Electronics II. Midterm #2

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1 The University of Toledo EECS:3400 Electronics I su4ms_elct7.fm Section Electronics II Midterm # Problems Points Total 0 Was the exam fair? yes no

2 The University of Toledo su4ms_elct7.fm Problem 8 points Given is the operational amplifier circuit model shown in Figure.. R v v + R v d + r d Av d + r o R L R 5kΩ R 30kΩ R L 0kΩ A85dB r d 40kΩ r o 3kΩ Figure. An operational circuit amplifier model. Parameter values of circuit elements in the given operational circuit amplifier are finite, and are given in Figure.. For the operational circuit model of Figure., demonstrate an ability to:. recognize the type of the feedback amplifier that it implements,. derive an expression for the amplifier s loop gain T in terms of the given circuit element parameters, 3. work with logarithmic units of gain/amplification. Solution 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 shown numerical results. An explicit demonstration of understanding the following solution steps is expected.. Recognize the type of the operational circuit whose model is shown in Figure., and mark below the name by which it is referred to in professional literature. For full credit, mark your answers yes, no, or not applicable for all offered answers! yes no not applicable x transresistance operational amplifier x inverting operational amplifier, x noninverting operational amplifier, x transconductance operational amplifier.. In the circuit model of Figure., show the positive reference direction for voltage v d. 7/0/4

3 The University of Toledo su4ms_elct7.fm 3.3 Calculate the value of the differential amplifier s magnitudescale voltage gain A. Show your calculation in the space reserved for equation (). A[dB] 0 A[dB] lga A Construct an auxiliary circuit for determining the loop gain of the feedback amplifier circuit shown in Figure.. Show the constructed circuit, with indicated positive reference directions of all relevant voltages, in the space reserved for Figure.. () R R r Av d d r b a v o d v + v 0V v i R 3a v v a + b + + R L Figure. Auxiliary circuit for determining the loop gain T of the amplifier whose circuit model is shown in Figure...5 Using the auxiliary circuit model of Figure., derive an expression for the loop gain T of the amplifier shown in Figure.. Show your calculation in the space reserved for equation (). R d R r d v i R d R +R d v a R a R L (R +R d ) R L (R +R d ) R L +R +R d ) v d v i v b Av d R a r o +R a T v b v i v d v v b a v a v i v d R a R d ()A R +R d ro +R a R R d L (R +R d ) ()(A) R +R d r o +R L (R +R d ) A R d R L r o (R L +R +R d )+R L (R +R d ) 7/0/4

4 The University of Toledo su4ms_elct7.fm 4.6 Calculate the numerical value of the loop gain T of the amplifier whose circuit model is shown in Figure.. Show your calculation in the space reserved for equation (3). R d R r d R r d R +r d 5 40 kω 5+40 (3) T A R d R L r o (R L +R +R d )+R L (R +R d ) ( )+ 0 4 ( ) ( ) ( ) /0/4

5 The University of Toledo su4ms_elct7.fm 5 Problem 7 points Given is the electric circuit model of a Reference Current Source cell shown in Figure.(a). S S M G M G D,D D,D R int M S I REF G + V SS M S R int G + V SS 0V (a) (b) Figure. MOSFET 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 MOSFETs,. determine an expression for the internal AC resistance of a given reference current source, R int. 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 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 six transistor terminals: S, G, D, S, G, D.. 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) Prepare the smallsignal equivalent circuit model of the MOSFET transistor, and show the prepared model in the space reserved for Figure.(a). 7/0/4

6 The University of Toledo su4ms_elct7.fm 6.4 Prepare the smallsignal, linearized AC, circuit model for the circuit model shown in Figure.(a), and show the prepared model in the space reserved for Figure.(b). S G D g m v gs g o v ds v gs v gs g m v gs S go i t v t g m v gs v g g o D,G D,G v ds v gs (a) Figure. Reference Current Source circuit models. (a) Smallsignal model of the MOSFET transistor. (b)smallsignal linearized AC model of the MOSFET Reference Current Source shown in Figure.(a). (b) S 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 S and S. 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 S and S, with its current direction into S..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. Since all energy sources in the circuit are current sources, use the S node, in Figure.(b), as the reference node, for preparing the normal form of Nodal Voltage Method equations (with unknown voltages designated by v t and v g. Show the necessary symbolic calculations in the space reserved for equations (). g o v g g o v t g m (v g + v gs ) g o v g + g o v t i t +g m v gs v gs v g v t g o v g g o v t g m (v g + v g v t ) g o v g + g o v t i t +g m (v g v t ) () (g o + g m )v g (g o + g m )v t 0 (g o + g m )v g + (g o + g m )v t i t 7/0/4

