Upload
mayur-venkateshs
View
225
Download
0
Embed Size (px)
Citation preview
8/12/2019 Low Level Measurements
1/247
Low Level Measurements Handbook
Precision DC Current, Voltage, and Resistance Measurements
6thEdition
www.kei thley.com LLM
A G R E A T E R M E A S U R E O F C O N F I D E N C E
8/12/2019 Low Level Measurements
2/247
Low LevelMeasuremen
HandbookPrecision DC Current, Voltag
and Resistance Measuremen
S I X T H E D I T I O N
8/12/2019 Low Level Measurements
3/247
8/12/2019 Low Level Measurements
4/247
SECTION 1 Low Level DC Measuring Instruments
1.1 Introduction .....................................................
1.2 Theoretical Measurement Limits.................
1.3 Instrument Definitions...................................
1.3.1 The Electrometer ...............................1.3.2 The DMM ...........................................1.3.3 The Nanovoltmeter ...........................1.3.4 The Picoammeter...............................1.3.5 The Source-Measure Unit .................1.3.6 The SourceMeter Instrument .........
1.3.7 The Low Current Preamp .................1.3.8 The Micro-ohmmeter.........................
1.4 Understanding Instrument Specifications 1.4.1 Definition of Accuracy Terms ...........1.4.2 Accuracy .............................................
1.4.3 Deratings ...........................................1.4.4 Noise and Noise Rejection ...............1.4.5 Speed .................................................
1.5 Circuit Design Basics .....................................1.5.1 Voltmeter Circuits .............................1.5.2 Ammeter Circuits ...............................1.5.3 Coulombmeter Circuits .....................1.5.4 High Resistance Ohmmeter Circuits .1.5.5 Low Resistance Ohmmeter Circuits .1.5.6 Complete Instruments.......................
TA B L E O F C O N T E N T S
8/12/2019 Low Level Measurements
5/247
2.3 Low Current Measurements.................................
2.3.1 Leakage Currents and Guarding ..............2.3.2 Noise and Source Impedance ..................2.3.3 Zero Drift ..................................................2.3.4 Generated Currents ..................................2.3.5 Voltage Burden ........................................2.3.6 Overload Protection ................................
2.3.7 AC Interference and Damping ................2.3.8 Using a Coulombmeter to Measure Low C
2.4 High Resistance Measurements .........................2.4.1 Constant-Voltage Method ........................2.4.2 Constant-Current Method ........................
2.4.3 Characteristics of High Ohmic Valued Res
2.5 Charge Measurements...........................................2.5.1 Error Sources............................................2.5.2 Zero Check ..............................................2.5.3 Extending the Charge Measurement Rang
of the Electrometer ..................................
2.6 General Electrometer Considerations ...............2.6.1 Making Connections ................................2.6.2 Electrostatic Interference and Shielding ..2.6.3 Environmental Factors..............................2.6.4 Speed Considerations ..............................2.6.5 Johnson Noise ..........................................2.6.6 Device Connections..................................2.6.7 Analog Outputs ........................................2.6.8 Floating Input Signals ..............................
6
8/12/2019 Low Level Measurements
6/247
3.3 Low Resistance Measurements...................
3.3.1 Lead Resistance and Four-Wire Metho3.3.2 Thermoelectric EMFs and
Offset Compensation Methods .........3.3.3 Non-Ohmic Contacts .........................3.3.4 Device Heating .................................3.3.5 Dry Circuit Testing.............................
3.3.6 Testing Inductive Devices .................
SECTION 4 Applications
4.1 Introduction .....................................................
4.2 Applications for Measuring Voltagefrom High Resistance Sources.....................4.2.1 Capacitor Dielectric Absorption .......4.2.2 Electrochemical Measurements.........
4.3 Low Current Measurement Applications .4.3.1 Capacitor Leakage Measurements .....4.3.2 Low Current Semiconductor Measur4.3.3 Light Measurements with Photomulti4.3.4 Ion Beam Measurements ...................4.3.5 Avalanche Photodiode Reverse Bias C
Measurements ...................................
4.4 High Resistance Measurement Applicatio4.4.1 Surface Insulation Resistance Testing
of Printed Circuit Boards...................4 4 2 R i ti it M t f I l ti
8/12/2019 Low Level Measurements
7/247
4.6.2 High Resolution Temperature Measureme
and Microcalorimetry ..............................
4.7 Low Resistance Measurement Applications ...4.7.1 Contact Resistance....................................4.7.2 Superconductor Resistance Measurement4.7.3 Resistivity Measurements of Conductive M
SECTION 5 Low Level Instrument Selection Guide
5.1 Introduction .............................................................
5.2 Instrument and Accessory Selector Guides .....
APPENDIX A Low Level Measurement Troubleshootin
APPENDIX B Cable and Connector Assembly
APPENDIX C Glossary
APPENDIX D Safety Considerations
INDEX
8/12/2019 Low Level Measurements
8/247
S E C T I O N 1
Low Level DC
Measuring
Instruments
8/12/2019 Low Level Measurements
9/247
FIGURE 1-1: Standard Symbols Used in this Text
UnitSymbol Quant
Quantities
V EMFvolts
PrefixSymbol Expon
Prefixes
yz
a
f
p
n
m
(none)
k
M
GT
P
E
Z
Y
yocto-zepto-
atto-
femto-
pico-
nano-
micro-
milli-
(none)
kilo-
mega-
giga-tera-
peta-
exa-
zetta-
yotta-
102
102
10
10
10
109
106
103
100
103
106
109
1012
1015
1018
102
1024
8/12/2019 Low Level Measurements
10/247
1.1 Introduction
DC voltage, DC current, and resistance are measuretal multimeters (DMMs). Generally, these instrummeasurements at signal levels greater than 1V or (See Figure 1-1 for standard symbols used in this texapproach the theoretical limits of sensitivity. For lowsitive instruments such as electrometers, picoam
meters must be used.Section 1 offers an overview of the theoretical
ments and the instruments used to make them. descriptions and basic instrument circuit designs. Finformation is organized into a number of subsectio
1.2 Theoretical Measurement Limits: A discussion
measurement limitations and instrument limitaturements.
1.3 Instrument Definitions: Descriptions of electrvoltmeters, picoammeters, source-measure unitments, low current preamps, and micro-ohmme
1.4 Understanding Instrument Specifications: A revused in instrument specifications, such as accutivity, transfer stability), deratings (temperaturenoise (NMRR and CMRR), and speed.
1.5 Circuit Design Basics: Describes basic circuit dcuits (electrometer, nanovoltmeter) and ammeteter, feedback picoammeter, high speed picpicoammeter).
1.2 Theoretical Measurement Limits
The theoretical limit of sensitivity in any measureme
8/12/2019 Low Level Measurements
11/247
input offset current1 when measuring voltage and lowecompared to more sensitive instruments intended for lourements. These characteristics cause errors in the mea
Sections 2 and 3 for further discussion of them.
Given these DMM characteristics, its not possible measure signals at levels close to theoretical measuremein Figure 1-3. However, if the source resistance is 1Mdesired resolution is no better than 0.1V (with low sousignal level isnt near theoretical limits, and a DMM is
voltage sensitivity is desired, and the source resistance isbecause of theoretical limitations), a nanovoltmeter prmeasuring at levels much closer to the theoretical limitWith very high source resistance values (for example, 1Tsuitable voltmeter. DMM input resistance ranges from 10
FIGURE 1-2: Theoretical Limits of Voltage Measurements
1kV
1V
1mV
1V
1nV
1pV
100 103 106 109 1012
1 1k 1M 1G 1T
Within theoretical limits
Near
theore
ticallim
its
Prohibitedby noise
NoiseVoltage
Source Resistance
8/12/2019 Low Level Measurements
12/247
(input burden), which affects low level current me
resolution is generally no better than 1nA. Thus, an emeter with its much lower input burden and betterat levels much closer to the theoretical (and practicmeasurements.
1.3 Instrument Definitions
A number of different types of instruments are avaiurements, including electrometers, DMMs, nanovolSMUs (source-measure units), SourceMeter instrumamps, and micro-ohmmeters. The following paragrpare the important characteristics of these instrume
1V
1mV
1V
1nV
1pV100 103 106 10
1 1k 1M 1G
NoiseVoltage
Source Resistan
DMM
Electrometer
nV PreAmpnVM
103
1m
FIGURE 1-3: Typical Digital Multimeter (DMM), NanovoltmPreamplifier (nV PreAmp), and Electrometer L
Various Source Resistances
8/12/2019 Low Level Measurements
13/247
2. Circuit loading must be minimized, such as when:
Measuring voltage from a source resistance of 100
Measuring current when input voltage drop (burfew hundred millivolts is required (when measusources of a few volts or less).
3. Charge measurement is required.
4. Measuring signals at or near Johnson noise limitatioFigure 1-2).
In addition to their versatility, electrometers are eaable, and rugged.
Voltmeter Function
The input resistance of an electrometer voltmeter is ex
cally greater than 100T (1014). Furthermore, the inpless than 3fA (31015A). These characteristics describemeasure voltage with a very small amount of circuit load
Because of the high input resistance and low offsettrometer voltmeter has minimal effect on the circuit beiresult, the electrometer can be used to measure voltage i
an ordinary multimeter would be unusable. For examplecan measure the voltage on a 500pF capacitor withoucharging the device; it can also measure the potential oftals and high impedance pH electrodes.
