Chapter 3, Problem 3.83HP

The so-called forward-bias i-v relationship for a silicon diode is:
   $i_D=I_{SAT}\left[e^{\left(v_D/V_{thermal}\right)}-1\right]$
where $I_{SAT}$ and $V_{thermal}$ are known as the saturation current and thermal voltage, respectively. At room temperature (20°C):
   $I_{SAT}={10}^{-12}A$ and $V_{thermal}=\frac{kT}{q}=25.3\text{mV}$
wherek is Boltzmann’s constant, T is absolute temperature in kelvins, and q is the charge of an electron. Consider the circuit shown in Figure P3.83. KVL applied around the loop results in a transcendental equation for the loop current $i=i_D$ . Such equations cannot be solved in terms of a closed-form expression $i=$ Instead, graphical or iterative procedures must be used.
a. Use graphical analysis to estimate the current through and the voltage across the diode. Assume $R_T=22\Omega$ and $V_T=12V$ .
b. Use the iterative algorithm depicted in the flowchart of Figure P3.83 to construct a computer program that solves for V and i. The algorithm relies upon the fact that $0<V<V_T$ to make an initial guess $V_{D1}=V_T\text{/}2$ for the voltage across the diode. The algorithm then determines whether the current $i_{D1}$ through $R_T$ is greater than, less than, or equal to the diode current $i_{D2}$ for the guessed diode voltage. In the first case, a new guess for $V_{D1}$ is set equal to the average value of $V_{D1}$ and $V_{D2}$ , which stores the most recent value of $V_{D1}$ that resulted in $i_{D2}>i_{D1}$ . The initial value $V_{D2}=V_T$ guarantees that $i_{D1}=0$ and, thus, $i_{D2}>i_{D1}$ , for the first pass through the iterative algorithm. The result is that $V_{D1}$ and $V_{D2}$ bracket the actual value of V. Each pass through the algorithm narrows the bracket until the difference $\left|i_{D1}-i_{D2}\right|<\epsilon$ , where $\epsilon$ is some sufficiently small error term.