# Electronics II. Midterm #1

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1 The University of Toledo EECS:3400 Electronics I su3ms_elct7.fm Section Electronics II Midterm # Problems Points Total 0 Was the exam fair? yes no

2 The University of Toledo su3ms_elct7.fm Problem 5 points Given is the operational circuit model shown in Figure.. i R R Av d i s R s Figure. An operational circuit model. Circuit elements in the circuit of Figure. are described by the following properties: (a) differential amplifier is accurately represented by the ideal differential amplifier model; that is A. 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 implemented amplifier s output voltage in terms of the circuit element parameters R s and R. 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 professuonal literature. For full credit, mark your answers yes, no, or not applicable for all offered answers! yes no not applicable x noninverting amplifier, x transresistance amplifier, x unity gain amplifier, x transconductance amplifier,. 5/7/4

3 The University of Toledo su3ms_elct7.fm 3. Show in in the circuit model of Figure. a positive reference direction for the current i R that flows through resistor R..3 Derive an expression for the output voltage,, of the amplifier circuit shown in Figure. Show your calculation in the space reserved for equation (). By KVL, R i R Since voltage at the operational circuit s input is the voltage of the virtual ground, 0V and R i R () Since, i R R s R s R i s R R s Rs R i s i s R R s.4 Derive an expression for the ratio of the voltage to the current i s, in the circuit model of Figure.. Show your calculation in the space reserved for equation (). i s R R s () 5/7/4

4 The University of Toledo su3ms_elct7.fm 4 Problem 6 points Given is the electric circuit model of a BJT single stage amplifier shown in Figure.(a). R C c R C C c V CC R L R 8kΩ R 6kΩ R C 4.3kΩ R E 0kΩ R L 0kΩ β o 75 B C V A 50V V CE 7.5V I C ma R C i o R L R B R RE C s E (a) (b) Figure. A single stage BJT amplifier circuit model. (a) The amplifier circuit model with connected signal source and resistive load. (b)amplifier s quivalent nonlinear AC circuit model. For the given electric circuit model of Figure.(a), demonstrate an ability to:. construct its nonlinear AC equivalent circuit,. construct its linearized AC model by replacing the transistor with its small signal model, 3. determine the values of the needed parameters in transistor s small signal linear model when the coordinates of the quiscent operating point of the transistor are known, 4. determine the values of the external small signal parameters of the given amplifier: voltage gain A v /, Solution input resistance R i /. 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.. Construct the nonlinear AC equivalent circuit model for the circuit model in Figure.(a), assuming that capacitances of all capacitors have infinite values. Show the constructed AC model in the space reserved for Figure.(b), and show the necessary calculations in the space reserved for equation (). R B R R R R R R R kΩ R CL R C R L R C R L R C R L kΩ () 5/7/4

5 The University of Toledo su3ms_elct7.fm 5. 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., B i b i c C i o r π ro R B v R be v ce CL β o i b E Figure. Given amplifier s linearized AC model in which the transistor has been replaced by its small signal linearized model. Hint # For a meaningfull process of performing the analysis in part.4, the positive reference directions of the voltages,, and the current must be shown in the circuit of Figure 3.. Failure to show these positive reference directions reduces the credit for this part to Determine which smal signal model s parameter values have not been given, and calculate them Show your calculation in the space reserved for equation (). r π β o r m β o V T I C Ω g m I C 03 V ms T () r o V A V CE I C kω.4 Using the constructed linearized AC model in Figure., determine the value of the voltage gain, A v, of the given amplifier circuit model. Show your calculation in the space reserved for equation (3). From the circuit model in Figure., i b r π r o R CL r o R CL r o R CL kΩ (3) β o i b r o R C β o r π r o R C A v vi vi β o r π r o R C /7/4

6 The University of Toledo su3ms_elct7.fm 6.5 Using the constructed linearized AC model of the given amplifier circuit shown in Figure., determine the value of the input resistance, R i, of the given amplifier circuit. Show your calculation in the space reserved for equation (4). By the circuit model in Figure., r π R B r π R B r π R B rπ R 8.4Ω B (4) R i r π R B 8.4Ω 5/7/4

