Low level seminar

A Greater Measure of Confidence

DC Voltage measurements, intro

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Voltage Measurements

Source

of

Voltage

Vs

A Greater Measure of Confidence

Voltage Measurements

VsSource of

VoltageV

A Greater Measure of Confidence

Voltmeter

DUT

Voltage Measurements

VoltmeterVs

Source

of

Voltage

V

A Greater Measure of Confidence

Goal: V = Vs

Voltage Measurements

VSource

of

Voltage

VoltmeterVs

Two main problems:

1. Source is not ideal, Vs is dependent upon load

2. Voltmeter is not ideal, it is not an absolute open

A Greater Measure of Confidence

Thevenin Equivalent Model

VoltmeterV

Rs

Ideal voltage

source Vs

• VS Open-Circuit Voltage

• RS Thevenin Equivalent Source Resistance

A Greater Measure of Confidence

Thevenin Equivalent Model

VoltmeterVRin

Rs

Source

of

Voltage

Vs

A Greater Measure of Confidence

Thevenin Equivalent Model

VoltmeterVRin

Rs

Source

of

Voltage

Vs

V = V

A Greater Measure of Confidence

S

Rin

R + RS in

Theoretical Limits of Voltage Measurement

The Rs provides a fundamental limit to how

well you can resolve Vs:

Vn = 4kTBRs

K - Boltzmann’s constant

T - absolute temperature of the source

B - noise bandwidth in hertz

R - resistance of the source in Ohms

A Greater Measure of Confidence

Theoretical Limits of Voltage Measurement

A Greater Measure of Confidence

Theoretical Limits of Voltage Measurement

A Greater Measure of Confidence

Theoretical Limits of Voltage Measurement

A Greater Measure of Confidence

How to reduce Vn

• Reduce temperature

• Reduce the bandwidth:

– Increasing response time of the instrument

– Noise speed trade off

Vn = 4kTBRs

A Greater Measure of Confidence

Voltage Measurements

VsSource of

Voltage

RsHI

LO

En

In

Cin RinV Ideal

Voltmeter

Voltmeter

A Greater Measure of Confidence

Voltage Measurements

VsSource

of

Voltage

Rs

V

R2

R1

Voltmeter

V = VS

A Greater Measure of Confidence

R1+ R2

R1

Voltage Measurements

RsHI En Voltmeter

Source of In Ideal

VoltageVs

Cin RinV

Voltmeter

LO

VsSource

of

Voltage

Rs

V

R2

R1

Voltmeter

A Greater Measure of Confidence

Noise Voltage vs. Source Resistance

A Greater Measure of Confidence

Typical Parameters

Instr. type

A Greater Measure of Confidence

RIN eN IN

DMM 1GΩ 1µV 100pA

nVmeter 1GΩ 10nV 50pA

Electrometer 10TΩ 10µV 10fA

PROBLEM: Measure 1 mV to within 3%

10MΩ

1mV

A Greater Measure of Confidence

To within

±3%

PROBLEM: Measure 1 mV to within 3%

10MΩ

1mV

To within

±3%

A Greater Measure of Confidence

PROBLEM: Measure 1 mV to within 3%

Instr. Type RIN eN IN

DMM

nVmeter

Electrometer

1GΩ

1GΩ

10TΩ

1µV

10nV

10µV

100pA

50pA

10fA

10MΩ

1mV

A Greater Measure of Confidence

PROBLEM: Measure 1 mV to within 3%

Instr. Type RIN eN IN

DMM

nVmeter

Electrometer

1µV

10nV

10µV

100pA

50pA

10fA

1GΩ-1%1GΩ

10TΩ

10MΩ

1mV

A Greater Measure of Confidence

PROBLEM: Measure 1 mV to within 3%

Instr. Type RIN eN IN

DMM

nVmeter

Electrometer

1GΩ-1%1GΩ

10TΩ

1µV±0.1%10nV

10µV

100pA

50pA

10fA

10MΩ

1mV

A Greater Measure of Confidence

PROBLEM: Measure 1 mV to within 3%

Instr. Type RIN eN IN

DMM

nVmeter

Electrometer

1GΩ-1%1GΩ

10TΩ

1µV±0.1%10nV

10µV

100pA10-10 A* 107 Ω = 10-3 V

50pA

10fA

±100%!!