Ammeter Function
As an ammeter, the electrometer is capable of measuring rents, limited only by theoretical limits or by the instrumcurrent. It also has a much lower voltage burden than co
With its extremely low input offset current and minburden, it can detect currents as low as 1fA (1015A). Be
8/12/2019 Low Level Measurements
14/247
Coulombmeter Function
Current integration and measurement of charge aremeter capabilities not found in multimeters. The eleter can detect charge as low as 10fC (1014C). Its integrator and, therefore, has low voltage burden, ty
The coulombmeter function can measure loammeter function can, because no noise is contribu
Currents as low as 1fA (1015
A) may be detected uSection 2.3.8 for further details.
1.3.2 The DMM
Digital multimeters vary widely in performance, fromdigit units to high precision system DMMs. While available from a wide variety of manufacturers, non
retical limits of measurement discussed previously. imply that DMMs are inadequate instruments; they sthat the vast majority of measurements are made atical limits, and DMMs are designed to meet these murement needs.
Although low level measurements are by definit
to theoretical limits, and are thus outside the rangetechnology are narrowing the gap between DMMs instruments. For example, the most sensitive DMMsas low as 10nV, resolve DC currents down to 10pA, aas high as 1G. While these characteristics still falsponding capabilities of more sensitive instrumentdescribed previously, all the measurement theory ations in this book apply to DMM measurements as wpicoammeter, electrometer, or SMU measurements. matter of degree; when making measurements closemeasurement considerations are vitally important. els far from theoretical limits only a few basic co
8/12/2019 Low Level Measurements
15/247
function instruments and are correspondingly les
electrometers.
1.3.4 The Picoammeter
A picoammeter is an ammeter built along the lines of theof an electrometer. When compared with an electromethas a similar low voltage burden, similar or faster speed,
a lower price. It may also have special characteristics, slogarithmic response or a built-in voltage source.
1.3.5 The Source-Measure Unit
As its name implies, a source-measure unit (SMU) has bosourcing capabilities. Adding current and voltage sourcinmeasuring instrument provides an extra degree of versalevel measurement applications. For example, very highcan be determined by applying a voltage across a device resulting current. The added sourcing functions also makvenient and versatile than using separate instruments foras generating I-V curves of semiconductors and other typ
The typical SMU provides the following four function
Measure voltage
Measure current
Source voltage
Source current
These functions can be used separately or they can bthe following combinations:
Simultaneously source voltage and measure curre
Si l l d l
8/12/2019 Low Level Measurements
16/247
1.3.6 The SourceMeter Instrument
The SourceMeter instrument is very similar to the many ways, including its ability to source and mevoltage and to perform sweeps. In addition, a Sourdisplay the measurements directly in resistance, current.
The typical SourceMeter instrument doesnt impedance or as low a current capability as a souSourceMeter instrument is designed for general-puduction test applications. It can be used as a sourlevel measurements and for research applications.
Unlike a DMM, which can make a measuremeSourceMeter instrument can be used to generate a fait has a built-in source. This is especially useful whetor devices and making materials measurements.
When used as a current source, a SourceMeter in conjunction with a nanovoltmeter to measure automatically reversing the polarity of the source to
1.3.7 The Low Current Preamp
Some SMUs and SourceMeter instruments may havpreamp. With this design, the sensitive amplifier cithe SMU or SourceMeter instrument. This makes most sensitive part of the instrument very close to tthereby eliminating a major source of error, the noicables themselves.
1.3.8 The Micro-ohmmeter
A micro-ohmmeter is a special type of ohmmeter
8/12/2019 Low Level Measurements
17/247
1.4 Understanding Instrument Specifications
Knowing how to interpret instrument specifications protant aspect of making good low level measurements. Altaccuracy is probably the most important of these specifseveral other factors to consider when reviewing specifnoise, deratings, and speed.
1.4.1 Definition of Accuracy Terms
This section defines a number of terms related to insSome of these terms are further discussed in subsequent1-1 summarizes conversion factors for various specificatioinstruments.
SENSITIVITY - the smallest change in the signal that can
RESOLUTION - the smallestportion of the signal that canREPEATABILITY - the closeness of agreement between su
ments carried out under the same conditions.
REPRODUCIBILITY - the closeness of agreement betweenthe same quantity carried out with a stated change i
ABSOLUTE ACCURACY - the closeness of agreement betw
measurement and its true value or accepted standais often separated into gain and offset terms.
RELATIVE ACCURACY - the extent to which a measureflects the relationship between an unknown and a
ERROR - thedeviation (difference or ratio) of a measurevalue. Note that true values are by their nature inde
RANDOM ERROR - the mean of a large number of measurby random error matches the true value.
SYSTEMATIC ERROR - the mean of a large number of menced by systematic errordeviates from the true val
8/12/2019 Low Level Measurements
18/247
a percentage of reading, or a combination of botaspects are covered in the following paragraphs.
Other factors such as input loading, leakage shielding, and guarding may also have a serious imp
These important measurement considerations areSections 2 and 3.
Measurement Instrument Specifications
Instrument accuracy is usually specified as a percencentage of range (or a number of counts of the lea
example, a typical DMM accuracy specification mayof reading + 0.002% of range). Note that the percennificant when the reading is close to full scale, whilemost significant when the reading is a small fraction
Accuracy may also be specified in ppm (parts pe
Percent PPM Digits Bits dBPortioof 10V
10% 100000 1 3.3 20 1 V
1% 10000 2 6.6 40 100mV
0.1% 1000 3 10 60 10mV
0.01% 100 4 13.3 80 1mV
0.001% 10 5 16.6 100 100 V
0.0001% 1 6 19.9 120 10 V
0.00001% 0.1 7 23.3 140 1 V
0.000001% 0.01 8 26.6 160 100 nV
0.000001% 0.001 9 29.9 180 10 nV
TABLE 1-1: Specification Conversion Factors
8/12/2019 Low Level Measurements
19/247
For example, the specification of (0.05% + 1 co
meter reading 10.000 volts corresponds to a total error out of 10V, or (0.05% of reading + 0.01% of reading)Generally, the higher the resolution, the better the accur
Sensitivity
The sensitivity of a measurement is the smallest change onal that can be detected. For example, voltage sensitivity
simply means that any change in input signal less than 1in the reading. Similarly, a current sensitivity of 10fA changes in current greater than that value will be detecte
The ultimate sensitivity of a measuring instrument dresolution and the lowest measurement range. For examof a 512-digit DMM with a 200mV measurement range is 1
Absolute and Relative Accuracy
As shown in Figure 1-4, absolute accuracy is the measaccuracy that is directly traceable to the primary standaInstitute of Standards and Technology (NIST). Absolutespecified as (% of reading + counts), or it can be stated
ing + ppm of range), where ppm signifies parts per mill
FIGURE 1-4: Comparison of Absolute and Relative Accuracy
NISTStandard
SecondaryStandard
Absolute
8/12/2019 Low Level Measurements
20/247
Transfer Stability
A special case of relative accuracy is the transfer instrument accuracy relative to a secondary referenshort time span and narrow ambient temperaturefive minutes and 1C). The transfer stability specifations where highly accurate measurements must beknown secondary standard.
Calculating Error Terms from Accuracy SpecifiTo illustrate how to calculate measurement errors fcations, assume the following measurement parame
Accuracy: (25ppm of reading + 5ppm of rangRange: 2V
Input signal: 1.5V
The error is calculated as:
Error= 1.5(25 106) + 2(5 106)= (37.5 106) + (10 106)
= 47.5 106
Thus, the reading could fall anywhere within47.5V, an error of 0.003%.
1.4.3 Deratings
Accuracy specifications are subject to deratings fordrift, as discussed in the following paragraphs.
Temperature Coefficient
The temperature of the operating environment can reason, instrument specifications are usually given oture range. Keithley accuracy specifications on newvoltmeters, DMMs, and SMUs are usually given ov28C. For temperatures outside of this range, a temp
8/12/2019 Low Level Measurements
21/247
instruments accuracy cannot be guaranteed. The time
the specifications, and is typically over specific incremenor one year. As noted previously, transfer stability specificfor a much shorter period of timetypically five or 10 m
1.4.4 Noise and Noise Rejection
Noise is often a consideration when making virtually anymeasurement, but noise problems can be particularly se
low level measurements. Thus, its important that noiseterms are well understood when evaluating the performment.
Normal Mode Rejection Ratio
Normal mode rejection ratio (NMRR) defines how w
rejects or attenuates noise that appears between the HIminals. Noise rejection is accomplished by using the inverter to attenuate noise at specific frequencies (usually 5passing low frequency or DC normal mode signals. As1-5, normal mode noise is an error signal that adds tosignal. Normal mode noise is detected as a peak noise orsignal. The ratio is calculated as:
peak normal mode noiseNMRR = 20 log _______________________________[ peak measurement deviation ]
FIGURE 1-5: Normal Mode Noise
MeasuringInstrument
HI
Noise
8/12/2019 Low Level Measurements
22/247
FIGURE 1-6: Common Mode Noise
Although the effects of common mode noise arenormal mode noise, this type of noise can still be asurement situations. To minimize common modeonly to a single point in the test system.
Noise Specifications
Both NMRR and CMRR are generally specified in dBare the interference frequencies of greatest interestfied at DC as well.) Typical values for NMRR and >120dB respectively.
Each 20dB increase in noise rejection ratio redurent by a factor of 10. For example, a rejection ratio
reduction by a factor of 104, while a ratio of 120dB smode noise would be reduced by a factor of 106. would be reduced to 100V with an 80dB rejectionwith a 120dB rejection ratio.
