Schmalzel. J.L. "instrume The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton CRC Press llc. 2000
Schmalzel, J.L.. “Instruments” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
108 struments 108.2 Physical Variables 108.3 Transducers 108.4 Instrument elements 108.5 Instrumentation System 108.6 Modeling Elements of an Instrumentation System 108.7 Summary of Noise Reduction Technique 108.8 Personal Computer-Based Instruments 108.9 Modeling PC-Based Instruments John L. Schmalzel e Effects of Sampling Rowan University 108.11 Other Factors 108.1 Introduction Instruments are the means for monitoring or measuring physical variables. The basic elements of an instru- mentation application are shown in Fig. 108. 1. A physical system produces a measurand, m(o), shown as time- varying, which is transformed by a transducer into an electrical signal, s(t), that is then processed by an instrument to yield the desired output information variable, i(t). Producing meaningful information from physical variables requires conversion and processing Electronic instruments require that physical variables be converted to electrical signals through a process of transduction, followed by signal conditioning and signal processing to obtain useful results 108.2 Physical variables The measurand can be one of many physical variables; the type depends on the application. For example, in process control, typical measurands can include pressure, temperature, and flow. Representative physical vari- ables with corresponding units are summarized in Table 108.1 108.3 Transducers Transducers convert one form of energy to another. To be useful for an electronic instrument, a transducer must produce an electrical output such as voltage or current to allow required signal conditioning and signal processing steps to be completed A variety of transducers are available to meet a measurement requirement; ome common examples are listed in Table 108.2. Transducers can be compared based on their operating principles, the measurand range, interface design, and reliability. Khazan [ 1994] gives a complete summary of transducer schemes c 2000 by CRC Press LLC
© 2000 by CRC Press LLC 108 Instruments 108.1 Introduction 108.2 Physical Variables 108.3 Transducers 108.4 Instrument Elements 108.5 Instrumentation System 108.6 Modeling Elements of an Instrumentation System 108.7 Summary of Noise Reduction Techniques 108.8 Personal Computer-Based Instruments 108.9 Modeling PC-Based Instruments 108.10 The Effects of Sampling 108.11 Other Factors 108.1 Introduction Instruments are the means for monitoring or measuring physical variables. The basic elements of an instrumentation application are shown in Fig. 108.1. A physical system produces a measurand, m(t), shown as timevarying, which is transformed by a transducer into an electrical signal, s(t), that is then processed by an instrument to yield the desired output information variable, i(t). Producing meaningful information from physical variables requires conversion and processing. Electronic instruments require that physical variables be converted to electrical signals through a process of transduction, followed by signal conditioning and signal processing to obtain useful results. 108.2 Physical Variables The measurand can be one of many physical variables; the type depends on the application. For example, in process control, typical measurands can include pressure, temperature, and flow. Representative physical variables with corresponding units are summarized in Table 108.1. 108.3 Transducers Transducers convert one form of energy to another. To be useful for an electronic instrument, a transducer must produce an electrical output such as voltage or current to allow required signal conditioning and signal processing steps to be completed. A variety of transducers are available to meet a measurement requirement; some common examples are listed in Table 108.2. Transducers can be compared based on their operating principles, the measurand range, interface design, and reliability. Khazan [1994] gives a complete summary of transducer schemes. John L. Schmalzel Rowan University
