Johnson-Nyquist Thermal Noise

By Mohammad Ali Ahmadi Pajouh

AUT 2007

Some Interesting Measurements

Noise

bull Noise is a complex composite of lots of things

1 Thermal or Johnson Noise2 Shot noise

3 Flicker or 1f noise

4 Environmental noise

History

bull In 1927 J B Johnson observed random fluctuations in the voltages across electrical resistors A year later H Nyquist published a theoretical analysis of this noise which is thermal in origin Hence this type of noise is variously called Johnson noise Nyquist noise or Thermal noise

bull At any non-zero temperature we can think of the moving charges as a sort of Electron Gas trapped inside the resistor box

bull The electrons move about in a randomised way mdash similar to Brownian motion mdash bouncing and scattering off one another and the atoms

bull At any particular instant there may be more electrons near one end of the box than the other

bull If we note the meter reading at regular intervals (eg every second) for a long period we can plot a histogram of the results

bull we choose a lsquobin widthrsquo dv and divide up the range of possible voltages into small lsquobinsrsquo of this size We then count up how often the measured voltage was in each bin divide those counts by the total number of measurements and plot a histogram

bull We can now use this plot to indicate the likelihood or probability that any future measurement of the voltage will give a result in any particular small range

bull NYQUIST EQUATION

bull ltV2gt = 4kTRf

For frequencies below a few gigahertz Equation 1 gives the relationship between the- ltV2gt the measured mean-squared voltage - (T) absolute temperature of the resistor - ( R) its resistance - f is the bandwidth in hertz over which the noise is measured For a resistor of 1kΩ at room temperature and a 10 kHz bandwidth the RMS noise voltage is 400 nV or 04 microvolts - kB is Boltzmanrsquos constant (138 x 10-23- JoulesKelvin)

POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONSbull The frequency content of the random fluctuations are characterized by the power spectral density (PSD)bull PSD = power per unit frequencybull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoisebull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1

- f2 ) where(f1 - f2) is the bandwidth of the measurement systembullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth

In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as

Thermal Noise for Capacitancesbull Johnson noise in an RC circuit can be

expressed more simply by using the capacitance value rather than the resistance and bandwidth values The rms voltage noise on a capacitance C is independent of the resistor value since bandwidth varies reciprocally with resistance in an RC circuit

Shot Noise

bull Shot Noise occurs whenever any phenomenon can be

considered as a series of independent events occuring at random This occurs for carriers falling through a potential in one direction only This is a non-equilibrium process and

bull requires DC current flow First seen in vacuum tubes The spectrum is white and has a Gaussian Amplitude distribution

Why

bull Arises because electrons are quanta of charge and flow of charge across a junction is therefore a multiple quanta event and has to be dealt with using statistics

Flicker or 1f Noise

bull Inversely proportional to frequencybull Cause not well understoodbull Recognized by frequency dependencebull Becomes significant in signals lt100 Hzbull Worst for 0 Hz or DC driftbull Better in wire-wound or metallic film resistors

worse in standard carbon resistors So can be improved by using different electronic components in your circuit

Where1 Current in Carbon Composition resistors2 Current in Thin Metal Films (in the past not today)3 Current in Ionic Solutions4 All Solid-State components but especially Si MOSFET

GaAs5 Body Sway6 The Earthrsquos wobble on its axis7 Magnitude of Ocean waves8 Magnitude of Earthquakes9 Magnitude of Thunder Storms10 Magnitude of Tornados11 Magnitude of Hurricanes12 Classical and Jazz Music13 Economic data

Environmental Noise

bull Every wire in your instrument can act like an antenna to pick up electromagnetic energy and convert it into an electrical signal inside your instrument

bull There are lots of things in the environment that are putting out Electromagnetic signals

bull There are two region that are relatively noise free 3Hz to 60Hz and 1 kHz to 500 kHz

bull Will often design instruments around these frequencies to take advantage to this low environmental noise

Hardware Solutions

bull Grounding and Shielding

bull Difference and Instrumentation Amplifiers

bull Analog Filtering

bull Modulation

bull Signal Chopping Chopping amplifiers

bull Noise from environment can often be dramatically reduced by shielding grounding and minimizing wire lengths Shielding - surrounding a circuit or the wires in the circuit with a conducting material then attaching that to ground

bull Environmental EM radiation canrsquot penetrate the conductor where it gets absorbed

bull Arranging optimum shielding is something of an art something of hit and miss

bull Very important in high resistance transducers (like glass electrodes or pH electrodes Here even tiny noise get dramatically amplified

bull Wiring ndashavoid loops to reduce parasitic inductance

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

Some Interesting Measurements

Noise

bull Noise is a complex composite of lots of things

1 Thermal or Johnson Noise2 Shot noise

3 Flicker or 1f noise

4 Environmental noise

History

bull In 1927 J B Johnson observed random fluctuations in the voltages across electrical resistors A year later H Nyquist published a theoretical analysis of this noise which is thermal in origin Hence this type of noise is variously called Johnson noise Nyquist noise or Thermal noise

bull At any non-zero temperature we can think of the moving charges as a sort of Electron Gas trapped inside the resistor box

bull The electrons move about in a randomised way mdash similar to Brownian motion mdash bouncing and scattering off one another and the atoms

bull At any particular instant there may be more electrons near one end of the box than the other

bull If we note the meter reading at regular intervals (eg every second) for a long period we can plot a histogram of the results

bull we choose a lsquobin widthrsquo dv and divide up the range of possible voltages into small lsquobinsrsquo of this size We then count up how often the measured voltage was in each bin divide those counts by the total number of measurements and plot a histogram

bull We can now use this plot to indicate the likelihood or probability that any future measurement of the voltage will give a result in any particular small range

bull NYQUIST EQUATION

bull ltV2gt = 4kTRf

For frequencies below a few gigahertz Equation 1 gives the relationship between the- ltV2gt the measured mean-squared voltage - (T) absolute temperature of the resistor - ( R) its resistance - f is the bandwidth in hertz over which the noise is measured For a resistor of 1kΩ at room temperature and a 10 kHz bandwidth the RMS noise voltage is 400 nV or 04 microvolts - kB is Boltzmanrsquos constant (138 x 10-23- JoulesKelvin)

POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONSbull The frequency content of the random fluctuations are characterized by the power spectral density (PSD)bull PSD = power per unit frequencybull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoisebull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1

- f2 ) where(f1 - f2) is the bandwidth of the measurement systembullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth

