Low Level Measurements Handbook

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the connecting cable. A practical voltmeter may be represented by an idealinfinite input-resistance voltmeter (V M ) in parallel with a resistor equal tothe specified input resistance (R IN ), as shown in Figure 2-1. When a sourcewhose Thevenin equivalent is V S in series with R S is connected to the input,the voltage (V M ) appearing across the meter input terminals is reduced bythe voltage divider action of R S and R IN as follows:RV INM = V S ––––––––––( RS + R IN)For example, assume R S = 100kΩ and R IN = 10MΩ. If V S = 5V, the actualvoltage measured by the meter is:10V 7M = 5 –––––––––––V M = 4.95V( 105 + 10 7 )Thus, input resistance loading would result in an error of 1% in thisexample.The meter input resistance should be much higher than the sourceresistance. For example, if the desired accuracy is 1%, then the meter resistancemust be more than 100 times the source resistance. For higher accuracy,this ratio must be correspondingly higher.The connecting cable ordinarily isn’t a factor, but with very high sourceresistances (>10GΩ) or under extreme environmental conditions, it canFIGURE 2-1: Effects of Input Resistance Loading on Voltage Measurement AccuracyHIR SV SR INInputResistanceV MLOVoltage SourceVoltmeter Measuring V SIndicating V MV M = V SR INR IN + R S<strong>Measurements</strong> from High Resistance Sources 2-3
cause significant loading errors. It may be possible to guard the cable andthus reduce its loading on the measurement. This is discussed in the paragraphson Shunt Resistance Loading and Guarding.Input Bias Current LoadingAnother consideration when measuring voltages from high resistancesources is the input bias current of the voltmeter. The input bias currentflows at the instrument input due to internal instrument circuitry and theinternal bias voltage. As shown in Figure 2-2, the input bias current (I BIAS )develops an error voltage across the source resistance (R S ). Thus, the actualmeasured voltage (V M ) differs from the source voltage (V S ) as follows:V M = V S ±I OFFSET R SFor example, assume the following parameters:I OFFSET = 1pA R S = 10GΩ V S = 10VThe actual voltage measured by the meter is:V M = 10 ± (10 –12 · 10 10 )V M = 10 ± 0.01V M = 9.99V or 10.01V (depending on the offset current polarity)Thus, the error caused by input offset current would be about 0.1% inthis example.Figure 2-2: Effects of Input Bias Current on Voltage Measurement AccuracyHIR SI BIASInputBiasCurrentV MV SLOVoltage SourceVoltmeter Measuring V SIndicating V MV M = V S – I BIAS R SDMMs and nanovoltmeters have bias currents from 1pA to 1nA, althoughDMM bias currents are not always specified. Electrometers are2-4 SECTION 2
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 10 and 11: 1.1 IntroductionDC voltage, DC curr
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: 2.1 IntroductionAs described in Sec
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
Page 61 and 62: FIGURE 2-15: Simplified Model of a
Page 63 and 64: time and/or temperature. Zero offse
Page 65 and 66: open-circuited, allow the reading t
Page 67 and 68: to equalize charges and minimize ch
Page 69 and 70: If insulators become contaminated,
Page 71 and 72: The input resistance of a feedback
Page 73 and 74: ence. However, in some cases, shiel
Page 75 and 76: FIGURE 2-27: Feedback Coulombmeter
Page 77 and 78: Advantages of Using a Coulombmeter
Page 79 and 80: FIGURE 2-30: Constant-Voltage Metho
Page 81 and 82: In addition to the voltage drop lim
Page 83 and 84: FIGURE 2-34a: Effects of Cable Resi
Page 85 and 86: Such devices require extreme care i
Page 87 and 88: charge will be lost through the zer
Page 89 and 90: FIGURE 2-40: Proper ConnectionCurre
Page 91 and 92: Figure 2-43 shows an example of AC
Page 93 and 94: 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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