MeasuringInstrument
HI
LO Rimbalance
(usually 1k)
8/12/2019 Low Level Measurements
23/247
1.5 Circuit Design Basics
Circuits used in the design of many low level measuwhether a voltmeter, ammeter, ohmmeter, or coulombmcircuits that can be understood as operational amplifiersa basic operational amplifier. The output voltage is given
VO = A (V1 V2)
FIGURE 1-7: Basic Operational Amplifier
The gain (A) of the amplifier is very large, a minimumoften 106. The amplifier has a power supply (not shown)common lead.
Current into the op amp inputs is ideally zero. The
properly applied is to reduce the input voltage differenc
1.5.1 Voltmeter Circuits
Electrometer Voltmeter
V2
+
V1 VO
A
VO= A (V1 V
COMMON
8/12/2019 Low Level Measurements
24/247
Nanovoltmeter Preamplifier
The same basic circuit configuration shown in Figurinput preamplifier for a nanovoltmeter. Much required, so the values of R
A
and RB
are set accordgain for a nanovoltmeter preamplifier is 103.
Electrometer and nanovoltmeter characteristictional amplifier requirements for these two types somewhat different. While the most important chatrometer voltmeter operational amplifier are low ihigh input impedance, the most important require
meter input preamplifier is low input noise voltage
1.5.2 Ammeter Circuits
There are two basic techniques for making current mthe shunt ammeter and the feedback ammeter techn
V2
+
V1
A
RA
R
VO = V2(1
FIGURE 1-8: Voltage Amplifier
8/12/2019 Low Level Measurements
25/247
values reduce the input time constant and result inresponse time. To minimize circuit loading, the input reammeter should be small, thus reducing the voltage burdnote that reducing the shunt resistance will degrade the si
FIGURE 1-9: Shunt Ammeter
Feedback AmmeterIn this configuration, shown in Figure 1-10, the input through the feedback resistor (RF). The low offset curre(A) changes the current (IIN) by a negligible amount. Thvoltage is calculated as:
VO = IINRF
Thus, the output voltage is a measure of input currensitivity is determined by the feedback resistor (RF). The l(V1) and corresponding fast rise time are achieved by thewhich forces V1 to be nearly zero.
V2
+
V1
A
RA
RB
RS
IIN
VO = IIN RS(1
8/12/2019 Low Level Measurements
26/247
Picoammeter amplifier gain can be changed as by using the combination shown in Figure 1-11. Hand RB forms a multiplier, and the output voltage
VO = IINRF (1 + RA/RB)
FIGURE 1-11: Feedback Ammeter with Selectable Voltage G
High Speed Picoammeter
The rise time of a feedback picoammeter is normaconstant of the feedback resistor (RF) and any shunbasic approach to high speed measurements is to mcapacitance through careful mechanical design of th
Remaining shunt capacitance can be effectively
V1
+
A
R
R
I IN
RF
VO = IINRF
8/12/2019 Low Level Measurements
27/247
FIGURE 1-12: Neutralizing Shunt Capacitance
FIGURE 1-13: Logarithmic Picoammeter
+VO
A
IIN
+A
RF
IIN
CF
C1
R1
8/12/2019 Low Level Measurements
28/247
Using a small-signal transistor in place of a diobetter performance. Figure 1-14 shows an NPN trasistor in the feedback path to provide dual polarity
FIGURE 1-14: Dual Polarity Log Current to Voltage Convert
Remote Preamp Circuit (Source V, Measure I M
Figure 1-15 illustrates a typical preamp circuit. In tmode, the SMU applies a programmed voltage an
flowing from the voltage source. The sensitive inpguard, which can be carried right up to the DUT forments. The remote preamp amplifies the low currenthe DUT; therefore, the cable connecting the remourement mainframe carries only high level signals, m
+
1000pF
Input
A
8/12/2019 Low Level Measurements
29/247
1.5.3 Coulombmeter Circuit
The coulombmeter measures electrical charge that hascapacitor or that might be produced by some charge gen
For a charged capacitor, Q = CV, where Q is the charthe capacitor, C is the capacitance in farads, and V is the pcapacitor in volts. Using this relationship, the basic scheme is to transfer the charge to be measured to a c
value and then measure the voltage across the knowQ = CV.
The electrometer is ideal for charge measurements, bset current wont alter the transferred charge during shand the high input resistance wont allow the charge to b
Electrometers use a feedback circuit to measure ch
Figure 1-16. The input capacitance of this configurationeffective values of input capacitance are obtained usingcapacitors for CF.
FIGURE 1-16: Feedback Coulombmeter
+V
O
A
CF
8/12/2019 Low Level Measurements
30/247
FIGURE 1-17: High Resistance Measurement Using Externa
Usually, this method requires two instrumentspicoammeter or electrometer. Some electrometers aever, have a built-in voltage source and are capable ance directly.
Electrometer Ohmmeter Using Built-In Current
Figure 1-18 shows the basic configuration of an atrometer ohmmeter. A built-in constant-current sourforces a known current through the unknown resistvoltage drop is proportional to the unknown resistathe meter as resistance, rather than voltage.
FIGURE 1-18: Electrometer Ohmmeter with Built-In Curren
Built-In Current Source
I = VS/R
VS
ElectPicoa
VS
RX
I
RX =VSI
HI
LO
8/12/2019 Low Level Measurements
31/247
The disadvantage of this method is that the voltage acis a function of its resistance, so it cannot be easily conresistances tend to have large voltage coefficients; therefomade with a constant voltage are more meaningful.response speed for resistances greater than 10Gwill blimitation can be partially overcome by guarding.
Electrometer Ohmmeter with Guarded Ohms Mode
Figure 1-19 shows a modification of the circuit in FigureHI input node is surrounded with a guard voltage froamplifier output. The amplifier has unity gain, so this gtually the same potential as V1 and the capacitance (CS) olargely neutralized, resulting in much faster measuremgreater than 10G.
FIGURE 1-19: Electrometer Ohmmeter with Guarded Ohms
+
A
Built-In Current Source
RX CS V1
R I
I = VS/R
V1 = I RX
VS
Guard
8/12/2019 Low Level Measurements
32/247
FIGURE 1-20: High Resistance Measurement Using ExternaElectrometer Voltmeter
If the current source has a buffered 1 outputmeter, such as a DMM, may be used to read the arrangement is shown in Figure 1-21.
FIGURE 1-21: High Resistance Measurement Using a True a DMM
RX
+
I V1 VO
1 OutputA
HI
LO
E
I V1RX
V1 = I RX
ExternalCurrentSource
HI
LO
8/12/2019 Low Level Measurements
33/247
DMM Ohmmeter
The typical DMM uses the ratiometric technique shownmake resistance measurements. When the resistance funseries circuit is formed between the ohms voltage sourceance (RREF), and the resistance being measured (RX). Thcurrent to flow through the two resistors. This current iresistances, so the value of the unknown resistance can measuring the voltage across the reference resistancunknown resistance and calculating as:
SENSE HI SENSE LORX= RREF
__________________________REF HI REF LO
FIGURE 1-22: Ratiometric Resistance Measurement
VREFRREF
RS
RS
Ref
Ref
VSENSE
Sense
Sense
Input HI
Sense HI
Sense LO
R
R3
R2
R1
RX
Four-wireconnection
only
8/12/2019 Low Level Measurements
34/247
Micro-ohmmeter
The micro-ohmmeter also uses the four-wire ratiomis shown in Figure 1-23. It doesnt have the internaDMM, so all four leads must be connected to makthe terminals that supply test current to the unknowSource HI and Source LO.
FIGURE 1-23: Micro-ohmmeter Resistance Measurement
The pulsed drive mode, shown in Figure 1ohmmeter to cancel stray offset voltages in the unk
RX
= RREF
VSENSE
VREF
VREFRREF
VSENSE
Source HI
Sense HI
Sense LO
Source LOR4
R3
R2
R1
RX
8/12/2019 Low Level Measurements
35/247
FIGURE 1-24: Micro-ohmmeter in Pulse Mode
RX = RREFVSENSE 1 VSENSE 2
VREF
VREFRREF
Ref HI
Ref LO
VSENSE
Sense HI
Sense LO
Source HI
Sense HI
Sense LO
Source LOR4
R3
R2
R1
RX VXVOS
where VSENSE 1is measured with S1closed, and is equal to
VSENSE 2is measured with S1open, and is equal to VOS.
VREFRREF
Ref HI
Ref LOSource HIR1
Sense HI
FIGURE 1-25: Micro-ohmmeter with Dry Circuit On
8/12/2019 Low Level Measurements
36/247
1.5.6 Complete Instruments
Digital Electrometers
Figure 1-26 is a block diagram of a typical digital esection is similar to the circuitry discussed previousamplifier is used at the input to increase sensitivityance. The output of the main amplifier is applied toand the A/D converter. Range switching and functio
RaAm
Zero
Check
+
HI
A
Amps
Coulombs
Volts
Ohms
Function/Range
Volts, Ohms
Amps, Coulombs
LO
Input
FIGURE 1-26: Typical Digital Electrometer
8/12/2019 Low Level Measurements
37/247
verter provides a DC analog signal for resistance measushunts are used to convert currents to voltages for the am
Once the input signal is appropriately processed, itstal information by the A/D converter. Digital data is then
and to the digital output port (IEEE-488, RS-232, or EtheNanovoltmeters
A nanovoltmeter is a sensitive voltmeter optimized to meages. As shown in Figure 1-28, the nanovoltmeter incorppreamplifier, which amplifies the signal to a level suitabsion (typically 23V full scale). Specially designed pr
ensure that unwanted noise, thermoelectric EMFs, and ofabsolute minimum.
