Low Level Measurements Handbook

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1.1 IntroductionDC voltage, DC current, and resistance are measured most often with digitalmultimeters (DMMs). Generally, these instruments are adequate formeasurements at signal levels greater than 1µV or 1µA, or less than 1GΩ.(See Figure 1-1 for standard symbols used in this text.) However, they don’tapproach the theoretical limits of sensitivity. For low level signals, more sensitiveinstruments such as electrometers, picoammeters, and nanovoltmetersmust be used.Section 1 offers an overview of the theoretical limits of DC measurementsand the instruments used to make them. It includes instrumentdescriptions and basic instrument circuit designs. For easier reference, thisinformation is organized into a number of subsections:1.2 Theoretical Measurement Limits: A discussion of both the theoreticalmeasurement limitations and instrument limitations for low level measurements.1.3 Instrument Definitions: Descriptions of electrometers, DMMs, nanovoltmeters,picoammeters, source-measure units, SourceMeter ® instruments,low current preamps, and micro-ohmmeters.1.4 Understanding Instrument Specifications: A review of the terminologyused in instrument specifications, such as accuracy (resolution, sensitivity,transfer stability), deratings (temperature coefficient, time drift),noise (NMRR and CMRR), and speed.1.5 Circuit Design Basics: Describes basic circuit design for voltmeter circuits(electrometer, nanovoltmeter) and ammeter circuits (shunt ammeter,feedback picoammeter, high speed picoammeter, logarithmicpicoammeter).1.2 Theoretical Measurement LimitsThe theoretical limit of sensitivity in any measurement is determined by thenoise generated by the resistances present in the circuit. As discussed inSections 2.6.5 and 3.2.2, voltage noise is proportional to the square root ofthe resistance, bandwidth, and absolute temperature. Figure 1-2 shows theoreticalvoltage measurement limits at room temperature (300K) with aresponse time of 0.1 second to ten seconds. Note that high source resistancelimits the theoretical sensitivity of the voltage measurement. While it’scertainly possible to measure a 1µV signal that has a 1Ω source resistance,it’s not possible to measure that same 1µV signal level from a 1TΩ source.Even with a much lower 1MΩ source resistance, a 1µV measurement is neartheoretical limits, so it would be very difficult to make using an ordinaryDMM.In addition to having insufficient voltage or current sensitivity (mostDMMs are no more sensitive than 1µV or 1nA per digit), DMMs have highLow Level DC Measuring Instruments 1-3
FIGURE 1-2: Theoretical Limits of Voltage Measurements1kV10 3NoiseVoltage1VWithin theoretical limits10 01mV1µV1nV1pVNear theoretical limitsProhibitedby noise10 –310 –610 –910 –1210 0 10 3 10 6 10 9 10 121Ω 1kΩ 1MΩ 1GΩ 1TΩSource Resistanceinput offset current 1 when measuring voltage and lower input resistancecompared to more sensitive instruments intended for low level DC measurements.These characteristics cause errors in the measurement; refer toSections 2 and 3 for further discussion of them.Given these DMM characteristics, it’s not possible to use a DMM tomeasure signals at levels close to theoretical measurement limits, as shownin Figure 1-3. However, if the source resistance is 1MΩ or less, or if thedesired resolution is no better than 0.1µV (with low source resistance), thesignal level isn’t “near theoretical limits,” and a DMM is adequate. If bettervoltage sensitivity is desired, and the source resistance is low (as it must bebecause of theoretical limitations), a nanovoltmeter provides a means ofmeasuring at levels much closer to the theoretical limits of measurement.With very high source resistance values (for example, 1TΩ), a DMM isn’t asuitable voltmeter. DMM input resistance ranges from 10MΩ to 10GΩ—severalorders of magnitude less than a 1TΩ source resistance, resulting insevere input loading errors. Also, input currents are typically manypicoamps, creating large voltage offsets. However, because of its much higherinput resistance, an electrometer can make voltage measurements at levelsthat approach theoretical limits. A similar situation exists for low levelcurrent measurements; DMMs generally have a high input voltage drop1Input current flows in the input lead of an active device or instrument. With voltage measurements, theinput current is ideally zero; thus, any input current represents an error. With current measurements, thesignal current becomes the input current of the measuring instrument. However, some background currentis always present when no signal current is applied to the instrument input. This unwanted currentis the input offset current (often called just the offset current) of the instrument.The source and test connections can also generate unwanted offset currents and offset voltages.A leakage current is another unwanted error current resulting from voltage across an undesired resistancepath (called leakage resistance). This current, combined with the offset current, is the total errorcurrent.1-4 SECTION 1
Page 1 and 2: www.keithley.comLLM6 th EditionLow
Page 4 and 5: TABLE OF C ONTENTSSECTION 1 Low Lev
Page 6 and 7: 3.3 Low Resistance Measurements....
