant circuit of the system that is decisive for a resonance, with the following steps:

• - selecting an eigenmode corresponding to a resonance of the system to be analyzed;
• - Approximate the resonance properties according to the selected eigenmode;
• - Calculation of the energy stored in the components of the network model acting as capacitances and inductances depending on the resonance properties of the selected eigenmode;
• - selecting the components with the highest stored energies by one or more of the components acting as capacitance or inductance;
• - Determine the relevant resonant circuit based on the selected components.

• - Berechnung der Verlustleistung in den als ohmsche Widerstände wirkenden Bauteilen des Netzwerkmodells abhängig von den Resonanzeigenschaften der ausgewählten Eigenmode; und
• - Auswählen der durch ein oder mehrere der als Kapazität oder Induktivität wirkenden Bauteile mit der/den höchsten gespeicherten Energien und der durch ein oder mehrere der als ohmsche Widerstand wirkenden Bauteile mit der/den höchsten Verlustleistungen.

Furthermore, the method can include the following steps:

• - Calculation of the power loss in the components of the network model acting as ohmic resistances depending on the resonance properties of the selected natural mode; and
• - Selection of the one or more components acting as capacitance or inductance with the highest stored energies and one or more components acting as ohmic resistance with the highest power loss.

In particular, the resonance properties can include a quality, an amplitude and a frequency of the selected natural mode. These resonance properties are the goal of optimization, i.e. increasing the damping of the mode or reducing the amplitude or shifting the resonance frequency.

In order to comply with the limit values of an EMC behavior of a measured variable, resonances in electrical or electronic systems often have to be considered and, if necessary, changed/optimized. It is usually the case with complex systems made up of constructive mechanical components, such as a Housing, an electrical machine and the like, and electronic components difficult to clearly identify the cause of resonances that occur without further ado.

For this purpose, simulations are usually provided that use a network model based on an equivalent circuit diagram to simulate the EMC behavior. To create the network model, an electronic circuit is converted into an equivalent circuit diagram made up of functional components. This is supplemented by parasitic components that result from the constructive embedding of the electronic circuit in an overall system and describe the interactions of the constructive features with the components of the electronic circuit. An extraction method for creating such a network model (equivalent circuit diagram) from structural components and an electronic circuit is known from the prior art, such as in Jonathan Stysch et al., "Broadband Finite-Element Impedance Computation for Parasitic Extraction Computer Science > Computational Engineering, Finance, and Science”, Submitted on 17 Sep 2020, https://arxiv.org/abs/2009.08232 and in Sebastian Schuhmacher, “Sensitivity of Lumped Parameters to Geometry Changes in Finite Element Models”, Scientific Computing in Electrical Engineering, pages 35 -42, Springer: 14 April 2018, Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 28) revealed.

With the help of the network model, parasitic or functional components responsible for a resonance can be determined, so that a designer can make specific adjustments to the system. The above method enables an analysis of an entire system using a network model to find a resonant circuit that is largely responsible for a resonance of interest at a specific frequency.

This is done by analyzing the network model for an eigenmode that represents the most likely candidate for the cause of the resonance.

The network model, which combines the electrical effect of constructive mechanical components and electronic components in a common network model, can be analyzed with the help of an eigenvalue decomposition. For this purpose, a corresponding eigenvalue decomposition is carried out to determine the potential and current distribution for the eigenmodes of the network model. However, it is not immediately possible to clearly identify the components that are decisive for the corresponding resonance and to quantify their contribution to the resonance behavior based on the potential and current distribution in the eigenmodes of the network model. However, the unambiguous identification of the contribution of components to a particular resonance at hand is important in order to optimize the overall system design.

In particular, the above method envisages first providing a network model which is constructed from a combination of constructive mechanical components and electronic or electrical components. The network model corresponds to an electrical network in which functional components of the electronic or electrical component of the system and constructive mechanical components converted into corresponding parasitic components are contained.

