Low Level Measurements

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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


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Low LevelMeasuremen

HandbookPrecision DC Current, Voltag

and Resistance Measuremen

S I X T H E D I T I O N


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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


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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


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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


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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


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S E C T I O N 1

Low Level DC

Measuring

Instruments


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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


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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


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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


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(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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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)


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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


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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


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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


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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


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FIGURE 1-12: Neutralizing Shunt Capacitance

FIGURE 1-13: Logarithmic Picoammeter

+VO

A

IIN

+A

RF

IIN

CF

C1

R1


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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

+


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S E C T I O N 2

Measurements fr

High Resistanc

Sources


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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.


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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


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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


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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


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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


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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


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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)


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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


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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


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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


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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


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FIGURE 2 13: Guarding the Leakage Resistance of a Cable with


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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


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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


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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


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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


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/ 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


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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


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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


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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


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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


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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


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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


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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


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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


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2.3.8 Using a Coulombmeter to Measure Low Cur

In most cases an ammeter or picoammeter is use


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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Such devices require extreme care in handling. Mecsignificantly alter the resistance by dislodging particles material. Its also important not to touch the resistance e


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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


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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.


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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


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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


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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


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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


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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


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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.


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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 (


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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


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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


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( ) ( ) ( )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


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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


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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


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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 =


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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)


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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)


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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


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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

Low Level Measurements

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