Electronics II. Midterm II


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1 The University of Toledo f4ms_elct7.fm  Section Electronics II Midterm II Problems Points Total 0 Was the exam fair? yes no
2 The University of Toledo f4ms_elct7.fm  Problem 7 points Given in Figure.(a) is a feedback amplifier circuit model that is to be designed. Figure.(b) shows an excerpt from the data sheet of the operational amplifier Integrated Circuit (IC) that is available to be used in the design and implementation of the circuit model of Figure.(a). A o = 40dB Σ A Midband voltage gain A fwo = 00dB DCzero frequency = 0Hz v i v f β v o HF Dominant pole frequency ω d = 6.8Krad/s Slew Rate = 0.5V/µs Power supply voltage V CC = 5V (a) (b) Figure. Feedback amplifier to be designed. (a)feedback amplifier s circuit model. (b)parameter values of the operational amplifier IC to be used as the forwardgain amplifier in the circuit of Fig..(a). For the operational amplifier IC whose parameter values are shown in Figure.(b), demonstrate an ability to:. recognize the definition of an IC operational amplifier parameters, and use their values to assess other performance metrics of the amplifier;. design the feedback amplifier, whose circuit model is shown in Figure., which will: (a) use the given IC amplifier as the forwardgain amplifier, (b) have the midband gain decreased by A o [db] WRT the given IC amplifier s; 3. analyze the feedback amplifier under design to determine: (a) bandwidth of the designed feedback amplifier, (b) fullpower bandwidth of the designed feedback amplifier. Solution Hint # For full credit, give answers to all questions, prepare all required circuit diagrams and all mathematical expressions in the space reserved for them; include all symbolic and numerical expressions whose evaluation produces the shown numerical results. An explicit demonstration of understanding the following solution steps is expected.. Calculate the value of reverse transmission factor β that will insure that the feedback amplifier of Figure. will have the midband voltage gain lesser by A o than the forwardgain IC amplifier. /3/4
3 The University of Toledo f4ms_elct7.fm  3 Show your calculation in the space reserved for equation(s) (). A fo [db] = A fwo [db]  A o = = 60 db A fo = 0 3 = 000 β A fo = 000 = 0.00 (). Prepare a drawing of the Bode plot of the asymptotic amplitude characteristic of the forward gain amplifier. Show your work in the space reserved for Figure.. 00 A fw (ω)[db] ω d A fo ω H lg ω ω d Figure. Asymptotic Bode Plot of the magnitude A fw (ω) of the given IC s transfer function A fw (s)..3 Using the prepared Bode plot of Figure., determine the bandwidth of the feedback amplifier of Figure. Show the result of your work inside the Figure., and show your calculation in the space reserved for equation(s) (). From Figure., the highfrequency corner of the midband frequency range is: ω H = 0 ω d = 0 6.8Krad/s = Krad/s = 6.8 Mrad/s BW = f H  0 = MHz 0 = MHz f H = MHz () /3/4
4 The University of Toledo f4ms_elct7.fm Determine the gainbandwidth product of the feedback amplifier of Figure.. Show your calculation in the space reserved for equation(s) (3). According to determined values of A fo and f H, GBW = A fo f H = = 0 9 = 000 MHz (3) Also, since GBW product is independent of frequency, GBW = A fwo f d = = 0 9 = 000 MHz.5 Determine the fullpower bandwidth of the feedback amplifier of Figure.. Show your calculation in the space reserved for equation(s) (4). With the railtorail output signal swing, BW fulpower = Slew rate π(v Omax  V Omin ) = Slew rate π(v CC  0) = π(50) (4) = 05 = 0.6 KHz 9.4 /3/4
5 The University of Toledo f4ms_elct7.fm  5 Problem 7 points Given is the electric circuit model of a Reference Current Source cell shown in Figure.(a). E +  V EB E +  V EB =0V C B +  V CC C B +  V CC=0V I REF I REF R int R int (a) (b) Figure. BJT Reference Current Source cell circuit model. (a) The complete circuit model. (b)nonlinear AC model for the model in Figure.(a). For the given electric circuit model of Figure.(a), demonstrate an ability to:. prepare and use in analysis the smallsignal linearized equivalent models of bipolar junction transistors (BJTs),. determine an expression for the internal AC resistance R int of a given reference current source,. Hint # For full credit, give answers to all questions, prepare all required circuit diagrams and all equations in the space reserved for them; include all symbolic and numerical expressions whose evaluation produces the shown numerical results. An explicit demonstration of understanding the following solution steps is expected Label on the circuit models in Figures.(a),.(b) and.(b) the locations of the transistor terminals: E, B, and C Prepare the nonlinear AC circuit model of the circuit model shown in Figure.(a). Show the prepared model in the space reserved for Figure.(b)..3 Prepare the smallsignal equivalent circuit model of the BJT, and show the prepared model in the space reserved for Figure.(a). /3/4