For example, the frequency behavior of an electronic circuit can be represented by capacitors, inductances and ohmic resistances in the form of an equivalent circuit diagram. Furthermore, constructive mechanical components, especially if they are conductive, can interact with the electronic circuit as additional parasitic components in the form of capacitances and inductances and can thus be taken into account in the network model together with the functional components. With the help of a suitable extraction method, a corresponding electronic equivalent circuit diagram can be constructed from CAD construction data, which can be combined with an electronic circuit diagram to form a corresponding network model.

The resulting network model can now be analyzed in order to obtain a modal representation of the system behavior through its eigenvalues and corresponding eigenvectors according to an eigenvalue decomposition. This enables the network model to be represented by its (decoupled) eigenmodes.

When analyzing the network model, certain resonances are of particular interest, the amplitude of which is significant, i.e. H. e.g., exceeds a predetermined threshold. For further individual analysis of each individual resonance, the eigenmode that is closest to the corresponding resonance is therefore examined more closely.

An analysis of the components of the network model is carried out for each of the selected eigenmodes. The aim of the analysis is to determine the power loss in ohmic components and the energy stored in energy-storing components, such as capacitive and inductive components, based on the current and potential distribution of the eigenmode. From the energy or power loss consideration, an order list of the components with the highest stored energies and the components with the highest power losses results. The resonant circuit can be identified based on these order lists of the components with the highest power losses and the highest stored energies.

In particular, the selection of the one or more components acting as a capacitance or inductance with the / the highest stored energies and / or the one or more components acting as an ohmic resistance with the / the highest power losses can be carried out by a for the selected natural mode The resonance frequency and a damping factor are determined, with the power losses and the stored energies being determined in each case as a function of the damping factor or the resonance frequency.

Furthermore, the relevant resonant circuit can be determined by determining the current flows through all components and determining the resonant circuit as a function of the current flows through the components.

In particular, the current flows through all components can be determined, with the components being sorted in an order list according to the magnitude of their current flows, with the components being successively added to the selected components depending on their positions in the order list, until a closed current loop with all selected components is found, where the closed current loop corresponds to the relevant resonant circuit.

The current paths can be determined by determining node potentials in the network model, with the currents through the components of the network model being determined as a function of the node potentials at connections of the relevant component.

character list

• 1 ein Blockdiagramm zur Veranschaulichung der Prozessschritte zur Durchführung eines Verfahrens zur Analyse eines Netzwerkmodells und zur Identifikation von für Resonanzen maßgeblichen Bauteilen;
• 2 ein System mit einem Gehäuse, in dem eine elektronische Schaltung eingesetzt ist; und
• 3 ein beispielhaftes Netzwerkmodell, das aus dem System zur Analyse des EMV-Verhaltens abgeleitet ist.

Embodiments are explained in more detail below with reference to the accompanying drawings. Show it:

• 1 a block diagram to illustrate the process steps for carrying out a method for analyzing a network model and for identifying components that are decisive for resonances;
• 2 a system having a housing in which an electronic circuit is inserted; and
• 3 an exemplary network model derived from the EMC behavior analysis system.

Description of Embodiments

1 FIG. 12 schematically shows a flowchart to illustrate a method for identifying components in an overall system that are decisive for a resonance.

An overall system 1 is shown as an example in 2 shown. The overall system 1 has in the example 2 an electronic circuit 2 with electronic components 21 and a housing 3 with partially conductive components 31 and electrical lines 32 . For example, the electronic circuit 2 can be inserted in the housing 3 in the form of a circuit board 22 .

With reference to the flowchart, a method for identifying components in the overall system 1 that are decisive for a resonance is carried out.

To examine the overall system 1, a network model 10 is created in step S1, which describes the components of the electronic circuit 2 and the housing 3 as an equivalent circuit diagram. The components of the electronic circuit 2 are combined into functional components with regard to their EMC effect. The electrically relevant (e.g. conductive or dielectric) components of the housing 2 are described with regard to their EMC effect by parasitic components 15.

As an example, the overall system 1 results in 2 with regard to the EMC behavior, a network model 10, which in 3 is shown. The network model has components relevant to the EMC behavior, such as capacitances 11, inductances 12 and ohmic resistances 13. In the network model 10, parasitic components 15 and functional components 14 are combined to form a common network model. The parasitic components 15 result from structural design properties of the housing 3 and electrical lines 32, while the functional components 14 result from the components of the electronic circuit 2.

