ECE3040 Assignment9. 1. The figures show inverting amplifier circuits.

Transcription

1 ECE3040 Assignment9 1. The figures show inverting amplifier circuits. (a) For the circuit of Fig. (a), specify R 1, R F,andR O for a voltage gain of 50, an input resistance of 2kΩ, and an output resistance of 1kΩ. If the op amp clips at a peak output voltage of 12 V, specify the maximum peak input voltage if the op amp is not to be driven into clipping. Answers: R 1 =2kΩ, R F = 100 kω, R O =1kΩ, and vi(peak) =0.24 V. (b) Fig. (b) shows the circuit of Fig. (a) with a load resistor connected to the output. Calculate the new voltage gain if R L = 1kΩ. What is the maximum peak output voltage if the op amp is not to clip? Answers: v O /v I = 25 and v O(peak) =6V. (c) Repeat part (b) if the circuit is modifiedasshowninfig. (c). Answers: v O /v I = 50 and vo(peak) =5.97 V. Hint, use voltage division to solve for vo(peak) in terms of. v 0 O(peak) 2. Fig. (a) shows an inverting amplifier with a T feedback network. Fig. (b) shows the amplifier with a Thévenin equivalent made looking into the feedback network from the input. The amplifier is to be designed for an input resistance of 1kΩ and a voltage gain of If R 2 = R 4 and R 3 = 100 Ω, specify the value of R 2 and R 4. Answers: R 1 =1kΩand R 2 = R 4 = kω. 3. The figure shows a current to voltage converter. The circuit is to be designed to convert an input current of 50 µa into an output voltage of +4 V. 1

2 (a) Calculate the required value of R F.Answer:R F =80kΩ. (b) If the op amp clips at a peak output voltage of 12 V, calculate the maximum peak input current. Answer: i 1(peak) = 150 µa. (c) The circuit is driven from an amplifier which can be modeled by a voltage-controlled voltage source with an open-circuit voltage gain of 10 and an output resistance of 2kΩ. Calculate the overall voltage gain of the two circuits in combination. Answer: v O /v I = The figure shows a non-inverting amplifier. The circuit is to be designed for an input resistance of 10 kω, and output resistance of 100 Ω, and an open-circuit voltage gain of 20. When the peak output voltage is 10 V, the current through R F and R 1 is to be 0.2mA. Specify the resistors in the circuit. Answers: R i =10kΩ, R O =100Ω, R 1 =2.5kΩ, andr F =47.5kΩ. 5. The figure shows a 4 input inverting summer. The circuit is to be designed for an output voltage given by v O = (2v I1 +4v I2 +6v I3 +8v I4 ). When the peak output voltage is 10 V, the current through R F is to be 0.5mA. Specify the resistors in the circuit. Answers: R F =20kΩ, R 1 =10kΩ, R 2 =5kΩ, R 3 =3.33 kω, andr 4 =2.5kΩ. 6. The figure shows a non-inverting summer. The gain v O /v + is specified to be 50. If R 3 = R 4 =1kΩ, specify R 1, R 2,andR F for an output voltage given by v O =5v I1 +2v I2.Answers: R F =49kΩ, R 1 =8.6kΩ, andr 2 =21.5kΩ. 2

3 7. Fig. (a) shows a differential amplifier. Fig. (b) shows the equivalent circuit for the special case R 1 = R 3 and R 2 = R F. It is desired to design the circuit so that v O =10(v I1 v I2 ).In addition, the input resistance seen between the two input nodes is to be 10 kω. (a) Specify the resistors in the circuit. Answers: R 1 = R 3 =5kΩ, R 2 = R F =50kΩ. (b) For v I2 =0, solve for the resistance seen looking into the v I1 input. Answer: 55 kω. (c) For v I1 =0, solve for the resistance seen looking into the v I2 input. Answer: 5kΩ. 8. The figure shows a differential amplifier with a source connected between its two inputs. The circuit elements values are the same as those found in problem 7. Solve for the voltage gain v O /v D, v I1, v I2, the voltage at each op amp input, and the common-mode input voltage v ICM. Answers: v O /v D =10, v I1 =5.5v D, v I2 =4.5v D, v + = v =5v D, v ICM = v O /2=5v D. 9. The figure shows a two op amp diff amp. Design the circuit for an output voltage given by v O =50(v I1 v I2 ). The input resistance to each input is to be 5kΩ. Answers: R 1 = R 2 = R F 1 = R 3 =5kΩ, R F 2 = 250 kω. 3

