****** Please it has to be solved by MATLAB ******

Explanation: The voltage-versus-current characteristic of a practical diode at forward biased region (v_D > 0) can be approximated by the Shockley diode equation:

i_D = I_S(e^(v_D^/(nV_T⁾⁾ - 1), (1)

where

• i_D is the current [A] through the diode,
• v_D is the diode voltage [V],
• I_S is the leakage (or reverse saturation) current, typically in the range of 10^-6 A to 10^-15 A,
• n is the empirical constant known as the emission coefficient or the ideality factor, whose value varies from 1 to 2,
• V_T is a constant called the thermal voltage.

The diode current i_D will be very small if the diode voltage v_D is less than a specific value V_TD, known as the threshold voltage or the cut-in voltage or the turn-on voltage (typically 0.7 = V). The diode conducts fully if v_D is higher than V_TD. Thus, the threshold voltage is the voltage at which a forward-biased diode begins to conduct fully. For v_D > 0.1 V, which is usually the case, i_D >> I_S, and Eq. (1) can be approximated by

i_D = I_S (e^(v_D^/(nV_T⁾⁾ - 1) I_S e^(v_D^/(nV_T⁾⁾ . (2)

Question: The voltage-versus-current characteristic of a diode at forward biased region (v_D > 0) is measured at a junction temperature of 25 C and the measured values are plotted in Figure 1 and given in the data file (fprdata.dat), where the first column is the voltage in V and the second column is the measured current in A. This diode is used in the RL circuit shown in Figure 2, where the switch is closed at t = t0. Formulate and write a code to calculate the current i(t), voltages v₁(t), v₂(t), and v_D(t) for V_S = 2 V, L=0.98 H, R = 14.2 , t₀ = 0 s, and i₀ = 0 A for the time interval t [0.600] ms using the step sizes t = 25 ms and t = 2.5 ms. Assume that v_D(0) = 0 V for t = 0 s.

Followings should be included:

1. Formulation for the initial value problem.
2. Formulation of the method used to handle the diode characteristic.
3. Plots of the current i(t), voltages v₁(t), v₂(t), and v_D(t) versus time t.

Figure 1: The measured voltage-current characteristic of a diode at forward biased region: (a) linear, (b) logarithmic scales.

Figure 2: Circuit for the final project.

4. Which methods are used? Explain why they are chosen.
5. Include all necessary values and figures (depending on the used methods).

*************** fprdata.dat *************

+4.60000E-01 +2.39944E-08

+5.00000E-01 +5.47030E-08

+9.70000E-01 +1.15987E-03

+1.21200E+00 +1.90309E-01

+1.24300E+00 +4.21568E-01

***************************************

0.5 10 0.4 102 203) Current [A] Current [A] 10+ 0.2 10-6 0.1 0 0.4 10-8 0.6 1.2 1.4 0.4 0.6 1.2 1.4 0.8 Voltage [V] 0.8 1 Voltage [V] t=ts (1) X, R + + (1) + V S (1) 3L 0.5 10 0.4 102 203) Current [A] Current [A] 10+ 0.2 10-6 0.1 0 0.4 10-8 0.6 1.2 1.4 0.4 0.6 1.2 1.4 0.8 Voltage [V] 0.8 1 Voltage [V] t=ts (1) X, R + + (1) + V S (1) 3L