FIGURE 1-28: Typical Nanovoltmeter
ACAttenuator
DCAttenuator
ACConverter
OhmsConverter
AC
DC
Ohms
AC
DC
Ohms
DD
Co
PreRef
PrecisionShunts
HI
Amps
LO
INPUT
FIGURE 1-27: DMM Block Diagram
8/12/2019 Low Level Measurements
38/247
In order to cancel internal offsets, an offset or cuit allows the preamplifier offset voltage to be m
phases of the measurement cycle. The resulting quently subtracted from the measured signal to maccuracy.
Once the preamplifier amplifies the signal, itinformation by the A/D converter. Digital data is thenthe IEEE-488 interface.
SMUs
The SMU provides four functions in one instrument:ure current, source voltage and source current. Gencan simultaneously source voltage and measure cusource current and measure voltage.
When configured to Source I and Measure V (asthe SMU will function as a high impedance curremeasure (and voltage limit) capability.
Selecting either local or remote sense determmeasurement will be made. In local sense, the voloutput of the SMU. In remote sense, the voltage is
under test, eliminating any voltage drops due to leaThe driven guard (1 Buffer) ensures that the G
minals are always at the same potential. Proper use inates leakage paths in the cable, test fixture, and coured to Source V and Measure I (as shown in Figufunction as a low impedance voltage source with curent limit) capability.
SourceMeter Instrument
Like an SMU, a SourceMeter instrument can source measure current and measure voltage. However, t
8/12/2019 Low Level Measurements
39/247
FIGURE 1-30: Source V Mode of SMU
FIGURE 1-29: Source I Mode of SMU
I Meter
1Buffer
Guard
V Meter
Local
Remote
Local
Remote
I Source
8/12/2019 Low Level Measurements
40/247
Sense circuitry is used to monitor the output voadjust the V Source as needed.
+
FIGURE 1-31: Source I Mode of a SourceMeter Instrument
FIGURE 1-32: Source V Mode of a SourceMeter Instrument
1
V Meter
Local
Remote
Local
Remote
I Source
I Meter
+
8/12/2019 Low Level Measurements
41/247
8/12/2019 Low Level Measurements
42/247
S E C T I O N 2
Measurements fr
High Resistanc
Sources
8/12/2019 Low Level Measurements
43/247
2.1 Introduction
As described in Section 1 of this handbook, measuremenresistance sources include low DC voltage, low DC curreand charge measurements. The instruments used to impedance measurements include electrometers, pisource-measure units (SMUs). While Section 1 describedof these instruments and their measurement functionsmore detailed information about these functions, variou
error sources, and ways to maximize the accuracy of mefrom high resistance sources. For easier reference, thSection 2 is organized into these subsections:
2.2 High Impedance Voltage Measurements: A discussioand the use of guarding to minimize these errors, as won insulating materials used for making high im
ments.2.3 Low Current Measurements: Information about mak
current measurements is described with such topicsand guarding, noise and source impedance, zero drrents, voltage burden, overload protection, and usinto measure low current.
2.4 High Resistance Measurements: Describes the coconstant-current methods for measuring high rincludes information on high valued resistors.
2.5 Charge Measurements: A discussion of the error sominimize them, zero check, and extending the range tion.
2.6 General Electrometer Considerations: A discussion error sources that affect high impedance measureSome of the topics include measurement connecinterference and shielding, environmental factors,tions, etc.
8/12/2019 Low Level Measurements
44/247
the connecting cable. A practical voltmeter may be infinite input-resistance voltmeter (VM) in parallel
the specified input resistance (RIN), as shown in Figwhose Thevenin equivalent is VS in series with RS is the voltage (VM) appearing across the meter input the voltage divider action of RS and RIN as follows:
RINVM = VS ( RS + RIN)For example, assume RS = 100k and RIN = 10M
al voltage measured by the meter is:
107VM = 5 ( 105 + 107)VM = 4.95V
Thus, input resistance loading would result inexample.
The meter input resistance should be much resistance. For example, if the desired accuracy is 1%ance must be more than 100 times the source resisracy, this ratio must be correspondingly higher.
The connecting cable ordinarily isnt a factor, buresistances (>10G) or under extreme environm
RSR
HI
FIGURE 2-1: Effects of Input Resistance Loading on Voltage
8/12/2019 Low Level Measurements
45/247
cause significant loading errors. It may be possible to guthus reduce its loading on the measurement. This is disc
graphs on Shunt Resistance Loading and Guarding.
Input Bias Current Loading
Another consideration when measuring voltages fromsources is the input bias current of the voltmeter. The flows at the instrument input due to internal instrumeninternal bias voltage. As shown in Figure 2-2, the input develops an error voltage across the source resistance (Ral measured voltage (VM) differs from the source voltage
VM = VS IOFFSETRS
For example, assume the following parameters:
IOFFSET = 1pA R S = 10G VS = 10V
The actual voltage measured by the meter is:
VM = 10 (1012 1010)
VM = 10 0.01
VM = 9.99V or 10.01V (depending on the offset c
Thus, the error caused by input offset current wouldthis example.
Figure 2-2: Effects of Input Bias Current on Voltage Measuremen
RS
IBIAS
InputBiasCurrent VM
HI
8/12/2019 Low Level Measurements
46/247
known for their low input bias current, which is usPicoammeters and SMUs also have very low input
usually not as low as an electrometers.
Although input bias current is a common sourcurrents generated by external circuits can also resuage drops across the source resistance. Typical sourents are insulators and cables.
Shunt Resistance Loading and Guarding
External shunt resistances, such as leaky cables analso cause loading errors.
Any external shunt resistance across the voltagthe measured voltage, as shown in Figure 2-3. As inance voltage loading, the shunt resistance (RSHUNTance (RS) form a voltage divider that reduces the mfollows:
RSHUNTVM = VS ( RSHUNT + RS)For example, assume RS = 10G and RSHUNT =
of 10V, the measured voltage (VM) is:
1011VM = 10 ( 1011 + 1010)VM = 9.09V
In this instance, the error due to shunt loading
HI
FIGURE 2-3: Effects of Shunt Resistance on Voltage Measu
8/12/2019 Low Level Measurements
47/247
8/12/2019 Low Level Measurements
48/247
also reduced, making the response speed of the circdiscussed in detail in the paragraphs on Shunt CaGuarding.
The source-measure unit (SMU) can also be us
from a high resistance source and the Guard termimprovement.
The circuit of the electrometer when used as ashown in Figure 2-6. The guard amplifier is a unity-high input impedance. The open-loop gain, AGUARD,The leakage resistance (RL) is multiplied by this gainage becomes:
AGUARDRLVM = VS ( RS + AGUARDRL)Example:Assume RS has a value of 10G and RL
Voltage Source
RL
GUARD
LO
RG IG
HI
Connecting Cable
CableShield
RS
VS
FIGURE 2-5: Guarded Configuration
8/12/2019 Low Level Measurements
49/247
FIGURE 2-7: Shunt Capacitance Loading
VS
RS
CSHUNT
HI
ShuntCapacitance
QIN
FIGURE 2-6: Guarding Leakage Resistance
+
VS
RS
Voltage Source
RL VM
HI
LO
Voltmeter with Guard
AGUARD =
A
VM = VSAGUARD
RS + AGU
104to 106
GUARD
8/12/2019 Low Level Measurements
50/247
this input capacitance consists of the meter inputwith the input cable capacitance. Even a small amou
can result in long settling times if the source resistple, a shunt capacitance of 100pF (including the inresistance of 20Gwill result in an RC time constaseconds must be allowed for the measurement to sefinal value.
Figure 2-7 demonstrates the effects of shunt cap
input of a typical high impedance voltmeter. The siged by VS and RS, the shunt capacitance is CSHUNT, anis VM. Initially, the switch is open, and CSHUNT holds
When the switch is closed, the source voltageinput, but the measured voltage across CSHUNT doesto its final value. Instead, the voltage rises exponen
VM = VS (1 et/RSCSHUNT)Also, the charge (QIN) transferred to the capacitor i
QIN = VSCSHUNT
The charging of CSHUNTyields the familiar expoFigure 2-8. After one time constant ( = RC), the m
within 63% of its final value; final values for various marized in Table 2-1.
FIGURE 2-8: Exponential Response of Voltage Across Shun
100
63
90
80
7060
40
30
20
50
Percent ofFinal Value
(VS)
8/12/2019 Low Level Measurements
51/247
Example:Assume RS = 10G and CSHUNT = 100pFresults in an RC time constant of one second. Thus, it w
onds for the circuit to settle to within less than 1% of finachange in VS, a total of 1nC of charge would be transferr
While the primary advantage of guarding is a reductishunt resistance, another important aspect is the reductishunt capacitance. As shown in Figure 2-9, the guard reduces the charging time of CSHUNT because of th
(AGUARD), which is typically 104
to 106
.With guarding, the rise time of the measured v
becomes:
VM = VS (1 etAGUARD/RSCSHUNT)
and the charge transferred to CSHUNT is:
VSCSHUNTQIN = ( AGUARD )Example:Assume RS = 10G and CSHUNT = 100pF,
ed example given previously. With a nominal value of 105
see the guarded RC settling time is reduced to approximaan insignificant period of time compared to the time it
instrument to process a single reading. Note that with athe charge transferred (QIN) is only 10fC, a reduction of
FIGURE 2-9: Guarding Shunt Capacitance
+
RS CSHUNT VM
HI
AG
GUARD
8/12/2019 Low Level Measurements
52/247
2.2.2 Insulation Resistance
Electrometers and some SMUs as voltmeters are charesistance. High resistance insulation in the test cirrequirements of making successful electrometer mknowledge of the various types of insulating matethem properly is important. To measure voltagesources accurately, the insulation leakage resistanceleads, and measuring voltmeter must be several ord
er than the Thevenin equivalent resistance of the ciring on the number of decades of precision, rrequired. If the insulation resistances arent decadeffects of the insulation will reduce the source voltdiscussed previously.