10MΩ

1mV

A Greater Measure of Confidence

PROBLEM: Measure 1 mV to within 3%

Instr. Type RIN eN IN

DMM

nVmeter

Electrometer

1GΩ-1%1GΩ-1%10TΩ

1µV±0.1%10nV

10µV

100pA10-10 A* 107 Ω = 10-3 V

50pA

10fA

±100%!!

10MΩ

1mV

A Greater Measure of Confidence

PROBLEM: Measure 1 mV to within 3%

Instr. Type RIN eN IN

DMM

nVmeter

Electrometer

1GΩ-1%1GΩ-1%10TΩ

1µV±0.1%10nV

±0.001%10µV

100pA10-10 A* 107 Ω = 10-3 V

50pA

10fA

±100%!!

10MΩ

1mV

A Greater Measure of Confidence

PROBLEM: Measure 1 mV to within 3%

Instr. Type RIN eN IN

DMM

nVmeter

Electrometer

1GΩ-1%1GΩ-1%10TΩ

1µV±0.1%10nV

±0.001%10µV

100pA

50pA5*10-11 *107 Ω= 5*10-4 V

10fA

10-10 A* 107 Ω = 10-3 V

±100%!!

±50%!!

10MΩ

1mV

A Greater Measure of Confidence

PROBLEM: Measure 1 mV to within 3%

Instr. Type RIN eN IN

DMM

nVmeter

Electromete

r

1GΩ-1%1GΩ-1%10TΩ

-0.0001%

1µV±0.1%10nV

±0.001%10µV

100pA

50pA5*10-11 *107 Ω= 5*10-4 V

10fA

10-10 A* 107 Ω = 10-3 V

±100%!!

±50%!!

10MΩ

1mV

A Greater Measure of Confidence

A Greater Measure of Confidence

PROBLEM: Measure 1 mV to within 3%

Instr. Type RIN eN IN

DMM

nVmeter

Electromete

r

1GΩ-1%1GΩ-1%10TΩ

-0.0001%

1µV±0.1%10nV

±0.001%10µV

±1%

100pA

50pA5*10-11 *107 Ω= 5*10-4 V

10fA

10-10 A* 107 Ω = 10-3 V

±100%!!

±50%!!

10MΩ

1mV

A Greater Measure of Confidence

PROBLEM: Measure 1 mV to within 3%

Instr. Type RIN eN IN

DMM

nVmeter

Electromete

r

1GΩ-1%1GΩ-1%10TΩ

-0.0001%

1µV±0.1%10nV

±0.001%10µV

±1%

100pA

50pA

10fA

10-10 A* 107 Ω = 10-3 V

±100%!!

5*10-11 *107 Ω= 5*10-4 V

±50%!!

10-14 A*107Ω =10-7V

=±0.01%!!

OK! ~ 1 % Error

10MΩ

1mV

Rs determines what instrument to choose

A Greater Measure of Confidence

• High Rs (Rs > 1 MΩ )– A limiting factor could be loading errors or voltage terms created by offset current In. Need a high input impedance voltmeter to reduce such errors: Electrometer. See high impedance voltage measurements.

• Low Rs (Rs < 1 MΩ )– For low Rs, very high input resistance not required, DMM could be a good solution. For low voltages, the limiting factor could be En. Use Nanovoltmeter

For More Information:

A Greater Measure of Confidence

Later segments of Keithley’s Low Level

Seminars:

• High impedance voltage measurements

• Low impedance voltage measurements

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A Greater Measure of Confidence

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