DE102021210303A1 - Method for modal analysis and optimization of resonance properties in an electromechanical product - Google Patents

Abstract

The invention relates to a computer-implemented method for analyzing a CAD model of an electronic or electrical system (1) to determine a distribution of at least one constructive resonance property sensitivity which indicates a constructive sensitivity of one or more resonance properties in an electronic or electrical system (1) with respect to a geometric position in the system (1) or a material property in the system (1), a network model (10) functional components (15) representing the electrical and electronic components, and parasitic components (14) representing the effective impedances of geometric structures of the system (1), described in an equivalent circuit. The invention also relates to a computer program product and a machine-readable storage medium.

Description

technical field

The invention relates to the targeted adaptation of electromechanical products whose behavior can be described by electronic circuit simulations. The invention further relates to the targeted adaptation of a corresponding representative CAD model, with the points or properties in the model responsible for the target properties of a resonance being identified quantitatively.

Technical background

The EMC behavior of an electrical or electronic system with an electronic circuit is usually determined by its geometric construction, its material properties, 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 indicate the electrical interaction of the geometric design features with the functional components.

In the product development of such electronic or electrical systems, a network model of functional components and parasitic components is created and simulated to accompany the 3D CAD model in order to determine their EMC behavior.

Disclosure of Invention

According to the invention, a method for analyzing and optimizing a CAD model of an electromechanical product with regard to at least one resonance property according to claim 1 and the device according to the independent claim are solved.

• - Auswählen einer Eigenmode entsprechend einer zu analysierenden Resonanz des Systems;
• - Approximieren einer oder mehrerer Resonanzeigenschaften der zu analysierenden Resonanz entsprechend der durch die Eigenschaften einer für die zu analysierende Resonanz verantwortliche Eigenmode;
• - Bestimmen der Resonanzeigenschaftssensitivitäten der einen oder der mehreren Resonanzeigenschaften bezüglich der Impedanz jedes der Parasitärbauteile abhängig von der einen oder der mehreren Resonanzeigenschaften der ausgewählten Eigenmode;
• - Ermitteln der konstruktiven Sensitivitäten der Impedanzen jedes der Parasitärbauteile bezüglich mindestens eines konstruktiven Parameters;
• - Bestimmen der mindestens einen konstruktiven Resonanzeigenschaftssensitivität abhängig von den Resonanzeigenschaftssensitivitäten der einen oder der mehreren Resonanzeigenschaften bezüglich der Impedanz jedes der Parasitärbauteile und den konstruktiven Sensitivitäten der Impedanzen jedes der Parasitärbauteile;
• - Anpassen des Aufbaus und/oder der Konfiguration des Systems abhängig von der mindestens einen konstruktiven Resonanzeigenschaftssensitivität.

According to a first aspect, a computer-implemented method for analyzing a CAD model of an electronic or electrical system to determine a distribution of at least one constructive resonance property sensitivity is provided, which is a sensitivity of one or more resonance properties in an electronic or electrical system with respect to a geometric position in the system or a material property in the system, the network model describing functional components, which represent the electrical and electronic components, and parasitic components, which represent the effective impedances of geometric structures of the system, in an equivalent circuit, the method having the following steps:

• - selecting an eigenmode corresponding to a resonance of the system to be analyzed;
• - approximation of one or more resonance properties of the resonance to be analyzed according to the properties of a responsible for the resonance to be analyzed eigenmode;
• - determining the resonance property sensitivities of the one or more resonance properties with respect to the impedance of each of the parasitic components depending on the one or more resonance properties of the selected eigenmode;
• - determining the constructive sensitivities of the impedances of each of the parasitic components with respect to at least one constructive parameter;
• - determining the at least one constructive resonance property sensitivity dependent on the resonance property sensitivities of the one or more resonance properties with respect to the impedance of each of the parasitic components and the constructive sensitivities of the impedances of each of the parasitic components;
• - Adjusting the structure and/or the configuration of the system depending on the at least one constructive resonance property sensitivity.

The at least one design parameter can include a geometric position in the system, a geometry of a functional component and/or a material property, in particular a permeability, a conductivity and/or a permittivity.

