Question 1.8: Objective: Determine the diode voltage and current for the c...
Objective: Determine the diode voltage and current for the circuit shown in Figure 1.28. Consider a diode with a given reverse-saturation current of I_{S} = 10^{−13} A
We can write Equation (1.23) as
V_{PS} = I_{S} R\left[e^{\left(\frac{V_{D}}{V_{T}} \right) } – 1\right] + V_{D} (1.23)
5 = (10^{-13}) (2 \times 10^{3}) \left[e^{\left(\frac{V_{D}}{0.026} \right) } – 1\right] + V_{D} (1.24)
If we first try V_{D} = 0.60 V the right side of Equation (1.24) is 2.7 V, so the equa-tion is not balanced and we must try again. If we next try V_{D} = 0.65 V the right side of Equation (1.24) is 15.1 V. Again, the equation is not balanced, but we can see that the solution for V_{D} is between 0.6 and 0.65 V. If we continue refining our guesses, we will be able to show that, when V_{D} = 0.619 V the right side of Equa-tion (1.29) is 4.99 V, which is essentially equal to the value of the left side of the equation
I_{DQ} = I_{S} e^{\left(\frac{V_{D}}{V_{T}} \right) } (1.29)
The current in the circuit can then be determined by dividing the voltage differ- ence across the resistor by the resistance, or
I_{D} = \frac{V_{PS} – V_{D}}{R} = \frac{5 – 0.619}{2} = 2.19 mAComment: Once the diode voltage is known, the current can also be determined from the ideal diode equation. However, dividing the voltage difference across a re-sistor by the resistance is usually easier, and this approach is used extensively in the analysis of diode and transistor circuits.