Component
Types of Components#
| Type | Symbol | Function | Linearized |
|---|---|---|---|
| Resistivity |  |
\(f_R(u,i)\) | \(u = U_0 + R \cdot i\) |
| Capacity |  |
\(f_C(u,q)\) | \(q = Q_0 + C \cdot u\) |
| Inductivity |  |
\(f_L(i,\Phi)\) | \(\Phi = \Phi_0 + L \cdot i\) |
| Memristivity |  |
\(f_M(q,\Phi)\) | \(\Phi = \Phi_0 + M \cdot q\) |
Two Terminals#
| Component | Function | Chart |
|---|---|---|
Open Circuit  |
\(u \in \R\) \(i = 0\) |  |
Short Circuit  |
\(u = 0\) \(i \in \R\) |  |
Voltage Source  |
\(u = U_0\) \(i \in \R\) |  |
Current Source  |
\(u \in \R\) \(i = I_0\) |  |
Nullator  |
\(u = 0\) \(i = 0\) |
 |
Norrator  |
\(u \in \R\) \(i \in \R\) |
 |
Resistor  |
\(u = R \cdot i\) \(i = \frac{1}{R} \cdot u\) |  |
Capacitor  |
\(I = C \cdot\dot U\) \(C = \frac{\diff Q}{\diff U}\) |
|
Inductor  |
\(U = L \cdot\dot I\) \(L = \frac{\diff \Phi}{\diff U}\) |
|
ideal Diode  |
\(\begin{array}{ll} u = 0 \text{ if } i > 0 \\ i = 0 \text{ if } u < 0\end{array}\) |  |
reale Diode  |
\(\begin{array}{ll} u_D = u_T \cdot \ln \left(\frac{i_D}{I_S} + 1 \right) \\ i_D = I_S \cdot \left( \exp \left(\frac{u_D}{U_T}\right) -1 \right) \end{array}\) | |
LED  |
\(i = I_S \cdot \left( \exp \left(\frac{u_D}{U_T}\right) -1 \right) - i_L\) |