The equivalent model of a certain op amp is shown in the figure given below, where R 1 = 2.8 MΩ, R 2 = 39 Ω, and A =


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1 The equivalent model of a certain op amp is shown in the figure given below, where R 1 = 2.8 MΩ, R 2 = 39 Ω, and A = Section Break Difficulty: Easy Learning Objective: Understand how real operational amplifiers (op amps) function. 1/28
2 1. Award: points Calculate the input resistance of the given circuit. The input resistance of the circuit is 2.8 ± 2% MΩ. The input resistance is the Thevenin equivalent resistance seen at the input terminals, that is R in = 2.8 MΩ. The input resistance of the circuit is 2.8 MΩ. Worksheet Difficulty: Easy Learning Objective: Understand how real operational amplifiers (op amps) function. 2/28
3 2. Award: points Calculate the output resistance of the given circuit. The output resistance of the given circuit is 39 ± 2% Ω. The output resistance is the Thevenin equivalent resistance seen at the output terminals, that is R out = 39 Ω. The output resistance of the given circuit is 39 Ω. Worksheet Difficulty: Easy Learning Objective: Understand how real operational amplifiers (op amps) function. 3/28
4 3. Award: points The openloop gain of an op amp is Calculate the output voltage when there are inputs of +10 μv on the inverting terminal and +20 μv on the noninverting terminal. The output voltage is 750 ± 2% mv. The output voltage is calculated as follows: v o = Av d = A(v 2 v 1 ) = (20 μv 10 μv) = 750 mv The output voltage is 750 mv. Worksheet Difficulty: Medium Learning Objective: Understand how real operational amplifiers (op amps) function. 4/28
5 4. Award: points The output voltage of an op amp is 1 V when the noninverting input is 1 mv. If the openloop gain of the op amp is , what is the inverting input? The inverting input of the op amp is ± 2% mv. The inverting input of the op amp is calculated as follows: v 0 = Av d = A(v 2 v 1 ) v 2 v 1 = V = mv 1 mv v 1 = mv v 1 = 1 mv ( ) = mv The inverting input of the op amp is mv. Worksheet Difficulty: Medium Learning Objective: Understand how real operational amplifiers (op amps) function. 5/28
6 5. Award: points For the op amp circuit given below, the op amp has an openloop gain of 90000, an input resistance of 14 kω, and an output resistance of 115 Ω. Find the voltage gain v 0 /v i using the nonideal model of the op amp. The voltage gain v 0 /v i of the op amp is ± 2%. The formula to find the voltage gain is derived as follows: v i + Av d + (R i + R 0 )I = 0 But v d = R i I v i + (R i + R o + R i A) I = 0 Av d R 0 I + v 0 = 0 The voltage gain is calculated as follows: 6/28
7 The voltage gain is Worksheet Difficulty: Medium Learning Objective: Understand how real operational amplifiers (op amps) function. 7/28
8 6. Award: points A 741 op amp shown in the circuit given below has an openloop voltage gain of 80000, an input resistance of 2 MΩ, and an output resistance of 110 Ω. Calculate the output voltage v 0 in the op amp circuit. The output voltage of the op amp is ± 2% mv. The formula to find the output voltage is derived as follows: (R 0 + R i )I + v i + Av d = 0 But v d = R i I v i + (R o + R i + R i A)I = 0 (1) Av d R 0 I + v o = 0 v o = Av d + R o I = (R o + R i A)I Substituting for I in equation(1), Then, the output voltage is calculated as follows: 8/28
9 v o = mv The output voltage is mv. Worksheet Difficulty: Medium Learning Objective: Understand how real operational amplifiers (op amps) function. The op amp in the circuit given below has R i = 100 kω, R 0 = 100 Ω, v S = 1 mv, and A = 100,000. Section Break Difficulty: Medium Learning Objective: Understand how real operational amplifiers (op amps) function. 9/28
10 7. Award: points Calculate the output voltage v o for the given op amp circuit. The output voltage v o for the given op amp circuit is ± 2% mv. At node V 1, which leads to At node V o, But, V d = V 1 and A = 100,000 so This gives us If V s = 1 mv, then V o = mv The output voltage v o for the given op amp circuit is mv. 10/28
11 Worksheet Difficulty: Medium Learning Objective: Understand how real operational amplifiers (op amps) function. 8. Award: points Calculate the differential voltage v d. The differential voltage v d is 9.90 ± 2% nv. The differential voltage is calculated as follows: v 0 = Av d = 100,000 v d Then,. The differential voltage v d is nv. Worksheet Difficulty: Medium Learning Objective: Understand how real operational amplifiers (op amps) function. 11/28
12 9. Award: points Calculate the output voltage v o for the given op amp circuit. The output voltage v o for the given op amp circuit is ± 2% mv. At node V 1, which leads to At node V o, But, V d = V 1 and A = 100,000 so This gives us If V s = 1 mv, then V o = mv The output voltage v o for the given op amp circuit is mv. 12/28
13 Worksheet Difficulty: Medium Learning Objective: Understand how real operational amplifiers (op amps) function. 10. Award: points Calculate the differential voltage v d. The differential voltage v d is 9.90 ± 2% nv. The differential voltage is calculated as follows: v 0 = Av d = 100,000 v d Then,. The differential voltage v d is nv. Worksheet Difficulty: Medium Learning Objective: Understand how real operational amplifiers (op amps) function. 13/28
14 11. Award: points Calculate the output voltage v o for the op amp circuit given below, where I = 1 ma and R = 3 kω. (Assume ideal op amp) The output voltage v o for the given op amp circuit is 3.0 ± 2% V. If v a and v b are the voltages at the inverting terminal and noninverting terminals of the op amp, v a = v b = 0 v 0 = V The output voltage v o for the given op amp circuit is V. Worksheet Difficulty: Easy Learning Objective: Understand that ideal op amps function nearly identical to real ones and that they can be used to effectively model them in a variety of circuit applications. 14/28
