Electronics I. Midterm #1

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1 The University of Toledo s6ms_elct7.fm - Electronics I Midterm # Problems Points Total 5 Was the exam fair? yes no

2 The University of Toledo s6ms_elct7.fm - 2 Problem 4 points For full credit, mark your answers yes, no, or not in all the given choices!. At room temperatures, the number of ionized donor/acceptor atoms in a semiconductor material doped for application in semiconductor devices, x depends on the concentration of donor/acceptor atoms. _ x is below 9% of all such atoms, x is close to 50% of all such atoms, x is above 99% of all such atoms, x depends on the intrinsic concentration of electron-hole pairs..2 When the reverse bias voltage v D = v AC = -2V is applied to a pn-junction diode, the electric field inside the depletion region of the diode s pn-junction: x opposes the transition of majority charge carriers through the depletion region, x opposes the transition of minority charge carriers through the depletion region x opposes the passage of holes through the depletion region in the direction from the p-region to the n-region, x opposes the passage of electrons through the depletion region in the direction from the n-region to the p-region,.3 Inside a semiconductor material: x diffusion current is caused by the presence of an external electric field, x drift current is caused by the presence of internal ionized atoms, _x diffusion current is caused by the presence of a gradient in the concentration of minority charge carriers, x drift current is caused by the presence of internal electric field,.4 The magnitude of the diffusion capacitance of a pn-junction diode under forward bias conditions: x depends on the concentration of donor atoms in the n-region, x depends on the magnitude of the current flowing through the diode, x is always greater than the junction capacitance of the diode, x depends on the temperature of the diode.

3 The University of Toledo s6ms_elct7.fm - 3 Problem 2 5 points Figure 2. shows the electrical circuit model with pn-junction diodes in it. The pn-junction diodes are v D i D I DD = 5mA R = 00Ω I DD V DD R V R Figure 2. Electrical circuit model with pn-junction diodes. identical, and have the following properties: a) at the room temperature of T o = 20 o C, diodes behave as "00mA devices", i.e. their currentvoltage relation is I DR (V DR =0.7V) =00mA; b) magnitude of the diodes breakdown voltage is V Z = 2V; c) temperature dependence of diodes reverse leakage current I L is described by: I L doubles for every 0 o K increase in diode s temperature; d) temperature dependence of diodes voltage drop v D under constant current is described by: Problem Statement v D decreases by 2mV for every o K increase in diode s temperature. Applied on the circuit model of Figure 2. demonstrate an ability to determine: - magnitude of the voltage V R when diodes are kept at temperature T o, V R (T o ). - value of the voltage drop across the current source when diodes are kept at temperature T o,v DD (T o ), - magnitude of the voltage V R when diodes are kept at temperature T = 95 o C, V R (T ). - value of the voltage drop across the current source when diodes are kept at temperature T, V DD (T ), Hint # For full credit: all equations, all answers to questions, all circuit models and other graphical representations are expected to be entered into the space designated for them; all shown numerical results must be preceded by the symbolic and numeric expressions whose evaluation produces the shown results. Problem Solution For full credit, explicit demonstration of understanding the following solution steps is expected. 2. Indicate in the electrical model of Figure 2.:

4 The University of Toledo s6ms_elct7.fm - 4 (a) positive reference directions of the voltage v D and current i D of one of the diodes, (b)active convention positive reference direction of the voltage V DD across the current source I DD. 2.2 Prepare an expression for, and calculate the value of, the indicated voltage across the resistor V R at temperature T o, V R (T o ), and show the work in the space reserved for equation (2-). Since the current through the resistor R is equal to the current of the current source I DD, by OL: V R (T o ) = R I DD = = V (2-) 2.3 Prepare an expression for, and calculate the value of, the current i D flowing through each one of the diodes in the circuit; show the process in the space reserved for equation (2-2) Since the diodes are identical, the current of the current source divides equally between the five diodes, so each diode carries the current i D I DD i D = = = ma 5 5 (2-2) 2.4 Prepare an expression for, and calculate the value of, the voltage v D (T o ) across the diodes in the circuit when diodes are kept at temperature T o ; show the process in the space reserved for equation (2-3). Since the diodes carry a lesser current i D = ma than their reference current at T o, I DR = 00mA the voltage drop across the diodes at temperature T o, is determined by v D (T o ) = V DR + v D V DR + V T 2.3 log = (-2) = = 85 = 585mV i D I DR = log = (2-3) 2.5 Prepare an expression for, and calculate the value of, the voltage drop V DD (T o ) across the current source in the circuit of Figure 2. when diodes are kept at temperature T o ; show the process in the space reserved for equation (2-4). At any temperature of the diodes, the voltage drop across the current source is given by KVL as therefore, V DD = v D + V R V DD (T o ) = v D (T o ) + V R (T o ) = 85 + =.085V (2-4)