The EMC network model is created using appropriate tools. For this purpose, an EMC network model of the electronic circuit (equivalent circuit) is created and this is supplemented with the help of a suitable extraction process to include parasitic components that result from the interaction between the housing and the electronic circuit. A network model is obtained from the parasitic components 15 and the functional components 14.

Furthermore, in step S2, the resonances of the overall system 1 are initially determined by simulating or observing a prototype on a test stand.

In step S3, all natural modes are determined for the network model 10 determined in step S1.

$$\mathbf{y}=\mathbf{C}x+\mathbf{D}u$$

angegeben werden. Der Zustandsvektor beinhaltet dabei die Zustandsvariablen x (bspw. Spannung am Kondensator oder Strom über die Induktivität). In der Form $$\left[\underset{\mathbf{W}}{\underbrace{\left(\begin{array}{cc}\tilde{C}& 0\\ 0& -\mathbf{L}\end{array}\right)}}+\underset{\mathbf{V}}{\underbrace{\left(\begin{array}{cc}\tilde{G}& {\mathbf{A}}_L\\ {\mathbf{A}}_{\text{L}}^{\text{T}}& -\mathbf{R}\end{array}\right)}}\right]\underset{x}{\underbrace{\left(\begin{array}{c}V\\ I\end{array}\right)}}=\underset{u}{\underbrace{\left(\begin{array}{c}{\overline{I}}_s\\ 0\end{array}\right)}}$$

lässt sich eine erweiterte Knotenpotentialanalyse in die obige Zustandsraumdarstellung mit der Systemmatrix A = -W^-1V und der Eingangsmatrix B = W^-1 mit $$B=W^{-1}I=\left(\begin{array}{cc}{\tilde{C}}^{-1}& 0\\ 0& -L^{-1}\end{array}\right),A=-W^{-1}V=\left(\begin{array}{cc}-{\tilde{C}}^{-1}\tilde{G}& -{\tilde{C}}^{-1}{A}_L\\ -L^{-1}{A}_L^T& -L^{-1}R\end{array}\right),$$

überführen.The network model can be obtained using the state space representation and the LAPLACE transform s $$s\mathbf{x}=\mathbf{A}x+\mathbf{B}\mathrm{and},$$

$$\mathbf{y}=\mathbf{C}x+\mathbf{D}\mathrm{and}$$

be specified. The state vector contains the state variables x (e.g. voltage at the capacitor or current through the inductance). In the shape $$\left[\underset{\mathbf{W}}{\underbrace{\left(\begin{array}{cc}\tilde{C}& 0\\ 0& -\mathbf{L}\end{array}\right)}}+\underset{\mathbf{V}}{\underbrace{\left(\begin{array}{cc}\tilde{G}& {\mathbf{A}}_L\\ {\mathbf{A}}_{\text{L}}^{\text{T}}& -\mathbf{R}\end{array}\right)}}\right]\underset{x}{\underbrace{\left(\begin{array}{c}V\\ I\end{array}\right)}}=\underset{\mathrm{and}}{\underbrace{\left(\begin{array}{c}{\overline{I}}_s\\ 0\end{array}\right)}}$$

an extended nodal potential analysis can be converted into the above state space representation with the system matrix A = -W ^-1 V and the input matrix B = W ^-1 $$B=W^{-1}I=\left(\begin{array}{cc}{\tilde{C}}^{-1}& 0\\ 0& -L^{-1}\end{array}\right),A=-W^{-1}V=\left(\begin{array}{cc}-{\tilde{C}}^{-1}\tilde{G}& -{\tilde{C}}^{-1}{A}_L\\ -L^{-1}{A}_L^T& -L^{-1}R\end{array}\right),$$

convict.

The matrix G̃ contains all resistances that occur parallel to inductances or capacitances in the circuit. All capacities are represented in the matrix C̃. The matrix _Ĩs represents the current sources. These matrices are set up in a manner known per se in the nodal potential analysis.