In particular, the resonance properties can include a quality, an amplitude and/or a frequency of the selected natural mode or depend on one or a combination of these variables. These resonance properties are either the individual goal of the optimization, i.e. increasing the damping or reducing the amplitude or shifting the resonance frequency, or part of a multi-objective optimization using at least one resonance property and at least one other target variable, for example another resonance property of the selected resonance or the Resonance property of another resonance.

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. As a rule, it is difficult to identify, analyze and optimize any resonances that occur in complex systems made up of constructive mechanical components, such as a printed circuit board, a housing, an electrical machine and the like, and electronic components

For this purpose, simulations are usually provided that use a network model based on an equivalent circuit diagram to simulate the EMC behavior. The equivalent circuit diagram of functional components on which the electronic circuit is based is used to create the network model. 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 (parasitic components) and components of an electronic circuit (functional components) is known from the prior art, such as in Jonathan Stysch et al., "Broadband finite-element impedance computation for parasitic extraction”, in Electrical Engineering, Springer, https://doi.org/10.1007/s00202-021-01348-9 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).

The above method enables an overall system to be analyzed using a network model in order to find a constructive sensitivity of a resonance property with respect to a constructive condition in the overall system that is largely responsible for a resonance to be examined at a specific frequency. The design constraint may include a position dependency and/or a material dependency.

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, based on the potential and current distribution of the eigenmodes of the network model, to quantify the constructive conditions that are decisive for the corresponding resonance and their influence on the resonance behavior. However, this quantification with regard to the structural conditions of the overall system is important for a specific existing resonance in order to optimize the overall system design.

In particular, the above method provides for first providing a network model, e.g. in the form of an electronic equivalent circuit, which is constructed from a combination of the parasitic electrical properties 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 structural 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. In particular, using a suitable extraction method from CAD design data, a corresponding electron ical equivalent circuit diagram can be constructed, which can be combined with an electronic circuit diagram to form a corresponding network model. In the same step, the sensitivity of these extracted parasitic components with regard to the geometric model parameters or the material parameters of the model can be determined using a suitable numerical method.

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 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, that natural mode is therefore selected and examined more closely, which is closest to the corresponding resonance in terms of frequency spacing.

A sensitivity analysis is carried out below, in which the resonance properties for each of the selected eigenmodes are determined with regard to their sensitivities with regard to the constructive property within the system. Depending on the sensitivities, one or more areas in the system can be identified that significantly influence the resonance of the system to be analyzed. These constructive sensitivities describe the dependence of the resonance properties on the geometric conditions in the model of the system to be analyzed and/or on the material properties present there. In order to determine these constructive sensitivities, sensitivities of one or more resonance properties with regard to their respective impedances are first determined for all parasitic components. These sensitivities relate to one or more resonance properties, e.g. B. the resonant frequency, the quality and the amplitude.

In a next step, the sensitivities of the impedances of the parasitic components are determined with regard to the structural conditions in the system. These sensitivities describe the dependency of the impedances of the parasitic components on the geometric conditions in the model of the system to be analyzed and/or on the material properties present there. For example, an inductance and its sensitivity with regard to model parameters such as the geometry or the material parameters of the model, i.e. depending on its course in the system, can be specified for a bonding wire using a suitable extraction method. A possible method for extracting the parasitic components and their sensitivities is given, for example, in S. Schuhmacher et al., "Adjoint technique for sensitivity analysis of coupling factors according to geometric variations", IEEE Transactions on Magnetics, Vol. 54, 2018.

From the resonance property sensitivity, which describes the dependence of the at least one resonance property on the respective impedances of the parasitic components, and the constructive sensitivities, which describe the dependence of the impedances of the parasitic components on the geometric model properties or the material properties of the model, the dependence of the at least one resonance property can now be determined can be determined from the geometric model properties or the material properties of the system model according to the generalized chain rule.

A sensitivity map results that represents the constructive sensitivity of one or more resonance properties (resonance property sensitivities with respect to a local area in the system) over a two-dimensional or three-dimensional representation of the system. From this, by finding areas with high resonance property sensitivities, the structures can be identified that lend themselves to a constructive change in the system in order to influence the resonance behavior of the system.

