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7.15 A 12-bit A/D converter having an E FSR ¼ 5 V has a relative accuracy of 0.03% FS (full-scale).
Estimate its quantization error in volts. What is the total possible error expected in volts? What value
of relative uncertainty might be used for this device?
7.16 A 16-bit A/D converter has a full-scale range of þ10 V. What is the resolution of this A/D in volts? If
this A/D were used to measure temperature using a sensor having a sensitivity of 0.1 mV/
C, what is
the resolution in
C?
7.17 An 8-bit single-ramp A/D converter with E FSR ¼ 10 V uses a 2.5-MHz clock and a comparator having
a threshold voltage of 1 mV. Estimate:
a. The binary output when the input voltage is E ¼ 6.000 V; when E ¼ 6.035 V.
b. The actual conversion time for the 6.000-V input and average conversion times.
c. The resolution of the converter.
7.18 Compare the maximum conversion times of a 10-bit successive approximation A/D converter to a
dual-slope ramp converter if both use a 1-MHz clock and E FSR ¼ 10 V.
7.19 An 8-bit D/A converter shows an output of 3.58 V when straight binary 10110011 is applied. What is
the output voltage when 01100100 is applied?
7.20 A 0- to 10-V, 4-bit successive approximation A/D converter is used to measure an input voltage of 4.9 V.
a. Determine the binary representation and its analog approximation of the input signal. Explain
your answer in terms of the quantization error of the A/D converter.
b. If we wanted to ensure that the analog approximation be within 2.5 mVof the actual input voltage,
estimate the number of bits required of an A/D converter.
7.21 Discuss the trade-offs between resolution and conversion rate for successive approximation, ramp,
and parallel converters.
7.22 A 0- to 10-V, 10-bit A/D converter displays an output in straight binary code of 1010110111.
Estimate the input voltage to within 1 LSB.
7.23 A Æ5-V, 8-bit A/D converter displays an output in twos-complement code of 10101011. Estimate the
input voltage to within 1 LSB.
7.24 A dual-slope A/D converter has 12-bit resolution and uses a 10-kHz internal clock. Estimate the
conversion time required for an output code equivalent to 2011 10 .
7.25 How long does it take an 8-bit single ramp A/D converter using a 1-MHz clock to convert the number
173 10 ?
7.26 A successive approximation A/D converter has a full-scale output of 0 to 10 V and uses an 8-bit
register. An input of 6.2 V is applied. Estimate the final register value.
7.27 A 12-bit A/D converter has a full-scale output of 0 to 10 V. A voltage measurement is performed, and
the register value is 010101001000. What is the value of the measured voltage?
7.28 The voltage from a 0- to 5-kg strain gauge balance scale is expected to vary from 0 to 3.50 mV. The
signal is to be recorded using a 12-bit A/D converter having a Æ5-V range with the weight displayed
on a computer monitor. Suggest an appropriate amplifier gain for this situation.
7.29 An aircraft wing oscillates under wind gusts. The oscillations are expected to be at about 2 Hz. Wingmounted strain-gauge sensors are connected to a Æ5-V, 12-bit A/D converter and data-acquisition
system to measure this. For each test block, 10 seconds of data are sampled.
a. Suggest an appropriate sample rate. Explain.
b. If the signal oscillates with an amplitude of 2 V, express the signal as a Fourier series,
306 Chapter 7 Sampling, Digital Devices, and Data Acquisition
14:43:59 Page 306
7.15 A 12-bit A/D converter having an E FSR ¼ 5 V has a relative accuracy of 0.03% FS (full-scale).
Estimate its quantization error in volts. What is the total possible error expected in volts? What value
of relative uncertainty might be used for this device?
7.16 A 16-bit A/D converter has a full-scale range of þ10 V. What is the resolution of this A/D in volts? If
this A/D were used to measure temperature using a sensor having a sensitivity of 0.1 mV/
C, what is
the resolution in
C?
7.17 An 8-bit single-ramp A/D converter with E FSR ¼ 10 V uses a 2.5-MHz clock and a comparator having
a threshold voltage of 1 mV. Estimate:
a. The binary output when the input voltage is E ¼ 6.000 V; when E ¼ 6.035 V.
b. The actual conversion time for the 6.000-V input and average conversion times.
c. The resolution of the converter.
7.18 Compare the maximum conversion times of a 10-bit successive approximation A/D converter to a
dual-slope ramp converter if both use a 1-MHz clock and E FSR ¼ 10 V.
7.19 An 8-bit D/A converter shows an output of 3.58 V when straight binary 10110011 is applied. What is
the output voltage when 01100100 is applied?
7.20 A 0- to 10-V, 4-bit successive approximation A/D converter is used to measure an input voltage of 4.9 V.
a. Determine the binary representation and its analog approximation of the input signal. Explain
your answer in terms of the quantization error of the A/D converter.
b. If we wanted to ensure that the analog approximation be within 2.5 mVof the actual input voltage,
estimate the number of bits required of an A/D converter.
7.21 Discuss the trade-offs between resolution and conversion rate for successive approximation, ramp,
and parallel converters.
7.22 A 0- to 10-V, 10-bit A/D converter displays an output in straight binary code of 1010110111.
Estimate the input voltage to within 1 LSB.
7.23 A Æ5-V, 8-bit A/D converter displays an output in twos-complement code of 10101011. Estimate the
input voltage to within 1 LSB.
7.24 A dual-slope A/D converter has 12-bit resolution and uses a 10-kHz internal clock. Estimate the
conversion time required for an output code equivalent to 2011 10 .
7.25 How long does it take an 8-bit single ramp A/D converter using a 1-MHz clock to convert the number
173 10 ?
7.26 A successive approximation A/D converter has a full-scale output of 0 to 10 V and uses an 8-bit
register. An input of 6.2 V is applied. Estimate the final register value.
7.27 A 12-bit A/D converter has a full-scale output of 0 to 10 V. A voltage measurement is performed, and
the register value is 010101001000. What is the value of the measured voltage?
7.28 The voltage from a 0- to 5-kg strain gauge balance scale is expected to vary from 0 to 3.50 mV. The
signal is to be recorded using a 12-bit A/D converter having a Æ5-V range with the weight displayed
on a computer monitor. Suggest an appropriate amplifier gain for this situation.
7.29 An aircraft wing oscillates under wind gusts. The oscillations are expected to be at about 2 Hz. Wingmounted strain-gauge sensors are connected to a Æ5-V, 12-bit A/D converter and data-acquisition
system to measure this. For each test block, 10 seconds of data are sampled.
a. Suggest an appropriate sample rate. Explain.
b. If the signal oscillates with an amplitude of 2 V, express the signal as a Fourier series,
306 Chapter 7 Sampling, Digital Devices, and Data Acquisition