15 12. Award: points Calculate the output voltage of the op amp circuit given below, where v 1 = 2.3 V and v 2 = 1.5 V. The output voltage of the op amp circuit is 0.8 ± 2% V. The output voltage is calculated as follows: Since v a = v b = 1.5 V and i a = 0, no current flows through the 10kΩ resistance. Using the compensatory circuit concept, from the given figure we get, v a v o = 0. v o = v a 2.3 = 1.5 V 2.3 V = V The output voltage of the op amp circuit is V. Worksheet Difficulty: Easy Learning Objective: Understand that ideal op amps function nearly identical to real ones and that they can be used to effectively model them in a variety of circuit applications. 15/28
16 16/28
17 13. Award: points Find the output voltage v o for the op amp circuit given below, where V = 11 V. The output voltage v o for the given op amp circuit is 9 ± 2% V. Let v a and v b be respectively the voltages at the inverting and the noninverting terminals of the op amp. v a = v b = 11 V At the inverting terminal, v o = 9 V The output voltage v o for the given op amp circuit is 9 V. Worksheet Difficulty: Easy Learning Objective: Understand that ideal op amps function nearly identical to real ones and that they can be used to effectively model them in a variety of circuit applications. 17/28
18 14. Award: points Find the voltage gain v 0 /v s of the circuit given below, where R 1 = 17 kω and R 2 = 14 kω. The voltage gain v 0 /v s of the circuit is 2.21 ± 2%. Since no current enters the op amp, the voltage at the input of the op amp is v s. Hence, The gain v 0 /v s of the circuit is Worksheet Difficulty: Medium Learning Objective: Understand that ideal op amps function nearly identical to real ones and that they can be used to effectively model them in a variety of circuit applications. 18/28
19 15. Award: points Calculate the voltage ratio v 0 /v s for the op amp circuit given below, where R = 11 kω. Assume that the op amp is ideal. The voltage ratio v 0 /v s for the op amp circuit is ± 2%. Step 1: Label the unknown nodes in the op amp circuit. Next we write the node equations and then apply the constraint v a = v b. Finally, solve for v o in terms of v s. Step 2: Thus, and or v b = 0 = v a or or v 0 /v s = The voltage ratio v 0 /v s is /28
20 Worksheet Difficulty: Medium Learning Objective: Understand that ideal op amps function nearly identical to real ones and that they can be used to effectively model them in a variety of circuit applications. Consider the op amp circuit given below, where R 1 = 19 kω and v s = 1 V. Section Break Difficulty: Medium Learning Objective: Understand that ideal op amps function nearly identical to real ones and that they can be used to effectively model them in a variety of circuit applications. 20/28
21 16. Award: points Calculate the output voltage v 0 for the given circuit. The output voltage v o is 2.48 ± 2% V. By voltage division, But v a = v b v o = 2.48 V The output voltage v o is 2.48 V. Worksheet Difficulty: Medium Learning Objective: Understand that ideal op amps function nearly identical to real ones and that they can be used to effectively model them in a variety of circuit applications. 21/28
22 17. Award: points Calculate the output current in the circuit. The output current in the circuit is ± 2% A. The output current is calculated as follows: The output current in the circuit is A. Worksheet Difficulty: Medium Learning Objective: Understand that ideal op amps function nearly identical to real ones and that they can be used to effectively model them in a variety of circuit applications. 22/28
23 18. Award: points Determine the output voltage v o in the op amp circuit given below, where I = 7 ma. The output voltage v o is ± 2% V. The transformation of a current source to a voltage source is shown below, where v S = 35 V. At node 1, But v 2 = 0. Hence, 140 V 4v 1 = v 1 + 2v 1 2v o 140 V = 7v 1 2v o (1) At node 2,, v 2 = 0 or v 1 = 2v o (2) From (1) and (2), 140 = 14v o 2v o 23/28
24 v o = V The output voltage is V. Worksheet Difficulty: Medium Learning Objective: Understand that ideal op amps function nearly identical to real ones and that they can be used to effectively model them in a variety of circuit applications. 24/28
25 19. Award: points In the circuit given below, R 1 = 20 kω, R 2 = 66 kω, and R 3 = 2 MΩ. Calculate the gain switch is in position 1, position 2, and position 3. when the The gain at the position 1 is 4.0 ± 2%. The gain at the position 2 is ± 2%. The gain at the position 3 is 400 ± 2%. The gain is calculated as follows: Position 1: Position 2: Position 3: The gain at the position 1 is The gain at the position 2 is The gain at the position 3 is /28
26 Worksheet Difficulty: Medium Learning Objective: Understand how the basic inverting op amp is the workhorse of the op amp family. 26/28
27 20. Award: points In the circuit given below, find k in the voltage transfer function v 0 = kv s. From the figure, v 1 = v 2. Node 1 is the inverting input and node 2 is the noninverting input. Applying KCL at node 1 gives (1) Applying KCL at node 2 gives Substituting (2) into (1) yields (2) Therefore, The expression for. 27/28
28 Hint #2 Multiple Choice Difficulty: Medium Learning Objective: Understand how the basic noninverting op amp works and how they can be analyzed in electrical circuit applications. 28/28
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