PHYSICAL Lm( TRANSDUCER Ls(D_ INSTRUMENT Li(t) SYSTEM FIGURE 108.1 Generalized block diagram of an instrument applied to a physical measurement. TABLE 108 1 Representative Physical Variables, Physical Variable Symbol SI Units, Abbreviations N EFQfLmPPRrtvv he flow rate, m /s hertz, Hz m kilogram, kg N/m2 Watt. w ohm. Q Temperature Velocity TABLE 108.2 Representative Transducers Measurand Transducer Operating Principles Displacement Resistive Change in resistance, capacitance, Capacitive inductance caused by linear or angular Inductive displacement of transducer element Force Strain gage Resistance, piezoresistivity Temperature Thermistor Resistance Thermocouple Peltier, seebeck effect Pressure Diaphragm motion sensed by a displacement technique. Differential pressure Pressure drop across restriction Turbine Angular velocity proportional to flow rate 108.4 Instrument elements ignal conditioning consists of amplification, filtering, limiting, and other operations that prepare the raw nstrument input signal for further operations. The signal may be the output of a transducer or it may be an electrical signal obtained directly from an electronic device or circuit Signal processing applies some algorithm to the basic signal in order to obtain meaningful information. Signal conditioning and processing operatic may be performed using analog or digital circuit techniques, or using a combination of methods. There are a variety of trade-offs between them. For example, analog methods offer bandwidth advantages, whereas digital techniques offer advanced algorithm support and long-term stability. The use of microprocessors within an instrument makes it possible to perform many useful functions including calibration, linearization, conversion, storage,display, and transmission. A block diagram of a representative microprocessor-based instrument is e 2000 by CRC Press LLC
© 2000 by CRC Press LLC 108.4 Instrument Elements Signal conditioning consists of amplification, filtering, limiting, and other operations that prepare the raw instrument input signal for further operations. The signal may be the output of a transducer or it may be an electrical signal obtained directly from an electronic device or circuit. Signal processing applies some algorithm to the basic signal in order to obtain meaningful information. Signal conditioning and processing operations may be performed using analog or digital circuit techniques, or using a combination of methods. There are a variety of trade-offs between them. For example, analog methods offer bandwidth advantages, whereas digital techniques offer advanced algorithm support and long-term stability. The use of microprocessors within an instrument makes it possible to perform many useful functions including calibration, linearization, conversion, storage, display, and transmission. A block diagram of a representative microprocessor-based instrument is shown in Fig. 108.2. FIGURE 108.1 Generalized block diagram of an instrument applied to a physical measurement. TABLE 108.1 Representative Physical Variables, Symbols, and Units Physical Variable Symbol SI Units, Abbreviations Current I ampere, A Energy E joule, J Force F newton, N Flow Q volume flow rate, m3 /s Frequency f hertz, Hz Length L meter, m Mass m kilogram, kg Pressure P N/m2 Power P Watt, W Resistance R ohm, W Temperature T Kelvin, K Time t second, s Velocity V m/s Voltage V volt, V TABLE 108.2 Representative Transducers Measurand Transducer Operating Principles Displacement Resistive Change in resistance, capacitance, or (Length) Capacitive inductance caused by linear or angular Inductive displacement of transducer element Force Strain gage Resistance, piezoresistivity Temperature Thermistor Resistance Thermocouple Peltier, seebeck effect Pressure Diaphragm Diaphragm motion sensed by a displacement technique. Flow Differential pressure Pressure drop across restriction Turbine Angular velocity proportional to flow rate
DISPLAY Physical TRANSDUCER TIONENO ESSING INPUTHOUTP MICROPROCESSOR WER SUPPL STORAGE FIGURE 108.2 Block diagram of generalized, microprocessor-based instrument. 108.5 Instrumentation System An instrument is never used in isolation. The instrumentation components contribute to an overall system response in a number of ways that are based on the measurement system elements present. These elements include:(1)sources,(2)interconnect, (3)device or system under test, (4)response measuring equipment, and (5)environmental variables. Figure 108.3 shows the elements of a typical instrumentation system 108.6 Modeling Elements of an Instrumentation System est results are achieved when the instrumentation system is clearly understood, and its effects compensated for when practical. Lumped parameter modeling of the elements shown in Fig. 108.3 provides a means for determining the contribution each element makes to the overall system behavior. Of particular importance are the input and output impedances of each element. In addition, the effects of interconnect and environmental variables can also be modeled to determine their influence on the system. The relative dimensions of the measurement system with respect to the highest frequencies encountered-whether signal or noise--determine whether simplified circuit theory models, or generalized solutions to Maxwell's equations must be used. theory models can be used. Operation in this regime also allows impedance matching to be largely ignored e.g., not requiring mandatory use of 50 Q2 sources, 50 Q2 transmission lines, and 50 Q2 terminations which is commonly encountered in high-frequency systems. Table 108.3 summarizes several common instruments and input or output impedance models corresponding to Fig 108.4. At low frequencies, interconnect can be modeled r ignoring the ver ce(Zsl, Zs2)terms, and considering only the shi TAL INTERCONNECT DEVICE UNDER INTERCONNECT I NSTRUMENTS MEASUREMENT SYSTEM FIGURE 108.3 Fundamental elements of an instrumentation system. e 2000 by CRC Press LLC