Detecting inferior insulation in test setups is dineous reading can appear well-behaved and steady.to measure the insulation resistance of the test fixtually with an electrometer ohmmeter to ensure their are discovered, either cleaning or replacement of thin order.
Choosing the Best Insulator
In evaluating an insulating material, consider these Volume resistivity: leakage of current direct
Surface resistivity: leakage across the surfaof surface contaminants.
Water absorption: leakage dependent on thhas been absorbed by the insulator.
Piezoelectric or stored charge effects:unbalances (and thus current flow or voltagecal stress.
Triboelectric effects: the creation of charge
8/12/2019 Low Level Measurements
53/247
1018
1017
1016
1015
1014
1013ivity(-cm)
FR
Teflo
n
ramics
ylon
FIGURE 2-10: Approximate Resistivity of Various Insulating Mat
________________________________
PROPERT
Material
VolumeResistivity(Ohm-cm)
Resistanceto Water
Absorption
MinimalPiezoelectric
Effects1
MTri
Sapphire >1018 + +
Teflon PTFE >1018 +
Polyethylene 1016
0 +Polystyrene >1016 0 0
Kel-F >1018 + 0
Ceramic 10141015 0
Nylon 10131014 0
Glass Epoxy 1013 0
PVC 5 1013 + 0
KEY: + Material very good in regard to 0 Material moderately good in re Material weak in regard to the
1 Stored charge effects in non-piezoelectric insulators.
TABLE 2-2: Properties of Various Insulating Materials
8/12/2019 Low Level Measurements
54/247
8/12/2019 Low Level Measurements
55/247
Quartz
Quartz has properties similar to sapphire, but considerelectric output, so its rarely used in electrometer circuit
Other Insulating Materials
Practically all other insulating materials have unaccepresistivity or unsatisfactory surface characteristics for Vinyl, nylon, and Lucite are markedly inferior to Teflon
ethylene, sapphire, or quartz.Keeping Insulators Clean
As with any high resistance device, mishandling can destinsulators. Oils and salts from the skin can degrade insuand contaminants in the air can be deposited on thereducing its resistance. Therefore, insulator handling sho
under no circumstances should the insulator be touchedwith any material that might contaminate the surface.
If the insulator becomes contaminated, either throuling or from deposits, it can be cleaned with a foam tippmethanol. After cleaning, the insulator should be allowehours at low humidity before use or be dried using dry n
2.3 Low Current Measurements
A number of error sources can have serious impacts on urement accuracy. For example, the ammeter may caerrors if not connected properly. (Refer to Sections 2.6.1 information on how to make properly shielded connec
ters voltage burden and input offset current may also aaccuracy. The source resistance of the device under test wperformance of a feedback ammeter. External sources oleakage current from cables and fixtures, as well as currtriboelectric or piezoelectric effects Section 2 3 addr
8/12/2019 Low Level Measurements
56/247
8/12/2019 Low Level Measurements
57/247
8/12/2019 Low Level Measurements
58/247
FIGURE 2 13: Guarding the Leakage Resistance of a Cable with
8/12/2019 Low Level Measurements
59/247
RL = Coax Cable Leakag
IL = Leakage Current
RDUT = Resistance of Devic
IM = IDUT+ IL
V
SMU
RL
Z
a) Unguarded Circuit
Force/Output HI
CoaxCable
IM
1
Force/Output LO
ILGuard
V
RL1Z
b) Guarded Circuit
Force/Output HI
TrCaIM
1
Force/Output LO
0VGuard
RL2
FIGURE 2-13: Guarding the Leakage Resistance of a Cable with
FIGURE 2-14: Test Fixture Guarding with an SMU
8/12/2019 Low Level Measurements
60/247
leakage current is added to the current from the D
Metal Shielded
IDUT
RD
RL
Metal Moun
IL=
V
SMU
Z
b) Guarded Circuit
Force/Output HI
1
Force/Output LO
0VGuard
IM
Metal Shielded
IDUT
StandoffInsulators
RDRL
Metal Moun
IL
V
SMU
Z
a) Unguarded Circuit
Force/Output HI
1
Force/Output LO
Guard
IM
FIGURE 2-14: Test Fixture Guarding with an SMU
FIGURE 2-15: Simplified Model of a Feedback Ammeter
8/12/2019 Low Level Measurements
61/247
Source Resistance
The source resistance of the DUT will affect the noise perfback ammeter. As the source resistance is reduced, theammeter will increase.
Figure 2-15 shows a simplified model of a feedbackCS represent the source resistance and source capacitancvoltage, and VNOISE is the noise voltage of the ammeter.are the feedback resistance and capacitance respectively.
The noise gain of the circuit can be given by the follo
Output VNOISE = Input VNOISE (1 + RF/RS)
Note that as R decreases in value the output noise in
+
RF
CS
VS
RS
CF
VNOISE
Current Source
ZF
ZS
Feedback Ammeter
FIGURE 2 15: Simplified Model of a Feedback Ammeter
TABLE 2-3: Minimum Recommended Source Resistance Va
8/12/2019 Low Level Measurements
62/247
Source Capacitance
DUT source capacitance will also affect the noise pertype ammeter. In general, as source capacitance incrgain.
To see how changes in source capacitance canagain refer to the simplified ammeter model in Figof interest for this discussion are the source capacitback capacitance (CF). Taking into account the capatwo elements, our previous noise gain formula must
Output VNOISE = Input VNOISE (ZF/ZS)
Here, ZF represents the feedback impedance mwhile ZS is the source impedance formed by RS and
and
Note that as CS increases in value, ZS decreincreasing the noise gain. Again, at the point where is amplified by a factor of two.
ZS=RS
(2f RSCS)2+ 1
ZF=RF
(2f RFCF)2+ 1
TABL 3: Minimum Recommended Source Resistance VaFeedback Ammeter
Minimum RecomRange Source Resist
pA 1 GnA 1 MA 1 k
mA 1
time and/or temperature. Zero offset over a time period
8/12/2019 Low Level Measurements
63/247
/ p prange will stay within the specified limits. Offset due to st
peratures may exceed the specification before settling. perature rates of change (1C/15 minutes) wont usually
Most electrometers include a means to correct for CHECK switch is used to configure most electrometers to display any internal voltage offsets. This feature allowsadjustment of the amplifier zero. Typically, the instrumen
while zero check is enabled. This procedure may needperiodically, depending on ambient conditions. Electromfunction with the touch of a button or upon command fr
In a picoammeter or electrometer ammeter, note tand ZERO CORRECT functions are used to correct for insets. SUPPRESS or REL controls are used to correct for exsets. For optimum accuracy, zero the instrument on the ra
measurement. Refer to Section 2.3.4 for a discussion of cnal offset current.
2.3.4 Generated Currents
Any extraneous generated currents in the test system willcurrent, causing errors. Currents can be internally gener
of instrument input offset current, or they can come fromsuch as insulators and cables. The following paragraphs types of generated currents.
Figure 2-16 summarizes the magnitudes of a numberents discussed in this section.
Offset Currents
Offset currents can be generated within an instrument (inor can be generated from external circuitry (external offs
Input Offset Current
FIGURE 2-16: Typical Magnitudes of Generated Currents
8/12/2019 Low Level Measurements
64/247
107
108
109
1010
1011
1012
1013
1014
1015
Standardcable
Lownoisecable
Dirtysurface
Epoxyboard
Cleansurface
Teflon
Ceramics
TriboelectricEffects
ElectrochemicEffects
MechanicalStressEffects
Current-Generating Phenome
TypicalCurrentGenerated(A)
FIGURE 2-17: Effects of Input Offset Current on Current M
VS
RS
HIIS
IO
open-circuited, allow the reading to settle and then enabl
8/12/2019 Low Level Measurements
65/247
Once the REL value is established, subsequent readings
ence between the actual input value and the REL value.
External Offset Current
External offset currents can be generated by ionic coninsulators connected to the ammeter. Offset currents canexternally from such sources as triboelectric and piezoshown in Figure 2-18, the external offset current also a
current, and the meter again measures the sum of the tw
FIGURE 2-18: Effects of External Offset Current on Current Mea
External offset currents can be suppressed with the cufeature (if available) of the instrument or they can be nulably stable and quiet external current source, as shown in
VS
RS
IM
HI
LO
DMM, Electromeor Picoammeter
Measuring CurreIndicating IM
IS
Current Source
IM = IS+ IOFFSE
IOFFSET
FIGURE 2-19: Using External Current Source to Suppress O
8/12/2019 Low Level Measurements
66/247
ductor and create a charge imbalance that causes thexample would be electrical currents generated by tors rubbing together in a coaxial cable, as shown in
FIGURE 2-20: Triboelectric Effect
Frictional motion atboundary due tocable motion
+ +Insulation
VS
RS
HI
LO
DMM, Eor Picoa
MeasuriIndicatin
IS
Current Source
IM = ISWhen IO
ISUPPRESSIOFFSET
to equalize charges and minimize charge generated by fbl l bl
8/12/2019 Low Level Measurements
67/247
cable movement. However, even low noise cable creates
subjected to vibration and expansion or contraction, should be kept short, away from temperature changes (wthermal expansion forces), and preferably supported by cable to a non-vibrating surface such as a wall, benstructure.