Furthermore, quantitative information from the determined sensitivities can also provide the basis for use in gradient-based optimization methods to automatically adapt the model geometrically or with regard to a material parameter optimization (e.g. the relative permeability) with regard to a resonance property.

Furthermore, the adaptation can also be adapted with regard to multiple resonance properties or multiple resonance properties of more than one resonance using a suitable multi-objective optimization method.

Provision can be made for at least one resonance property sensitivity of the one or more resonance properties with regard to the impedance of at least one functional component to be determined as a function of the one or more resonance properties of the selected natural mode, with the adjustment of the structure and/or the configuration of the system with regard to the the at least one functional component specific resonance property sensitivity is carried out.

character list

• 1 ein Blockdiagramm zur Veranschaulichung der Prozessschritte zur Durchführung eines Verfahrens zur Analyse und Anpassung bzw. Optimierung eines CAD Modells für die Analyse und Optimierung von Resonanzeigenschaften;
• 2 ein System mit einer Platine, auf der eine elektronische Schaltung aufgebaut ist; und
• 3 ein beispielhaftes Netzwerkmodell, das aus dem System zur Analyse des EMV-Verhaltens abgeleitet ist;
• 4a-4c Karten zur Darstellung von konstruktiven Resonanzeigenschaftssensitivitäten zur Veranschaulichung von geometrischen Bereichen des elektronischen bzw. elektrischen Systems, die die Resonanzeigenschaften bei Veränderung maßgeblich beeinflussen;
• 5a und 5b die Änderung des Leiterplattendesigns zur Anpassung einer Resonanzamplitude; und
• 6 eine Darstellung von Amplitudenverläufen über der Frequenz für das ursprüngliche und das geänderte Leiterplattendesign.

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 the analysis and adjustment or optimization of a CAD model for the analysis and optimization of resonance properties;
• 2 a system having a circuit board on which an electronic circuit is built; and
• 3 an exemplary network model derived from the EMC behavior analysis system;
• 4a-4c Maps for the representation of constructive resonance property sensitivities to illustrate geometric areas of the electronic or electrical system, which significantly influence the resonance properties when changing;
• 5a and 5b changing the circuit board design to adjust a resonance amplitude; and
• 6 a representation of amplitude curves versus frequency for the original and the modified circuit board design.

Description of Embodiments

1 FIG. 12 schematically shows a flowchart to illustrate a method for identifying geometric positions 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 a voltage converter as an electronic circuit 2 with electronic components 21 and a printed circuit board 3 with electrically active areas 31 (solder points) and electrical lines 32 (conductor tracks). For example, the electronic circuit 2 can be constructed with SMD components on the printed circuit board 3 .

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 printed circuit board 3 as an equivalent circuit diagram. The components 21 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 circuit board 3 are described with regard to their EMC effect by parasitic components 14.

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 10 has components relevant to the EMC behavior, such as capacitances 11, inductances 12 and ohmic resistances 13. In the network model 10, parasitic components 14 and functional components 15, which include the components 21, are combined to form a common network model 10. The parasitic components 14 result from structural design properties of the printed circuit board 3 with the electrically active areas 31 and the electrical lines 32, while the functional components 11, 12, 13 result from the components of the electronic circuit 2.

The EMV network model 10 is created using suitable tools. For this purpose, an EMC network model of the electronic circuit (equivalent circuit) is created and this is supplemented by the parasitic components 14 using a suitable extraction method, which result from the interaction between the constructs ven conditions and the electronic circuit. A network model is obtained from the parasitic components 14 and the functional components 15.

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

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

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

The state space representation describes the behavior of the network model and can be brought into the following form using the Laplace transformation and the Laplace parameter s: $$sx=\mathbf{A}x+\mathbf{B}\mathrm{and},$$

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

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

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 capacitances are represented in the matrix C̃. The matrix Ĩ _S 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.