The extended node potential analysis is known per se and is used to determine the node voltages and branch currents.

bestimmt werden. Diese wird modale Darstellung genannt. Da die Systemmatrix dadurch diagonalisiert wird, sind die einzelnen Moden entkoppelt.The state vector x consists of the node voltages V and the currents through the inductances I. Since voltage sources can be transformed into equivalent current sources, the excitation vector u consists only of the current sources Ĩ _s , at the nodes. Using the eigenvalue decomposition (diagonal eigenvalue matrix Λ, eigenvector matrix E) of the above state space representation, the state variables x for each value of s can be calculated using $$X\left(s\right)=\mathbf{E}{\left(s\mathbf{I}-\Lambda \right)}^{-1}{\mathbf{E}}^{-1}\mathbf{B}\mathrm{and}$$

to be determined. This is called modal representation. Since the system matrix is thereby diagonalized, the individual modes are decoupled.

dargestellt werden. Mit den Eigenwerten $${\lambda }_i={\xi }_i{\omega }_{\mathrm{0,}i}\pm {\omega }_{\mathrm{0,}i}\sqrt{1-{\xi }_i}$$

wobei ξ_i einer Dämpfung und ω_0,i einer natürlichen Resonanzfrequenz entsprechen.With Y = E ^-1 and Bu = b, the decoupled system of equations can now be summed up $$X\left(s\right)={\displaystyle \sum _{i=1}^N\frac{y_i^{T}b}{s-{\lambda }_i}}{e}_i$$

being represented. with the intrinsic values $${\lambda }_i={\xi }_i{\omega }_{\mathrm{0,}i}\pm {\omega }_{\mathrm{0,}i}\sqrt{1-{\xi }_i}$$

where ξ _i corresponds to a damping and ω _0,i to a natural resonance frequency.

N stands for the number of eigenvectors in E or eigenvalues in Λ. The electrical network can thus be described as a superposition of all eigenmodes.

In a subsequent step S4, the resonant frequency or the resonant frequencies of the determined resonances are compared with the natural frequencies of the determined natural modes. A relevant natural mode can now be selected for a specific resonance frequency, according to the frequency spacing between the resonance and the natural frequency.

For resonances of sufficiently high quality, the resonant frequency is close to the natural frequency of the associated mode.

∀ω in der Nähe der i-ten Resonanz.Each resonance of the system can be approximated by the respectively associated eigenmode $$x\left(\omega \right)={\displaystyle {\sum }_{\mathcal{l}=1}^N\frac{y_{\mathcal{l}}^{T}b}{j\omega -{\lambda }_{\mathcal{l}}}}{e}_{\mathcal{l}}\approx \frac{y_i^{T}b}{j\omega -{\lambda }_i}{e}_i$$

∀ω near the i-th resonance.

und die Resonanzamplitude berechnet sich näherungsweise zu $$X=\frac{y_i^{T}b}{{\xi }_i{\omega }_{\mathrm{0,}i}}{e}_i$$

The maximum of the i-th complex mode is thus at $${\omega }_i={\omega }_{\mathrm{0,}i}\sqrt{1-{\xi }_i}$$

and the resonance amplitude is calculated approximately to $$X=\frac{y_i^{T}b}{{\xi }_i{\omega }_{\mathrm{0,}i}}{e}_i$$

mit dem Vektor y_i ∈ Y = E^-1 der Anregung b = Bu und der natürlichen Frequenz ω_0,i und der Form der Mode e_i (Eigenvektor).This term consists of the damping factor ξ _i , the excitation factor $\frac{y_i^{T}b}{{\xi }_i{\omega }_{\mathrm{0,}i}}$

with the vector y _i ∈ Y = E ^-1 of the excitation b = Bu and the natural frequency ω _0,i and the shape of the mode e _i (eigenvector).

1. 1. Die Resonanzfrequenz zu ${\omega }_i={\omega }_{\mathrm{0,}i}\sqrt{1-{\xi }_i}$
   
2. 2. Der Dämpfungsfaktor ξ_i und damit die Güte $Q_i=\frac{1}{2{\xi }_i}$
   
3. 3. Die frequenzunabhängige Resonanzamplitude $X=\frac{y_i^{T}b}{{\xi }_i{\omega }_{\mathrm{0,}i}}{e}_i$
   

The approximation of the resonance of a system variable via the maximum of the (nearby) eigenmode also enables a direct calculation of the resonance properties.