There are a variety of other solutions to movement alems:
Removal or mechanical decoupling of the soMotors, pumps, and other electromechanical devsources.
Stabilization of the test hookup. Securely mounttronic components, wires, and cables. Shielding s
Triboelectric effects can also occur in other insulatothat touch each other. Therefore, its important to between insulators as well as conductors in constructinconnections for low current and high impedance.
Table 2-2 in Section 2.2.2 summarizes the triboelecous insulating materials.
Piezoelectric and Stored Charge Effects
Piezoelectric currents are generated when mechanical scertain crystalline materials when used for insulated teconnecting hardware. In some plastics, pockets of storematerial to behave in a manner similar to piezoelectric mple of a terminal with a piezoelectric insulator is shown
To minimize the current due to this effect, its impmechanical stresses from the insulator and use insulatminimal piezoelectric and stored charge effects. Sectio2-2 summarize the piezoelectric properties of various in
FIGURE 2-21: Piezoelectric Effect
8/12/2019 Low Level Measurements
68/247
FIGURE 2-22: Electrochemical Effects
I
PrintedWiring
Flux orother chemica
track andmoisture+
I
I
Metalterminal
+
+
Appliedforce
Piezoelectricinsulator
If insulators become contaminated, apply a cleanmethanol to all interconnecting circuitry Its importan
8/12/2019 Low Level Measurements
69/247
methanol to all interconnecting circuitry. Its importan
contaminants once theyre dissolved in the solvent, so thposited. Use only very pure solvents for cleaning; lower gcontaminants that leave an electrochemical film.
Dielectric Absorption
Dielectric absorption in an insulator can occur when a
insulator causes positive and negative charges within theize because various polar molecules relax at different ratage is removed, the separated charges generate a decayincircuits connected to the insulator as they recombine.
To minimize the effects of dielectric absorption onments, avoid applying voltages greater than a few volts t
used for sensitive current measurements. In cases wheunavoidable, it may take minutes or even hours in somerent caused by dielectric absorption to dissipate.
Table 2-2 in Section 2.2.2 summarizes the relative diof various insulating materials.
2.3.5 Voltage Burden
An ammeter may be represented by an ideal ammeter (Inal resistance, in series with a resistance (RM), as showWhen a current source whose Thevenin equivalent circuin series with a source resistance (RS) is connected toammeter, the current is reduced from what it would
ammeter (RM = 0). This reduction is caused by the (RM), which creates an additional voltage drop called t(VB).
FIGURE 2-23: Effects of Voltage Burden on Current Measu
8/12/2019 Low Level Measurements
70/247
The percent error in the measured reading due
Example: In this circuit, VS = 0.7V, IS = 100Assuming RS = 10k and the voltage burden at full
d h id l
IM=
0.7V 0.2V
10k
100A200A
= 60A
% error =
VB
VS
ISIFS
100%
VS
RS RM
IM
HI
LO
DMM, Electrometeror Picoammeter
V
Current Source
IM = R
VIM = RS
VS VBor
The input resistance of a feedback picoammeter or eter is less than the ratio of the specified voltage burde
8/12/2019 Low Level Measurements
71/247
ter is less than the ratio of the specified voltage burde
current: Voltage BurdenInput Resistance < _____________________
Full Scale Current
When determining the voltage burden of an SMU, ththe voltage source range being used must be included. Tto use the lowest possible voltage source range in order
2.3.6 Overload ProtectionElectrometers, picoammeters, and SMUs may be damageage is applied to the input. Most instruments have a spmaximum allowable voltage input. In some applicatiovoltage may be unavoidably exceeded. Some of theseinclude leakage current of capacitors, reverse diode leak
resistance of cables or films. If the component or materiathe voltage would be applied to the ammeters input, posIn these cases, additional overload protection is requiredthe input circuitry of the instrument.
Electrometer or Picoammeter Overload Protection
Figure 2-24 shows a protection circuit for an electrom
picoammeter, consisting of a resistor and two diodes (1Nof the 1N3595 diode is generally less than one picoampof forward bias, so the circuit wont interfere with measurmore. This diode is rated to carry 225mA (450mA repeatevoltage burden of the electrometer ammeter or picoam1mV, the diodes wont conduct. With two diodes in parallcircuit will provide protection regardless of the signal po
FIGURE 2-24: Overload Protection Circuit for Electrometers and
R
8/12/2019 Low Level Measurements
72/247
8/12/2019 Low Level Measurements
73/247
2.3.8 Using a Coulombmeter to Measure Low Cur
In most cases an ammeter or picoammeter is use
8/12/2019 Low Level Measurements
74/247
In most cases, an ammeter or picoammeter is use
However, for femtoamp-level currents, it may be betfunction of an electrometer to measure the change inuse those charge measurements to determine the cusion of charge measurements can be found in Sectio
Basic Charge Measurement Methods
Charge is difficult to measure directly; it must be reured quantity. One commonly used method of maurement is to measure the voltage across a capacitcharge is related to capacitor voltage as follows:
Q = CV
where: Q = capacitor charge (coulombs)
C = capacitor value (farads)V = voltage across capacitor (volts)
Once the rate of change in charge is known, thdetermined from the charge measurement. The instsimply:
dQ
i =
____
dt
while the long-term average current is defined
QIAVG =
____t
Thus, we see that charge can be measured an
mined simply by making a series of voltage measure
Using a Feedback Coulombmeter to Measure C
Charge can be measured directly with a feedback
FIGURE 2-27: Feedback Coulombmeter Equivalent Circuit
8/12/2019 Low Level Measurements
75/247
iM = CF(dVOUT/dt) = dQM/dt
The long-term average current (IAVG) can be calculatein output voltage over a specific time period:
VOUTCF QIAVG =__________ = ____
t t
To make calculations easier, set a one-second meatime in the one-shot trigger mode. The REL or zero futrometer may be used to reset the readings.
Fixed Integration Time Period Method
The fixed integration time method shown in Figure 2-determine current and is a variation of the feedback conique In this instance the increasing charge value is m
QM = CFVOUT
iM = CF(dVOUT/dt) = dQM/dt
VOUTCF
tIAVG
= = QM
t
+IS
CF
VOUT
A
FIGURE 2-28: Fixed Integration Time Method of Determini
8/12/2019 Low Level Measurements
76/247
Q
t
IAVGQ
tFixed time intervals
FIGURE 2-29: Fixed Threshold Method of Determining Cur
t
Q
tt1
Fixed threshold
Qt
IAVG=
Advantages of Using a Coulombmeter to Measure C
There are several advantages to using a coulombmeter in
8/12/2019 Low Level Measurements
77/247
e e a e se e a ad a tages to us g a cou o b ete
ter for measuring current in certain situations: Lower Current Noise: The ammeter uses a feedb
will have significant Johnson noise. For charge resistor is replaced by a capacitor, which theJohnson noise. Consequently, the charge methosurement results in lower noise than measuring
with a feedback ammeter. Thus, the charge mewhen current noise performance less than 1fA p-pto Figure 2-52 in Section 2.6.5 and note that fehigher than 1012 arent very practical.)
Faster Settling Times: The speed of a feedback by the time constant of its feedback circuit (RFCF)feedback resistances greater than 10G, stray response times to tens of milliseconds. In contragrator will respond immediately and is limited onthe operational amplifier.
Random Pulses Can Be Integrated: The averageper unit time of random pulse trains can be evaluthe current pulse train for a given period of time
rent amplitudes can then be expressed as the totathe time period involved in the measurement. especially useful when averaging very small, unsteduty cycle is known, the pulse height can also be
The Noise Effects of Input Shunt CapacitancNoise gain is mainly determined by CIN/CF, and C
a coulombmeter than in an ammeter, so much latance values can be tolerated. This characteristic measuring from high capacitance sources or whecables are used.
source are required. Some electrometers and picosources built into the instrument and automatic
8/12/2019 Low Level Measurements
78/247
unknown resistance.The basic configuration of the constant-voltage
trometer or picoammeter is shown in Figure 2-302-30b, an SMU can also be used for making high reusing the constant voltage method.
In this method, a constant voltage source (V) is p
unknown resistor (R) and an ammeter (IM). Since the ammeter is negligible, essentially all the test voThe resulting current is measured by the ammeter aculated using Ohms Law (R= V/I).
High resistance is often a function of the appliethe constant-voltage method preferable to the consttesting at selected voltages, a resistance vs. voltage cand a voltage coefficient of resistance can be dete
Some of the applications that use this method minal high resistance devices, measuring insulationmining the volume and surface resistivity of inSection 4 for descriptions of these applications.
The constant-voltage method requires measurintechniques and error sources described in SectMeasurements) apply to this method. The two mostwhen measuring high resistance are electrostatic incurrent. As described in Section 2.6.2, electrostatic iimized by shielding the high impedance circuitry. Inage current can be controlled by guarding as descri
2.4.2 Constant-Current Method
High resistance measurements using the constant-cmade using either an electrometer voltmeter and cu
FIGURE 2-30: Constant-Voltage Method for Measuring High Res
a) Using an Electrometer or Picoammeter
8/12/2019 Low Level Measurements
79/247
V
SMU
b) Using an SMU
Force/Output HI
Force/Output LO
IM
R
V
a) Using an Electrometer or Picoammeter
and a Voltage Source
IMElectromePicoamme
HI
LO
FIGURE 2-31: Constant-Current Method Using a Separate CurrenVoltmeter
compared with a source resistance to keep the loadable limits. Typically, the input impedance of an el
14
8/12/2019 Low Level Measurements
80/247
about 1014
. Also, the output resistance of the cmuch greater than the unknown resistance for the ear. The voltage across the sample depends uponwhich makes it difficult to account for voltage coeconstant-current method. If voltage coefficient is a cthe constant-voltage method. When using the elemake high resistance measurements, all the techni
described in Section 2.2 (Voltage MeasurementsSources) apply to these measurements. The electroseparate current source are used when determiningconductor materials using the four-point probe or vThese methods of determining the resistivity of semidescribed in more detail in Section 4.4.3.
