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 open-loop 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 open-loop 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 open-loop 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 open-loop 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 10-kΩ 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

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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 non-inverting 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

ECE2262 Electric Circuits. Chapter 4: Operational Amplifier (OP-AMP) Circuits

ECE2262 Electric Circuits. Chapter 4: Operational Amplifier (OP-AMP) Circuits ECE2262 Electric Circuits Chapter 4: Operational Amplifier (OP-AMP) Circuits 1 4.1 Operational Amplifiers 2 4. Voltages and currents in electrical circuits may represent signals and circuits can perform