Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

--- circuit_design:uebung_2.1.4 [2023/03/09 15:25] – mexleadmin
+++ circuit_design:uebung_2.1.4 [2023/03/27 14:20] (aktuell) – mexleadmin
@@ Zeile 4: / Zeile 4: @@
 <imgcaption imageIdealizedDiode | Idealized Diode>
 </imgcaption>
-{{drawio>ImageIdealizedDiode}}
+{{drawio>ImageIdealizedDiode.svg}}
 </WRAP>
-The differential resistance $r_D$ of a diode was already described in the chapter. This is necessary if a diode is to be simulated via a simplified diode model (voltage source + resistor + ideal diode, if applicable). In <imgref imageIdealizedDiode>, see the differential conductance $g_D={{1}\over{r_D}}$ as the local slope at the desired operating point.
+The differential resistance $r_\rm D$ of a diode was already described in the chapter. This is necessary if a diode is to be simulated via a simplified diode model (voltage source + resistor + ideal diode, if applicable). In <imgref imageIdealizedDiode>, see the differential conductance $g_{\rm D}={{1}\over{r_\rm D}}$ as the local slope at the desired operating point.
-Calculate the differential resistance $r_D$ at forward current $I_D=15 mA$ for room temperature ($T=293~K$) and $m=1$ from Shockley's equation: ${I_F = I_S(T)\cdot (e^{\frac{U_F}{m\cdot U_T}}-1)}$ with $U_T = \frac{k_B \cdot T}{e}$.
+Calculate the differential resistance $r_\rm D$ at forward current $I_\rm D=15 ~\rm mA$ for room temperature ($T=293~\rm K$) and $m=1$ from Shockley's equation: ${I_{\rm F} = I_{\rm S}(T)\cdot ({\rm e}^{\frac{U_\rm F}{m\cdot U_\rm T}}-1)}$ with $U_{\rm T} = \frac{k_{\rm B} \cdot T}{q}$ with $q=1~\rm e$.
-To do this, first calculate the general formula for the differential resistance $r_D$.
+To do this, first, calculate the general formula for the differential resistance $r_\rm D$.
 Steps:
-  - First, simplify Shockley's equation for $U_F \gg U_T$
+  - First, simplify Shockley's equation for $U_{\rm F} \gg U_\rm T$
-  - Find a formula for $\frac {d I_F}{d U_F}$.
+  - Find a formula for $\frac {{\rm d} I_{\rm F}}{{\rm d} U_\rm F}$.
-  - Again, replace part of the result with $I_F$ and rotate the fraction to calculate the differential resistance by $r_D = \frac {d U_F}{d I_F}$. \\ As a result, you should now have $r_D = \frac {d U_F}{d I_F} = \frac {m \cdot U_T}{I_F} $
+  - Again, replace part of the result with $I_\rm F$ and rotate the fraction to calculate the differential resistance by $r_{\rm D} = \frac {{\rm d} U_\rm F}{{\rm d} I_\rm F}$. \\ As a result, you should now have $r_{\rm D} = \frac {{\rm d} U_\rm F}{{\rm d} I_\rm F} = \frac {m \cdot U_\rm T}{I_\rm F} $
-  - Calculate $r_D$.
+  - Calculate $r_\rm D$.
 </WRAP></WRAP></panel>