7 The University of Toledo su4ms_elct7.fm 7.7 Solve the resulting equations of section.6 for the ratio v t /i t. Show the necessary symbolic calculations in the space reserved for equations (). Hint #3 For full credit use the determinant method for solving the equations. In the case when a different solution method is used, and the resulting solution is incorrect, the credit for this section will be 0.. (g o + g m ) (g o + g m ) (g o + g m ) (g o + g m ) (g (g o + g m ) (g o + g m ) o + g m ) (g o + g m ) 0 t (g o + g m ) i t (g o + g m ) i t () v t t it (go + gm ) (g o + g m ) i t go + g m R int v t g o + g m i t r o r m r o + r m r o r m. 7/0/4

8 The University of Toledo su4ms_elct7.fm 8 Problem 3 5 points Given is the electric circuit model of a BJT differential amplifier shown in Figure 3.(a). +V CC v I + R C R C v R C R o v o C v o v o v i od C ic Q Q + i E i E i b Q i b i e i Q + e v + I v d I + v be v EE be + R EE v e R EE v d (a) (b) Figure 3. A BJT differential amplifier circuit model. (a) The circuit model with connected signal sources. (b) Equivalent AC circuit model for AC analysis of the circuit in Figure 3.(a). For the given amplifier s circuit model of Figure 3.(a), demonstrate an ability to use:. AC analysis of a BJT differential amplifier to determine the potential at the node to which both emitters are connected.. draw the conclusions suggested by the performed analysis. 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 shown numerical results. Solution An explicit demonstration of understanding the following solution steps is expected. 3. In the space reserved for Figure 3.(b), prepare the AC equivalent circuit model of the circuit model shown in Figure 3.(a). 3. In the circuits of Figure 3.(b) and 3.(b) indicate the positive reference directions for: base currents of the two transistors, emitter currents of the two transistors, base to emitter voltages of the two transistors, emitter to ground voltage. 7/0/4

9 The University of Toledo su4ms_elct7.fm Prepare the smallsignal hybridπ equivalent model of the BJT. Show the prepared model in the space reserved for Figure 3.(a). R C R C B v be i b r π β o i b E i c C v ce v d B B + C C + i b r π V BE E v e β o i b i e β o i b i e i b r π V BE E + R EE v d (a) (b) Figure 3. BJT differential amplifier circuit models. (a) Hybridπ equivalent model of the BJT. (b) Linearized equivalent AC circuit model for the differential amplifier circuit of Figure 3.(a). 3.4 Prepare the linearized AC equivalent model of the differential amplifier by replacing the transistor symbols in the circuit model of Figure3.(b) by the hybridπ equivalent model of the BJT from Figure 3.(a). Show the prepared model in the space reserved for Figure 3.(b). Hint # Check the correctness of expressions that are shown in the space reserved for equations (3). Make sure that you will be using the correct expressions in the sequel. i b g π v be i b g π v be β o i b g m r π i b g m v be β o i b g m r π i b g m v be (3) i e (+β o )i b (g π +g m )v be i e (+β o )i b (g π +g m )v be 7/0/4

10 The University of Toledo su4ms_elct7.fm Prepare the KCL equation for the emitter node in the circuit model of Figure 3.(b), followed by: substitution of emitter currents by their correct expressions from equations (3), and determining the solution of KCL equation for the emitter voltage v e. Show your calculation in the space reserved for equation (3). KCL: i e + i e + G EE v e 0 (g π +g m )v be (g π + g m )v be + G EE v e 0 (g π +g m )(v be + v be ) + G EE v e 0 (3) Voltages v be and v be are related to the voltage v e as, Therefore, (g π +g m )v e + G EE v e 0 v e 0 v d v be v d v e v be v e CONCLUSION v e 0V In the circuit model of Figure 3.(b), Emitter node has the same potential as the ground node. This fact is often reffered to by the statement: "In the Equivalent AC Circuit Model of a DiffAmp, Emitter node is a virtual ground." 7/0/4

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