# 7.7: Problems

## 1.8.1: Review Questions

1. What are the advantages of using decibels over the ordinary scheme?

2. How do decibel power and voltage gain calculations differ?

3. What does the third letter in a decibel-based signal measurement indicate (as in dBV or dBm)?

4. What is a Bode plot?

5. What is a lead network? What general response does it yield?

6. What is a lag network? What general response does it yield?

7. What do the terms $$f_1$$ and $$f_2$$ indicate about a system’s response?

8. What are the rolloff slopes for lead and lag networks?

9. What are the phase changes produced by individual lead and lag networks?

10. How is rise time related to upper break frequency?

11. How do multiple lead or lag networks interact to form an overall system response?

12. What is SPICE?

13. What is common-mode rejection?

14. What is a current mirror?

## 1.8.2: Problems

### Analysis Problems - dB emphasis

1. Convert the following power gains into dB form:

a) 10

b) 80

c) 500

d) 1

e) 0.2

f) 0.03.

2. Convert the following dB power gains into ordinary form:

a) 0 dB

b) 12 dB

c) 33.1 dB

d) 0.2 dB

e) −5.4 dB

f) −20 dB.

3. An amplifier has an input signal of 1 mW, and produces a 2 W output. What is the power gain in dB?

4. A hi-fi power amplifier has a maximum output of 50 W and a power gain of 19 dB. What is the maximum input signal power?

5. An amplifier with a power gain of 27 dB is driven by a 25 mW source. Assuming the amplifier doesn’t clip, what is the output signal in watts?

6. Convert the following voltage gains into dB form:

a) 10

b) 40

c) 250

d) 1

e) 0.5

f) 0.004

7. Convert the following dB voltage gains into ordinary form:

a) 0.5 dB

b) 0 dB

c) 46 dB

d) 10.7 dB

e) −8 dB

f) −14.5 dB

8. A guitar pre-amp has a gain of 44 dB. If the input signal is 12 mV, what is the output signal?

9. A video amplifier has a 140 mV input and a 1.2 V output. What is the voltage gain in dB?

10. The pre-amp in a particular tape deck can output a maximum signal of 4 V. If this amplifier has a gain of 18 dB, what is the maximum input signal?

11. Convert the following powers into dBW:

a) 1 W

b) 23 W

c) 6.5 W

d) 0.2W

e) 2.3 mW

f) 1.2 kW

g) 0.045 mW

h) 0.3 $$\mu$$W

i) 5.6E−18 W.

12. Repeat Problem 11 for units of dBm.

13. Repeat Problem 11 for units of dBf.

14. Convert the following voltages into dBV:

a) 12.4 V

b) 1 V

c) 0.25 V

d) 1.414 V

e) 0.1 V

f) 10.6 kV

g) 13 mV

h) 2.78 $$\mu$$V.

15. A two stage power amplifier has power gains of 12 dB and 16 dB. What is the total gain in dB and in ordinary form?

16. If the amplifier of Problem 15 has an input of −18 dBW, what is the final output in dBW? in dBm? in watts?

17. Referring to Figure 1.2.1, what are the various stages’ outputs if the input is changed to −4 dBm? to −34 dBW?

18. Which amplifier has the greatest power output?

a) 50 watts

b) 18 dBW

c) 50 dBm.

19. Which amplifier has the greatest power output?

a) 200 mW

b) −10 dBW

c) 22 dBm.

20. A three stage amplifier has voltage gains of 20 dB, 5 dB, and 12 dB respectively. What is the total voltage gain in dB and in ordinary form?

21. If the circuit of Problem 20 has an input voltage of −16 dBV, what are the outputs of the various stages in dBV? In volts?

22. Repeat Problem 21 for an input of 12 mV.

23. Which amplifier produces the largest output voltage?

a) 15 V

b) 16 dBV

### Analysis Problems – Bode plot emphasis

24. Given a lead network critical at 3 kHz, what are the gain and phase values at 100 Hz, 3 kHz, and 40 kHz?

25. Given a lag network tuned to 700 kHz, what are the gain and phase values at 50 kHz, 700 kHz, and 10 MHz? What is the rise time?

26. A noninverting amplifier has a midband voltage gain of 18 dB and a single lag network at 200 kHz. What are the gain and phase values at 30 kHz, 200 kHz, and 1 MHz. What is the rise time?

27. Repeat Problem 26 for an inverting (−180 degrees) amplifier.

28. Draw the Bode plot for the circuit of Problem 26.

29. Draw the Bode plot for the circuit of Problem 27.

30. An inverting (−180 degrees) amplifier has a midband gain of 32 dB and a single lead network critical at 20 Hz (assume the lag network $$f_c$$ is high enough to ignore for low frequency calculations). What are the gain and phase values at 4 Hz, 20Hz, and 100 Hz?

