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
$$i = I_S \cdot \left( \exp \left(\frac{u_D}{U_T}\right) -1 \right) - i_L$$

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