4 10. The figure shows a three op amp instrumentation amplifier. (a) Design the circuit such that v O1 v O2 =10(v I1 v I2 ) and v O =10(v O1 v O2 ). Answers: 1+2R F 1 /R 1 =10,choose R 1 = 2kΩ and R F 1 = 9kΩ, R F 2 /R 2 = 10, choose R F 2 = 10kΩ, and R 2 = 1kΩ. (b) For v I1 =0.03 V and v I2 =0.01 V, calculate v O1, v O2,andv O. Answers: v O1 =0.12 V, v O2 = 0.08 V, andv O =2V. 11. The figure shows a balanced output amplifier. Design the circuit so that v O1 = v O2 =6v I. When v O1 = ±12 V and v O2 = 12 V, the current through R F 1 and R F 2 is not to exceed 1mA.Answers:for1mA, R 1 =2kΩ, R F 1 =10kΩ, andr F 2 =12kΩ. 12. For the circuit shown, use superposition of v 1 and v 2 to show that v O is given by µ v O = v 1 1+ R 4 R2 + R µ 2 + v 2 1+ R 2 + R 4 R 2 R 3 kr 5 R 1 R 5 R 1 kr 5 R 5 R 1 4

5 13. Solve for the transfer function for / for the circuit below. Sketch the Bode plot, label the break frequencies, and label the gain on the zero-slope asymptotes. Answer: = Z F R 1 = R 2 R 1 1+R 3 Cs 1+(R 2 + R 3 ) Cs The circuit is to be designed as a lag-lead compensator for a motor control system. The specifications are low-frequency asymptotic gain: 2, input resistance: 10 kω, pole frequency: 1Hz, zero frequency: 10 Hz. Specify the element values. Answers: R 1 =10kΩ, R 2 =20kΩ, R 3 = Ω, andc = µf. 14. Solve for / for the circuits below. Sketch and label the Bode magnitude plots. Answers: (a) The transfer function is a low-pass shelving function with a dc gain of and a high-frequency gain of R 2 + R 3 K dc = R 1 + R 2 + R 3 K = R 2 + R 3 kr 4 R 1 + R 2 + R 3 kr 4 5

6 The transfer function is R 2 + R 3 = R 1 + R 2 + R 3 1+(R 2 kr 3 + R 4 ) Cs 1+[(R 1 + R 2 ) kr 3 + R 4 ] Cs (b) The transfer function is a high-pass shelving function. The zero-frequency gain is The high-frequency gain is The transfer function is given by = µ Vf K dc =1+ R 1 + R 2 R 3 K =1+ R 2 R 3 1 µ = 1+ R 1 + R 2 1+[(R2 + R 3 ) kr 1 ] Cs R 3 1+R 1 Cs 15. Solve for the voltage-gain transfer function for the circuit below Sketch and label the Bode magnitude plot. Answer: = R 3 Z 1 = R 3 R 1 + R 2 1+R 2 Cs 1+(R 1 kr 2 ) Cs 16. Using a single 100 µf capacitor, design a single op amp circuit which has the voltage-gain transfer function =10 1+s/10 1+s/100 Sketch and label the Bode magnitude plot. One possible answer is the circuit below. where µ V 1 µ o Vf = = 1+ R 3 1+(R1 kr 3 + R 2 ) Cs R 1 1+R 2 Cs The element values are R 1 =1kΩ, R 2 = 100 Ω, R 3 =9kΩ, andc =15.92 µf. 6

7 17. For the circuit shown, show that = R 2 R R 2 Cs 18. For the circuit shown, show that = 1+(R 1 + R 2 ) Cs 1+R 1 Cs 19. For the potentiometer circuit shown, let the resistance below the wiper be xr p and the resistance above the wiper be (1 x) R p.show that = x 1+x (1 x) RCs Show that the circuit has a minimum bandwidth when x =0.5 and that the corresponding pole frequency is given by f pole = 1 πrc 7

8 20. For the circuit shown, show that = µ 1+ R F R 1 + R 2 1+[R1 k (R 2 + R F )] Cs 1+(R 1 kr 2 ) Cs 21. The figure shows a Schmidt trigger. It is given that V SAT =12Vand R F =10kΩ. Solvefor V REF and R 1 for V A = 4V and V B =+2V.Answers:R 1 =3.33 kω, V REF = 1.33 V. 8