The University of Toledo Section s7ms_elct7.fm - Electronics I Midterm # Problems Points. 4 2. 5 3. 6 Total 5 Was the exam fair? yes no
The University of Toledo s7ms_elct7.fm - 2 Problem 4 points For full credit, mark your answers yes, no, or not in all the given choices!. The number of ionized donor/acceptor atoms in a semiconductor material doped for application in semiconductor devices, at room temperatures, 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 In a pn-junction diode: x the terminal connected to the n-region of the junction is called the anode, x the atoms of the doping material added to the intrinsic semiconductor to form the p-region of the junction are called the donor atoms, x the atoms of the doping material added to the intrinsic semiconductor to form the p-region of the junction are called the acceptor atoms, x the terminal connected to the n-region of the junction is called the cathode.. 3 By raising the anode terminal to a potential of 0.V above the cathode terminal s potential, x the height of the potential barrier of a silicon pn-junction diode is increased by 0.V, x a silicon pn-junction diode s current i D reaches a value which satisfies the inequality: i D >50I S, x a silicon pn-junction diode becomes reverse biased, x the height of the potential barrier of a silicon pn-junction diode is decreased by 0.V..4 In a bridge-rectifier circuit which is "rectifying" the current of an AC energy source whose voltage is given by v s = V sm sinωt, the maximum reverse bias voltage of any diode is equal to: x _ 0.5V sm, i.e. one half of the amplitude V sm of the AC voltage v s, x V sm, i.e. one amplitude of the AC voltage v s, x 2V sm, i.e. two amplitudes V sm of the AC voltage v s, x 4V sm, i.e. four amplitudes V sm of the AC voltage v s,
The University of Toledo s7ms_elct7.fm - 3 Problem 2 5 points Given is the electrical circuit model shown in Figure 2.(a) and the constant voltage drop large-signal model of the pn-junction diode in Figure 2.(b) i D i D V DD - v D V DD = 30V R V R V Z = 30V R = MΩ -V Z 0 V DR v D (a) (b) Figure 2. A pn-junction diode circuit description. (a) PN-junction diode circuit model. (b) the constant voltage drop large-signal model of the pn-junction diode. The silicon pn-junction diode in the electrical circuit model of Figure 2.(a) has the following properties: (a) diode is "00mA devices", i.e. I DR (V DR =0.7V) =00mA; (b) diode s reverse saturation current parameter I S, measured at temperature T o =293K, has the value I So = I S (T o =293K) =0-5 A, (c) temperature dependence of diode s reverse saturation current is described by: I S doubles for every 5 o K increase in diode s temperature, (d) temperature dependence of diode s leakage current I L is described by: I L doubles for every 0 o K increase in diode s temperature; (e) the value of diode s leakage current at room temperature is not known, but the voltage V R has been measured at temperature T o =293K, and its value has been found to be V Ro =.5V. Problem Statement On the electrical circuit model of Figure 2. demonstrate an ability to determine the value of the voltage V R, to which the voltage V R in the circuit model of Figure 2. will be equal at temperature T = 333K 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. Calculate the value I Lo of diode s leakage current at temperature T o =293 o K Show your calculation in the space reserved for equation (2-). That the diode in the circuit of Figure 2. is reverse biased should be obvious after five weeks spent studying pn-junctions and diodes. That the diode does not operate in the breakdown region follows from the voltage division between the diode and the resistor. Therefore, the current which creates the voltage
The University of Toledo s7ms_elct7.fm - 4 drop V R across the resistor R in the circuit of Figure 2. is the reverse leakage current of the diode. Ohm s law provides the reverse leakage current I Lo at temperature T o =293K, V Ro.5 I Lo = = R 0 6 =.5 0-6 =.5µA (2-) 2.2 Calculate the increase in temperature T between the temperature T o at which the reverse leakage current of the diode has been calculated under 2.2 above, and the temperature T at which the value of the voltage V R ought to be determined. Show your calculation in the space reserved for equation (2-2). T = T - T o = 333-293 = 40 o K (2-2) 2.3 Determine the number of decades of degrees Kelvin in the temperature increase T. Show your calculation in the space reserved for equation (2-3). This calculation is straight forward, T 40 n 0 = = = 4 (2-3) 0K 0 2.4 Determine the ratio of the diode s reverse leakage currents at temperatures T =333K and T o =293K Show your calculation in the space reserved for equation (2-4). By the diode s property b), and by the calculated number of decades of degrees Kelvin of temperature increase. I L n = 2 0 = 2 4 = 6 I Lo (2-4) 0.5 2.5 Determine the reverse leakage current of the diode at temperature T =333K. Show your calculation in the space reserved for equation (2-5). Solving the equation (2-4) for I L I L = 6I L0 = 6.5 0-6 = 24µA (2-5) 2. 6 Determine the value of the voltage V R at temperature T =333K. Show your calculation in the space reserved for equation (2-6). By Ohm s law, V R = R I L = 0 6 24 0-6 (2-6) = 24V
The University of Toledo s7ms_elct7.fm - 5 Problem 3 6 points Given is the electrical model of a circuit with two ideal diodes shown in Figure 3.. R 2 D 2 R V M - - V V 2 V N D - V M =3V V N =9V R =8kΩ R 2 =2kΩ Figure 3. A circuit with two 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 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.
The University of Toledo s7ms_elct7.fm - 6 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. R 2 A 2 C 2 R V M - - I D2 I A C I 2 - V N V M =3V V N =9V R =8kΩ R 2 =2kΩ I D2 Figure 3.2 The circuit from Figure 3. when ideal diodes are replaced by their linear models for the states guessed in Section 3.. Substituting the ideal diodes D and D 2 by their 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). 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. Show your calculation in the space reserved for equations (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.. To formally check the guess that both diodes are forward biased, we ought to determine the direction of the currents flowing through the diodes in the circuit model of Figure 3.2. If these currents flow in the positive reference direction (anode to cathode), then the diodes are indeed forward biased in the circuit model of Figure 3.; otherwise, the guess is incorrect. Writing and solving the mesh current system of equations for the circuit of Figure 3.2, one obtains, I R 2 - I 2 0 = V M V M 3 I = = =.5mA R2 2 0 3 -I 0 I 2 R = V N V N 9 I 2 = = R 8 0 3 =.25mA The diode currents are then determined from their relations to the mesh currents as, (3-) I D = I -I 2 =.5 -.25 = 0.375 ma I D2 = I =.5mA The obtained positive values of diode currents imply that both diodes are forward biased, which confirms that the guessed bias conditions of both diodes are correct.
The University of Toledo s7ms_elct7.fm - 7 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. 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 below the values of the voltages V and V 2 which are indicated in the circuit of Figure 3.. Show your calculation in the space reserved for equations (3-2). Since both diodes are forward biased, v D = v D2 = 0V (3-2) and consequently, V 2 = v D = 0V V = v D2 V 2 = 00 = 0V 3.6 When the biasing conditions of all diodes have been guessed correctly, determine and write into the space reserved below the values of the currents flowing through diodes D and D 2 in the circuit model of Figure 3.. Show your calculation in the space reserved for equations (3-3). Since both guesses which led to the equivalent circuit of Figure 3.2 have been found correct, the results of the analysis performed on the circuit in Figure 3.2 are valid for the circuit of Figure 3.. (3-3) Consequently, by equations (3-), I D = 0.38Α I D2 =.5mA