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 ampliFer is frequency dependent as shown in ±igure 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 ampliFer. 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 ampliFer? - + + - + - + - A (s) V (s) d d V (s) o d V (s) Figure 1: Operational amplifer with ±requency dependent gain. Using the operational ampliFer model in ±igure 1, the non-inverting ampliFer in ±igure 2(a) can be represented by the block diagram in ±igure 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 /ω+1 s 1 Figure 2: (a) Non-inverting amplifer confguration. (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 ampliFer 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 ampliFer. What is the 3 dB bandwidth of the non-inverting ampliFer response? 7. (1 point) Calculate the GBW of the non-inverting ampliFer. How does it compare to the GBW of the open-loop operational ampliFer? 8. (2 point) ±or the non-inverting ampliFer circuit, calculate the transfer function V d ( s ) /V i ( s ) using the block diagram representation in ±igure 2(b). In the limit as A o as approaches inFnity, what is V d ( s )? Now consider what happens when the output of the operational ampliFer is connected to the non-inverting input of the operational ampliFer as shown in ±igure 3(a). Using the model in ±igure 1, the circuit in ±igure 3(a) is represented using the block diagram in ±igure 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 amplifer 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 ±igure 3(a) BIBO stable?
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This note was uploaded on 07/23/2008 for the course EE 350 taught by Professor Schiano,jeffreyldas,arnab during the Fall '07 term at Penn State.

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

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