Page 8 and 9: SECTION 1Low Level DCMeasuringInstr
Page 12 and 13: FIGURE 1-3: Typical Digital Multime
Page 14 and 15: Coulombmeter FunctionCurrent integr
Page 16 and 17: 1.3.6 The SourceMeter ® Instrument
Page 18 and 19: TABLE 1-1: Specification Conversion
Page 20 and 21: Transfer StabilityA special case of
Page 22 and 23: FIGURE 1-6: Common Mode NoiseMeasur
Page 24 and 25: FIGURE 1-8: Voltage Amplifier+-V 2A
Page 26 and 27: Picoammeter amplifier gain can be c
Page 28 and 29: Using a small-signal transistor in
Page 30 and 31: FIGURE 1-17: High Resistance Measur
Page 32 and 33: FIGURE 1-20: High Resistance Measur
Page 34 and 35: Micro-ohmmeterThe micro-ohmmeter al
Page 36 and 37: FIGURE 1-26: Typical Digital Electr
Page 38 and 39: In order to cancel internal offsets
Page 40: Sense circuitry is used to monitor
Page 43 and 44: 2.1 IntroductionAs described in Sec
Page 45 and 46: cause significant loading errors. I
Page 47 and 48: Cable leakage resistance is a commo
Page 49 and 50: FIGURE 2-6: Guarding Leakage Resist
Page 51 and 52: Example: Assume R S = 10GΩ and C S
Page 53 and 54: MaterialTABLE 2-2: Properties of Va
Page 55 and 56: QuartzQuartz has properties similar
Page 57 and 58: FIGURE 2-11: Guarding as Applied to
Page 59 and 60: FIGURE 2-13: Guarding the Leakage R
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FIGURE 2-15: Simplified Model of a
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time and/or temperature. Zero offse
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open-circuited, allow the reading t
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to equalize charges and minimize ch
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If insulators become contaminated,
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The input resistance of a feedback
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ence. However, in some cases, shiel
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FIGURE 2-27: Feedback Coulombmeter
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Advantages of Using a Coulombmeter
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FIGURE 2-30: Constant-Voltage Metho
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In addition to the voltage drop lim
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FIGURE 2-34a: Effects of Cable Resi
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Such devices require extreme care i
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charge will be lost through the zer
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FIGURE 2-40: Proper ConnectionCurre
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Figure 2-43 shows an example of AC
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fering voltage or current. A guard
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esponse is the rise time of the ins
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FIGURE 2-47: Shunt Capacitance Effe
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Resistance Measurements (Constant-C
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FIGURE 2-52: Noise Voltage vs. Band
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Source ResistanceAfter the bandwidt
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a. ConfigurationShieldCenterconduct
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• Shielding and Guarding: The fix
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floating circuits, a second grounde
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3.1 IntroductionLow voltage and low
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Thermoelectric EMFsThermoelectric v
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Reversing Sources to Cancel Thermoe
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quency spectrum of these interferen
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ment is almost entirely determined
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FIGURE 3-9: Low Voltages Generated
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FIGURE 3-11a: Multiple Grounds (Gro
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Common-Mode Reversal ErrorsReversin
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FIGURE 3-14: Two-Wire Resistance Me
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FIGURE 3-16: Canceling Thermoelectr
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Both V A and V B are affected by th
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If using a micro-ohmmeter or DMM to
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FIGURE 3-20: Dry Circuit Testing Us
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SECTION 4Applications
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For timing and integrating applicat
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FIGURE 4-2:Using an Electrometer to
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If current flows, the electrodes wi
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4.3 Low Current Measurement Applica
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DC. The Model 6517A can also be use
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voltage (V DS ) and measures the re
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The Keithley Model 248 High Voltage
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FIGURE 4-16: Ion Collector with Gro
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Figure 4-19 shows a Model 6430 conn
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FIGURE 4-21: SIR Test System to Mea
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FIGURE 4-22: Volume ResistivityElec
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these problems, the Alternating Pol
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FIGURE 4-25: Four-Point Collinear P
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Using two electrometers eliminates
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A plot of this function is shown in
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FIGURE 4-31: van der Pauw Measureme
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Through interactive programming, th
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objects. As discussed in Section 2.
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FIGURE 4-36: Faraday CupOutside Ele
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FIGURE 4-38: Connections for Standa
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FIGURE 4-40: Microcalorimeter with
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Measurement MethodFigure 4-42 illus
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FIGURE 4-43: Using a Nanovoltmeter
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exceed the critical current of the
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equation for V/I. Most materials ha
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FIGURE 4-49: van der Pauw Connectio
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5.1 IntroductionChoosing a specific
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TABLE 5-1a: Low Current/High Resist
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Table 5-1b: Source-Measure Instrume
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Table 5-2: High Speed Power Supplie
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Table 5-3: Connectors, Adapters, an
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Table 5-4: CablesTERMINATIONS LENGT
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Table 5-5: Test Leads and ProbesMOD
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Table 5-6: Switching Cards for the
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APPENDIX ALow LevelMeasurementTroub
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Measurement Type andTypical Applica
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Proper cable and connector assembly
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APPENDIX CGlossary
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channels. For matrix cards, a chann
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R. Buckminster Fuller. Sometimes ca
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NORMAL-MODE REJECTION RATIO (NMRR).
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SOURCEMETER. A SourceMeter instrume
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APPENDIX DSafetyConsiderations
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The types of product users are:Resp
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are the same. Other components that
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1/f noise, 3-7 to 3-83dB point, 2-5
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Normal mode rejection ratio (NMRR),
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Specifications are subject to chang
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Specifications are subject to chang
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