7 The University of Toledo su3ms_elct7.fm 7 Problem 3 9 points Given is the electric model of a MOSFET single stage amplifier circuit shown in Figure 3.(a). R R D C c C D R c v R R v L R RS V DD R L 4kΩ R v 75kΩ R 4MΩ vi g m 5mS r o 0kΩ R G S R S R D 4kΩ R S 330Ω R 4MΩ i o R D R L (a) (b) Figure 3. A single stage MOSFET amplifier circuit model. (a) The amplifier circuit model with connected signal source and resistive load. (b)amplifier s quivalent AC circuit model. For the given amplifier model of Figure 3.(a), demonstrate an ability to:. draw its AC equivalent circuit,. prepare the linearized AC model of the given amplifier in which the transistor has been replaced by its small signal equivalent model, 3. determine the values of the given amplifier s small signal external parameters: voltage gain A v /, output resistance R o /i o. 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. Construct the nonlinear AC equivalent circuit model for the circuit model in Figure 3.(a) assuming that capacitances of all capacitors have infinite values. Show the constructed model in the space reserved for Figure 3.(b), and show the necessary calculations in the space reserved for equation (3). R G R R R R R R R 4 4 MΩ R DL R D R L R D R L RD R L 4 4 kω (3) 5/7/4

8 The University of Toledo su3ms_elct7.fm 8 3. 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 3.. R v G D i o R G v gs g m v gs S i S r o R DL v s R S Figure 3. :Lnearized AC model of the given amplifier circuit. Hint # For a meaningfull process of performing the analysis in parts 3.3 and 3.4, the positive reference directions of these voltages,, and the current must be shown in the circuit of Figure 3.. Failure to show these positive reference directions reduces the credit for these parts to Using the constructed linearized AC model of the given amplifier shown in Figure 3., determine the value of the voltage gain, A v, of the given amplifier circuit. Show your calculation in the space reserved for equation (3). From the circuit model in Figure 3., v g and i s g m v gs r o R S r o R DL v s i s R S ( g m v r o gs )R RS r o R S g m v r gs o R S DL R S r o R DL v gs v g v s g m v gs i s g m r o R S r v o R gs DL r o R S R S r vgs o R DL g m r o R S R S r o R DL g m r o g m r o R S r g m r o R o R DL S RS r o R DL g m r o R S RS r o R DL (3) i s R DL g m r o R DL (g m r o )R S r o R DL A v vi g m r o R DL (g m r o )R S r o R DL 5/7/4

9 The University of Toledo su3ms_elct7.fm Using the constructed linearized AC model shown in Figure 3., determine the value of the input resistance, R i, of the given amplifier circuit. Show your calculation in the space reserved for equation (33). R i R G kω (33) 3.5 Construct the auxhiliary linearized circuit model for determining the output resistance of the given amplifier circuit in which the output port is driven by an independent energy source. Show the constructed model in the space reserved for Figure 3.3. R v G D i x r o D i x 0V R G v gs v s v g g m v gs S i S R S r o R D R x R o r o g m v gs v x S v s R S R x v x v x (a) Figure 3.3 Auxiliary linearized circuit models for determining the output resistance of the given amplifier circuit. (a)model with the current source g m v gs.(b)model wherein the Norton s equivalen circuit with the current source g m v gs has been replaced by its Thevenin s equivalent circuit. (b) 3.6 Using the constructed linearized AC model of the given amplifier circuit shown in Figure 3.3, determine the value of the output resistance, R o, of the given amplifier circuit. Show your calculation in the space reserved for equation (34). In the circuit model of Figure 3.3(b), v g 0V, v gs v g v s 0 v s v s, Removing R D from the auxiliary circuit model of Figure 3.3(b) simplifies the calculation of the resistance R x at the small cost of adding a simple calculation of R o R D R x. KVL: (R S r o )i x v x r o g m v gs v gs v s v s R S i x } v gs R S i x (R S r o )i x v x r o g m R S i x (34) (r o g m R S R S r o )i x v x R x v x i x (r o g m )R S r o ( ) ,830Ω 7kΩ R o R D R x kΩ 5/7/4

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