# Computing Capacitances Matrix with Flux PEEC – Power Module Example

Different applications now need to evaluate the capacitive behaviors of their devices. Power modules, for instance, are now working at high frequencies and a capacitive behavior appears in  addition to the resistive-inductive aspects. Unfortunately these effects may have undesirable effects on the devices and generate additional losses. In order to observe and analyze these effects, the value of the capacitances between each conductor has to be computed. From electrostatic computations with different methods and tools described below, these capacitances can be obtained as capacitances matrices.

Three different matrices exist from electrostatic computation results to direct the capacitance value between two “conductors”. Before beginning any computation, these “conductor” regions have to be defined, corresponding to the elements to be connected with the computed capacitances. The methods are described with Flux PEEC .

The three matrices:

“Maxwell” matrix: contains the results of electrostatic computations. This matrix CMaxwell corresponds to this equation:
Q=CMaxwell*V where V is the absolute electrical potential of the conductor. This matrix has no circuit equivalent.

“Kirchhoff” matrix (obtained from Maxwell): contains the capacitances between the “conductors” regions and the capacitances between each region and an infinite reference point.
CKirchhoff corresponds to this equation: Q= CKirchhoff*(Vi-Vj) where Vi is the absolute electrical potential of the conductor and Vj the potential of a reference infinite point. This matrix has a circuit equivalent (cf. Fig 1) Figure 1 & 2: Equivalent circuit with Kirchhoff & “capacitance” matrix elements between two capacitive regions.

“Capacitance” matrix (obtained from Kirchhoff): contains the capacitances between each “conductors” regions only, including the self-capacitances. Capacitance corresponds to this equation:
Q= CCapacitance*(Vi-Vj) where Vi and Vj are the absolute electrical potentials of the conductors. This matrix has a circuit equivalent (cf. Fig 2).

Depending on the reason for capacitance computation, both Kirchhoff and “Capacitance” may be useful. To study the capacitive behavior of the global system, the Kirchhoff will better take account of the common-mode currents flowing through the capacitances. However, some users will only want to estimate the value of the capacitances between two conductors to design the dielectric material in the device. Those users will prefer the “Capacitance”matrix.

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“To study the capacitive behavior of the global system, the “Kirchhoff” matrix will better take account of the common-mode currents flowing through the capacitances.”

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Integrated computation and connection with Flux PEEC

Flux PEEC is a specific tool to compute inductances of electrical interconnections and power modules and it allows the resistive-inductive-capacitive behavior of these devices to be simulated. Its specific Partial Element Equivalent Circuit method permits solving very quickly and easily devices composed of conductors and analyzing their resistive-inductive properties. Flux PEEC now includes the capacitive effects in this process thanks to an integrated computation before solving the whole system.

Dedicated applications can handle this computation to enhance the accuracy of results when working with high frequencies. As explained in the introduction, from a project with conductors and circuit-ready, the first step consists in defining the different “Capacitive regions” which will be connected with capacitances. These regions can include multiple conductors that should be grouped according to geometry and relative distances. Some conductors can be ignored for performing capacitance computation even though they play an important role in the whole system (e.g.: vias and bondings can be ignored in a power module).

Next, the definition of dielectric material is important. There might be volumes in the geometry that are not conductors but have a specific relative permittivity. Those regions can be defined as “Dielectric” regions for computation and affect electrostatic computations (insulation, for example). After meshing the capacitive and dielectric regions, an integrated computation returns the  three matrices described in the introduction.

One specific advantage of Flux PEEC is that these matrices can consequently be converted into an equivalent circuit. Thanks to the connection wizard, the user can add the capacitances recently computed on the global circuit containing the conductors. Then the user can select the right matrix and different connection options such as “Pi” or “T” connection, or a threshold value. The  wizard adds capacitances with values from the matrix and smartly connects them correctly with the terminals of the existing conductors.
After this operation, the project is ready to be solved with a complete circuit, taking into account both resistive-inductive behaviors of the conductors, and capacitive effects thanks to capacitances connected between them.

In the post-processing context, results of this RLC behavior can be observed according to the solving frequency. For example, impedance probes perfectly illustrate the different reactions of the devices with various frequencies. This device can then be observed in any system simulation software since it is possible to export an equivalent RLC macro block of the device to SPICE or  solidThinking Activate.
Flux PEEC provides a full solution to compute and observe the capacitive effects in a power electronics device. Figure 6: Input impedance of a power module according to the solving frequency, illustration of the two behaviors in low and high frequencies. 