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 figure 1, see the differential conductance $g_D={{1}\over{r_D}}$ 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 ($T=293K$) and $m=1$ from Shockley's equation: ${I_F = I_S(T)\cdot (e^{\frac{U_F}{m\cdot U_T}}-1)}$ with $U_T = \frac{k_B \cdot T}{e}$. To do this, first calculate the general formula for the differential resistance $r_D$.

Steps:

1. First, simplify Shockley's equation for $U_F >> U_T$
Solution

2. Find a formula for $\frac {d I_F}{d U_F}$.
Solution

3. 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 $r_D = \frac {d U_F}{d I_F} = \frac {m \cdot U_T}{I_F}$.
Solution

4. Calculate $r_D$.
Solution

Final result