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.

bestimmt werden. Diese wird modale Darstellung genannt. Da die Systemmatrix dadurch diagonalisiert wird, sind die einzelnen Moden entkoppelt.Using the eigenvalue decomposition (diagonal eigenvalue matrix A, eigenvector matrix E) of the above state space representation, the state variables x for each value of s can be calculated using $$x\left(s\right)=\mathbf{E}{\left(s\mathbf{I}-\mathrm{\Lambda }\right)}^{-1}{\mathbf{E}}^{-1}\mathbf{B}\mathrm{and}$$

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

über alle Eigenmoden i=1...N dargestellt werden. Mit den Eigenwerten $${\lambda }_i=-{\xi }_i{\omega }_{\mathrm{0,}i}\pm {\omega }_{\mathrm{0,}i}\sqrt{1-{\xi }_i^2}$$

wobei ξi 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 $$x\left(s\right)={\displaystyle \sum _{i=1}^N\frac{y_i^{T}b}{s-{\lambda }_i}{e}_i}$$

can be represented over all eigenmodes i=1...N. with the intrinsic values $${\lambda }_i=-{\xi }_i{\omega }_{\mathrm{0,}i}\pm {\omega }_{\mathrm{0,}i}\sqrt{1-{\mathrm{<figure-callout\; id="2"\; label="\xi \; i"\; filenames="DE102021210303A1\_0029.png,DE102021210303A1\_0034.png"\; state="\{\{state\}\}">\xi </figure-callout>}}_i^{}}$$

where ξi 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 A. The behavior of the electrical network can thus be described by a weighted 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.

in der Nähe der i-ten Resonanz.The behavior of the system in the vicinity of each resonance of sufficiently high quality can be approximated by the associated eigenmode $x\left(\omega \right)={\displaystyle {\sum }_{\mathcal{l}=1}^N\frac{y_{\mathcal{l}}^{T}b}{j\omega -{\lambda }_{\mathcal{l}}}e\mathcal{l}\approx \frac{y_i^{T}b}{j_{\omega }-{\lambda }_i}{e}_i\forall \mathrm{\omega }}$

near the i-th resonance.

und die Resonanzamplitude X 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 $${\omega }_i={\mathrm{<figure-callout\; id="0"\; label="\omega "\; filenames="DE102021210303A1\_0034.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_{\mathrm{0,}i}\sqrt{1-{\mathrm{<figure-callout\; id="2"\; label="\xi \; i"\; filenames="DE102021210303A1\_0029.png,DE102021210303A1\_0034.png"\; state="\{\{state\}\}">\xi </figure-callout>}}_i^{}}$$

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

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 ${\omega }_i={\mathrm{<figure-callout\; id="0"\; label="\omega "\; filenames="DE102021210303A1\_0034.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_{\mathrm{0,}i}\sqrt{1-{\mathrm{<figure-callout\; id="2"\; label="\xi \; i"\; filenames="DE102021210303A1\_0029.png,DE102021210303A1\_0034.png"\; state="\{\{state\}\}">\xi </figure-callout>}}_i^{}}$
   
2. 2. Der Dämpfungsfaktor ξ_iund 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 ${\omega }_i={\mathrm{<figure-callout\; id="0"\; label="\omega "\; filenames="DE102021210303A1\_0034.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_{\mathrm{0,}i}\sqrt{1-{\mathrm{<figure-callout\; id="2"\; label="\xi \; i"\; filenames="DE102021210303A1\_0029.png,DE102021210303A1\_0034.png"\; state="\{\{state\}\}">\xi </figure-callout>}}_i^{}}$
   
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 $X=\frac{y_i^{T}b}{{\xi }_i{\omega }_{\mathrm{0,}i}}{e}_i$
   

mit der Systemmatrix A in zur Resonanz assoziierten Eigenwerten λ_i und Eigenvektoren ei. Für die Sensitivitätsberechnung müssen somit lediglich die Eigenvektoren numerisch bestimmt werden. Die Ableitung der Systemmatrix A kann symbolisch erfolgen. Dadurch kann die Sensitivität der Resonanzfrequenz bezüglich der Änderung der Netzwerkelemente effizient und präzise bestimmt werden.In step S5, the derivations of the resonance properties are first determined according to the impedance variables z of the network elements, which can be either an ohmic resistance R, an inductance L or a capacitance C. For the sensitivity of the resonance frequency follows: $$\frac{\mathrm{i.e}{\omega }_i}{\mathrm{i.e}\mathrm{e.g}}=\frac{\mathrm{i.e}\text{In the}\left({\lambda }_i\right)}{\mathrm{i.e}\mathrm{e.g}}=\text{In the}\left(y_i^T\frac{\mathrm{i.e}\mathbf{A}}{\mathrm{i.e}\mathrm{e.g}}{e}_i\right)$$

with the system matrix A in eigenvalues λ _i and eigenvectors ei associated to the resonance. For the sensitivity calculation only the eigenvectors have to be determined numerically. The derivation of the system matrix A can be done symbolically. As a result, the sensitivity of the resonant frequency with regard to the change in the network elements can be determined efficiently and precisely.