© 2000 by CRC Press LLC 108.5 Instrumentation System An instrument is never used in isolation. The instrumentation components contribute to an overall system response in a number of ways that are based on the measurement system elements present. These elements include: (1) sources, (2) interconnect, (3) device or system under test, (4) response measuring equipment, and (5) environmental variables. Figure 108.3 shows the elements of a typical instrumentation system. 108.6 Modeling Elements of an Instrumentation System Best results are achieved when the instrumentation system is clearly understood, and its effects compensated for when practical. Lumped parameter modeling of the elements shown in Fig. 108.3 provides a means for determining the contribution each element makes to the overall system behavior. Of particular importance are the input and output impedances of each element. In addition, the effects of interconnect and environmental variables can also be modeled to determine their influence on the system. The relative dimensions of the measurement system with respect to the highest frequencies encountered—whether signal or noise—determine whether simplified circuit theory models, or generalized solutions to Maxwell's equations must be used. Generally, if measurement system dimensions are on the order of 1/20 of the shortest wavelength, simple circuit theory models can be used. Operation in this regime also allows impedance matching to be largely ignored; e.g., not requiring mandatory use of 50 W sources, 50 W transmission lines, and 50 W terminations which is commonly encountered in high-frequency systems. Table 108.3 summarizes several common instruments and input or output impedance models corresponding to Fig. 108.4.At low frequencies, interconnect can be modeled by ignoring the very low series resistance and inductance (Zs1, Zs2) terms, and considering only the shunt FIGURE 108.2 Block diagram of generalized, microprocessor-based instrument. FIGURE 108.3 Fundamental elements of an instrumentation system
CASSINI SPACECRAFT O ne of NASAs latest planetary systems research segments is called the Discovery Program. This program is an effort to develop frequent, small planetary missions that perform high quality scientific investigations. Discovery missions planned for 1997 include the sending of a Mars lander to the planet and launching the Lunar Prospector to map the moon's surface composition. The principle planetary mission of NASAs Discovery Program is the 1997 launch of Cassini. Cassini is a joint project of NASA, the European Space Agency(ESA), and the Italian Space Agency, and managed by the Jet Propulsion Laboratory (PL) The flight vehicle consists of the main Cassini spacecraft and the ESA-built Huygens Probe, a 750-pound, six instrument package that will descend into the atmosphere of Saturns moon Titan, which is believed to be chemically similar to the atmosphere of early Earth Launched towards the end of 1997, Cassini will make flybys of Venus and Jupiter en route to a rendezvous with Saturn in July 2004. Cassini will release the Huygens Probe during its first orbit, then make approximately 40 revolutions over a span of four years, while the spacecrafts 12 instruments onduct a detailed exploration of the whole Saturnian system, including Titan and the planets other icy moons. (Courtesy of National Aeronautics and Space Administration. This artist,'s concept shows the Cassini spacecraft orbiting around Saturn just after deploying a probe that will descend into the atmosphere of Saturns moon Titan. Launched October 1997, Cassini will reach Saturn in July 2004 and orbit the planet for four years thereafter.(Photo courtesy of National Aeronautics and Space Administration. capacitance(Zp) which is in the range of 50 to 150 pF/m for different types of cable. At high frequencies, the haracteristic impedance of the interconnect is used;e.g, 50 Q2 or 75 @2 for commonly used coaxial cables; 120 Q2 for twisted pair The response of an entire instrumentation system can be modeled by interconnecting the individual me elements. Figure 108.5 shows an le that was obtained by substituting models for an operational amplifier e 2000 by CRC Press LLC
