Saturating magnetic capacitor (Capacitorsat)
Saturating magnetic capacity from [1] (chap 7) with state \(\phi\in [-\phi_{sat}, \phi_{sat}]\) and parameters described below. The energy is
\begin{equation*}
H(\phi) = \frac{1}{C_{0}} \, \left( \frac{\phi^2}{2} + C_{sat} H_{sat}(\phi)\right),
\end{equation*}
with
\begin{equation*}
H_{sat}(\phi) = - \frac{8 \phi_{sat}}{\pi \left(4-\pi\right)} \, \left(\frac{\pi^{2} \phi^{2}}{8\phi_{sat}^{2}} + \log{\left (\cos{\left (\frac{\pi \phi}{2 \phi_{sat}} \right)} \right)}\right).
\end{equation*}
The resulting magnetomotive force is:
\begin{equation*}
\psi(\phi)= \frac{d\,H(\phi)}{d \phi} = \frac{ 1}{C_{0}} \left(\phi + C_{sat} \frac{d\,H_{sat}(\phi)}{d \phi}\right),
\end{equation*}
with
\begin{equation*}
\frac{d\,H_{sat}(\phi)}{d \phi}= \frac{4}{4- \pi} \left(\tan{\left (\frac{\pi \phi}{2 \phi_{sat}} \right )} - \frac{\pi \phi}{2\phi_{sat}} \right).
\end{equation*}
Saturating magnetic capacitor (Capacitorsat)
Saturating magnetic capacity from [1] (chap 7) with state \(\phi\in [-\phi_{sat}, \phi_{sat}]\) and parameters described below. The energy is
\begin{equation*}
H(\phi) = \frac{1}{C_{0}} \, \left( \frac{\phi^2}{2} + C_{sat} H_{sat}(\phi)\right),
\end{equation*}
with
\begin{equation*}
H_{sat}(\phi) = - \frac{8 \phi_{sat}}{\pi \left(4-\pi\right)} \, \left(\frac{\pi^{2} \phi^{2}}{8\phi_{sat}^{2}} + \log{\left (\cos{\left (\frac{\pi \phi}{2 \phi_{sat}} \right)} \right)}\right).
\end{equation*}
The resulting magnetomotive force is:
\begin{equation*}
\psi(\phi)= \frac{d\,H(\phi)}{d \phi} = \frac{ 1}{C_{0}} \left(\phi + C_{sat} \frac{d\,H_{sat}(\phi)}{d \phi}\right),
\end{equation*}
with
\begin{equation*}
\frac{d\,H_{sat}(\phi)}{d \phi}= \frac{4}{4- \pi} \left(\tan{\left (\frac{\pi \phi}{2 \phi_{sat}} \right )} - \frac{\pi \phi}{2\phi_{sat}} \right).
\end{equation*}
Power variables
flux: Magnetic flux variation (mfv) \(\frac{d\,\phi}{dt}\) (V)
effort: Magnetomotive force (mmf) \(\psi\) (A)
Arguments
- label : str
- Capacitorsat label.
- nodes : ('N1', 'N2')
- Component terminals with positive flux N1->N2.
- parameters : keyword arguments
- Component parameters
| Key | Description | Unit | Default |
|---|---|---|---|
| C0 | Magnetic capacitance around zero | H | 1000.0 |
| Csat | Nonlinearity parameter | d.u. | 1000.0 |
| phisat | Magnetic capacitance | Wb | 0.1 |
Usage
capa = Capacitorsat('capa', ('N1', 'N2'), C0=1000.0, Csat=1000.0, phisat=0.1)
Netlist line
magnetics.capacitorsat capa ('N1', 'N2'): C0=1000.0; Csat=1000.0; phisat=0.1;
Example
>>> # Import dictionary
>>> from pyphs.dictionary import magnetics
>>> # Define component label
>>> label = 'capa'
>>> # Define component nodes
>>> nodes = ('N1', 'N2')
>>> # Define component parameters
>>> parameters = {'C0': 1000.0, # Magnetic capacitance around zero (H)
... 'Csat': 1000.0, # Nonlinearity parameter (d.u.)
... 'phisat': 0.1, # Magnetic capacitance (Wb)
... }
>>> # Instanciate component
>>> component = magnetics.Capacitorsat(label, nodes, **parameters)
>>> # Graph dimensions
>>> len(component.nodes)
2
>>> len(component.edges)
1
Reference
| [1] | (1, 2) Antoine Falaize. Modelisation, simulation, generation de code et correction de systemes multi-physiques audios: Approche par reseau de composants et formulation hamiltonienne a ports. PhD thesis, ecole Doctorale d'Informatique, Telecommunication et electronique de Paris, Universite Pierre et Marie Curie, Paris 6, EDITE UPMC ED130, july 2016. |