In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as

Thermal Noise for Capacitancesbull Johnson noise in an RC circuit can be

expressed more simply by using the capacitance value rather than the resistance and bandwidth values The rms voltage noise on a capacitance C is independent of the resistor value since bandwidth varies reciprocally with resistance in an RC circuit

Shot Noise

bull Shot Noise occurs whenever any phenomenon can be

considered as a series of independent events occuring at random This occurs for carriers falling through a potential in one direction only This is a non-equilibrium process and

bull requires DC current flow First seen in vacuum tubes The spectrum is white and has a Gaussian Amplitude distribution

Why

bull Arises because electrons are quanta of charge and flow of charge across a junction is therefore a multiple quanta event and has to be dealt with using statistics

Flicker or 1f Noise

bull Inversely proportional to frequencybull Cause not well understoodbull Recognized by frequency dependencebull Becomes significant in signals lt100 Hzbull Worst for 0 Hz or DC driftbull Better in wire-wound or metallic film resistors

worse in standard carbon resistors So can be improved by using different electronic components in your circuit

Where1 Current in Carbon Composition resistors2 Current in Thin Metal Films (in the past not today)3 Current in Ionic Solutions4 All Solid-State components but especially Si MOSFET

GaAs5 Body Sway6 The Earthrsquos wobble on its axis7 Magnitude of Ocean waves8 Magnitude of Earthquakes9 Magnitude of Thunder Storms10 Magnitude of Tornados11 Magnitude of Hurricanes12 Classical and Jazz Music13 Economic data

Environmental Noise

bull Every wire in your instrument can act like an antenna to pick up electromagnetic energy and convert it into an electrical signal inside your instrument

bull There are lots of things in the environment that are putting out Electromagnetic signals

bull There are two region that are relatively noise free 3Hz to 60Hz and 1 kHz to 500 kHz

bull Will often design instruments around these frequencies to take advantage to this low environmental noise

Hardware Solutions

bull Grounding and Shielding

bull Difference and Instrumentation Amplifiers

bull Analog Filtering

bull Modulation

bull Signal Chopping Chopping amplifiers

bull Noise from environment can often be dramatically reduced by shielding grounding and minimizing wire lengths Shielding - surrounding a circuit or the wires in the circuit with a conducting material then attaching that to ground

bull Environmental EM radiation canrsquot penetrate the conductor where it gets absorbed

bull Arranging optimum shielding is something of an art something of hit and miss

bull Very important in high resistance transducers (like glass electrodes or pH electrodes Here even tiny noise get dramatically amplified

bull Wiring ndashavoid loops to reduce parasitic inductance

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

Noise

bull Noise is a complex composite of lots of things

1 Thermal or Johnson Noise2 Shot noise

3 Flicker or 1f noise

4 Environmental noise

History

bull In 1927 J B Johnson observed random fluctuations in the voltages across electrical resistors A year later H Nyquist published a theoretical analysis of this noise which is thermal in origin Hence this type of noise is variously called Johnson noise Nyquist noise or Thermal noise

bull At any non-zero temperature we can think of the moving charges as a sort of Electron Gas trapped inside the resistor box

bull The electrons move about in a randomised way mdash similar to Brownian motion mdash bouncing and scattering off one another and the atoms

bull At any particular instant there may be more electrons near one end of the box than the other

bull If we note the meter reading at regular intervals (eg every second) for a long period we can plot a histogram of the results

bull we choose a lsquobin widthrsquo dv and divide up the range of possible voltages into small lsquobinsrsquo of this size We then count up how often the measured voltage was in each bin divide those counts by the total number of measurements and plot a histogram

bull We can now use this plot to indicate the likelihood or probability that any future measurement of the voltage will give a result in any particular small range

bull NYQUIST EQUATION

bull ltV2gt = 4kTRf

For frequencies below a few gigahertz Equation 1 gives the relationship between the- ltV2gt the measured mean-squared voltage - (T) absolute temperature of the resistor - ( R) its resistance - f is the bandwidth in hertz over which the noise is measured For a resistor of 1kΩ at room temperature and a 10 kHz bandwidth the RMS noise voltage is 400 nV or 04 microvolts - kB is Boltzmanrsquos constant (138 x 10-23- JoulesKelvin)

POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONSbull The frequency content of the random fluctuations are characterized by the power spectral density (PSD)bull PSD = power per unit frequencybull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoisebull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1

- f2 ) where(f1 - f2) is the bandwidth of the measurement systembullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth

In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as

Thermal Noise for Capacitancesbull Johnson noise in an RC circuit can be

expressed more simply by using the capacitance value rather than the resistance and bandwidth values The rms voltage noise on a capacitance C is independent of the resistor value since bandwidth varies reciprocally with resistance in an RC circuit

Shot Noise

bull Shot Noise occurs whenever any phenomenon can be

considered as a series of independent events occuring at random This occurs for carriers falling through a potential in one direction only This is a non-equilibrium process and

bull requires DC current flow First seen in vacuum tubes The spectrum is white and has a Gaussian Amplitude distribution

Why

bull Arises because electrons are quanta of charge and flow of charge across a junction is therefore a multiple quanta event and has to be dealt with using statistics

Flicker or 1f Noise

bull Inversely proportional to frequencybull Cause not well understoodbull Recognized by frequency dependencebull Becomes significant in signals lt100 Hzbull Worst for 0 Hz or DC driftbull Better in wire-wound or metallic film resistors

worse in standard carbon resistors So can be improved by using different electronic components in your circuit

Where1 Current in Carbon Composition resistors2 Current in Thin Metal Films (in the past not today)3 Current in Ionic Solutions4 All Solid-State components but especially Si MOSFET

GaAs5 Body Sway6 The Earthrsquos wobble on its axis7 Magnitude of Ocean waves8 Magnitude of Earthquakes9 Magnitude of Thunder Storms10 Magnitude of Tornados11 Magnitude of Hurricanes12 Classical and Jazz Music13 Economic data

Environmental Noise

bull Every wire in your instrument can act like an antenna to pick up electromagnetic energy and convert it into an electrical signal inside your instrument

bull There are lots of things in the environment that are putting out Electromagnetic signals

bull There are two region that are relatively noise free 3Hz to 60Hz and 1 kHz to 500 kHz

bull Will often design instruments around these frequencies to take advantage to this low environmental noise