© 2000 by CRC Press LLC capacitance (Zp) which is in the range of 50 to 150 pF/m for different types of cable. At high frequencies, the characteristic impedance of the interconnect is used; e.g., 50 W or 75 W for commonly used coaxial cables; 120 W for twisted pair. The response of an entire instrumentation system can be modeled by interconnecting the individual model elements. Figure 108.5 shows an example that was obtained by substituting models for an operational amplifier CASSINI SPACECRAFT ne of NASA’s latest planetary systems research segments is called the Discovery Program. This program is an effort to develop frequent, small planetary missions that perform high quality scientific investigations. Discovery missions planned for 1997 include the sending of a Mars lander to the planet and launching the Lunar Prospector to map the moon’s surface composition. The principle planetary mission of NASA’s Discovery Program is the 1997 launch of Cassini. Cassini is a joint project of NASA, the European Space Agency (ESA), and the Italian Space Agency, and is managed by the Jet Propulsion Laboratory (JPL). The flight vehicle consists of the main Cassini spacecraft and the ESA-built Huygens Probe, a 750-pound, six instrument package that will descend into the atmosphere of Saturn’s moon Titan, which is believed to be chemically similar to the atmosphere of early Earth. Launched towards the end of 1997, Cassini will make flybys of Venus and Jupiter en route to a rendezvous with Saturn in July 2004. Cassini will release the Huygens Probe during its first orbit, then make approximately 40 revolutions over a span of four years, while the spacecraft’s 12 instruments conduct a detailed exploration of the whole Saturnian system, including Titan and the planet’s other icy moons. (Courtesy of National Aeronautics and Space Administration.) This artist’s concept shows the Cassini spacecraft orbiting around Saturn, just after deploying a probe that will descend into the atmosphere of Saturn’s moon Titan. Launched October 1997, Cassini will reach Saturn in July 2004 and orbit the planet for four years thereafter. (Photo courtesy of National Aeronautics and Space Administration.) O
108.3 Summary of Common Instruments and Their Lumped-Parameter Models ent Description, Model, Manufacturer Input Impedance, Zi Output Impedance, Z Function generator, FG501A, Tektronix 50 Multimeter, DM501A. Tektronix 10 MQ2(Volts mode) Oscilloscope, 54601A, Hewlett Packard I MQ213 PF Output Impedance Series Impedances Input Impedance SOURCE MODEL FIGURE 108.4 Simplified output and input models for instrument elements. Output Impedan Output Impedance -Zoo Zi SOURCE MODEL LOAD MODEL P AMP INPUT )P AMP OUTPUT IOX PROBE LOAD MODEL FIGURE 108.5 Model of representative instrumentation system. Each variable would be substituted as required. For example, Vs= 1.0sin2r1000t for a 0.707 Vrms, I kHz sine wave; Zo= 50 ]2 for the FG501A; Zi= 1 kQ2 for an op amp configured as an inverting amplifier with Ri= 1 kQ and gain of 10; AcVi=-100sin2r1000t; Zo= 1 Q2 for low current utput; Zi=9 MQ2lI1 4 PF for a compensated 10X probe; and with Zi= 1 MQ2ll13 PF for the input model of the HP54601A oscilloscope. (op amp)circuit(corresponds to the device under test in Fig. 1083)that was driven by a function generator for the source, and that measured the response with an oscilloscope connected to the output of the op amp using a 10X probe In this application, the impedance of the interconnect between the source and op amp can be neglected since the frequencies are low and the input impedance of the op amp is much greater than that of the cable. The circuit model of the compensated 10x probe contains a very high series impedance (9 MQ2lI1 14 pF)relative to the oscilloscope(1 MQ2 l13 pF)so it cannot be ignored. The models can be used to determine the frequency response of the complete system which describes the magnitude and phase response of the system to sinusoidal, steady-state inputs. This can reveal the contribution of each element to the overall response and helps indicate which elements produce the dominant response The graphical results of the frequency response analysis is termed a Bode plot. If each of n elements has an individual transfer function, H Go), i=1 to N, then a composite transfer function can be found for the total ystem, Tio), which is generally not the simple product of each transfer function, H, Go).H, Go).... HGo) due to loading effects between elements. The use of a circuit simulation program such as PSpice(MicroSim Corp )simplifies the investigation into instrument behavior. A library of subcircuit models can be developed for each instrumentation and interconnect element to support measurement system loading effects analy For example, a PSpice subcircuit definition for the HP54601A oscilloscope is SUBCKT HP54601A 1 2 Cin 1 2 13p in 1 2 1MEG ENDS e 2000 by CRC Press LLC