6 The University of Toledo f4ms_elct7.fm Prepare the smallsignal, linearized AC, circuit model for the circuit model shown in Figure.(a., Show the prepared model in the space reserved for Figure.(b). B i b i c C v r π be β o i b r ο v ce i t v t R int C i c B i b βo i b r ο rπ E E (a) (b) Figure. Reference Current Source circuit models. (a) Smallsignal model of the BJT transistor. (b)smallsignal linearized AC model of the BJT Reference Current Source shown in Figure.(a). Hint # Notice that in the equivalent circuits of Figures.(b) and.(b) the internal AC resistance, R int, of the analyzed Reference Current Source appears between nodes C and E. As a consequence, the remaining steps for determining R int are:.5 through.7..5 Modify the circuit model of Figure.(b) by connecting a test current source, i t, between the nodes C and E, with its current direction into C..5.6 Prepare the equations that solve the modified circuit of Figure.(b) for the voltage v t that appears across the current source i t, and has the active convention positive reference direction with respect to i t. Show the necessary symbolic calculations in the space reserved for equations (). Since the base current i b in the circuit of Figure.(b) has the value i b = 0A all of the current i t flows through resistance r o, and consequently, v t = r o i t ().7 Solve the resulting equation(s) of section.6 for the ratio v t /i t. Show the necessary symbolic calculations in the space reserved for equations (). Solving equation () gives, R int = v t i t = r o () /3/4
7 The University of Toledo f4ms_elct7.fm  7 Problem 3 6 points Given is the electric circuit model of a MOSFET differential amplifier shown in Figure 3.(a). +V DD R D =5kΩ +V DD v G +  R D R D V ID OD I D M M I S I S +  V TN =.V R D R D I SS =ma k n = 48µA/V I D I D V DD =8V M M v G I S I S v G = V GS I SS V GS V GS I SS V GS (a) (b) Figure 3. A MOSFET differential amplifier circuit model. (a) The circuit model with connected signal sources. (b)equivalent DC circuit model. for determining the quiescent operating points of the transistors in the circuit of Figure 3.(a). For the given amplifier s circuit model of Figure 3.(a), demonstrate an ability to determine:. operating point of the matched transistors in the circuit of a differential amplifier,. small signal parameters of the transistors, Hint #For full credit, give answers to all questions, prepare all required circuit diagrams and all equations in the space reserved for them; include in due succession all symbolic and numerical expressions whose evaluation produces the shown results. Solution An explicit demonstration of understanding the following solution steps is expected. 3. In the space reserved for Figure 3.(b), prepare the DC equivalent circuit model for determining the quiescent operating points of the transistors in the circuit of Figure 3.(a). 3. Calculate the drain current values of the transistors in the amplifier s circuit model of Figure 3.(b). Show your calculation in the space reserved for equation (3). I D = I S =  I SS = I SS = 03 = A (3) /3/4
8 The University of Toledo f4ms_elct7.fm Calculate the indicated gate to source voltage, V GS, of the transistor(s) in the amplifier s circuit model of Figure 3.. Show your calculation in the space reserved for equation (3) V GS = V TN + I D (3) = k =. + 5 = 6.9V n Calculate the common value of the drain to source voltages, V DS and V DS, of the transistors in the amplifier s circuit model of Figure 3.. Show your calculation in the space reserved for equation (33). KVL: V DS =  I D R D + V DD + V GS =  I SS = = 4.9V R D + V DD + V GS = (33) 3.5 In the space reserved for Figure 3., show the unilateral lowfrequency smallsignal circuit model of the MOSFET transistor. G i d D v gs g m v gs ro v ds S 3.6 Using the given values of circuit element parameters and currents, determine the value of the small signal transconductance, g m, of the transistors in the given amplifier circuit. Show your calculation in the space reserved for equation (34). I D g m = V GS V = = A/V TN (34) /3/4
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