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FET1 kth bit of input, bk 23-kR1
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to op-amp inverting input
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1557 The voltage range of feedback signal from a
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process is 5 V to +15 V, and a resolution of 005 percent of the voltage range is required How many bits are required for the DAC
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1558 Eight channels of analog information are being
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used by a computer to close eight control loops Assume that all analog signals have identical frequency content and are multiplexed into a single ADC The ADC requires 100 s per conversion The closed-loop software requires 500 s of computation and output time for four of the loops, and for the other four it requires 250 s What is the maximum frequency content that the analog signal can have according to the Nyquist criterion
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1549 The unsigned decimal number 34510 is inputted
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to a 12-bit DAC Given that RF = R0 /4,095, logic 1 corresponds to 10 V, and logic 0 to 0 V,
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Part II
Electronics
1559 A rotary potentiometer is to be used as a remote
rotational displacement sensor The maximum displacement to be measured is 180 , and the potentiometer is rated for 10 V and 270 of rotation a What voltage increment must be resolved by an ADC to resolve an angular displacement of 05 How many bits would be required in the ADC for full-range detection b The ADC requires a 10-V input voltage for full-scale binary output If an ampli er is placed between the potentiometer and the ADC, what ampli er gain should be used to take advantage of the full range of the ADC
Vhigh + Vin Vlow +
Vout
1560 Suppose it is desired to digitize a 250-kHz analog
signal to 10 bits using a successive-approximation ADC Estimate the maximum permissible conversion time for the ADC
Vout
Window Vlow Vhigh Vin
1561 A torque sensor has been mounted on a farm
tractor engine The voltage produced by the torque sensor is to be sampled by an ADC The rotational speed of the crankshaft is 800 rev/min Because of speed uctuation caused by the reciprocating action of the engine, frequency content is present in the torque signal at twice the shaft rotation frequency What is the minimum sampling period that can be used to ensure that the Nyquist criterion is satis ed
Figure P1565
1566 Design a Schmitt trigger to operate in the
1562 The output voltage of an aircraft altimeter is to be
sampled using an ADC The sensor outputs 0 V at 0 m altitude and outputs 10 V at 10,000 m altitude If the allowable error in sensing ( 1 LSB) is 10 m, nd the 2 minimum number of bits required for the ADC
presence of noise with peak amplitude = 150 mV The circuit is to switch around the reference value 1 V Assume an op-amp with 10-V supplies (Vsat = 85 V)
1567 In the circuit of Figure P1567, R1 = 100 ,
1563 Consider a circuit that generates interrupts at
xed time intervals Such a device is called a real-time clock and is used in control applications to establish the sample period as T seconds for control algorithms Show how this can be done with a square wave (clock) that has a period equal to the desired time interval between interrupts
R2 = 56 k , Ri = R1 R2 , and vin is a 1-V peak-to-peak sine wave Assuming that the supply voltages are 15 V, determine the threshold voltages (positive and negative v + ) and draw the output waveform
Ri vi R2
+ vo
1564 What is the minimum number of bits required to
digitize an analog signal with a resolution of: a 5% b 2% c 1%
Section 5: Timing Circuits 1565 A useful application that exploits the open-loop
characteristics of op amps is known as a comparator One particularly simple example known as a window comparator is shown in Figures P1565(a) and (b) Show that Vout = 0 whenever Vlow < Vin < Vhigh and that Vout = +V otherwise
Figure P1567
1568 The circuit in Figure P1568 shows how a
Schmitt trigger might be constructed with an op-amp Explain the operation of this circuit
15
Electronic Instrumentation and Measurements
Vout + Rin Vin RF
+ V Green Red
R2 R1
Figure P1568
1569 Consider again the circuit of Figure P1568 Let
Figure P1571
the op-amp be an LM741 with 15 V bias supplies, and suppose RF is chosen to be 104 k Assume Vin is a 1-kHz sinusoidal signal with 1-V amplitude a Determine the appropriate value for Rin if the output is to be high whenever |Vin | 025 V b Sketch the input and output waveforms
1572 For the circuit of Figure P1572, vin is a 100-mV
peak sine wave at 5 kHz, R = 10 k , and D1 and D2 are 62-V Zener diodes Draw the output voltage waveform
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