© 2000 by CRC Press LLC (op amp) circuit (corresponds to the device under test in Fig. 108.3) that was driven by a function generator for the source, and that measured the response with an oscilloscope connected to the output of the op amp using a 10X probe. In this application, the impedance of the interconnect between the source and op amp can be neglected since the frequencies are low and the input impedance of the op amp is much greater than that of the cable. The circuit model of the compensated 10X probe contains a very high series impedance (9 MW||1.14 pF) relative to the oscilloscope (1 MW||13 pF) so it cannot be ignored. The models can be used to determine the frequency response of the complete system which describes the magnitude and phase response of the system to sinusoidal, steady-state inputs. This can reveal the contribution of each element to the overall response and helps indicate which elements produce the dominant response. The graphical results of the frequency response analysis is termed a Bode plot. If each of N elements has an individual transfer function, Hi (jw), i = 1 to N, then a composite transfer function can be found for the total system, T(jw), which is generally not the simple product of each transfer function, H1(jw)·H2(jw)·…·HN(jw) due to loading effects between elements. The use of a circuit simulation program such as PSpice (MicroSim Corp.) simplifies the investigation into instrument behavior. A library of subcircuit models can be developed for each instrumentation and interconnect element to support measurement system loading effects analysis. For example, a PSpice subcircuit definition for the HP54601A oscilloscope is: .SUBCKT HP54601A 1 2 Cin 1 2 13p Rin 1 2 1MEG .ENDS TABLE 108.3 Summary of Common Instruments and Their Lumped-Parameter Models Instrument Description, Model, Manufacturer Input Impedance, Zi Output Impedance, Zo Function generator, FG501A, Tektronix 50 W Multimeter, DM501A, Tektronix 10 MW (Volts mode) Oscilloscope, 54601A, Hewlett Packard 1 MW||13 pF FIGURE 108.4 Simplified output and input models for instrument elements. FIGURE 108.5 Model of representative instrumentation system. Each variable would be substituted as required. For example, Vs = 1.0sin2p1000t for a 0.707 Vrms, 1 kHz sine wave; Zo = 50 W for the FG501A; Zi = 1 kW for an op amp configured as an inverting amplifier with Ri = 1 kW; and gain of 10; AcVi = -10.0sin2p1000t; Zo = 1 W for low current output; Zi = 9 MW||1.4 pF for a compensated 10X probe; and with Zi = 1 MW||13 pF for the input model of the HP54601A oscilloscope
TABLE 108. 4 Noise Reduction Checklist Source Interconnect Response Shield enclosures Shield leads Shield Filter inputs and outputs Minimize loop area(twist leads) Filter inputs and outputs Limit bandwidth Keep signal leads near ground Limit bandwidth Separate low, high-level signals Mi Keep signal and ground leads short Low f Use single ground High f: Use multiple grounds Source: H W. Ott, Noise Reduction Techniques in Electronic Systems, 2nd ed, New York: John Wiley Sons, 1988. With permission. This network model would be added as a load to the output of the device under test in order to predict its 108.7 Summary of Noise Reduction Techniques Elimination of undesired measurement errors benefits from a systematic approach to identifying and solving noise problems. Source, interconnect, and response elements of a measurement system can be treated individ ually. Some techniques, such as shielding, are applicable to all three. Various combinations of techniques should be tried to achieve best results. There are many choices of grounding techniques that vary depending on whether elements are floating or ground-referred, and based on bandwidth. In general, multiple ground connections that create ground loops should be avoided. Difficult ground loop problems may require isolation or other techniques to interrupt the ground connection between elements. Table 108.4 summarizes a checklist of noise eduction techni 108.8 Personal Computer-Based Instruments Many instrument functions are available for interface to personal computer(PC)systems. These range from plug-in cards that reside on the PC backplane to standalone instruments that communicate with the PC over standard interfaces such as RS-232 or IEEE-488 Software to control data acquisition, analysis, and display completes the computer-based instrument. Examples of such software include Lab Windows or Lab View (National Instruments), HP VEE(Hewlett-Packard), and Testpoint(Keithley-Metrabyte). Figure 108.6 shows a block diagram of an output screen developed using Lab Windows for an acoustic measurement application.a GRAPH OF SPL CURVESK TITLE: PND MEDIUM Lmax ED3-LINE DISPLAY IGRAPH OF DATA) TEXT DISPLAY AREA: FILE NAME FIGURE 108.6 Example block diagram of a virtual instrument user interface. e 2000 by CRC Press LLC
