![background image](http://html2.mh-extra.com/html/keithley/2182/2182_user-manual_3982763273.webp)
Measurement Considerations
C-5
Johnson noise equation
The amount of noise present in a given resistance is defined by the Johnson noise equation as
follows:
where: E
RMS
= rms value of the noise voltage
k = Boltzmann's constant (1.38
×
10
–23
J/K)
T = Temperature (K)
R = Source resistance (ohms)
F = Noise bandwidth (Hz)
At a room temperature of 293K (20°C), the above equation simplifies to:
Since the peak to peak noise is five times the rms value 99% of the time, the peak to peak
noise can be equated as follows:
For example, with a source resistance of 10k
Ω
, the noise over a 0.5Hz bandwidth at room
temperature will be:
Minimizing source resistance noise
From the above examples, it is obvious that noise can be reduced in several ways: (1) lower
the temperature; (2) reduce the source resistance; and (3) narrow the bandwidth. Of these three,
lowering the resistance is the least practical because the signal voltage will be reduced more than
the noise. For example, decreasing the resistance of a current shunt by a factor of 100 will also
reduce the voltage by a factor of 100, but the noise will be decreased only by a factor of 10.
Very often, cooling the source is the only practical method available to reduce noise. Again,
however, the available reduction is not as large as it might seem because the reduction is related
to the square root of the change in temperature. For example, to cut the noise in half, the
temperature must be decreased from 293K to 73.25K, a four-fold decrease.
E
RMS
4kTRF
=
E
RMS
1.27
10
10
–
×
RF
=
E
p
p
–
6.35
10
10
–
×
RF
=
E
p
p
–
6.35
10
10
–
×
10
10
3
×
(
)
0.5
(
)
=
E
p
p
–
45nV
=
Summary of Contents for 2182
Page 1: ...www tek com keithley Model 2182 2182A Nanovoltmeter User s Manual 2182A 900 01 Rev B May 2017...
Page 18: ......
Page 22: ......
Page 23: ...1 Getting Started Getting Started...
Page 41: ...2 VoltageandTemperature Measurements Voltageand Temperature Measurements...
Page 68: ...2 28 Voltage and Temperature Measurements...
Page 69: ...3 Range Digits Rate andFilter Range Digits Rate andFilter...
Page 82: ...3 14 Range Digits Rate and Filter...
Page 83: ...4 Relative mX b and Percent Relative mX b andPercent...
Page 91: ...5 RatioandDelta Ratioand Delta...
Page 117: ...6 Buffer Buffer...
Page 123: ...7 Triggering Triggering...
Page 140: ...7 18 Triggering...
Page 141: ...8 Limits Limits...
Page 149: ...9 SteppingandScanning Steppingand Scanning...
Page 168: ...9 20 Stepping and Scanning...
Page 169: ...10 AnalogOutput Analog Output...
Page 175: ...11 RemoteOperation Remote Operation...
Page 205: ...12 CommonCommands Common Commands...
Page 221: ...13 SCPISignalOriented Measurement Commands SCPISignalOri entedMeasure ment Commands...
Page 225: ...14 SCPIReferenceTables SCPIRefer enceTables...
Page 239: ...15 AdditionalSCPI Commands Additional SCPICom mands...
Page 260: ...15 22 Additional SCPI Commands...
Page 261: ...A Specifications Specifications...
Page 263: ...B Statusand ErrorMessages StatusandError Messages...
Page 268: ...B 6 Status and Error Messages...
Page 269: ...C Measurement Considerations Measurement Consider ations...
Page 278: ...C 10 Measurement Considerations...
Page 279: ...D Model182Emulation Commands Model182 EmulationCom mands...
Page 284: ...D 6 Model 182 Emulation Commands...
Page 285: ...E Example Programs ExamplePro grams...
Page 293: ...F IEEE 488 BusOverview IEEE 488Bus Overview...
Page 307: ...G IEEE 488andSCPI ConformanceInformation IEEE 488and SCPIConform anceInforma tion...
Page 310: ...G 4 IEEE 488 and SCPI Conformance Information...
Page 311: ...H Measurement Queries Measurement Queries...
Page 316: ...H 6 Measurement Queries...
Page 317: ...I Delta PulseDelta and DifferentialConductance Delta Pulse Deltaand Dif ferentialCon ductance...