so dass man die Sensitivität der Amplitude der Zustandsgrößen beliebiger Systemgrößen bezüglich einer Änderung der Impedanz der Netzwerkelemente erhält.Furthermore, the sensitivity of the resonance amplitude X is calculated using the product rule as follows: $$\begin{array}{c}\frac{\mathrm{i.e}X}{\mathrm{i.e}\mathrm{e.g}}=\frac{\mathrm{i.e}}{\mathrm{i.e}\mathrm{e.g}}\left(\frac{y_i^{T}b}{{\xi }_i{\omega }_{\mathrm{0,}i}}{e}_i\right)\\ =\frac{\mathrm{i.e}{y}_i^T}{\mathrm{i.e}\mathrm{e.g}}\frac{b}{{\xi }_i{\omega }_{\mathrm{0,}i}}{e}_i+\frac{y_i^T}{{\xi }_i{\omega }_{\mathrm{0,}i}}\frac{\mathrm{i.e}b}{\mathrm{i.e}\mathrm{e.g}}{\text{e}}_{\text{i}}+\frac{y_i^{T}b}{{\xi }_i{\omega }_{\mathrm{0,}i}{}^2}\frac{\mathrm{i.e}{e}_i}{\mathrm{i.e}\mathrm{e.g}}-\frac{y_i^{T}b}{\left({\xi }_i{\omega }_{\mathrm{0,}i}\right)}\frac{\mathrm{i.e}\left({\xi }_i{\omega }_{\mathrm{0,}i}\right)}{\mathrm{i.e}\mathrm{e.g}}{e}_i\end{array}$$

so that one obtains the sensitivity of the amplitude of the state variables of any system variables with regard to a change in the impedance of the network elements.

Furthermore, the sensitivity of the quality of the selected eigenmode can be determined from the derivation of the eigenvalue. Applying the chain rule follows $$\frac{\mathrm{i.e}{\xi }_i}{\mathrm{i.e}\mathrm{e.g}}=-\frac{\mathrm{i.e}}{\mathrm{i.e}\mathrm{e.g}}\left(\frac{\text{re}\left({\lambda }_i\right)}{{\mathrm{<figure-callout\; id="0"\; label="\omega "\; filenames="DE102021210303A1\_0034.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_{\mathrm{0,}i}}\right)=-{\mathrm{<figure-callout\; id="0"\; label="\omega "\; filenames="DE102021210303A1\_0034.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_{\mathrm{0,}i}^{-1}\frac{\mathrm{i.e}\text{re}\left({\lambda }_i\right)}{\mathrm{i.e}\mathrm{e.g}}+{\mathrm{<figure-callout\; id="0"\; label="\omega "\; filenames="DE102021210303A1\_0034.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_{\mathrm{0,}i}^{-2}\text{re}\left({\lambda }_i\right)\frac{\mathrm{i.e}{\mathrm{<figure-callout\; id="0"\; label="\omega "\; filenames="DE102021210303A1\_0034.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_{\mathrm{0,}i}}{\mathrm{i.e}\mathrm{e.g}}$$