© 2000 by CRC Press LLC This network model would be added as a load to the output of the device under test in order to predict its loaded behavior. 108.7 Summary of Noise Reduction Techniques Elimination of undesired measurement errors benefits from a systematic approach to identifying and solving noise problems. Source, interconnect, and response elements of a measurement system can be treated individually. Some techniques, such as shielding, are applicable to all three.Various combinations of techniques should be tried to achieve best results. There are many choices of grounding techniques that vary depending on whether elements are floating or ground-referred, and based on bandwidth. In general, multiple ground connections that create ground loops should be avoided. Difficult ground loop problems may require isolation or other techniques to interrupt the ground connection between elements. Table 108.4 summarizes a checklist of noise reduction techniques. 108.8 Personal Computer-Based Instruments Many instrument functions are available for interface to personal computer (PC) systems. These range from plug-in cards that reside on the PC backplane to standalone instruments that communicate with the PC over standard interfaces such as RS-232 or IEEE-488. Software to control data acquisition, analysis, and display completes the computer-based instrument. Examples of such software include Lab Windows or Lab View (National Instruments), HP VEE (Hewlett-Packard), and Testpoint (Keithley-Metrabyte). Figure 108.6 shows a block diagram of an output screen developed using Lab Windows for an acoustic measurement application. A TABLE 108.4 Noise Reduction Checklist Source Interconnect Response Shield enclosures Shield leads Shield enclosures Filter inputs and outputs Minimize loop area (twist leads) Filter inputs and outputs Limit bandwidth Keep signal leads near ground Limit bandwidth Minimize loop areas Separate low-, high-level signals Minimize loop areas Keep signal and ground leads short Low f: Use single ground High f: Use multiple grounds Source: H.W. Ott, Noise Reduction Techniques in Electronic Systems, 2nd ed., New York: John Wiley & Sons, 1988. With permission. FIGURE 108.6 Example block diagram of a virtual instrument user interface
FIGURE 108.7 Sampling a continuous-time signal yields a discrete-time signal. menu bar provides pull-down options. Several windows simultaneously display selection options and present results graphically and with text. 108.9 Modeling pc-based instruments The approach outlined previously for modeling conventional measurement systems can be extended to PC- based instruments with one major difference: PC-based instruments by their nature are digital machines and perform functions in discrete time. Best performance of PC-based instrument systems must therefore consider Impled data effects. Figure 108.7 shows a data acquisition system modeled using an ideal sampler which instantaneously samples a continuous signal, s(o), every T seconds. This yields a sequence, s(nT), of discrete values that represent the value of the continuous signal at integer multiples of T seconds 108.10 The Effects of Sampling The Fourier transform of a sampled signal yields a frequency domain function that is periodic in frequency, with a period that is 1/fs. The sampling theorem states that in order to unambiguously preserve information, the sampling frequency fs =1/T, must be at least twice the highest frequency present in the continuous-time ignal. If f is less than twice the highest frequency, aliasing will occur. Aliased frequencies are indistinguishable om one another. A useful method for visualizing this result is through the use of an aliasing diagram.An example is shown in Fig. 108.8. Note that the Nyquist frequency is defined to be f/2. 108.11 Other Factors Other important factors that should be considered when using PC-based instruments over manual counterparts are summarized in Table 108.5. Perhaps the most important choice is the selection of a minimum sampling rate for the data acquisition process. It must be chosen to meet the requirements of the Nyquist frequency. However, in order to ensure that no higher frequencies are present, an anti-aliasing low pass filter that eliminates energy above the Nyquist frequency should be employed. In order to provide sufficient transition bandwidth for the filter, a slightly higher sampling rate should generally be employed. A factor of 1. 25 to 5 times the minimum f, is a good compromise. Automated equipment may introduce substantial transients into the measurement system. Sufficient time must be provided for the resulting transients to settle to an acceptable error bound: for exam Fn=Fs/2 3Fn=3Fs/2 fIb FIGURE 108.8 Aliasing diagram. The two baseband frequencies, fl and f2, have aliases at frequencies that intersect the vertical dashed lines. For example, using a sampling frequency of 10 kHz(F.=5 kHz) with fl 1 kHz and f2=3.5 kHz, ignals at 9 kHz(,a)and 11 kHz(f,b)would be aliased to 1 kHz(f,, while signals at 6.5 kHz(, )and 13. 5 kHz(f, b )would be aliased to 3.5 kHz(f,) e 2000 by CRC Press LLC