Using an SMU in the Source I, Measure V Mode
An SMU can measure high resistance in the source cmode by using either a two-wire (local sense) or fomethod. Figure 2-32 illustrates an SMU in four-wir
FIGURE 2-32: Using the SMU in the Four-Wire Mode to M
V
Force HI
Sense HI
Sense LO
Source I, Measure V Mode
In addition to the voltage drop limitation, some SMremote sensing resistors located between the HI Force a
8/12/2019 Low Level Measurements
81/247
nals and between the LO Force and LO Sense terminalslimit the use of a single SMU in remote mode for certainas semiconductor resistivity. If this is the case, use thesource in the two-wire mode, and use a separate voltmthe voltage difference. See Section 4.4.3 for further infor
Using the Electrometer Ohmmeter
When using the electrometer ohmmeter, measuremenaffected by a variety of factors. In the following paragrapthe most important considerations for making accurameasurements.
Basic Configuration
Figure 2-33 shows the electrometer ohmmeter measurinThe ohmmeter uses an internal current source and electto make the measurement. It automatically calculates andured resistance. Notice that this is a two-wire resistance mpared to using the electrometer voltmeter and externwhich can make a four-wire measurement. This is besource is internally connected to the voltmeter and
separately.
FIGURE 2-33: Electrometer Ohmmeter for Measuring High Res
R
HI
Electrometer Ohmmeter
V I
across the DUT. If we assume that the meter has infinmeasured resistance is then computed from Ohms
8/12/2019 Low Level Measurements
82/247
VMRM =____IR
However, since the cable leakage resistance (Rthe actual measured resistance (RM) is reduced, aequivalent circuit of Figure 2-34b. The measured re
RLRM = RS ____________( RS + RL)The loading effects of cable resistance (and oth
can be virtually eliminated by driving the cable samplifier, as shown in Figure 2-34c. Since the voltially zero, all the test current (IR) now flows thro
resistance value can be accurately determined. Ththrough the cable-to-ground leakage path (RG) mathat current is supplied by the low impedance outrather than by the current source (IR).
Settling Time
The settling time of the circuit is particularly impor
resistance measurements. The settling time of the mby the shunt capacitance, which is due to the conning, and the DUT. As shown in Figure 2-35, the shumust be charged to the test voltage by the currenrequired for charging the capacitor is determined b(one time constant, = RSCSHUNT), and the familiFigure 2-36 results. Thus, it becomes necessary to
constants to achieve an accurate reading. When meance values, the settling time can range up to minuamount of shunt capacitance in the test system. Foonly 10pF a test resistance of 1T will result in a t
FIGURE 2-34a: Effects of Cable Resistance on High Resistance M
8/12/2019 Low Level Measurements
83/247
RS
ElectromMeasurin
Indicatin
UnknownResistanceof DUT
RM
HI
LO
RL
VM
FIGURE 2-34b: Equivalent Circuit of Figure 2-34a Showing LoadLeakage Resistance RL.
RS RMRL RM = RS
FIGURE 2-34c: Guarding Cable Shield to Eliminate Leakage Resis
8/12/2019 Low Level Measurements
84/247
Such devices require extreme care in handling. Mecsignificantly alter the resistance by dislodging particles material. Its also important not to touch the resistance e
8/12/2019 Low Level Measurements
85/247
penvelope that surrounds it; doing so could change its rescreation of new current paths or small electrochemically g
The resistors are coated to prevent water films from fface. Therefore, if a resistor acquires surface films from cadeposits from air contaminants, it should be cleaned with aand methanol. After cleaning, the resistor should be dried
atmosphere for several hours to allow any static charges to
2.5 Charge MeasurementsCharge is the time integral of current, q =idt. Chargeon a quantity of particles, on a surface, or on a componeitor. Sometimes, the charge is measured on a continu
when using the coulombmeter to measure very low curreSection 2.3.8.
An electrometer makes an ideal coulombmeter becainput offset current and high input resistance. The couloof the electrometer measures charge by integrating theintegrating capacitor is used in the feedback loop of the
to Section 1.5.3 for a more detailed discussion of the couof the electrometer.
2.5.1 Error Sources
Charge measurements made with an electrometer are suof error sources, including input offset current, voltage currents, and low source impedance.
Input Offset Current
With an electrometer, the input offset current is very lowcharge levels, even this small current may be a significant
If the source voltage is at least 10mV, the typicoulombs mode will integrate the current accuratelymuch lower, the voltage burden may become a prob
8/12/2019 Low Level Measurements
86/247
noise will be amplified so much that accurate measu
Generated Currents
Generated currents from the input cable or induceficient shielding can cause errors in charge measurcharge levels of 100pC or less. To minimize gene
noise cable and electrostatically shield all connectioSource Impedance
The magnitude of the source impedance can affectof the feedback coulombmeter. Figure 2-37 showscircuit connected to a source impedance. In a couloimpedance is a capacitor. From this diagram, the noi
meter can be calculated from the following equatio
Output Noise = Input Noise (1 + ZF/ZS)
where:ZS is the source impedanceZF is the feedback impedance of the coulomInput Noise is the noise of the input stage o
FIGURE 2-37: Generalized Feedback Circuit
+ZS
ZFInputNoise
charge will be lost through the zero check impedance aured by the electrometer. Thats because when zero cheinput resistance of the electrometer is about 10M.
8/12/2019 Low Level Measurements
87/247
Opening the zero check switch will produce a suddereading known as zero hop. To eliminate the effects oreading just after the zero check is disabled, then subtracsubsequent readings. An easy way to do this is to enablafter zero check is disabled, which nulls out the charge the hop.
2.5.3 Extending the Charge Measurement Range of th
The charge measurement range of most electrometersusing external feedback. The external feedback mode device to be used as the feedback element of the electroelectrometer in the volts mode and then enabling externes the feedback circuit from an internal network to a feenected to the preamp output.
To extend the coulombs ranges, an external capacfeedback element.
As illustrated in Figure 2-38, an external feedback between the preamp output terminal and the HI input tetrometer. To prevent electrostatic interference, the capashielded test fixture.
FIGURE 2-38: Connections for Using External Feedback Capacito
HI
PUnknownChargeto be
Determined
ExternalFeedbackCapacitor
where: Q = charge (coulombs)C = capacitance of the external feedback caV = voltage on display of electrometer (vol
8/12/2019 Low Level Measurements
88/247
For example, using an external feedback capacuring 5V on the display of the electrometer, the calc
The capacitance of the feedback element shouavoid errors due to stray capacitance and noise gain
To ensure low leakage current and low dielectr
back capacitor should be made of a suitable dielectrstyrene, polypropylene, or Teflon.
More information on the measurement proceduinstruction manual of the electrometer.
2.6 General Electrometer Considerations
So far, we have discussed considerations specific toance, and charge measurements. The following pasiderations that apply to all types of electrometer aon high resistance sources.
2.6.1 Making Connections
To avoid measurement errors, its critical to make p
the electrometer, SMU, or picoammeter to the devconnect the high resistance terminal of the meteance point of the circuit under test.
Figure 2-39 shows an electrometer connected consists of a voltage source in series with a resistor.usually has a significant level (often several volts) of
mode voltage. As shown in Figure 2-40, this will cathrough the low to ground capacitance of the electr
FIGURE 2-39: Connecting the HI Terminal of the Ammeter
FIGURE 2-40: Proper Connection
Current Source
8/12/2019 Low Level Measurements
89/247
R
Current Source
HI
LO
IM
i
FIGURE 2-41: Improper Connection
R
Current Source
LO
HI
IM
i
See Section 2.6.6 for details on appropriate cablfor electrometer measurements.
2 6 2 Electrostatic Interference and Shielding
8/12/2019 Low Level Measurements
90/247
2.6.2 Electrostatic Interference and ShieldingElectrostatic coupling or interference occurs whenobject approaches the input circuit under test. At loweffects of the interference arent noticeable becausrapidly. However, high resistance materials dont alquickly, which may result in unstable measuremen
ings may be due to either DC or AC electrostaticshielding will help minimize the effects of these fiel
DC fields can produce noisy readings or undetecan be detected when movement near an experimment of the person operating the instrument or ovicinity) causes fluctuations on the electrometersquick check for interference, place a piece of chacomb, near the circuit. A large change in the meter ficient shielding.
AC fields can be equally troublesome. These arpower lines and RF fields. If the AC voltage at the insignal is rectified, producing an error in the DC signcan be checked by observing the analog output
picoammeter with an oscilloscope. A clipped wavefimprove electrostatic shielding. Figure 2-42 illustrataken from the 2V analog output of an electrometeamount of clipping reduced the DC current reading
Figure 2-43 shows an example of AC electrostatic trostatic voltage source in the vicinity of a conductor, suchon a PC board, generates a current proportional to the ravoltage and of the coupling capacitance This current can
8/12/2019 Low Level Measurements
91/247
voltage and of the coupling capacitance. This current canthe following equation:
i = C dV/dt + V dC/dt
For example, two conductors, each with 1cm2 areapart by air, will have almost 0.1pF of capacitance. With a
of 100V between the two conductors and a vibration cacapacitance of 0.01pF/second (a 10% fluctuation betweeof 1pA AC will be generated.
