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6.25 What internal impedance is needed for the bridge circuit of Figure 6.18 for the loading error to be
under 1% if the bridge resistances change by
dR 1 ¼ þ40 V dR 2 ¼ À40 V dR 3 ¼ þ40 V dR 4 ¼ À40 V
6.26 The input to a subwoofer loudspeaker is to pass through a passive low-pass Butterworth filter having
a cutoff frequency of 100 Hz. Specify a filter that meets the following specifications: At 50 Hz, the
signal magnitude ratio should be at least at 0.95 and at 200 Hz, the magnitude ratio should be no more
than 0.01. The sensor and load resistances are 10 V. You will need to specify the number of even
stages and the values for the components.
6.27 For the application in Problem 6.26, repeat using a Linkwitz-Riley topology to specify the reactive
element values in both a 4th-order low-pass filter and high-pass filter for 10 V speakers.
6.28 A high-pass Butterworth filter with cutoff frequency of 5000 Hz is used as a crossover to a highfrequency loudspeaker. Specify a filter such that at 2500 Hz, the attenuation should be at least
À20 dB. The source and load resistances are 10 V. You need to specify the number of stages and the
values for the components.
6.29 Design an active-RC low-pass first-order Butterworth filter for a cutoff frequency of 10 kHz, and a
passband gain of 20. Use a 741 op-amp and 0.1-mF capacitors for your design. Program Lowpass
Butterworth Active Filter can be used.
6.30 Design an active-RC first-order high-pass filter for a cutoff frequency of 10 kHz and passband gain of
10. Use a 741 op-amp.
6.31 Use the LabView program Oscilloscope to explore the workings of an actual oscilloscope. Vary
between channel A and B.
a. Characterize each signal by its waveform (i.e., triangle, square, sine). Determine the amplitude
and the period of both signals.
b. Vary the signal gain (volts/division). Explain the effect on the displayed signals.
c. Vary the time base (ms/div). Explain the effect on the displayed signals.
d. Make sure channel B is active. With the trigger source set to channel B, vary the trigger level dial.
Explain the function of the trigger level. Why do the waveforms disappear at some settings of the
trigger?
e. Repeat c, but now vary the trigger slope. Explain the effect on the signals.
6.32 Use the LabView program Butterworth_Filters to explore the behavior of low-pass, bandpass, and
high-pass Butterworth filters chosen for their flat amplitude passband. In this program, the signal
y(t) ¼ 2 sin 2pft is passed through the filter and it is the filtered signal y
Ã
t
ð Þ ¼ B sin 2pf t þ f f
ð Þ
½
that is displayed. The single-tone results show the effect at the input frequency f. The amplitude
spectrum results show the effect over the full-frequency band of interest. Describe the amplitude
behavior of the filtered signal as the single input frequency is increased. Pay particular attention near
the filter cutoff frequencies, which are set at 300 and 500 Hz.
6.33 Use the LabView program Bessel_Filters to explore the behavior of low-pass, bandpass, and highpass Bessel filters. Using the information from Problem 6.32, describe the amplitude behavior of
the filtered signal as a single-input frequency is increased from 1 to 1000 Hz.
6.34 The program Filtering_Noise demonstrates the effect of using a low-pass Butterworth filter to treat a
signal containing high-frequency noise. Set the signal frequency at 5 Hz. Set the cutoff frequency at
10 Hz. Discuss the behavior of the filter as the number of stages is increased. Then incrementally
258 Chapter 6 Analog Electrical Devices and Measurements
11:55:9 Page 258
6.25 What internal impedance is needed for the bridge circuit of Figure 6.18 for the loading error to be
under 1% if the bridge resistances change by
dR 1 ¼ þ40 V dR 2 ¼ À40 V dR 3 ¼ þ40 V dR 4 ¼ À40 V
6.26 The input to a subwoofer loudspeaker is to pass through a passive low-pass Butterworth filter having
a cutoff frequency of 100 Hz. Specify a filter that meets the following specifications: At 50 Hz, the
signal magnitude ratio should be at least at 0.95 and at 200 Hz, the magnitude ratio should be no more
than 0.01. The sensor and load resistances are 10 V. You will need to specify the number of even
stages and the values for the components.
6.27 For the application in Problem 6.26, repeat using a Linkwitz-Riley topology to specify the reactive
element values in both a 4th-order low-pass filter and high-pass filter for 10 V speakers.
6.28 A high-pass Butterworth filter with cutoff frequency of 5000 Hz is used as a crossover to a highfrequency loudspeaker. Specify a filter such that at 2500 Hz, the attenuation should be at least
À20 dB. The source and load resistances are 10 V. You need to specify the number of stages and the
values for the components.
6.29 Design an active-RC low-pass first-order Butterworth filter for a cutoff frequency of 10 kHz, and a
passband gain of 20. Use a 741 op-amp and 0.1-mF capacitors for your design. Program Lowpass
Butterworth Active Filter can be used.
6.30 Design an active-RC first-order high-pass filter for a cutoff frequency of 10 kHz and passband gain of
10. Use a 741 op-amp.
6.31 Use the LabView program Oscilloscope to explore the workings of an actual oscilloscope. Vary
between channel A and B.
a. Characterize each signal by its waveform (i.e., triangle, square, sine). Determine the amplitude
and the period of both signals.
b. Vary the signal gain (volts/division). Explain the effect on the displayed signals.
c. Vary the time base (ms/div). Explain the effect on the displayed signals.
d. Make sure channel B is active. With the trigger source set to channel B, vary the trigger level dial.
Explain the function of the trigger level. Why do the waveforms disappear at some settings of the
trigger?
e. Repeat c, but now vary the trigger slope. Explain the effect on the signals.
6.32 Use the LabView program Butterworth_Filters to explore the behavior of low-pass, bandpass, and
high-pass Butterworth filters chosen for their flat amplitude passband. In this program, the signal
y(t) ¼ 2 sin 2pft is passed through the filter and it is the filtered signal y
Ã
t
ð Þ ¼ B sin 2pf t þ f f
ð Þ
½
that is displayed. The single-tone results show the effect at the input frequency f. The amplitude
spectrum results show the effect over the full-frequency band of interest. Describe the amplitude
behavior of the filtered signal as the single input frequency is increased. Pay particular attention near
the filter cutoff frequencies, which are set at 300 and 500 Hz.
6.33 Use the LabView program Bessel_Filters to explore the behavior of low-pass, bandpass, and highpass Bessel filters. Using the information from Problem 6.32, describe the amplitude behavior of
the filtered signal as a single-input frequency is increased from 1 to 1000 Hz.
6.34 The program Filtering_Noise demonstrates the effect of using a low-pass Butterworth filter to treat a
signal containing high-frequency noise. Set the signal frequency at 5 Hz. Set the cutoff frequency at
10 Hz. Discuss the behavior of the filter as the number of stages is increased. Then incrementally
258 Chapter 6 Analog Electrical Devices and Measurements