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1086 ⏐⏐⏐ DECIBELS, FILTERS, AND BODE PLOTS dB
+
V i
–
Vi = 10 mV
+
V i
–
+
–
R
2.2 k�
R
4.7 k�
C 0.02 mF
FIG. 23.99
Problem 19.
R
1 k�
FIG. 23.100
Problem 20.
C
FIG. 23.101
Problem 22.
C 0.01 mF
500 pF
+
V o
–
+
V o
–
+
V o
–
11. If a 2-W speaker is replaced by one with a 40-W output,
what is the increase in decibel level?
12. Determine the dBm level for an output power of 120 mW.
13. Find the dBv gain of an amplifier that raises the voltage
level from 0.1 mV to 8.4 mV.
14. Find the output voltage of an amplifier if the applied voltage
is 20 mV and a dBv gain of 22 dB is attained.
15. If the sound pressure level is increased from 0.001 mbar to
0.016 mbar, what is the increase in dBs level?
16. What is the required increase in acoustical power to raise
a sound level from that of quiet music to very loud music?
Use Fig. 23.5.
17. a. Using semilog paper, plot XL versus frequency for a
10-mH coil and a frequency range of 100 Hz to 1 MHz.
Choose the best vertical scaling for the range of XL. b. Repeat part (a) using log-log graph paper. Compare
to the results of part (a). Which plot is more informative?
c. Using semilog paper, plot XC versus frequency for a
1-mF capacitor and a frequency range of 10 Hz to
100 kHz. Again choose the best vertical scaling for the
range of XC. d. Repeat part (a) using log-log graph paper. Compare
to the results of part (c). Which plot is more informative?
18. a. For the meter of Fig. 23.6, find the power delivered to
a load for an 8-dB reading.
b. Repeat part (a) for a �5-dB reading.
SECTION 23.5 R-C Low-Pass Filter
19. For the R-C low-pass filter of Fig. 23.99:
a. Sketch Av � Vo/Vi versus frequency using a log scale
for the frequency axis. Determine Av � Vo/Vi at 0.1fc, 0.5fc, fc, 2fc, and 10fc. b. Sketch the phase plot of v versus frequency, where v is
the angle by which Vo leads Vi. Determine v at f �
0.1fc, 0.5fc,fc, 2fc, and 10fc. *20. For the network of Fig. 23.100:
a. Determine Vo at a frequency one octave above the critical
frequency.
b. Determine Vo at a frequency one decade below the critical
frequency.
c. Do the levels of parts (a) and (b) verify the expected
frequency plot of Vo versus frequency for the filter?
21. Design an R-C low-pass filter to have a cutoff frequency of
500 Hz using a resistor of 1.2 k�. Then sketch the resulting
magnitude and phase plot for a frequency range of
0.1fc to 10fc. 22. For the low-pass filter of Fig. 23.101:
a. Determine fc. b. Find Av � Vo/Vi at f � 0.1fc, and compare to the maximum
value of 1 for the low-frequency range.
c. Find Av � Vo/Vi at f � 10fc, and compare to the minimum
value of 0 for the high-frequency range.
d. Determine the frequency at which Av � 0.01 or Vo �
1
Vi. � 100