© 2000 by CRC Press LLC menu bar provides pull-down options. Several windows simultaneously display selection options and present results graphically and with text. 108.9 Modeling PC-Based Instruments The approach outlined previously for modeling conventional measurement systems can be extended to PCbased instruments with one major difference: PC-based instruments by their nature are digital machines and perform functions in discrete time. Best performance of PC-based instrument systems must therefore consider sampled data effects. Figure 108.7 shows a data acquisition system modeled using an ideal sampler which instantaneously samples a continuous signal, s(t), every T seconds. This yields a sequence, s(nT), of discrete values that represent the value of the continuous signal at integer multiples of T seconds. 108.10 The Effects of Sampling The Fourier transform of a sampled signal yields a frequency domain function that is periodic in frequency, with a period that is 1/fs . The sampling theorem states that in order to unambiguously preserve information, the sampling frequency, fs = 1/T, must be at least twice the highest frequency present in the continuous-time signal. If fs is less than twice the highest frequency, aliasing will occur. Aliased frequencies are indistinguishable from one another. A useful method for visualizing this result is through the use of an aliasing diagram. An example is shown in Fig. 108.8. Note that the Nyquist frequency is defined to be fs/2. 108.11 Other Factors Other important factors that should be considered when using PC-based instruments over manual counterparts are summarized in Table 108.5. Perhaps the most important choice is the selection of a minimum sampling rate for the data acquisition process. It must be chosen to meet the requirements of the Nyquist frequency. However, in order to ensure that no higher frequencies are present, an anti-aliasing low pass filter that eliminates energy above the Nyquist frequency should be employed. In order to provide sufficient transition bandwidth for the filter, a slightly higher sampling rate should generally be employed. A factor of 1.25 to 5 times the minimum fs is a good compromise. Automated equipment may introduce substantial transients into the measurement system. Sufficient time must be provided for the resulting transients to settle to an acceptable error bound; for example, 1%. FIGURE 108.7 Sampling a continuous-time signal yields a discrete-time signal. FIGURE 108.8 Aliasing diagram. The two baseband frequencies, f1 and f2, have aliases at frequencies that intersect the vertical dashed lines. For example, using a sampling frequency of 10 kHz (Fn = 5 kHz) with f1 = 1 kHz and f2 = 3.5 kHz, signals at 9 kHz (f1a) and 11 kHz (f1b) would be aliased to 1 kHz (f1), while signals at 6.5 kHz (f2a) and 13.5 kHz (f2b) would be aliased to 3.5 kHz (f2)
TABLE 108.5 Automated Measurement Factors Factor Consideration Frequency response measurements require use of a leveled generator. Alternatively, store a calibration curve. plexing multiple nodes require lead switching to shared instruments; consider these effects. Sampling frequency Must exceed the Nyquist frequency Include an anti-aliasing filter Manual instruments typically use od noise rejection over integer numbers f line cycles. Faster sampling rates for ATE are achieved using successive-approximation or other chniques. User may have to perform averaging as a post-processing step in order to achieve acceptable signal-to-noise ratios. Allow sufficient time for transients to settle for both stimulus/response instruments and device under test. Automatic measurements can produce large arrays of data at high speeds. Actual throughput to a hard disk may be much less than the maximum sampling rate of a data acquisition element(plug- in board, external instrument) Triggering Choices between free-running, external, and internal. Defining Terms Instrument: The means for monitoring or measuring physical variables Usually includes transducers, signal Measurement system: The sum of all stimulus and response instrumentation, device under test, interconnect, nvironmental variables, and th among the element Transducer: A device that transforms one form of energy to an electrical output that can be processed by an Instrument Virtual instrument: An instrument created through computer control of instrumentation resources with analysis and display of the data collected. Related Topics 3.1 Voltage and Current Laws.8.5 Sampled Data.73.2 Noise. 