5 The University of Toledo s6ms_elct7.fm Prepare an expression, and calculate the value of the voltage V R at temperature T, V R (T ), and show the work in the space reserved for equation (2-5). Since the current through the resistor R is equal to the current of the current source I DD, and the current of the current source does not depend on the temperature of the diodes, V R (T ) = V R (T o ) = V (2-5) 2.7 Prepare an expression for, and calculate the value of, the voltage drop v D (T ) across the diodes in the circuit of Figure 2. when diodes are kept at temperature T = 95 o C; show the process in the space reserved for equation(2-6). Since the current source drives the same current through the diodes at all temperatures, the diodes voltage is influenced by the diodes temperature in the way specified by the property (d) of the diodes. (2-6) v D (T ) = v D (T o ) + T(-0.002V) = v D (T o ) + (T T o )(-0.002V) = = (95-20)(-2) = = 435 mv 2.8 Prepare an expression for, and calculate the value of, the voltage drop V DD (T ) across the current source in the circuit of Figure 2. when diodes are kept at temperature T = 95 o C; show the process in the space reserved for equation (2-7). V DD (T ) = v D (T ) + V R (T ) = = 0.935V (2-7)

6 The University of Toledo s6ms_elct7.fm - 6 Problem 3 6 points Given is the electrical circuit model with two ideal diodes shown in Figure 3.. V M D R 2 R 2 -+ V D V 2 -+ V N R =2kΩ R 2 =kω V M =8V V N =7V Figure 3. A circuit with ideal diodes. Problem Statement On the electrical circuit model of Figure 3., demonstrate an ability to:. apply the piece-wise linear models of non linear electrical circuit elements in the process of analysis of nonlinear electrical circuits, 2. apply the large signal method of analysis to nonlinear electrical circuits that contain 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 flowing through diodes in the circuit model of Figure 3., - values of the positive reference direction voltage drops across diodes in the circuit model of Figure 3.. Hint # For full credit: all equations, all answers to questions, all circuit models and other graphical representations are expected to be entered into the space designated for them; all shown numerical results must be preceded by the symbolic and numeric expressions whose evaluation produces the shown results. Problem Solution For full credit, 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 diode D is forward biased, x diode D is reverse biased, x diode D 2 is forward biased, x iode D 2 is reverse biased.

7 The University of Toledo s6ms_elct7.fm Construct the linear circuit which results when the ideal diodes in the circuit of Figure 3. are replaced by their large-signal models for the biasing conditions 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 large-signal equivalent circuits 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 is infinite). R A 2 C 2 R 2 V M vd2 A - + V V I D 2 -+ C V N Figure 3.2 The circuit with ideal diodes replaced by their models for the biasing conditions guessed in Section 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. Show your work in the space reserved for equation (3-). Hint #2 For a meaningful process of performing the analysis, the positive reference directions of these voltages/currents must be shown in the circuit of Figure 3.2. Failure to show those positive reference directions reduces the credit for this part to 0.. Since no current flows through the resistance R 2 in the circuit of Figure 3.2, the voltage V 2 at cathode C 2 is equal to the emf of the ideal voltage source V N. At the same time, the voltage V across the forward biased diode D is equal to 0V. V C2 = V 2 = V N = 7V V = V A2 = V A = V D = 0V V D2 = V A2 - V C2 = 0-7 = -7V (3-) Which shows that the potential at A 2 is 7V below the potential of C 2, confirming that diode D 2 is reverse biased in the circuit of Figure 3.2. To formally check the guessed bias condition of diode D, one ought to determine the direction of current flowing through D in the circuit of Figure 3.2. If the current of D is in the positive reference direction (anode to cathode), diode D is forward biased; otherwise, the guess would be wrong. Writing the KVL equation for the loop containing V M, R, and D, by summing the voltage

8 The University of Toledo s6ms_elct7.fm - 8 rises in the positive reference direction of the current i D one obtains, V M - I D R - V = 0 when solved for I D, (3-) I D = V M - V 8-0 = = 4mA R The obtained positive value of the current i D means that the current flows through D in the positive reference current direction, which confirms that diode D is forward biased in the circuit of Figure 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. 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 and write into the space reserved for equations (3-2) the values of the voltages V and V 2 which are indicated in the circuit of Figure 3.. Show your determination process in the space reserved for equations (3-2). Since both guesses which led to the equivalent circuit of Figure 3.2 have been found correct, the results of analysis performed on the circuit in Figure 3.2 are also valid for the circuit of Figure 3.. Consequently, by equations (3-), (3-2) V = 0V V 2 = 7V 3.6 When the biasing conditions of all diodes have been guessed correctly, determine and write into the space reserved for equations (3-3) the values of the currents flowing through diodes D and D 2 in the circuit of Figure 3.. Show your determination process in the space reserved for equations (3-3). Since the diode D 2 is reverse biased, it does not conduct any current, so I D2 =0A. The current through diode D has been determined by equations (3-); hence, the two currents, I D = 4mA I D2 = 0A (3-3)

Electronics I. Midterm #1

Electronics I. Midterm #1 EECS:3400 Electronics I s5ms_elct7.fm - Section Electronics I Midterm # Problems Points. 4 2. 5 3. 6 Total 5 Was the exam fair? yes no EECS:3400 Electronics I s5ms_elct7.fm - 2 Problem 4 points For full