Hardware Solutions

bull Grounding and Shielding

bull Difference and Instrumentation Amplifiers

bull Analog Filtering

bull Modulation

bull Signal Chopping Chopping amplifiers

bull Noise from environment can often be dramatically reduced by shielding grounding and minimizing wire lengths Shielding - surrounding a circuit or the wires in the circuit with a conducting material then attaching that to ground

bull Environmental EM radiation canrsquot penetrate the conductor where it gets absorbed

bull Arranging optimum shielding is something of an art something of hit and miss

bull Very important in high resistance transducers (like glass electrodes or pH electrodes Here even tiny noise get dramatically amplified

bull Wiring ndashavoid loops to reduce parasitic inductance

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

History

bull In 1927 J B Johnson observed random fluctuations in the voltages across electrical resistors A year later H Nyquist published a theoretical analysis of this noise which is thermal in origin Hence this type of noise is variously called Johnson noise Nyquist noise or Thermal noise

bull At any non-zero temperature we can think of the moving charges as a sort of Electron Gas trapped inside the resistor box

bull The electrons move about in a randomised way mdash similar to Brownian motion mdash bouncing and scattering off one another and the atoms

bull At any particular instant there may be more electrons near one end of the box than the other

bull If we note the meter reading at regular intervals (eg every second) for a long period we can plot a histogram of the results

bull we choose a lsquobin widthrsquo dv and divide up the range of possible voltages into small lsquobinsrsquo of this size We then count up how often the measured voltage was in each bin divide those counts by the total number of measurements and plot a histogram

bull We can now use this plot to indicate the likelihood or probability that any future measurement of the voltage will give a result in any particular small range

bull NYQUIST EQUATION

bull ltV2gt = 4kTRf

For frequencies below a few gigahertz Equation 1 gives the relationship between the- ltV2gt the measured mean-squared voltage - (T) absolute temperature of the resistor - ( R) its resistance - f is the bandwidth in hertz over which the noise is measured For a resistor of 1kΩ at room temperature and a 10 kHz bandwidth the RMS noise voltage is 400 nV or 04 microvolts - kB is Boltzmanrsquos constant (138 x 10-23- JoulesKelvin)

POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONSbull The frequency content of the random fluctuations are characterized by the power spectral density (PSD)bull PSD = power per unit frequencybull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoisebull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1

- f2 ) where(f1 - f2) is the bandwidth of the measurement systembullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth

In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as

Thermal Noise for Capacitancesbull Johnson noise in an RC circuit can be

expressed more simply by using the capacitance value rather than the resistance and bandwidth values The rms voltage noise on a capacitance C is independent of the resistor value since bandwidth varies reciprocally with resistance in an RC circuit

Shot Noise

bull Shot Noise occurs whenever any phenomenon can be

considered as a series of independent events occuring at random This occurs for carriers falling through a potential in one direction only This is a non-equilibrium process and

bull requires DC current flow First seen in vacuum tubes The spectrum is white and has a Gaussian Amplitude distribution

Why

bull Arises because electrons are quanta of charge and flow of charge across a junction is therefore a multiple quanta event and has to be dealt with using statistics

Flicker or 1f Noise

bull Inversely proportional to frequencybull Cause not well understoodbull Recognized by frequency dependencebull Becomes significant in signals lt100 Hzbull Worst for 0 Hz or DC driftbull Better in wire-wound or metallic film resistors

worse in standard carbon resistors So can be improved by using different electronic components in your circuit

Where1 Current in Carbon Composition resistors2 Current in Thin Metal Films (in the past not today)3 Current in Ionic Solutions4 All Solid-State components but especially Si MOSFET

GaAs5 Body Sway6 The Earthrsquos wobble on its axis7 Magnitude of Ocean waves8 Magnitude of Earthquakes9 Magnitude of Thunder Storms10 Magnitude of Tornados11 Magnitude of Hurricanes12 Classical and Jazz Music13 Economic data

Environmental Noise

bull Every wire in your instrument can act like an antenna to pick up electromagnetic energy and convert it into an electrical signal inside your instrument

bull There are lots of things in the environment that are putting out Electromagnetic signals

bull There are two region that are relatively noise free 3Hz to 60Hz and 1 kHz to 500 kHz

bull Will often design instruments around these frequencies to take advantage to this low environmental noise

Hardware Solutions

bull Grounding and Shielding

bull Difference and Instrumentation Amplifiers

bull Analog Filtering

bull Modulation

bull Signal Chopping Chopping amplifiers

bull Noise from environment can often be dramatically reduced by shielding grounding and minimizing wire lengths Shielding - surrounding a circuit or the wires in the circuit with a conducting material then attaching that to ground

bull Environmental EM radiation canrsquot penetrate the conductor where it gets absorbed

bull Arranging optimum shielding is something of an art something of hit and miss

bull Very important in high resistance transducers (like glass electrodes or pH electrodes Here even tiny noise get dramatically amplified

bull Wiring ndashavoid loops to reduce parasitic inductance

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

bull At any non-zero temperature we can think of the moving charges as a sort of Electron Gas trapped inside the resistor box

bull The electrons move about in a randomised way mdash similar to Brownian motion mdash bouncing and scattering off one another and the atoms

bull At any particular instant there may be more electrons near one end of the box than the other

bull If we note the meter reading at regular intervals (eg every second) for a long period we can plot a histogram of the results

bull we choose a lsquobin widthrsquo dv and divide up the range of possible voltages into small lsquobinsrsquo of this size We then count up how often the measured voltage was in each bin divide those counts by the total number of measurements and plot a histogram

bull We can now use this plot to indicate the likelihood or probability that any future measurement of the voltage will give a result in any particular small range

bull NYQUIST EQUATION

bull ltV2gt = 4kTRf

For frequencies below a few gigahertz Equation 1 gives the relationship between the- ltV2gt the measured mean-squared voltage - (T) absolute temperature of the resistor - ( R) its resistance - f is the bandwidth in hertz over which the noise is measured For a resistor of 1kΩ at room temperature and a 10 kHz bandwidth the RMS noise voltage is 400 nV or 04 microvolts - kB is Boltzmanrsquos constant (138 x 10-23- JoulesKelvin)

POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONSbull The frequency content of the random fluctuations are characterized by the power spectral density (PSD)bull PSD = power per unit frequencybull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoisebull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1

- f2 ) where(f1 - f2) is the bandwidth of the measurement systembullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth

In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as

Thermal Noise for Capacitancesbull Johnson noise in an RC circuit can be

expressed more simply by using the capacitance value rather than the resistance and bandwidth values The rms voltage noise on a capacitance C is independent of the resistor value since bandwidth varies reciprocally with resistance in an RC circuit