112.1 Introduction References N. Ahmed and T. Natarajan, Discrete-Time Signals and Systems, Reston, Vir ; Reston Publishing, 1983 E.O. Doebelin, Measurement Systems: Application and Design, 4th ed, New York: McGraw-Hill, 1990 J.P. Holman, Experimental Methods for Engineers, 6th ed, New York: McGraw-Hill, 1994 A D. Khazan, Transducers and Their Elements: Design and Application, Englewood Cliffs, N J. Prentice-Hall, 1994. H.W. Ott, Noise Reduction Techniques in Electronic Systems, 2nd ed, New York: John wiley Sons, 1988 w.J. Tompkins and J.G. Webster, Eds, Interfacing Sensors to the IBM PC, Englewood Cliffs, N J. Prentice-Hall, Further information The monthly journals, IEEE Transactions on Instrumentation and Measurement, and IEEE Transactions on Biomedical Instrumentation, report advances in instrumentation. For subscription information, contact: IEEE Service Center, 445 Hoes Lane, PO Box 1331, Piscataway, NJ 08855-1331.(800)678-IEEE. Information about automatic test equipment and software for data ition, analysis, and display, can be obtained from several vendors; for example, Hewlett-Packard, Englewood, CO,(800)-829-4444; Keithley Metrabyte, Taunton, MA, (800)348-0033; and National Instruments, Austin, TX, (512)794-0100. Information about transducers can be obtained from Omega International, Stamford, CT, (203)359-1660 e 2000 by CRC Press LLC
© 2000 by CRC Press LLC Defining Terms Instrument: The means for monitoring or measuring physical variables. Usually includes transducers, signal conditioning, signal processing, and display. Measurement system: The sum of all stimulus and response instrumentation, device under test, interconnect, environmental variables, and the interaction among the elements. Transducer: A device that transforms one form of energy to an electrical output that can be processed by an instrument. Virtual instrument: An instrument created through computer control of instrumentation resources with analysis and display of the data collected. Related Topics 3.1 Voltage and Current Laws • 8.5 Sampled Data • 73.2 Noise • 112.1 Introduction References N. Ahmed and T. Natarajan, Discrete-Time Signals and Systems, Reston, Vir.:, Reston Publishing, 1983. E.O. Doebelin, Measurement Systems: Application and Design, 4th ed., New York: McGraw-Hill, 1990. J.P. Holman, Experimental Methods for Engineers, 6th ed., New York: McGraw-Hill, 1994. A.D. Khazan, Transducers and Their Elements: Design and Application, Englewood Cliffs, N.J.: Prentice-Hall, 1994. H.W. Ott, Noise Reduction Techniques in Electronic Systems, 2nd ed., New York: John Wiley & Sons, 1988. W.J. Tompkins and J.G. Webster, Eds., Interfacing Sensors to the IBM PC, Englewood Cliffs, N.J.: Prentice-Hall, 1988. Further Information The monthly journals, IEEE Transactions on Instrumentation and Measurement, and IEEE Transactions on Biomedical Instrumentation, report advances in instrumentation. For subscription information, contact: IEEE Service Center, 445 Hoes Lane, PO Box 1331, Piscataway, NJ 08855-1331. (800) 678-IEEE. Information about automatic test equipment and software for data acquisition, analysis, and display, can be obtained from several vendors; for example, Hewlett-Packard, Englewood, CO, (800)-829-4444; KeithleyMetrabyte, Taunton, MA, (800) 348-0033; and National Instruments, Austin, TX, (512) 794-0100. Information about transducers can be obtained from Omega International, Stamford, CT, (203) 359-1660. TABLE 108.5 Automated Measurement Factors Factor Consideration Leveling Frequency response measurements require use of a leveled generator. Alternatively, store a calibration curve. Multiplexing Measurements from multiple nodes require lead switching to shared instruments; consider these effects. Sampling frequency Must exceed the Nyquist frequency. Include an anti-aliasing filter. Manual instruments typically use integrating (dual-slope) analog-to-digital converters which give good noise rejection over integer numbers of line cycles. Faster sampling rates for ATE are achieved using successive-approximation or other techniques. User may have to perform averaging as a post-processing step in order to achieve acceptable signal-to-noise ratios. Settling time Allow sufficient time for transients to settle for both stimulus/response instruments and device under test. Storage Automatic measurements can produce large arrays of data at high speeds. Actual throughput to a hard disk may be much less than the maximum sampling rate of a data acquisition element (plug-in board, external instrument). Triggering Choices between free-running, external, and internal