f4ms_elct7.fm - Electronics I Midterm I Examination Problems Points. 4 2. 5 3. 6 Total 5 Was the exam fair? yes no
f4ms_elct7.fm - 2 Problem 4 points For full credit, mark your answers yes, no, or not for all the given choices! For full credit, mark your answers yes, no, or not in all the given choices!. In a pn-junction diode: x majority charge carriers on the p-side of the junction are free electrons, x minority charge carriers on the p-side of the junction are holes, x majority charge carriers on the n-side of the junction are holes, x minority charge carriers on the n-side of the junction are free electrons,.2 The electric field inside the depletion region of a silicon pn-junction diode is directed: x from the donor to the acceptor ions, x from the p-region to the n-region of the pn-junction, x from the acceptor to the donor ions, x from the cathode to the anode side of the pn-junction.3 The height of the potential barrier of the pn-junction is, x unaffected by the application of a reverse bias voltage to the junction, x increased by the application of a forward bias voltage to the junction, x decreased by the application of a forward bias voltage to the junction, x decreased by the application of a reverse bias voltage to the junction..4 Under reverse bias, the reverse current of a silicon pn-junction diode is given by -i D =I S +I L, where I S is the reverse saturation current, and I L is the reverse leakage current of the diode. With e denoting the base of natural logarithms, and assuming that T=(T 2 -T ) o K>0, the nonlinear temperature dependence of I L can be mathematically described by, T x I L (T 2 ) = I L (T ) 2 5, x I L (T 2 ) = I L (T ) e T, T x I, L (T 2 ) = I L (T ) 2 0 T x I L (T. 2 ) = I L (T ) e 0 9/26/4
f4ms_elct7.fm - 3 Problem 2 5 points Given is the nonlinear electric circuit model shown in Figure 2., which includes a pn-junction diode. i D R =.2 MΩ V DD = 30V i D V DD + - v D (a) R V R (T) T o =293 o K V R (T o ) = V R0 = 0V V Z = 28V V DR = 0.7V -V Z 0 V DR (b) v D Figure 2. A nonlinear circuit model containing a pn-junction diode. (a) The circuit model. (b)the diode s piece-wise-linear model. The pn-junction diode in the circuit model of Figure 2. is described by the following properties: (a) diode is accurately represented by its large-signal piece-wise-linear "constant voltage drop" model shown in Figure 2.(b); (b) temperature dependence of the diode s reverse leakage current I L is described by: I L doubles for every 0 o K increase in diode s temperature. Problem statement For the electric circuit model of Figure 2., demonstrate an ability to:. indicate the positive reference directions of the diode s current flow and voltage drop; 2. determine the value of the voltage V R (T ) = V R, to which the voltage V R in the circuit of Figure 2. will change when the diode s temperature changes to the value T =273K. Solution Hint # For full credit, give answers to all questions, prepare all required circuit diagrams, write all equations for which the space is reserved, and show all symbolic and numerical expressions whose evaluation produces the shown numerical results. An explicit demonstration of understanding the following solution steps is expected. 2. Show in the electrical model of Figure 2.(a) the positive reference directions for diode s voltage v D and current i D. 2.2 Calculate the diode s voltage V D0 at temperature T o. Show your calculation in the space reserved for equation (2-0). At temperature T o, the voltage drop across the resistor is known; therefore by KVL, V D0 = V R0 - V DD = 0-30 = -20V > -28V = -V Z (2-0) 9/26/4
f4ms_elct7.fm - 4 2.3 Based on the result of calculation in part 2., indicate the operating region of the diode at temperature T o by checking the conditions on all three lines below, x the diode is forward biased, x the diode is reverse biased, x the diode is in its breakdown region. 2.4 Calculate the value of I L0, the diode s reverse leakage current at temperature T o. Show your calculation in the space reserved for equation (2-). That the diode in the circuit of Figure 2. is reverse biased, but not in the breakdown region at temperature T o, has been established above. Therefore, the current which creates the voltage drop V R0 in the circuit of Figure 2. is the reverse leakage current of the diode. Ohm s law provides the reverse leakage current I L0 at temperature T o, I L0 = V R0 = R 0.2 0 6 = 8.3 0-6 = 8.3µA (2-) 2.5 Calculate T, the change in temperature between T o at which the reverse leakage current of the diode has been calculated under 2.3 above, and at the given temperature T. Show your calculation in the space reserved for equation (2-2). T= T - T o = 273-293 = -20K (2-2) 2.6 Determine n 0K, the number of decades of degrees Kelvin in the calculated temperature increase T. Show your calculation in the space reserved for equation (2-3). This calculation is straight forward. n 0K = T 0-20 = 0 = -2 (2-3) 2.7 Determine the ratio of the diode s reverse leakage currents at temperatures T and T o. Show your calculation in the space reserved for equation (2-4) By the diode s property (a), and by the calculated temperature increase, I L = I L0 2 n 0K (2-4) 9/26/4