bestimmen. Dadurch erhält man die Sensitivität der Resonanzgüte beliebiger Systemgrößen bezüglich einer Änderung der Impedanz der Netzwerkelemente.The derivative of the quality is the sum of the derivative of the real part of the eigenvalue and the derivative of the natural frequency ω ₀ with $$\frac{\mathrm{<figure-callout\; id="0"\; label="i.e\; \omega "\; filenames="DE102021210303A1\_0034.png"\; state="\{\{state\}\}">i.e</figure-callout>}{\omega }_{}{}_{\mathrm{0,}i}}{\mathrm{i.e}\mathrm{e.g}}=\frac{\mathrm{i.e}\text{Section}\left({\lambda }_i\right)}{\mathrm{i.e}\mathrm{e.g}}={\text{Section}}^{-1}\left({\lambda }_i\right)\left(\text{re}\left({\lambda }_i\right)\frac{\mathrm{i.e}\text{re}\left({\lambda }_i\right)}{\mathrm{i.e}\mathrm{e.g}}+\text{In the}\left({\lambda }_i\frac{\mathrm{i.e}\text{In the}\left({\lambda }_i\right)}{\mathrm{i.e}\mathrm{e.g}}\right)\right)$$

determine. This gives the sensitivity of the resonance quality of any system variable with regard to a change in the impedance of the network elements.

The derivation of the eigenvectors and eigenvalues can be done, for example, as described in N. Van der Aa et al., "Computation of eigenvalue and eigenvector derivatives for a general complex-valued eigensystem", The Electronic Journal of Linear Algebra ELA 16(1) (http: //dx.doi.org/10.13001/1081-3810.1203).

In step S6, the sensitivities of the impedances of the individual parasitic components with regard to the geometric parameters or the material parameters of the model in the system can be determined from the extraction model.

A possible method for extracting the parasitic components and their sensitivities is given, for example, in S. Schuhmacher et al., "Adjoint technique for sensitivity analysis of coupling factors according to geometric variations", IEEE Transactions on Magnetics, Vol. 54, 2018.

For example, the partial inductance of a piece of line and its sensitivities are calculated as follows. With the help of a system of equations derived from Maxwell's equations, the electrical potential difference can be calculated when a current density profile is impressed at both ends of the line section. The numerical solution of this system of equations can be determined, for example, by a finite element analysis. The impedance and thus the partial inductance of this piece of line can then be calculated from the impressed total current and the potential difference. The sensitivity of this impedance with regard to the underlying model parameters, such as the conductivities or the conductor geometry, can be calculated using an adjoint method, for example.

For example, the capacitance between two galvanic bodies can be calculated from the electrostatic approximation of Maxwell's equation in the potential representation by solving the field equation in a finite element analysis. Electrostatic potentials are impressed on the galvanic bodies as a boundary condition for the partial differential equations. By associating the stored energy in a capacitor with a capacity to be determined and a given voltage difference and the electric field energy determined with the help of the field solution, an equivalent capacity between the galvanic bodies can be calculated. Likewise, the sensitivity of this calculated capacity with regard to the underlying model parameters can then be calculated for this equation using the adjoint method.

To determine the constructive sensitivity of resonance properties (constructive resonance property sensitivity), in step S7 according to the generalized chain rule from the resonance property sensitivities Q(z(p)) determined above for each of the parasitic components and the N constructive sensitivities of the impedances z _j (p) of the parasitic components Sensitivities of the resonance properties can be determined via the geometric parameters and material parameters p of the model of the electromechanical system (geometric resonance property sensitivities). It results for each resonance property sensitivity: $$\frac{\mathrm{i.e}Q\left(\mathrm{e.g}\left(p\right)\right)}{\mathrm{i.e}{p}_i}={\displaystyle \sum _{j=1}^N\frac{\partial Q\left(\mathrm{e.g}\left(p\right)\right)}{\partial {\mathrm{e.g}}_j\left(p\right)}\frac{\mathrm{i.e}{\mathrm{e.g}}_j\left(p\right)}{\mathrm{i.e}{p}_i}}$$

This can be done, for example, using the maps such. Am 4a-4c shown, are illustrated, from which one recognizes the areas of the electronic or electrical system that are responsible for the occurrence of a high sensitivity of a resonance property. 4a shows for the example of 2 the areas B1 of maximum sensitivity of the resonance frequency, 4b the areas B2 of maximum sensitivity of the resonance quality and 4c the areas B3 of maximum sensitivity of the resonance amplitude.