Shot Noise

bull Shot Noise occurs whenever any phenomenon can be

considered as a series of independent events occuring at random This occurs for carriers falling through a potential in one direction only This is a non-equilibrium process and

bull requires DC current flow First seen in vacuum tubes The spectrum is white and has a Gaussian Amplitude distribution

Why

bull Arises because electrons are quanta of charge and flow of charge across a junction is therefore a multiple quanta event and has to be dealt with using statistics

Flicker or 1f Noise

bull Inversely proportional to frequencybull Cause not well understoodbull Recognized by frequency dependencebull Becomes significant in signals lt100 Hzbull Worst for 0 Hz or DC driftbull Better in wire-wound or metallic film resistors

worse in standard carbon resistors So can be improved by using different electronic components in your circuit

Where1 Current in Carbon Composition resistors2 Current in Thin Metal Films (in the past not today)3 Current in Ionic Solutions4 All Solid-State components but especially Si MOSFET

GaAs5 Body Sway6 The Earthrsquos wobble on its axis7 Magnitude of Ocean waves8 Magnitude of Earthquakes9 Magnitude of Thunder Storms10 Magnitude of Tornados11 Magnitude of Hurricanes12 Classical and Jazz Music13 Economic data

Environmental Noise

bull Every wire in your instrument can act like an antenna to pick up electromagnetic energy and convert it into an electrical signal inside your instrument

bull There are lots of things in the environment that are putting out Electromagnetic signals

bull There are two region that are relatively noise free 3Hz to 60Hz and 1 kHz to 500 kHz

bull Will often design instruments around these frequencies to take advantage to this low environmental noise

Hardware Solutions

bull Grounding and Shielding

bull Difference and Instrumentation Amplifiers

bull Analog Filtering

bull Modulation

bull Signal Chopping Chopping amplifiers

bull Noise from environment can often be dramatically reduced by shielding grounding and minimizing wire lengths Shielding - surrounding a circuit or the wires in the circuit with a conducting material then attaching that to ground

bull Environmental EM radiation canrsquot penetrate the conductor where it gets absorbed

bull Arranging optimum shielding is something of an art something of hit and miss

bull Very important in high resistance transducers (like glass electrodes or pH electrodes Here even tiny noise get dramatically amplified

bull Wiring ndashavoid loops to reduce parasitic inductance

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

bull At any particular instant there may be more electrons near one end of the box than the other

bull If we note the meter reading at regular intervals (eg every second) for a long period we can plot a histogram of the results

bull we choose a lsquobin widthrsquo dv and divide up the range of possible voltages into small lsquobinsrsquo of this size We then count up how often the measured voltage was in each bin divide those counts by the total number of measurements and plot a histogram

bull We can now use this plot to indicate the likelihood or probability that any future measurement of the voltage will give a result in any particular small range

bull NYQUIST EQUATION

bull ltV2gt = 4kTRf

For frequencies below a few gigahertz Equation 1 gives the relationship between the- ltV2gt the measured mean-squared voltage - (T) absolute temperature of the resistor - ( R) its resistance - f is the bandwidth in hertz over which the noise is measured For a resistor of 1kΩ at room temperature and a 10 kHz bandwidth the RMS noise voltage is 400 nV or 04 microvolts - kB is Boltzmanrsquos constant (138 x 10-23- JoulesKelvin)

POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONSbull The frequency content of the random fluctuations are characterized by the power spectral density (PSD)bull PSD = power per unit frequencybull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoisebull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1

- f2 ) where(f1 - f2) is the bandwidth of the measurement systembullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth

In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as

Thermal Noise for Capacitancesbull Johnson noise in an RC circuit can be

expressed more simply by using the capacitance value rather than the resistance and bandwidth values The rms voltage noise on a capacitance C is independent of the resistor value since bandwidth varies reciprocally with resistance in an RC circuit

Shot Noise

bull Shot Noise occurs whenever any phenomenon can be

considered as a series of independent events occuring at random This occurs for carriers falling through a potential in one direction only This is a non-equilibrium process and

bull requires DC current flow First seen in vacuum tubes The spectrum is white and has a Gaussian Amplitude distribution

Why

bull Arises because electrons are quanta of charge and flow of charge across a junction is therefore a multiple quanta event and has to be dealt with using statistics

Flicker or 1f Noise

bull Inversely proportional to frequencybull Cause not well understoodbull Recognized by frequency dependencebull Becomes significant in signals lt100 Hzbull Worst for 0 Hz or DC driftbull Better in wire-wound or metallic film resistors

worse in standard carbon resistors So can be improved by using different electronic components in your circuit

Where1 Current in Carbon Composition resistors2 Current in Thin Metal Films (in the past not today)3 Current in Ionic Solutions4 All Solid-State components but especially Si MOSFET

GaAs5 Body Sway6 The Earthrsquos wobble on its axis7 Magnitude of Ocean waves8 Magnitude of Earthquakes9 Magnitude of Thunder Storms10 Magnitude of Tornados11 Magnitude of Hurricanes12 Classical and Jazz Music13 Economic data

Environmental Noise

bull Every wire in your instrument can act like an antenna to pick up electromagnetic energy and convert it into an electrical signal inside your instrument

bull There are lots of things in the environment that are putting out Electromagnetic signals

bull There are two region that are relatively noise free 3Hz to 60Hz and 1 kHz to 500 kHz

bull Will often design instruments around these frequencies to take advantage to this low environmental noise

Hardware Solutions

bull Grounding and Shielding

bull Difference and Instrumentation Amplifiers

bull Analog Filtering

bull Modulation

bull Signal Chopping Chopping amplifiers

bull Noise from environment can often be dramatically reduced by shielding grounding and minimizing wire lengths Shielding - surrounding a circuit or the wires in the circuit with a conducting material then attaching that to ground

bull Environmental EM radiation canrsquot penetrate the conductor where it gets absorbed

bull Arranging optimum shielding is something of an art something of hit and miss

bull Very important in high resistance transducers (like glass electrodes or pH electrodes Here even tiny noise get dramatically amplified

bull Wiring ndashavoid loops to reduce parasitic inductance

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

bull If we note the meter reading at regular intervals (eg every second) for a long period we can plot a histogram of the results

bull we choose a lsquobin widthrsquo dv and divide up the range of possible voltages into small lsquobinsrsquo of this size We then count up how often the measured voltage was in each bin divide those counts by the total number of measurements and plot a histogram

bull We can now use this plot to indicate the likelihood or probability that any future measurement of the voltage will give a result in any particular small range

bull NYQUIST EQUATION

bull ltV2gt = 4kTRf

For frequencies below a few gigahertz Equation 1 gives the relationship between the- ltV2gt the measured mean-squared voltage - (T) absolute temperature of the resistor - ( R) its resistance - f is the bandwidth in hertz over which the noise is measured For a resistor of 1kΩ at room temperature and a 10 kHz bandwidth the RMS noise voltage is 400 nV or 04 microvolts - kB is Boltzmanrsquos constant (138 x 10-23- JoulesKelvin)

POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONSbull The frequency content of the random fluctuations are characterized by the power spectral density (PSD)bull PSD = power per unit frequencybull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoisebull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1

- f2 ) where(f1 - f2) is the bandwidth of the measurement systembullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth

In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as

Thermal Noise for Capacitancesbull Johnson noise in an RC circuit can be

expressed more simply by using the capacitance value rather than the resistance and bandwidth values The rms voltage noise on a capacitance C is independent of the resistor value since bandwidth varies reciprocally with resistance in an RC circuit

Shot Noise

bull Shot Noise occurs whenever any phenomenon can be

considered as a series of independent events occuring at random This occurs for carriers falling through a potential in one direction only This is a non-equilibrium process and

bull requires DC current flow First seen in vacuum tubes The spectrum is white and has a Gaussian Amplitude distribution

Why

bull Arises because electrons are quanta of charge and flow of charge across a junction is therefore a multiple quanta event and has to be dealt with using statistics

Flicker or 1f Noise

bull Inversely proportional to frequencybull Cause not well understoodbull Recognized by frequency dependencebull Becomes significant in signals lt100 Hzbull Worst for 0 Hz or DC driftbull Better in wire-wound or metallic film resistors

worse in standard carbon resistors So can be improved by using different electronic components in your circuit

Where1 Current in Carbon Composition resistors2 Current in Thin Metal Films (in the past not today)3 Current in Ionic Solutions4 All Solid-State components but especially Si MOSFET

GaAs5 Body Sway6 The Earthrsquos wobble on its axis7 Magnitude of Ocean waves8 Magnitude of Earthquakes9 Magnitude of Thunder Storms10 Magnitude of Tornados11 Magnitude of Hurricanes12 Classical and Jazz Music13 Economic data

Environmental Noise

bull Every wire in your instrument can act like an antenna to pick up electromagnetic energy and convert it into an electrical signal inside your instrument

bull There are lots of things in the environment that are putting out Electromagnetic signals

bull There are two region that are relatively noise free 3Hz to 60Hz and 1 kHz to 500 kHz

bull Will often design instruments around these frequencies to take advantage to this low environmental noise

Hardware Solutions

bull Grounding and Shielding

bull Difference and Instrumentation Amplifiers

bull Analog Filtering

bull Modulation

bull Signal Chopping Chopping amplifiers

bull Noise from environment can often be dramatically reduced by shielding grounding and minimizing wire lengths Shielding - surrounding a circuit or the wires in the circuit with a conducting material then attaching that to ground

bull Environmental EM radiation canrsquot penetrate the conductor where it gets absorbed

bull Arranging optimum shielding is something of an art something of hit and miss

bull Very important in high resistance transducers (like glass electrodes or pH electrodes Here even tiny noise get dramatically amplified

bull Wiring ndashavoid loops to reduce parasitic inductance

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

bull We can now use this plot to indicate the likelihood or probability that any future measurement of the voltage will give a result in any particular small range

bull NYQUIST EQUATION

bull ltV2gt = 4kTRf

For frequencies below a few gigahertz Equation 1 gives the relationship between the- ltV2gt the measured mean-squared voltage - (T) absolute temperature of the resistor - ( R) its resistance - f is the bandwidth in hertz over which the noise is measured For a resistor of 1kΩ at room temperature and a 10 kHz bandwidth the RMS noise voltage is 400 nV or 04 microvolts - kB is Boltzmanrsquos constant (138 x 10-23- JoulesKelvin)

POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONSbull The frequency content of the random fluctuations are characterized by the power spectral density (PSD)bull PSD = power per unit frequencybull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoisebull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1

- f2 ) where(f1 - f2) is the bandwidth of the measurement systembullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth

In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as

Thermal Noise for Capacitancesbull Johnson noise in an RC circuit can be

expressed more simply by using the capacitance value rather than the resistance and bandwidth values The rms voltage noise on a capacitance C is independent of the resistor value since bandwidth varies reciprocally with resistance in an RC circuit

Shot Noise

bull Shot Noise occurs whenever any phenomenon can be

considered as a series of independent events occuring at random This occurs for carriers falling through a potential in one direction only This is a non-equilibrium process and

bull requires DC current flow First seen in vacuum tubes The spectrum is white and has a Gaussian Amplitude distribution

Why

bull Arises because electrons are quanta of charge and flow of charge across a junction is therefore a multiple quanta event and has to be dealt with using statistics

Flicker or 1f Noise

bull Inversely proportional to frequencybull Cause not well understoodbull Recognized by frequency dependencebull Becomes significant in signals lt100 Hzbull Worst for 0 Hz or DC driftbull Better in wire-wound or metallic film resistors

worse in standard carbon resistors So can be improved by using different electronic components in your circuit

Where1 Current in Carbon Composition resistors2 Current in Thin Metal Films (in the past not today)3 Current in Ionic Solutions4 All Solid-State components but especially Si MOSFET

GaAs5 Body Sway6 The Earthrsquos wobble on its axis7 Magnitude of Ocean waves8 Magnitude of Earthquakes9 Magnitude of Thunder Storms10 Magnitude of Tornados11 Magnitude of Hurricanes12 Classical and Jazz Music13 Economic data

Environmental Noise

bull Every wire in your instrument can act like an antenna to pick up electromagnetic energy and convert it into an electrical signal inside your instrument

bull There are lots of things in the environment that are putting out Electromagnetic signals

bull There are two region that are relatively noise free 3Hz to 60Hz and 1 kHz to 500 kHz

bull Will often design instruments around these frequencies to take advantage to this low environmental noise