1. 1. The resonant frequency too ${\omega }_i={\omega }_{\mathrm{0,}i}\sqrt{1-{\xi }_i}$
   
2. 2. The damping factor ξ _i and thus the quality $Q_i=\frac{1}{2{\xi }_i}$
   
3. 3. The frequency-independent resonance amplitude $X=\frac{y_i^{T}b}{{\xi }_i{\omega }_{\mathrm{0,}i}}{e}_i$
   

In step S5, the power loss of the components that act as ohmic resistances is first set in relation to the total power loss of the mode. Subsequently, an energy consideration the contributions of the energy-storing components, such as capacitances and inductances, are set in relation to the total energy stored in the mode. The loss consideration and the energy consideration make it possible to identify the relevant components of the resonant circuit and to quantify their influence on the resonance behavior.

To quantify the resonance-damping components, the relationship between quality/damping factor and power loss of the series and parallel resistors is considered based on the state variables of the eigenvector belonging to the selected eigenmode. The following relationship results: $$Q_i=\frac{1}{2{\xi }_i}={\omega }_{\mathrm{0,}i}\frac{V_i^T\tilde{C}{\overline{V}}_i}{V_i^T\tilde{G}{\overline{V}}_i+I_i^{T}R\overline{I_i}}=\frac{1}{2}{\omega }_{\mathrm{0,}i}\frac{W_Q}{P_V}$$

With the stored modal energy W _Q,i and the modal losses P _v,i of the i-th eigenmode, which is made up of the power losses and the stored energies in the circuit elements.

The above equation represents an eigenvector-based equation of the resonance quality of the eigenmode. The individual terms of the losses are calculated by $$P=R\cdot {\left|I\right|}^2={\left|u\right|}^2\text{/}R$$

The currents I _Rj and voltages U _Gj are determined directly from the eigenvectors. In order to reduce the power losses P _{G j PR j} To make the components comparable, they are normalized with regard to the modal power loss P _V of the natural mode: $$p_{G_j}=\frac{P_{G_j}}{P_V}\text{or}.p_{R_j}=\frac{P_{R_j}}{P_V}$$

P _V is the absolute total power dissipation and, P _{G j} and _{PR j} are the absolute power losses of the parallel and series resistances, as well as p _{G j} and p _{R j} the associated normalized power losses.

Thus, the contribution of each component to the overall damping/quality of the resonance can be evaluated as a percentage. This allows the influence of all resistive components on the damping to be quantified and the components relevant to the resonance to be determined.

Furthermore, a relationship between the mode resonance frequency and the inductive and capacitive components of the network circuit is to be established. The basis is the energy analysis of the inductive and capacitive components based on the state variables of the eigenvectors belonging to the eigenmode.

According to the above relationships, the following applies: $$V^T\tilde{C}\overline{V}={\mathbf{I}}^T\mathbf{L}\overline{I}$$

sowie für die Gesamtenergie W_L der Induktivitäten: $$W_L={\mathbf{I}}^T\mathbf{L}\overline{I}={\displaystyle \sum _{j=1}^{n_L}{\mathbf{L}}_j}{\left|I_{L_j}\right|}^2+{\displaystyle \sum _{\begin{array}{l}j=1\\ j\ne k\end{array}}^{n_L}{\displaystyle \sum _{\begin{array}{l}k=1\\ k\ne j\end{array}}^{n_L}{M}_{jk}}{I}_j}{I}_k$$

mit der Gegeninduktivität $$M_{jk}=k_{ij}\sqrt{L_i{L}_j}$$

The following applies to the total energy W _C of the capacitances C: $${\text{W}}_C={\mathbf{V}}^T\tilde{C}\overline{V}={\displaystyle \sum _{j=1}^{n_c}{C}_j}{\left|V_{C_j}\right|}^2$$