By adapting the geometric construction or structure according to the quantitative size of the sensitivity in this identified area of the system, either the resonance frequency can be shifted, the damping increased and/or the resonance amplitude reduced in step S8. In particular, the geometric construction or the structure of the printed circuit board 3 can be changed by widening or narrowing the interconnects, reducing or increasing the area of soldering points, lengthening or shortening bonding wires in order to adapt the resonance properties.

For example, the 5a and 5b changing the circuit board design to adjust a resonance amplitude. You can see that the width of a trace in area B has been increased. 6 shows the amplitude curve U over the frequency f with curves K1 and K2, the reduction of the maximum resonance amplitude by changing the circuit board design 5b .

In an alternative application, material parameters of the model could be changed according to the predictions of the sensitivity analysis to make analogous adjustments. If, for example, the sensitivity analysis of one of the resonance properties, e.g. the damping factor, with respect to the permittivity of the material of the printed circuit board substrate gives a negative value, choosing a new material with a lower permittivity would lead to a larger resonance property, e.g. the damping factor.

Instead of calculating the modal sensitivities of the CAD model directly in a complex field simulation (solving the coupled Maxwell equations, including all functional components), the modal network sensitivities are first calculated in one step. In a second step, the parasitic network elements and their constructive sensitivities are determined in an efficient extraction without further consideration of the functional components of the equivalent circuit. In an efficient third step, these two sensitivities are combined with the extended chain rule to obtain the constructive resonance property sensitivities.

By considering the constructive sensitivity of the resonance frequency, potential positions in the geometry of the system can be identified for optimization so that the resonance can be pushed out of a critical frequency range. This can be useful, for example, for emitted interference, in which hard limits often only apply in very narrow frequency bands (e.g. medium wave: 530 - 1700 kHz). Shifting the resonance to frequencies without fixed requirements is very helpful here. By changing the resonance through the above 3D sensitivity analysis and modifying the product based on it, the requirements can be met cost-effectively.

Furthermore, a sorted list of the design parameters with regard to their influence on the resonance amplitude can be calculated using the sensitivity analysis, for example. By changing the design parameters according to this list, the amplitude of the resonance can be increased or decreased. A reduction in the resonance amplitude often corresponds to an improvement in the interference immunity and/or interference emission of the product at the resonance frequency.

Such a procedure lends itself, for example, to the interference immunity optimization of sensors. These must withstand high interference levels in a wide frequency range. Shifting the resonance is not helpful here. In addition, it is usually not possible to introduce further damping into the system via functional components. For this reason, a targeted change in the resonance excitation should be made as described here.

It becomes apparent that resonance optimization makes sense depending on the application and product in EMC with regard to various resonance properties (amplitude, damping, frequency).

Claims (10)

Computer-implemented method for analyzing a CAD model of an electronic or electrical system (1) to determine a distribution of at least one constructive resonance property sensitivity, which is a constructive sensitivity of one or more resonance properties in an electronic or electrical system (1) with respect to a geometric position in the System (1) or a material property in the system (1), with a network model (10) functional components (15) representing the electrical and electronic components, and parasitic components (14) representing the effective impedances of geometric structures of the system ( 1) described in an equivalent circuit, with the following steps: - selecting (S4) a natural mode corresponding to a resonance of the system (1) to be analyzed; - approximation of one or more resonance properties of the resonance to be analyzed according to the properties of a responsible for the resonance to be analyzed eigenmode; - determining (S5) the resonance property sensitivities $\left(\frac{\mathrm{i.e}X}{\mathrm{i.e}\mathrm{e.g}},\frac{\mathrm{i.e}{\xi }_i}{\mathrm{i.e}\mathrm{e.g}},\frac{\mathrm{i.e}{\omega }_{\mathrm{0,}i}}{\mathrm{i.e}\mathrm{e.g}}\right)$

the one or more resonant characteristics related to the impedance of each of the parasitic devices (14) depending on the one or more resonant characteristics of the selected eigenmode; - Determination (S6) of the constructive sensitivities $\left(\frac{\mathrm{i.e}{\mathrm{e.g}}_j\left(p\right)}{\mathrm{i.e}{p}_i}\right)$