f4ms_elct7.fm - 5 2.8 Calculate the reverse leakage current of the diode at temperature T. Show your calculation in the space reserved for equation (2-5) Solving equation (2-4) for I L yields, I L = 2 n 0K I L0 = 2-2 8.3 0-6 = 2.08µA (2-5) 2.9 Determine the value of the voltage V R =V R (T ). Show your calculation in the space reserved for equation (2-6). V R = R I L =.2 0 6 2.08 0-6 = 2.5V (2-6) I L = 2.µA V R = 2.5V 9/26/4
f4ms_elct7.fm - 6 Problem 3 6 points Given is an electric circuit model with two diodes, shown in Figure 3.. Both diodes in the circuit of R D 2 R 2 V M - V + D V + 2 - V N V M = 8V V N =7V R =2kΩ R 2 =kω Figure 3. A circuit with ideal diodes. Figure 3. are accurately modeled by the large-signal piecewise-linear "ideal diode" model. Problem statement For the electric circuit model of Figure 3., demonstrate an ability to:. apply the piece-wise linear models of non linear circuit elements in the process of analysis of nonlinear circuits, 2. apply the large signal method of analysis to nonlinear electric circuits containing diodes in order to determine: - values of the voltages V and V 2 whose positive reference directions are indicated in the circuit model of Figure 3.. - values of the positive reference direction currents of the diodes in the circuit model of Figure 3.. Hint # For full credit, give answers to all questions, prepare all required circuit diagrams, write all equations for which the space is reserved, and show all symbolic and numerical expressions whose evaluation produces the shown numerical results. Solution An explicit demonstration of understanding the following solution steps is expected. 3. Make an educated guess as to the bias conditions of the two diodes in the circuit of Figure 3., and show your guess by checking the conditions on all four lines below, x the diode D is forward biased, x the diode D is reverse biased, x the diode D 2 is forward biased, x the diode D 2 is reverse biased. 9/26/4
f4ms_elct7.fm - 7 3.2 Construct the linear circuit which results when the ideal diodes in the circuit of Figure 3. are replaced by their models for the biasing condition guessed in Section 3., and draw the electrical model of the constructed circuit in the space reserved for Figure 3.2 Substituting the ideal diodes D and D 2 by their equivalent circuit models for the states guessed in Section 3., gives the circuit of Figure 3.2 (by the definition of an ideal diode, a forward biased diode has an internal resistance of zero Ohms, and the internal resistance of a reverse biased diode has the infinite value). R A 2 C 2 R 2 V M A V D2 +- V v V + 2 C D - V N Figure 3.2 The circuit with ideal diodes replaced by their models for the biasing conditions vguessed D in Section 3. 3.3 To check the validity of the guesses made in Section 3., perform an analysis of the circuit of Figure 3.2 to determine the voltage across the diodes which were guessed reverse biased, and to determine the current through the diodes which were guessed forward biased. Hint #2 For a meaningful process of performing the analysis, the positive reference directions of these voltages/currents must be shown in the circuit model of Figure 3.2. Failure to show these positive reference directions reduces the credit for this part to 0.. V A = -V M = -8V (3.3-) V A2 = V A = -V M = -8V (3.3-4) V C = 0V (3.3-2) V C2 = V N = 7V (3.3-5) V D = V A - V C = -8-0 = -8V (3.3-3) V D2 = V A2 - V C2 = -8-7 = -5V (3.3-6) Both diodes in the circuit have been guessed reverse biased, and expressions (3.3-) through (3.3-6) show that their anodes are at a lower potential than their cathodes, so that both diodes are indeed reverse biased in the circuit of Figure 3.2. 3.4 Compare the result of the analysis performed in Section 3.3 with the guesses made in Section 3., to make a conclusion as to whether the bias conditions of both diodes were guessed correctly. Indicate your conclusion by appropriate checks on both lines below, x the biasing condition of both diodes has been guessed correctly, x the biasing condition of one, or more diodes has been guessed incorrectly. 9/26/4
f4ms_elct7.fm - 8 Since, now, booth guesses of Section 3., have been shown valid for the equivalent piece-wise linear circuit of Figure 3.2, their validity for the circuit in Figure 3. has also been confirmed. If the biasing condition of at least one diode is incorrect, repeat the steps of Sections 3. through 3.4 using the free space on the opposite page. 3.5 When the biasing conditions of all diodes have been guessed correctly, determine the values of the voltages V and V2 which are indicated in the circuit of Figure 3.. Show your calculation in the space reserved for equations (3-2). After the guesses which led to the construction of the circuit of Figure 3.2 have been shown correct, all results of the analysis of the circuit of Figure 3.2 are also valid for the circuit of Figure 3.. Therefore, by equations (3.3-) through (3.3-6), V = V A = -8V V 2 = V C2 = 7V V = -8V V 2 = 7V (3-2) 3.6 When the biasing conditions of all diodes have been guessed correctly, determine the values of the currents flowing through diodes D and D 2 in the circuit of Figure 3.. Show your calculation in the space reserved for equations (3-3). After the guesses which led to the construction of the linearized circuit model of Figure 3.2 have been proven correct, all results of the analysis of the circuit of Figure 3.2 are also valid for the circuit model of Figure 3.. Therefore, since both diodes are reverse biased, their currents have the value of zero Amperes, I D = 0A I D2 = 0A (3-3) 9/26/4