"Matrix equations"

Matrix equations

The MNA matrix equation for the RC network is:

Matrix equation:

\begin{equation} \left[\begin{matrix}1\\0\\0\end{matrix}\right]=\left[\begin{matrix}0 & 1 & 0\\1 & \frac{1}{R} & - \frac{1}{R}\\0 & - \frac{1}{R} & C s + \frac{1}{R}\end{matrix}\right]\cdot\left[\begin{matrix}I_{V1}\\V_{N001}\\V_{out}\end{matrix}\right] \end{equation}

The vector with independent variables is:

\begin{equation} I_{v}=\left[\begin{matrix}1\\0\\0\end{matrix}\right] \end{equation}

The MNA matrix is:

\begin{equation} M=\left[\begin{matrix}0 & 1 & 0\\1 & \frac{1}{R} & - \frac{1}{R}\\0 & - \frac{1}{R} & C s + \frac{1}{R}\end{matrix}\right] \end{equation}

The vector with dependent variables is:

\begin{equation} D_{v}=\left[\begin{matrix}I_{V1}\\V_{N001}\\V_{out}\end{matrix}\right] \end{equation} \begin{equation} \frac{V_{out}}{V_{1}}=\frac{1}{C R s + 1} \end{equation}

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Last project update: 2021-04-04 13:40:27