and for the total energy W _L of the inductances: $$W_L={\mathbf{I}}^T\mathbf{L}\overline{I}={\displaystyle \sum _{j=1}^{n_L}{\mathbf{L}}_j}{\left|I_{L_j}\right|}^2+{\displaystyle \sum _{\begin{array}{l}j=1\\ j\ne k\end{array}}^{n_L}{\displaystyle \sum _{\begin{array}{l}k=1\\ k\ne j\end{array}}^{n_L}{M}_{jk}}{I}_j}{I}_k$$

with the mutual inductance $$M_{jk}=k_{ij}\sqrt{L_i{L}_j}$$

The quantities n _L and nc indicate the number of capacitances and inductances with the capacitance voltages V _{C j} ∈ V
and the inductance currents I _{L j} ∈ I

die Resonanzfrequenz ist somit umgekehrt proportional zur in den Induktivitäten und Kapazitäten gespeicherten Energie in der i-ten Mode Die Einzelterme aus obigem Zusammenhang mit $$W_{C_j}=C_j{\left|V_{C_j}\right|}^2=\frac{1}{2}{C}_j{\left|{\widehat{V}}_{C_j}\right|}^2$$

können direkt aus den Eigenvektoren bestimmt werden. Um die Energien der Bauteile vergleichbar zu machen, werden diese bzgl. der Gesamtenergie normiert durch $$w_{C_j}=\frac{W_{C_j}}{W_C}$$

With the known relationships from the described loss analysis follows $${\omega }_{\mathrm{0,}i}\sqrt{1-{\mathrm{<figure-callout\; id="2"\; label="\xi \; i"\; filenames="DE102021208276A1\_0029.png"\; state="\{\{state\}\}">\xi </figure-callout>}}_i^{}}=Im\left({\lambda }_i\right)=\frac{j2Im\left({\overline{V}}^T{A}_{L}I\right)}{W_C+W_L}\stackrel{W_C=W_L}{=}\frac{jIm\left({\overline{V}}^T{A}_{L}I\right)}{W_C}$$

the resonant frequency is thus inversely proportional to the energy stored in the inductances and capacitances in the i-th mode. The individual terms from the above connection with $$W_{C_j}=C_j{\left|V_{C_j}\right|}^2=\frac{1}{2}{C}_j{\left|{\widehat{V}}_{C_j}\right|}^2$$

can be determined directly from the eigenvectors. In order to make the energies of the components comparable, they are normalized with regard to the total energy by $$w_{C_j}=\frac{W_{C_j}}{W_C}$$

mit der in der Gegeninduktivität M_jk gespeicherten Energie $$W_{M_{jk}}=M_{jk}\cdot \overline{I_{L_j}}\cdot I_{L_k}+M_{kj}\cdot \overline{I_{L_k}}\cdot I_{L_j}$$

The following calculation rule is selected for the energy calculation of the inductance $$W_{L_j}=L_j{\left|I_{L_j}\right|}^2+{\displaystyle \sum _{\begin{array}{l}k=1\\ k\ne j\end{array}}^{n_L}\frac{L_j{\left|I_{L_j}\right|}^2}{L_j{\left|I_{L_j}\right|}^2+L_k{\left|I_{L_k}\right|}^2}}\cdot W_{M_{jk}}$$

with the energy stored in the mutual inductance M _jk $$W_{M_{jk}}=M_{jk}\cdot \overline{I_{L_j}}\cdot I_{L_k}+M_{kj}\cdot \overline{I_{L_k}}\cdot I_{L_j}$$

In order to make the energies of the components comparable, they are normalized with regard to the total energy: $$w_{L_j}=\frac{W_{L_j}}{W_L}$$

Since Wc = W _L applies, the inductances and capacitances can also be compared with one another. In this way, the contribution of each component to the resonant frequency of the selected natural mode and thus to the resonant frequency of the system size can be evaluated as a percentage.

In a subsequent step S6, the components for which the power losses were identified and the components for which the stored energy was determined are sorted and in step S7 a number of components with the highest power losses and a number of components with the highest stored Energies are determined as components of a resonant circuit that is decisive for the resonance.

