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ps11 - EE 350 PROBLEM SET 11 DUE 17 December 2007 Reading...

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EE 350 PROBLEM SET 11 DUE: 17 December 2007 Reading assignment: Lathi Chapter 7, Sections 7.1 and 7.2 Recitation sections meet the week of December 3. Problem 55: (20 points) The gain of an open-loop operational amplifier is frequency dependent as shown in Figure 1. Assume that the transfer function A d ( s ) has a single real pole at s = - ω 1 and that A o is the DC gain A d ( s ) = A o s/ω 1 + 1 , where both A o and ω 1 are positive real numbers. 1. (3 points) Sketch the Bode plot of the open-loop frequency response function V o ( ω ) /V d ( ω ) of the operational amplifier. What is the 3 dB bandwidth of the open-loop response? 2. (1 point)The gain bandwidth (GBW) product is the product of the DC gain and the 3 dB bandwidth. What is the GBW product of the open-loop operational amplifier? - + + - + - + - A (s) V (s) d d V (s) o d V (s) Figure 1: Operational amplifier with frequency dependent gain. Using the operational amplifier model in Figure 1, the non-inverting amplifier in Figure 2(a) can be represented by the block diagram in Figure 2(b). R 1 R 2 i V (s) V (s) o V (s) o i V (s) (b) + + - + (a) K + - - - Σ V (s) d Α ο +1 s 1 Figure 2: (a) Non-inverting amplifier configuration. (b) Equivalent block diagram.
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3. (2 point) What is the value of K in terms of R 1 and R 2 ? 4. (2 points) Calculate the transfer function V o ( s ) /V i ( s ) of the non-inverting amplifier circuit. 5. (1 point) Is the system described by V o ( s ) /V i ( s ) bounded-input bounded-output stable? 6. (3 points) Sketch the Bode plot of the frequency response function V o ( ω ) /V i ( ω ) of the non-inverting amplifier. What is the 3 dB bandwidth of the non-inverting amplifier response? 7. (1 point) Calculate the GBW of the non-inverting amplifier. How does it compare to the GBW of the open-loop operational amplifier? 8. (2 point) For the non-inverting amplifier circuit, calculate the transfer function V d ( s ) /V i ( s ) using the block diagram representation in Figure 2(b). In the limit as A o as approaches infinity, what is V d ( s )? Now consider what happens when the output of the operational amplifier is connected to the non-inverting input of the operational amplifier as shown in Figure 3(a). Using the model in Figure 1, the circuit in Figure 3(a) is represented using the block diagram in Figure 3(b). R 1 R 2 i V (s) V (s) o V (s) o i V (s) (b) + + (a) K - - Σ V (s) d Α ο /ω+1 s 1 + - + - Figure 3: (a) Operational amplifier circuit. (b) Equivalent block diagram. 9. (2 point) What is the value of K in terms of R 1 and R 2 ? 10. (2 point) Calculate the transfer function V o ( s ) /V i ( s ) of the circuit. 11. (1 point) Based on the result in part 10, is the circuit in Figure 3(a) BIBO stable?
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