Electronics II. Final Examination

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1 The University of Toledo f17fs_elct27.fm 1 Electronics II Final Examination Problems Points Total 40 Was the exam fair? yes no

2 The University of Toledo f17fs_elct27.fm 2 Problem 1 11 points Given is the electric circuit model of a MOSFET single stage amplifier shown in Figure 1.1(a). R L 2.2kΩ g m 4mS R S 330 Ω V R v 1.5kΩ r o 20kΩ DD R 1 2MΩ R 2 2MΩ R 1 R v C c v v v i R 2 R v C c v D R v S R L v i R G G i i S i o R SL (a) (b) Figure 1.1 A single stage MOSFET amplifier circuit model. (a) The amplifier circuit model with connected signal source and resistive load. (b)amplifier s equivalent AC circuit model. Problem Statement For the given singlestage amplifier circuit model of Figure 1.1(a), demonstrate an ability to: 1. draw its nonlinear AC equivalent circuit, 2. prepare the linearized AC model of the given amplifier in which the transistor has been replaced by its linearized smallsignal equivalent circuit model, 3. determine the values of the given amplifier s external smallsignal parameters: voltage gain A v /v i, input resistance R i v i /i i, Hint #1 For full credit, give answers to all questions, prepare all required circuit diagrams, write all equations for which the space has been reserved, and show all symbolic and numerical expressions whose evaluation produces shown numerical results. Problem Solution An explicit demonstration of understanding the following solution steps is expected Construct the nonlinear AC equivalent circuit model for the circuit model in Figure 2.1(a) assuming that capacitances of all capacitors have infinite values. Show the constructed model in the space reserved for Figure 2.1(b), and show the necessary calculations in the space reserved for equations (11). R G R 12 R 1 R 2 R 1 R R1 R R S R L R SL R S R L RS R L MΩ 290Ω (11)

3 The University of Toledo f17fs_elct27.fm Construct the given amplifier s linearized AC model of in which the transistor has been replaced by its small signal equivalent model. Show the constructed model in the space reserved for Figure 1.2. R v i i G v gs v v v i R G v s g m v gs S r o i o R SL D Figure 1.2 Linearized AC model of the given amplifier circuit. Hint #2 For a meaningful process of performing the analysis in parts 3.3 and 3.4, the positive reference directions of these voltages v i,, and the current i i must be shown in the circuit of Figure 3.2. Failure to show these positive reference directions reduces the credit for these parts to Using the constructed linearized AC model, determine the value of the voltage gain, A v, of the given amplifier circuit. Show your calculation in the space reserved for equation (12). r From the circuit model in Figure 3.2, v i o g m g v i and gs r o R SL r o v s i o R SL ( g m v gs )R SL g m v r gs o R SL r o R SL r o R SL g m v gs R SLo with, R SLo r o R SL ro R SL Ω v gs v g v s v i g m v gs R SLo v i v gs 1 gm R SLo (12) i o g m r o r v v r o R gs g o i m SL r 1 g o R SL m R SLo g m v i 1 g m R SLo r o r o R SL i o R SL g m v i r o RSL 1 g m R SLo r o R SL g m R SLo v i 1 g m R SLo A v vi g m R SLo 1 g m R SLo

4 The University of Toledo f17fs_elct27.fm Using the constructed linearized AC model shown in Figure 1.2, determine the value of the input resistance, R i, of the given amplifier circuit. Show your calculation in the space reserved for equation (13). R i v i i i R G 1MΩ (13)

5 The University of Toledo f17fs_elct27.fm 5 Problem 2 14 points The electric circuit model of the basic current mirror is shown in Figure 2.1. V CC Reminder I REF I O R O I C I S e V T (1 VCE ) Q1 I C1 I B1 I B2 I C2 Q2 β F I C I B β FO (1 V CE ) V CC 0V Figure 2.1 Basic current mirror circuit model. Problem Statement Based on the shown current mirror s electrical circuit model of Figure 3.1, demonstrate an ability to derive: 1. The defining symbolic expression of the Mirror Ratio (MR) of a current mirror circuit; 2. the symbolic expression of the Mirror Ratio in the circuit of the basic current mirror of Figure 2.1. Hint #1 For full credit, give answers to all questions, prepare all required circuit diagrams, write all equations for which the space has been reserved, and show all symbolic and numerical expressions whose evaluation produces shown numerical results. Problem Solution For full credit, explicit demonstration of understanding the following solution steps is expected Prepare the defining symbolic expression of the quality metric Mirror Ratio (MR) of current mirror circuits. Show the prepared expression in the space reserved for equation (21). MR I O I REF (21) Indicate in the basic current mirror s circuit model of Figure 2.1 the positive reference directions of the base and collector currents of transistors Q 1 and Q 2.

6 The University of Toledo f17fs_elct27.fm Prepare the relation between the collectoremitter voltage V CE1 of the transistor Q 1.and the voltage indicated in the circuit model of Figure 3.1 Show the prepared expressions in the space reserved for equation (22) V CE1 1 2 (22) Based on the relations shown in Reminder section of Figure 2.1, prepare the expressions of the base and collector currents of transistors Q 1 and Q 2. Show the prepared expressions in the space reserved for equations (23). 1 I C1 I S e V T (1 VCE1 ) 2 I C2 I S e V T (1 VCE2 ) I B1 I C1 β F I S 1 e V T (1 V CE1 ) β FO (1 V CE1 ) V I BE S β e V T FO (23) I B2 V I BE S β e V T FO Prepare the KCL equation for the node of the collector terminal of transistor Q 1 and solve it for the current I REF ; then substitute into it the expressions for collector and base currents derived under (33), and simplify/rearrange the result. Show your work in the space reserved for equations (24). I REF I C1 I B1 I B2 I S (24) I e V T (1 VCE1 S ) 2I S β FO V T e I S e V T V CE1 (1 2 ) β FO