Hardware Solutions

bull Grounding and Shielding

bull Difference and Instrumentation Amplifiers

bull Analog Filtering

bull Modulation

bull Signal Chopping Chopping amplifiers

bull Noise from environment can often be dramatically reduced by shielding grounding and minimizing wire lengths Shielding - surrounding a circuit or the wires in the circuit with a conducting material then attaching that to ground

bull Environmental EM radiation canrsquot penetrate the conductor where it gets absorbed

bull Arranging optimum shielding is something of an art something of hit and miss

bull Very important in high resistance transducers (like glass electrodes or pH electrodes Here even tiny noise get dramatically amplified

bull Wiring ndashavoid loops to reduce parasitic inductance

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

bull NYQUIST EQUATION

bull ltV2gt = 4kTRf

For frequencies below a few gigahertz Equation 1 gives the relationship between the- ltV2gt the measured mean-squared voltage - (T) absolute temperature of the resistor - ( R) its resistance - f is the bandwidth in hertz over which the noise is measured For a resistor of 1kΩ at room temperature and a 10 kHz bandwidth the RMS noise voltage is 400 nV or 04 microvolts - kB is Boltzmanrsquos constant (138 x 10-23- JoulesKelvin)

POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONSbull The frequency content of the random fluctuations are characterized by the power spectral density (PSD)bull PSD = power per unit frequencybull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoisebull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1

- f2 ) where(f1 - f2) is the bandwidth of the measurement systembullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth

In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as

Thermal Noise for Capacitancesbull Johnson noise in an RC circuit can be

expressed more simply by using the capacitance value rather than the resistance and bandwidth values The rms voltage noise on a capacitance C is independent of the resistor value since bandwidth varies reciprocally with resistance in an RC circuit

Shot Noise

bull Shot Noise occurs whenever any phenomenon can be

considered as a series of independent events occuring at random This occurs for carriers falling through a potential in one direction only This is a non-equilibrium process and

bull requires DC current flow First seen in vacuum tubes The spectrum is white and has a Gaussian Amplitude distribution

Why

bull Arises because electrons are quanta of charge and flow of charge across a junction is therefore a multiple quanta event and has to be dealt with using statistics

Flicker or 1f Noise

bull Inversely proportional to frequencybull Cause not well understoodbull Recognized by frequency dependencebull Becomes significant in signals lt100 Hzbull Worst for 0 Hz or DC driftbull Better in wire-wound or metallic film resistors

worse in standard carbon resistors So can be improved by using different electronic components in your circuit

Where1 Current in Carbon Composition resistors2 Current in Thin Metal Films (in the past not today)3 Current in Ionic Solutions4 All Solid-State components but especially Si MOSFET

GaAs5 Body Sway6 The Earthrsquos wobble on its axis7 Magnitude of Ocean waves8 Magnitude of Earthquakes9 Magnitude of Thunder Storms10 Magnitude of Tornados11 Magnitude of Hurricanes12 Classical and Jazz Music13 Economic data

Environmental Noise

bull Every wire in your instrument can act like an antenna to pick up electromagnetic energy and convert it into an electrical signal inside your instrument

bull There are lots of things in the environment that are putting out Electromagnetic signals

bull There are two region that are relatively noise free 3Hz to 60Hz and 1 kHz to 500 kHz

bull Will often design instruments around these frequencies to take advantage to this low environmental noise

Hardware Solutions

bull Grounding and Shielding

bull Difference and Instrumentation Amplifiers

bull Analog Filtering

bull Modulation

bull Signal Chopping Chopping amplifiers

bull Noise from environment can often be dramatically reduced by shielding grounding and minimizing wire lengths Shielding - surrounding a circuit or the wires in the circuit with a conducting material then attaching that to ground

bull Environmental EM radiation canrsquot penetrate the conductor where it gets absorbed

bull Arranging optimum shielding is something of an art something of hit and miss

bull Very important in high resistance transducers (like glass electrodes or pH electrodes Here even tiny noise get dramatically amplified

bull Wiring ndashavoid loops to reduce parasitic inductance

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

For frequencies below a few gigahertz Equation 1 gives the relationship between the- ltV2gt the measured mean-squared voltage - (T) absolute temperature of the resistor - ( R) its resistance - f is the bandwidth in hertz over which the noise is measured For a resistor of 1kΩ at room temperature and a 10 kHz bandwidth the RMS noise voltage is 400 nV or 04 microvolts - kB is Boltzmanrsquos constant (138 x 10-23- JoulesKelvin)

POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONSbull The frequency content of the random fluctuations are characterized by the power spectral density (PSD)bull PSD = power per unit frequencybull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoisebull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1

- f2 ) where(f1 - f2) is the bandwidth of the measurement systembullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth

In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as

Thermal Noise for Capacitancesbull Johnson noise in an RC circuit can be

expressed more simply by using the capacitance value rather than the resistance and bandwidth values The rms voltage noise on a capacitance C is independent of the resistor value since bandwidth varies reciprocally with resistance in an RC circuit

Shot Noise

bull Shot Noise occurs whenever any phenomenon can be

considered as a series of independent events occuring at random This occurs for carriers falling through a potential in one direction only This is a non-equilibrium process and

bull requires DC current flow First seen in vacuum tubes The spectrum is white and has a Gaussian Amplitude distribution

Why

bull Arises because electrons are quanta of charge and flow of charge across a junction is therefore a multiple quanta event and has to be dealt with using statistics

Flicker or 1f Noise

bull Inversely proportional to frequencybull Cause not well understoodbull Recognized by frequency dependencebull Becomes significant in signals lt100 Hzbull Worst for 0 Hz or DC driftbull Better in wire-wound or metallic film resistors

worse in standard carbon resistors So can be improved by using different electronic components in your circuit

Where1 Current in Carbon Composition resistors2 Current in Thin Metal Films (in the past not today)3 Current in Ionic Solutions4 All Solid-State components but especially Si MOSFET

GaAs5 Body Sway6 The Earthrsquos wobble on its axis7 Magnitude of Ocean waves8 Magnitude of Earthquakes9 Magnitude of Thunder Storms10 Magnitude of Tornados11 Magnitude of Hurricanes12 Classical and Jazz Music13 Economic data

Environmental Noise

bull Every wire in your instrument can act like an antenna to pick up electromagnetic energy and convert it into an electrical signal inside your instrument

bull There are lots of things in the environment that are putting out Electromagnetic signals

bull There are two region that are relatively noise free 3Hz to 60Hz and 1 kHz to 500 kHz

bull Will often design instruments around these frequencies to take advantage to this low environmental noise

Hardware Solutions

bull Grounding and Shielding

bull Difference and Instrumentation Amplifiers

bull Analog Filtering

bull Modulation

bull Signal Chopping Chopping amplifiers

bull Noise from environment can often be dramatically reduced by shielding grounding and minimizing wire lengths Shielding - surrounding a circuit or the wires in the circuit with a conducting material then attaching that to ground

bull Environmental EM radiation canrsquot penetrate the conductor where it gets absorbed

bull Arranging optimum shielding is something of an art something of hit and miss

bull Very important in high resistance transducers (like glass electrodes or pH electrodes Here even tiny noise get dramatically amplified

bull Wiring ndashavoid loops to reduce parasitic inductance

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONSbull The frequency content of the random fluctuations are characterized by the power spectral density (PSD)bull PSD = power per unit frequencybull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoisebull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1

