Subsections

Special time-domain models

AM modulated AC source

An AC voltage source in the time-domain is characterized by its frequency $ f$, the initial phase $ \phi$ and the amplitude $ A$. During amplitude modulation the modulation level $ M$ must be considered. The output voltage of the source is determined by the following equation.

$\displaystyle V_1\left(t\right) - V_2\left(t\right) = \left(1 + M\cdot V_3\left(t\right)\right)\cdot A\cdot \sin{\left(\omega\cdot t + \phi\right)}$ (6.103)

Figure 6.7: AM modulated AC source
\includegraphics[width=0.3\linewidth]{vam}

The appropriate MNA matrix entries during the transient analysis decribing a simple linear operation can be written as

$\displaystyle \begin{bmatrix}. & . & . & 1\\ . & . & . & -1\\ . & . & . & 0\\ 1...
..._3\left(t\right)\\ A\cdot \sin{\left(\omega\cdot t + \phi\right)} \end{bmatrix}$ (6.104)

PM modulated AC source

The phase modulated AC source is also characterized by the frequency $ f$, the amplidude $ A$ and by an initial phase $ \phi$. The output voltage in the time-domain is determinded by the following equation

$\displaystyle V_1\left(t\right) - V_2\left(t\right) = A\cdot\sin{\left(\omega\cdot t + \phi + M\cdot V_3\left(t\right)\right)}$ (6.105)

whereas $ M$ denotes the modulation index and $ V_3$ the modulating voltage.

Figure 6.8: PM modulated AC source
\includegraphics[width=0.3\linewidth]{vpm}

The component is non-linear in the frequency- as well in the time-domain. In order to prepare the source for subsequent Newton-Raphson iterations the derivative

$\displaystyle g = \dfrac{\partial \left(V_1 - V_2\right)}{\partial V_3} = M\cdot A\cdot\cos{\left(\omega\cdot t + \phi + M\cdot V_3\right)}$ (6.106)

is required. With this at hand the MNA matrix entries of the PM modulated AC voltage source during the transient analysis can be written as

$\displaystyle \begin{bmatrix}. & . & . & +1\\ . & . & . & -1\\ . & . & . & 0\\ ...
...V_3 - A\cdot \sin{\left(\omega\cdot t + \phi + M\cdot V_3\right)} \end{bmatrix}$ (6.107)


This document was generated by Stefan Jahn on 2007-12-30 using latex2html.