31. Repeat Problem 29 with a noninverting amplifier.

32. Draw the Bode plot for the circuit of Problem 30.

33. Draw the Bode plot for the circuit of Problem 31.

34. A noninverting amplifier used for ultrasonic applications has a midband gain of 41 dB, a lag network critical at 250 kHz, and a lead network critical at 30 kHz. Draw its gain Bode plot.

35. Find the gain and phase at 20 kHz, 100 kHz, and 800 kHz for the circuit of Problem 34.

36. If the circuit of Problem 34 has a second lag network added at 300 kHz, What are the new gain and phase values at 20 kHz, 100 kHz, and 800 kHz?

37. Draw the gain Bode plot for the circuit of Problem 36.

38. What are the maximum and minimum phase shifts across the entire frequency spectrum for the circuit of Problem 36?

39. A noninverting DC amplifier has a midband gain of 36 dB, and lag networks at 100 kHz, 750 kHz, and 1.2 MHz. Draw its gain Bode plot.

40. What are the maximum and minimum phase shifts across the entire frequency spectrum for the circuit of Problem 39?

41. What is the maximum rate of high frequency attenuation for the circuit of Problem 39 in dB/decade?

42. If an amplifier has two lead networks, what is the maximum rate of low frequency attenuation in dB/octave?

### Analysis Problems – Differential amplifier emphasis

43. Given the circuit of Figure 1.6.4, determine the single-ended input/singleended output gain for the following values: $$R_B = 5 k\Omega, R_T = 7.5 k\Omega, R_C = 12 k\Omega, V_{CC} = 25 V, V_{EE} = −9 V, r_E = 50 \Omega$$.

44. Determine the differential voltage gain in the circuit of Figure 1.6.13 if $$R_B = 15 k\Omega, R_1 = 5 k\Omega, R_2 = 7 k\Omega, R_3 = 10 k\Omega, R_C = 20 k\Omega, V_{CC} = 22 V, V_{EE} = −12 V, r_E = 75 \Omega$$.

45. For the circuit of Problem 44, determine the output at collector 2 if $$V_{in1}(t) = 0.001 \sin 2\pi 1000t$$ and $$V_{in2}(t) = −0.001 \sin 2\pi 1000t$$.

46. Determine the differential voltage gain in the circuit of Figure 1.6.15 if $$R_b = 8 k\Omega, R_{mirror} = 22 k\Omega, R_C = 10 k\Omega, V_{CC} = 18 V, V_{EE} = −15 V, r_E = 25 \Omega$$.

47. For the circuit of Problem 46, determine the output at collector 1 if $$V_{in1}(t) = −0.005 \sin 2\pi 2000t$$ and $$V_{in2}(t) = 0.005 \sin 2\pi 2000t$$.

48. Determine the tail and emitter currents in the circuit of Figure 1.6.17 if $$R_B = 6 k\Omega, R_{mirror} = 50 k\Omega, V_{CC} = 15 V, V_{EE} = −15 V, r_E = 0\Omega$$.

### Challenge Problems

49. You would like to use a voltmeter to take dBm readings in a 600 $$\Omega$$ system. What voltage should produce 0 dBm?

50. Assuming that it takes about an 8 dB increase in sound pressure level in order to produce a sound that is subjectively “twice as loud” to the human ear, can a hi-fi using a 100 W amplifier sound twice as loud as one with a 40 W amplifier (assuming the same loudspeakers)?

51. Hi-fi amplifiers are often rated with a “headroom factor” in dB. This indicates how much extra power the amplifier can produce for short periods of time, over and above its nominal rating. What is the maximum output power of a 250 W amplifier with 1.6 dB headroom?

52. If the amplifier of Problem 34 picks up an extraneous signal that is a −10 dBV sine wave at 15 kHz, what is the output?

53. If the amplifier of Problem 39 picks up a high frequency interference signal at 30 MHz, how much is it attenuated over a normal signal? If this input signal is measured at 2 dBV, what should the output be?

54. If an amplifier has two lag networks, and both are critical at 2 MHz, is the resulting $$f_2$$ less than, equal to, or greater than 2 MHz?

55. If an amplifier has two lead networks, and both are critical at 30 Hz, is the resulting $$f_1$$ less than, equal to, or greater than 30 Hz?

### Computer Simulation Problems

56. Use a simulator to plot the Bode gain response of the circuit in Problem 39.

57. Use a simulator to plot the Bode phase response of the circuit in Problem 34.

58. Use a simulation program to generate a Bode plot for a lead network comprised of a 1 k$$\Omega$$ resistor and a 100 nF capacitor.