- f2 ) where(f1 - f2) is the bandwidth of the measurement systembullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth

In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as

Thermal Noise for Capacitancesbull Johnson noise in an RC circuit can be

expressed more simply by using the capacitance value rather than the resistance and bandwidth values The rms voltage noise on a capacitance C is independent of the resistor value since bandwidth varies reciprocally with resistance in an RC circuit

Shot Noise

bull Shot Noise occurs whenever any phenomenon can be

considered as a series of independent events occuring at random This occurs for carriers falling through a potential in one direction only This is a non-equilibrium process and

bull requires DC current flow First seen in vacuum tubes The spectrum is white and has a Gaussian Amplitude distribution

Why

bull Arises because electrons are quanta of charge and flow of charge across a junction is therefore a multiple quanta event and has to be dealt with using statistics

Flicker or 1f Noise

bull Inversely proportional to frequencybull Cause not well understoodbull Recognized by frequency dependencebull Becomes significant in signals lt100 Hzbull Worst for 0 Hz or DC driftbull Better in wire-wound or metallic film resistors

worse in standard carbon resistors So can be improved by using different electronic components in your circuit

Where1 Current in Carbon Composition resistors2 Current in Thin Metal Films (in the past not today)3 Current in Ionic Solutions4 All Solid-State components but especially Si MOSFET

GaAs5 Body Sway6 The Earthrsquos wobble on its axis7 Magnitude of Ocean waves8 Magnitude of Earthquakes9 Magnitude of Thunder Storms10 Magnitude of Tornados11 Magnitude of Hurricanes12 Classical and Jazz Music13 Economic data

Environmental Noise

bull Every wire in your instrument can act like an antenna to pick up electromagnetic energy and convert it into an electrical signal inside your instrument

bull There are lots of things in the environment that are putting out Electromagnetic signals

bull There are two region that are relatively noise free 3Hz to 60Hz and 1 kHz to 500 kHz

bull Will often design instruments around these frequencies to take advantage to this low environmental noise

Hardware Solutions

bull Grounding and Shielding

bull Difference and Instrumentation Amplifiers

bull Analog Filtering

bull Modulation

bull Signal Chopping Chopping amplifiers

bull Noise from environment can often be dramatically reduced by shielding grounding and minimizing wire lengths Shielding - surrounding a circuit or the wires in the circuit with a conducting material then attaching that to ground

bull Environmental EM radiation canrsquot penetrate the conductor where it gets absorbed

bull Arranging optimum shielding is something of an art something of hit and miss

bull Very important in high resistance transducers (like glass electrodes or pH electrodes Here even tiny noise get dramatically amplified

bull Wiring ndashavoid loops to reduce parasitic inductance

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as

Thermal Noise for Capacitancesbull Johnson noise in an RC circuit can be

expressed more simply by using the capacitance value rather than the resistance and bandwidth values The rms voltage noise on a capacitance C is independent of the resistor value since bandwidth varies reciprocally with resistance in an RC circuit

Shot Noise

bull Shot Noise occurs whenever any phenomenon can be

considered as a series of independent events occuring at random This occurs for carriers falling through a potential in one direction only This is a non-equilibrium process and

bull requires DC current flow First seen in vacuum tubes The spectrum is white and has a Gaussian Amplitude distribution

Why

bull Arises because electrons are quanta of charge and flow of charge across a junction is therefore a multiple quanta event and has to be dealt with using statistics

Flicker or 1f Noise

bull Inversely proportional to frequencybull Cause not well understoodbull Recognized by frequency dependencebull Becomes significant in signals lt100 Hzbull Worst for 0 Hz or DC driftbull Better in wire-wound or metallic film resistors

worse in standard carbon resistors So can be improved by using different electronic components in your circuit

Where1 Current in Carbon Composition resistors2 Current in Thin Metal Films (in the past not today)3 Current in Ionic Solutions4 All Solid-State components but especially Si MOSFET

GaAs5 Body Sway6 The Earthrsquos wobble on its axis7 Magnitude of Ocean waves8 Magnitude of Earthquakes9 Magnitude of Thunder Storms10 Magnitude of Tornados11 Magnitude of Hurricanes12 Classical and Jazz Music13 Economic data

Environmental Noise

bull Every wire in your instrument can act like an antenna to pick up electromagnetic energy and convert it into an electrical signal inside your instrument

bull There are lots of things in the environment that are putting out Electromagnetic signals

bull There are two region that are relatively noise free 3Hz to 60Hz and 1 kHz to 500 kHz

bull Will often design instruments around these frequencies to take advantage to this low environmental noise

Hardware Solutions

bull Grounding and Shielding

bull Difference and Instrumentation Amplifiers

bull Analog Filtering

bull Modulation

bull Signal Chopping Chopping amplifiers

bull Noise from environment can often be dramatically reduced by shielding grounding and minimizing wire lengths Shielding - surrounding a circuit or the wires in the circuit with a conducting material then attaching that to ground

bull Environmental EM radiation canrsquot penetrate the conductor where it gets absorbed

bull Arranging optimum shielding is something of an art something of hit and miss

bull Very important in high resistance transducers (like glass electrodes or pH electrodes Here even tiny noise get dramatically amplified

bull Wiring ndashavoid loops to reduce parasitic inductance

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

Thermal Noise for Capacitancesbull Johnson noise in an RC circuit can be

expressed more simply by using the capacitance value rather than the resistance and bandwidth values The rms voltage noise on a capacitance C is independent of the resistor value since bandwidth varies reciprocally with resistance in an RC circuit

Shot Noise

bull Shot Noise occurs whenever any phenomenon can be

considered as a series of independent events occuring at random This occurs for carriers falling through a potential in one direction only This is a non-equilibrium process and

bull requires DC current flow First seen in vacuum tubes The spectrum is white and has a Gaussian Amplitude distribution

Why

bull Arises because electrons are quanta of charge and flow of charge across a junction is therefore a multiple quanta event and has to be dealt with using statistics