the impedances of each of the parasitic components (14) in the system (1) with respect to at least one design parameter (p); - Determining (S7) the at least one constructive resonance property sensitivity depending on the at least one resonance property sensitivity $\left(\frac{\mathrm{i.e}X}{\mathrm{i.e}\mathrm{e.g}},\frac{\mathrm{i.e}{\xi }_i}{\mathrm{i.e}\mathrm{e.g}},\frac{\mathrm{i.e}{\omega }_{\mathrm{0,}i}}{\mathrm{i.e}\mathrm{e.g}}\right)$

with respect to the impedance of each of the parasitic components (14), and as a function of the at least one constructive sensitivity $\left(\frac{\mathrm{i.e}{\mathrm{e.g}}_j\left(p\right)}{\mathrm{i.e}{p}_i}\right)$

the impedance with respect to the at least one constructive parameter (p); - Adjusting the structure and/or the configuration of the system (1) depending on the at least one constructive resonance property sensitivity. procedure after claim 1 , wherein the at least one design parameter (p) comprises a geometric position in the system (1), a geometry of a functional component, and/or a material property, in particular a permeability, a conductivity and/or a permittivity. procedure after claim 1 or 2 , wherein the adjustment of the structure and/or the configuration of the system (1) comprises an adjustment of that geometric structure at which the constructive resonance property sensitivity for at least one of the one of the plurality of resonance properties is highest. Procedure according to one of Claims 1 until 3 , wherein the resonance properties include a quality (Q _i ) or an attenuation (ξ _i ), an amplitude (X) and/or a frequency of the selected eigenmode or depend on one or a combination of these quantities. Procedure according to one of Claims 1 until 4 , wherein determining the at least one constructive resonance property sensitivity by applying a generalized chain rule in derivatives of composite functions to the determined resonance property sensitivities $\left(\frac{\mathrm{i.e}X}{\mathrm{i.e}\mathrm{e.g}},\frac{\mathrm{i.e}{\xi }_i}{\mathrm{i.e}\mathrm{e.g}},\frac{\mathrm{i.e}{\omega }_{\mathrm{0,}i}}{\mathrm{i.e}\mathrm{e.g}}\right)$

regarding the impedances of each parasitic component (14) and the constructive sensitivities $\left(\frac{\mathrm{i.e}{\mathrm{e.g}}_j\left(p\right)}{\mathrm{i.e}{p}_i}\right)$

of the impedances of each of the parasitic components (14). Procedure according to one of Claims 1 until 5 , with the further steps: extracting parasitic components (14) from a CAD model using an extraction method; - Combination (S1) of the networks of the parasitic components (14) and functional components (15) in the network model (10), which describes the behavior of the electromechanical system (1); - Determining (S2, S3) one or more eigenmodes, in particular via a state space representation of the network model (10); - selecting (S4) the eigenmode from the one or more eigenmodes. Procedure according to one of Claims 1 until 6 , wherein at least one resonance property sensitivity $\left(\frac{\mathrm{i.e}X}{\mathrm{i.e}\mathrm{e.g}},\frac{\mathrm{i.e}{\xi }_i}{\mathrm{i.e}\mathrm{e.g}},\frac{\mathrm{i.e}{\omega }_{\mathrm{0,}i}}{\mathrm{i.e}\mathrm{e.g}}\right)$

the one or more resonance properties $\left(\frac{\mathrm{i.e}X}{\mathrm{i.e}\mathrm{e.g}},\frac{\mathrm{i.e}{\xi }_i}{\mathrm{i.e}\mathrm{e.g}},\frac{\mathrm{i.e}{\omega }_{\mathrm{0,}i}}{\mathrm{i.e}\mathrm{e.g}}\right)$

with regard to the impedance of at least one functional component (15) is determined as a function of the one or more resonance properties of the selected natural mode, with the adaptation of the structure and/or the configuration of the system (1) with regard to the resonance property sensitivity determined by the at least one functional component (15). is carried out. Device that is designed, one of the methods according to one of Claims 1 until 7 to execute. Computer program product, comprising instructions that are required when the program is executed by a computer, in particular by the device claim 8 , cause this, the steps of the method according to any one of Claims 1 until 7 to execute. Machine-readable storage medium, comprising instructions that, when executed by a computer, in particular by the device claim 8 , cause this, the steps of the method according to any one of Claims 1 until 7 to execute.

Images