To reduce the effects of the fields, a shield can be bcircuit being measured. The easiest type of shield to makbox or meshed screen that encloses the test circuit. Shiel
available commercially.
FIGURE 2-43: Electrostatic Coupling
V
C
Electrostaticvoltage source
GroundReferenceSignalConducto
i
Couplingcapacitance
i = C + VdV
dt
dC
dt
FIGURE 2-44: Shielding a High Impedance Device
R
8/12/2019 Low Level Measurements
92/247
FIGURE 2-45: Electrostatic Shielding
To summarize, follow these guidelines to minim
Shield Shield
V
Source-to-shieldcapacitance
Shield-to-cablecapacitance
Noise
current
Electrostaticvoltage source
V
R
fering voltage or current. A guard doesnt necessarily Guarding is described further in Section 2.2.1 for voltmefor ammeters, and Section 2.4.2 for ohmmeters.
8/12/2019 Low Level Measurements
93/247
2.6.3 Environmental Factors
A stable test environment is essential when making accururements. This section addresses important environmenaffect the accuracy of low level measurements.
Temperature and Temperature StabilityVarying temperatures can affect low level measuremenincluding causing thermal expansion or contraction of iducing noise currents. Also, a temperature rise can causeinput bias current of the meter. As a general rule, JFET gadoubles for every 10C increase in temperature, but mostemperature compensated to minimize input current vartemperature range.
To minimize errors due to temperature variations, system in a thermally stable environment. Keep sensitivefrom hot locations (such as the top of a rack) and allowtem to achieve thermal stability before making measuinstruments zero or suppress feature to null offsets onachieved thermal stability. Repeat the zeroing process went temperature changes. To ensure optimum accuracy, zon the same range as that to be used for the measureme
Humidity
Excess humidity can reduce insulation resistance on PC
connection insulators. A reduction in insulation resistanhave a serious effect on high impedance measurements. Iity or moisture can combine with any contaminants prestrochemical effects that can produce offset currents.
Ionization Interference
Current measurements made at very low levels (
8/12/2019 Low Level Measurements
94/247
ionization interference from sources such as alpha particle generates a track of from 30,000 to 70,00ions per cm, which may be polarized and moved abfields. Also, ions that strike a current-sensing node hop of about 10fC per ion.
There are several ways to minimize noise in the
ization interference. First, minimize the volume oaround sensitive input nodes. Also, keep sensitiveintensity electric fields.
RFI (Radio Frequency Interference)
Interference from radio frequency sources can aftrometer measurement. This type of interference ma
den change in the reading for no apparent reason.
A non-linear device or junction in the input cienergy and cause significant errors. Sources of sucmitters, contactors, solenoid valves, and even cportable two-way radios.
Once the source is identified, the RF energy m
nated by shielding and adding snubber networks opoints. Consult Section 3.2.1 for further discussion
2.6.4 Speed Considerations
Time and Frequency Relationships
Although this handbook stresses DC measurements,instrument response speed requires a brief discussicy relationships in electronic circuits.
A steady-state DC signal applied to a voltmeter
response is the rise time of the instrument. Bandwidth oused to describe the instruments response to time-varyi
Rise time of an analog instrument (or analog oudefined as the time necessary for the output to rise from
8/12/2019 Low Level Measurements
95/247
g ( gdefined as the time necessary for the output to rise fromfinal value when the input signal rises instantaneously ffixed value. This relationship is shown in Figure 2-46. step function with an assumed rise time of zero is sho2-46b shows the instruments response and the associatime, frequency response, and the RC time constant of a
are related. The 3dB point is given by the relationship:
1f3dB =
_______2RC
Rise time (tr) is related to the RC time constant as follow
tr = t90 t10
where: t90 = 2.3RCt10 = 0.1RC
Thus, tr= 2.2RC.
FIGURE 2-46: Instrument Response to Step Input
Time
Max.
0
a: Step Input Function
For example, the rise time of a circuit with a soand capacitance of 100pF will be approximately:
tr= (2.2) (1012
) (100 1012
) = 220 seconds
8/12/2019 Low Level Measurements
96/247
( ) ( ) ( )Using this with the above relationship between RC
2.2 0.35tr=
________ or tr=_______
2f3dB f3dB
Thus, the 1T source resistance and 100pF capacita
to:
0.35 0.35f3dB =
______ = _____ = 0.0016Hztr 220
Rise time affects the accuracy of the measuremeorder of magnitude as the period of the measuremeallowed before taking the reading is equal to theapproximately 10% will result, since the signal will of its final value. To reduce the error, more time musthe error to 1%, about two rise times must be allowerror to 0.1% would require roughly three rise timeconstants).
Beyond the 0.1% error level (and occasionally
order effects come into play. For example, more tgenerally required to settle to within 0.01% of finalabsorption in insulators and other second-order eff
In summary, an analog instruments responseresponse of most digital instruments) to a changingtion of its bandwidth, since frequency response an
related. To ensure accurate measurements, sufficienallowed for the source, the connection to the instrment itself to settle after the input signal is applied
FIGURE 2-47: Shunt Capacitance Effect of High Impedance Volta
RS
8/12/2019 Low Level Measurements
97/247
Thus, the familiar exponential curve of Figure 2-48becomes necessary to wait four or five time constants to a
reading. In the case of large resistors and capacitance,range up to minutes. While increased shunt capacitance increase, it does filter out noise produced in the sourceing cable simply by reducing the effective bandwidth of t
FIGURE 2-48: Exponential Response to Step Input
Time
1
0 1.0 2.0 3.0 4.0 5
1/e = 0.63
RSC
VS
VM
VS VMC IN
FIGURE 2-49: Shunt Type Ammeter
8/12/2019 Low Level Measurements
98/247
FIGURE 2-50: Feedback Electrometer Ammeter
If A, the gain of the amplifier, is large, then VOarrangement, CIN doesnt shunt RFB, and has only awould have with a shunt picoammeter The resultin
VS
+
A
IIN
RFB
Input CIN
IS C RS
Shunt Amm
IN
Resistance Measurements (Constant-Current Method
Input capacitance also affects resistance measurements (F
same manner. Again, CIN must be charged by the curresame equation applies. (See Section 2.4.2 for more inform
8/12/2019 Low Level Measurements
99/247
q pp (stant-current method.)
FIGURE 2-51: Constant-Current Resistance Measurement
Electrometer Rise Time Summary
For most measurements of high resistance sources, rise trequire minimizing the capacitance shunting the meter inshown that doing so also minimizes noise gain. In broadeimpedance should be large compared to the feedback meter.
The most effective method of minimizing input cap
nect the electrometer, SMU, or picoammeter to the sigshielded cable that is as short as possible. When measurinhigh source resistance, or when measuring high resistaminimize the effects of input capacitance by driving the
IRRS C
Electrometer Oh
IN
Metallic conductors approach this theoretical nmaterials produce somewhat higher noise. Johnsonoped in a resistor (R) is:
4kTRB volts, rmsE =
8/12/2019 Low Level Measurements
100/247
and Johnson current noise (I) developed by a resist
Statistical considerations show that peak-to-pefive times the rms noise more than 99% of the time;is commonly multiplied by five to convert to peakperature (300K), the previous equations become:
All real voltage and current sources contain therefore, they exhibit Johnson noise. Figure 2-5voltage versus source resistance for various bandwroom temperature.
For current measurements, Figure 2-53 showserated by various resistances at various bandwidths.decreases with increasing resistance, while voltage n
Johnson noise imposes a theoretical limit to acrent resolution. The previous equations suggest sevJohnson noise. It might be possible to reduce the
temperature, or the source resistance.
Bandwidth
Johnson noise is uniformly distributed over a wid
Ep-p= 6.4 1010 RB
Ip-p= 6.4 1010 BR
I =R
4kTRBamperes, rms
,
FIGURE 2-52: Noise Voltage vs. Bandwidth at Various Source Re
3 5s 350ms 35ms 3 5ms 350s 35Rise Time (seconds)
8/12/2019 Low Level Measurements
101/247
represents the smallest of the above alternative noise btions In this case noise bandwidth is:
0.1 1 10 100 1k 10
100
101
102
103
104
105
106
107
108
109
1010
3.5s 350ms 35ms 3.5ms 350s 35
R=10
12
R=10
10
R=10
8
R=10
6
R=10
4
R=10
2
R=10
0
Bandwidth (Hz)
Noise
Voltage(p-p)
8/12/2019 Low Level Measurements
102/247
Source Resistance
After the bandwidth and temperature, the remaining fac
the system noise is the effective source resistance. Thresistance includes the device under test as well as the mCh i h i i ll i i
8/12/2019 Low Level Measurements
103/247
ment. Changing the source resistance is usually impractiction. However, if a change can be made, the equations sbe lowered to decrease voltage noise or raised to decrea
In voltage measurements, the voltage source resistwith the voltmeter input resistance (see Figure 2-1). The
normally much larger than the source resistance; henceance value usually determines the Johnson noise voltage
In current measurements, the source resistance andance both contribute noise. The effective resistance is thetion of the source resistance and the feedback (or shunt) Feedback ammeters with high value sensing resistors in
have lower Johnson current noise and thus greater senammeters with lower resistance shunts.
Excess Current Noise
The Johnson noise of a resistor is related only to the reperature, and the bandwidth. When current passes thronoise will increase above the calculated Johnson noisenoise is sometimes referred to as excess current noiresisto