In step S8, based on the corresponding selected components, a resonant circuit is then determined by the identified components with the aid of a circuit identification. This requires making the correct connection between the identified components, which is not trivial, especially in complex structures.

In an electrical oscillating circuit, a charge exchange takes place through electrons. The charge exchange is described by the currents along the components. The resonant circuit can thus be identified by taking into account the edges of the network circuit with the highest currents in terms of magnitude. The currents of the inductances or series resistances are already included in the eigenvectors. The missing currents of the capacitances and parallel resistances can be calculated from the node potentials and the capacitance or resistance matrix.

The resonant circuits result in particular from those current paths between two selected components that carry the highest current.

Thus, the current paths with the highest currents are identified between the identified components in order to close the current flow circuits and thereby identify the resonant circuit. A resonant circuit identified in this way, which can be regarded as decisive for the resonance to be examined, now enables a person skilled in the art to make appropriate changes to suppress interference in the system. In particular, the components of the resonant circuit that correspond to parasitic components can be assigned to the actual structural housing properties and components that correspond to functional components, to the electronic circuit, so that the person skilled in the art can make targeted changes in order to optimize the resonance, in particular to dampen or suppress it .

In particular, all current flows through all components of the network model can be determined, with the components being sorted in an order list according to the magnitude of their current flows. The components are successively added to the components selected in step S7, depending on their positions in the order list, until a closed current loop is found with all selected components, the closed current loop corresponding to the relevant resonant circuit. The current paths can be determined by determining node potentials in the network model, with the currents through the components of the network model being determined as a function of the node potentials at connections of the relevant component.

Claims (10)

Computer-implemented method for analyzing an electrical network model (10) for simulating the behavior of an electronic or electrical system (1) and for identifying a resonant circuit of the system (1) that is decisive for a resonance, with the following steps: - selecting (S4) a natural mode corresponding to a resonance of the system (1) to be analyzed; - approximation of resonance properties according to the selected eigenmode; - Calculating (S5) the energy stored in the components of the network model (10) acting as capacitances and inductances as a function of the resonance properties of the selected natural mode; - Selection (S7) of the components (11, 12, 14) acting as capacitance or inductance with the/the highest stored energies; - Determination (S8) of the relevant resonant circuit based on the selected components. procedure after claim 1 , with the further steps: - Calculation of the power loss in the components (13) of the network model (10) acting as ohmic resistances as a function of the resonance properties of the selected natural mode; and - selecting the one or more of the components (11, 12) acting as capacitance or inductance with the highest stored energies and the one or more of the components (14) acting as ohmic resistance with the/the highest power losses. procedure after claim 1 or 2 , wherein the resonance properties include a quality or an attenuation, an amplitude and/or a frequency of the selected natural mode. procedure after claim 2 , wherein the selection of the one or more components (11, 12) acting as a capacitance or inductance with the/the highest stored energies and/or the one or more components acting as an ohmic resistance (13) with the/the highest power losses is/are carried out is determined by determining a resonant frequency and a damping factor for the selected natural mode, with the power losses and the stored energies being determined as a function of the damping factor or the resonant frequency Procedure according to one of Claims 1 until 4 , the relevant resonant circuit being determined by determining the current flows through all the components (11, 12, 13, 14) and determining the resonant circuit as a function of the current flows through the components. procedure after claim 5 , where the current flows through all components are determined and where the components are sorted in an ordered list according to the magnitude of their current flows, with the components being successively added to the selected components depending on their positions in the ordered list, until a closed current loop with all selected components is found, where the closed current loop corresponds to the relevant resonant circuit. procedure after claim 5 or 6 , the current paths being determined by determining node potentials in the network model (10), the currents through the components of the network model (10) being determined as a function of the node potentials at connections of the relevant component. Device that is designed one of the methods according to one of Claims 1 until 7 to execute. Computer program product, comprising instructions which, when the program is executed by a computer, cause the latter to carry out the steps of the method according to one of Claims 1 until 7 to execute. A machine-readable storage medium comprising instructions which, when executed by a computer, cause the computer to perform the steps of the method of any one of Claims 1 until 7 to execute.

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