7 The University of Toledo f17fs_elct27.fm Using the so far prepared relations and expressions, prepare the expression of the Mirror Ratio for the Basic current mirror circuit of Figure 2.1. Show your calculation in the space reserved for equation (25). MR I O I REF I C2 I REF I C2 I C1 I B1 I B2 I S I e V S T e V T (1 V CE2 ) V CE1 (1 2 ) β FO V CE2 1 VA 1 2 β FO (25)

8 The University of Toledo f17fs_elct27.fm 8 Problem 3 6 points Given is the electric circuit model of the non inverting feedback amplifier shown in Figure 3.1(a). v i v d r d Av d ro R 2 A 80 db r d 25 kω r o 1 kω R 1 10 kω R 2 91 kω R 1 Figure 3.1 Electric circuit model of the nonirritating feedback amplifier circuit. Problem Statement On the example of the feedback amplifier circuit model of Figure 3.1, demonstrate an ability to: 1. determine the loop gain of a feedback amplifier circuit, 2. apply Blackman s theorem to determine impedance between two nodes in a feedback amplifier circuit; specifically in this case, the impedance Z i between the ground and the plus input terminal of the differential amplifier in the circuit model of Figure 3.1. Hint #1 For full credit, give answers to all questions, prepare all required circuit diagrams, write all equations for which the space has been reserved, and show all symbolic and numerical expressions whose evaluation produces shown numerical results. Problem Solution For full credit, explicit demonstration of understanding the following solution steps is expected In the space reserved for equation (31(a) show the mathematical expression of the Blackman s theorem, as applied to the input impedance of feedback amplifier s circuit model of Figure 3.1. Z i Z io F(0) F( ) Z io (a) 1 T SC F(0) R 1 T i R io OC F( ) R 1 T SC io 1 T OC (b) (31) 3.2 Observing that there are no reactive circuit elements in the circuit model of Figure 3.1, and realizing that therefore the circuit s input impedance Z i ought to be resistive, rewrite the expression (31)(a) into a resistive form expression and place this expression into the space reserved for equation (31)(b).

9 The University of Toledo f17fs_elct27.fm Prepare the auxiliary circuit model in which one could measure the passive resistance R io between the input terminals of the feedback amplifier circuit of Figure 3.1. Show the prepared model in the space reserved for Figure 3.2. A0 r d Av d ro Setting A0, passivates the amplifier circuit by removing its amplification action. R io R 2 R 1 Figure 3.2 Auxiliary circuit model in which one could measure the passive resistance between the input terminals of the feedback amplifier circuit model of Figure Determine the expression (in terms of the circuit parameters) for the resistance R io which is seen from the input terminals of the amplifier model in the circuit model of Figure 3.2, and calculate its value. Show the prepared expression in the space reserved for equation (32). R io r d R 1 (R 2 r o ) 2510 (911) kΩ (32) Prepare an auxiliary circuit model for determining the opencircuit loop gain T OC of the feedback amplifier circuit of Figure 3.1. Show the prepared model in the space reserved for Figure 3.3. v d r d Av d ro a b R 2 v a R a R v 1 b Figure 3.3 Auxiliary circuit model for determining the opencircuit loop gain T OC of the operational amplifier circuit of Figure 3.1.

10 The University of Toledo f17fs_elct27.fm Determine the expression (in terms of the circuit parameters) for the opencircuit loop gain T OC of the amplifier model in the circuit model of Figure 3.3, and calculate its value. Show the prepared expression in the space reserved for equations (33). In the circuit model of Figure 3.3, (a) no current flows through resistor r d, therefore v d 0V (b) as v d 0V, the voltage, as determined by the voltage divider formula is R 2 R 1 R a r o R 2 R 1 R a Av d 0V (c) as 0V, the voltage v b, as determined by the voltage divider formula is (33) v b R 1 R a R 2 R 1 R a 0V (d) which finally yields the opencircuit loop gain T OC value as, T OC v b v a 0V v a Prepare an auxiliary circuit model for determining the shortcircuit loop gain T SC of the feedback amplifier circuit of Figure 3.1. Show the prepared model in the space reserved for Figure 3.4. v d r d Av d ro v a a b v b R a R 1 R 2 Figure 3.4 Auxiliary circuit model for determining the shortcircuit loop gain T SC of the operational amplifier circuit of Figure 3.1.

11 The University of Toledo f17fs_elct27.fm Determine the expression (in terms of the circuit parameters) for the shortcircuit loop gain T SC of the amplifier model in the circuit model of Figure 3.4, and calculate its value. Show the prepared expression in the space reserved for equations (34). In the circuit model of Figure 3.4, (a) the voltage drop v d from the to input terminals of the diffamp is v d v a (b) the resistance R a through which node a is connected to ground is R a r d (c) by the voltage divider formula, voltage is determined as (34) Av d R 2 R 1 R a r o R 2 R 1 R a (d) by the voltage divider formula, voltage v b is determined as v b R 1 R a R 2 R 1 R a (e) combining relations (a) through (d), the shortcircuit loop gain T SC is determined as v b v T SC v b v d a v d v a R 1 R a R 2 R 1 R a R 2 R 1 R a r o R 2 R 1 R a A (1) A R 1 R a r o R 2 R 1 R a R A 1 R a ro R 2 R 1 R a Calculate the value of the input resistance of the feedback amplifier of Figure 3.1 by entering into formula (31)(b) the derived values for R io, T SO and T SC ;. Show your work in the space reserved for equations (35). R i R 1 T SC io T OC MΩ (35)

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