Electronics II. Midterm #2

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1 The University of Toledo EECS:3400 Electronics I Section sums_elct7.fm - StudentName Electronics II Midterm # Problems Points Total 0 Was the exam fair? yes no

2 The University of Toledo sums_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 kω R 30kΩ R L 0kΩ A8dB 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: 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. 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. 7/6/

3 The University of Toledo sums_elct7.fm Calculate the value of the differential amplifier s magnitude-scale 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 a 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... 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 ) 7/6/

4 The University of Toledo sums_elct7.fm 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 40 kω 40 (-3) T A R d R L r o (R L R R d )R L (R R d ) ( ) 0 4 ( ) ( ) 0 4 ( ) /6/

5 The University of Toledo sums_elct7.fm - Problem points Figure. shows the electric circuit model of a multiple current sorce circuit, which is a part of the analog voltage amplifier circuit that was built on an Integrated Circuit that was manufactured on a CMOS tecnology processing line. V DD V DD I REF I O I O I O3 I O4 V DD V M M 0 v GS M3 M4 60 M V DD 0V I REF 0µA V SS, Figure. Multiple current source circuit. Problem Statement For the given electric circuit model of Figure., demonstrate an ability to:. recognize its two constituent parts: - the the reference voltage transistor, and - the current sources transistors,. determine the current sources currents of four current sources in the circuit model of Figure... 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 shown results. Problem Solution An explicit demonstration of understanding the following solution steps is expected.. In the list of transistor designations shown in the space reserved for equation (-), circle the transistor designation of the reference voltage transistor in the circuit of Figure.. M M M3 M4 M (-) 7/6/

6 The University of Toledo sums_elct7.fm - 6. Determine the value of the current source current I O in the circuit model of Figure.. Show the the necessary calculations in the space reserved for equation (-). The following relation is indicated in Figure.: v GS v GS v GS3 v GS4 v GS v GS Therefore, for all X x, 3, 4, : I O(X-) I REF k nx (v GSX - V TN ) k n (v GS - V TN ) k nx k n k n k n Therefore, for calculating thecurrent I O, X x applies: W X- L X- W L (-) I O I REF W 0 k n L I REF 0 0 k -6 n W L A.3 Determine the value of the current source current I O in the circuit model of Figure.. Show the the necessary calculations in the space reserved for equation (-3). I O I REF W 3 k n3 L I 3 REF 0 0 k -6 n W L A (-3).4 Determine the value of the current source current I O3 in the circuit model of Figure.. Show the the necessary calculations in the space reserved for equation (-4). I O3 I REF W 4 60 k n4 L I 4 REF 0 0 k -6 n W L A. Determine the value of the current source current I O4 in the circuit model of Figure.. Show the the necessary calculations in the space reserved for equation (-). I O4 I REF W k n L I REF 0 0 k -6 n W L A (-4) (-) 7/6/

7 The University of Toledo sums_elct7.fm - 7 Problem 3 7 points Given is the electric circuit model of a BJT differential amplifier shown in Figure 3.(a). V CC R C v o v o R C I C I C Q I E I E Q - V - BE V BE vi I EE R EE v I R C kω R EE 0kΩ I EE ma β o 90 I S fa V A 9V V CC V V EE V V CC R C v o v o R C I C I C Q I EE I E I E Q - V - BE V BE vi 0V R EE v I 0V (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 quiscent operaring points of the transistors in the circuit of Figure 3.(a). Problem Statement 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 shown results. Problem 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 quiscent operaring points of the transistors in the circuit of Figure 3.(a). 7/6/

8 The University of Toledo sums_elct7.fm Calculate the collector current values of the transistors in the amplifier s circuit miodel of Figure 3.(b). Show your calculation in the space reserved for equation (3-). Since R EE >> R C, the component of I EE that flows through R EE can be neglected in this calculation. I EE -(I E I E ) -I I E I E EE I I E I E } C -I E I EE A (3-) 3.3 Calculate the indicated base to emitter voltage, V BE, of the transistors in the amplifier s circuit miodel of Figure 3.. Show your calculation in the space reserved for equation (3-). V BE V T ln I C I S 0-3 ln V (3-) 3.4 Calculate the the common value of the collector to emitter voltages, V CE and V CE, of the transistors in the amplifier s circuit miodel of Figure 3.. Show your calculation in the space reserved for equation (3-3). V CE R C I C V CC - V B V BE V (3-3)./. 3. In the space reserved for Figure 3., show the unilateral low-frequency hybrid-π small-signal circuit model of the BJT transistor. B i i i o C v i r π β o i i r o v o E Figure 3. Unilateral small signal low-frequency hybrid-π circuit model of the BJT transistor. 7/6/

9 The University of Toledo sums_elct7.fm Using the known 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 (3-4). g m I C V T mA/V (3-4) 3.7 Using the known values of circuit element parameters and currents, determine the value of the input resistance r π of the transistors in the given amplifier circuit. Show your calculation in the space reserved for equation (3-). r π β o g m kω (3-) 7/6/

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