Flicker or 1f Noise

bull Inversely proportional to frequencybull Cause not well understoodbull Recognized by frequency dependencebull Becomes significant in signals lt100 Hzbull Worst for 0 Hz or DC driftbull Better in wire-wound or metallic film resistors

worse in standard carbon resistors So can be improved by using different electronic components in your circuit

Where1 Current in Carbon Composition resistors2 Current in Thin Metal Films (in the past not today)3 Current in Ionic Solutions4 All Solid-State components but especially Si MOSFET

GaAs5 Body Sway6 The Earthrsquos wobble on its axis7 Magnitude of Ocean waves8 Magnitude of Earthquakes9 Magnitude of Thunder Storms10 Magnitude of Tornados11 Magnitude of Hurricanes12 Classical and Jazz Music13 Economic data

Environmental Noise

bull Every wire in your instrument can act like an antenna to pick up electromagnetic energy and convert it into an electrical signal inside your instrument

bull There are lots of things in the environment that are putting out Electromagnetic signals

bull There are two region that are relatively noise free 3Hz to 60Hz and 1 kHz to 500 kHz

bull Will often design instruments around these frequencies to take advantage to this low environmental noise

Hardware Solutions

bull Grounding and Shielding

bull Difference and Instrumentation Amplifiers

bull Analog Filtering

bull Modulation

bull Signal Chopping Chopping amplifiers

bull Noise from environment can often be dramatically reduced by shielding grounding and minimizing wire lengths Shielding - surrounding a circuit or the wires in the circuit with a conducting material then attaching that to ground

bull Environmental EM radiation canrsquot penetrate the conductor where it gets absorbed

bull Arranging optimum shielding is something of an art something of hit and miss

bull Very important in high resistance transducers (like glass electrodes or pH electrodes Here even tiny noise get dramatically amplified

bull Wiring ndashavoid loops to reduce parasitic inductance

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

Shot Noise

bull Shot Noise occurs whenever any phenomenon can be

considered as a series of independent events occuring at random This occurs for carriers falling through a potential in one direction only This is a non-equilibrium process and

bull requires DC current flow First seen in vacuum tubes The spectrum is white and has a Gaussian Amplitude distribution

Why

bull Arises because electrons are quanta of charge and flow of charge across a junction is therefore a multiple quanta event and has to be dealt with using statistics

Flicker or 1f Noise

bull Inversely proportional to frequencybull Cause not well understoodbull Recognized by frequency dependencebull Becomes significant in signals lt100 Hzbull Worst for 0 Hz or DC driftbull Better in wire-wound or metallic film resistors

worse in standard carbon resistors So can be improved by using different electronic components in your circuit

Where1 Current in Carbon Composition resistors2 Current in Thin Metal Films (in the past not today)3 Current in Ionic Solutions4 All Solid-State components but especially Si MOSFET

GaAs5 Body Sway6 The Earthrsquos wobble on its axis7 Magnitude of Ocean waves8 Magnitude of Earthquakes9 Magnitude of Thunder Storms10 Magnitude of Tornados11 Magnitude of Hurricanes12 Classical and Jazz Music13 Economic data

Environmental Noise

bull Every wire in your instrument can act like an antenna to pick up electromagnetic energy and convert it into an electrical signal inside your instrument

bull There are lots of things in the environment that are putting out Electromagnetic signals

bull There are two region that are relatively noise free 3Hz to 60Hz and 1 kHz to 500 kHz

bull Will often design instruments around these frequencies to take advantage to this low environmental noise

Hardware Solutions

bull Grounding and Shielding

bull Difference and Instrumentation Amplifiers

bull Analog Filtering

bull Modulation

bull Signal Chopping Chopping amplifiers

bull Noise from environment can often be dramatically reduced by shielding grounding and minimizing wire lengths Shielding - surrounding a circuit or the wires in the circuit with a conducting material then attaching that to ground

bull Environmental EM radiation canrsquot penetrate the conductor where it gets absorbed

bull Arranging optimum shielding is something of an art something of hit and miss

bull Very important in high resistance transducers (like glass electrodes or pH electrodes Here even tiny noise get dramatically amplified

bull Wiring ndashavoid loops to reduce parasitic inductance

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

Why

bull Arises because electrons are quanta of charge and flow of charge across a junction is therefore a multiple quanta event and has to be dealt with using statistics

Flicker or 1f Noise

bull Inversely proportional to frequencybull Cause not well understoodbull Recognized by frequency dependencebull Becomes significant in signals lt100 Hzbull Worst for 0 Hz or DC driftbull Better in wire-wound or metallic film resistors

worse in standard carbon resistors So can be improved by using different electronic components in your circuit

Where1 Current in Carbon Composition resistors2 Current in Thin Metal Films (in the past not today)3 Current in Ionic Solutions4 All Solid-State components but especially Si MOSFET

GaAs5 Body Sway6 The Earthrsquos wobble on its axis7 Magnitude of Ocean waves8 Magnitude of Earthquakes9 Magnitude of Thunder Storms10 Magnitude of Tornados11 Magnitude of Hurricanes12 Classical and Jazz Music13 Economic data

Environmental Noise

bull Every wire in your instrument can act like an antenna to pick up electromagnetic energy and convert it into an electrical signal inside your instrument

bull There are lots of things in the environment that are putting out Electromagnetic signals

bull There are two region that are relatively noise free 3Hz to 60Hz and 1 kHz to 500 kHz

bull Will often design instruments around these frequencies to take advantage to this low environmental noise

Hardware Solutions

bull Grounding and Shielding

bull Difference and Instrumentation Amplifiers

bull Analog Filtering

bull Modulation

bull Signal Chopping Chopping amplifiers

bull Noise from environment can often be dramatically reduced by shielding grounding and minimizing wire lengths Shielding - surrounding a circuit or the wires in the circuit with a conducting material then attaching that to ground

bull Environmental EM radiation canrsquot penetrate the conductor where it gets absorbed

bull Arranging optimum shielding is something of an art something of hit and miss

bull Very important in high resistance transducers (like glass electrodes or pH electrodes Here even tiny noise get dramatically amplified

bull Wiring ndashavoid loops to reduce parasitic inductance

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

Flicker or 1f Noise

bull Inversely proportional to frequencybull Cause not well understoodbull Recognized by frequency dependencebull Becomes significant in signals lt100 Hzbull Worst for 0 Hz or DC driftbull Better in wire-wound or metallic film resistors

worse in standard carbon resistors So can be improved by using different electronic components in your circuit

Where1 Current in Carbon Composition resistors2 Current in Thin Metal Films (in the past not today)3 Current in Ionic Solutions4 All Solid-State components but especially Si MOSFET

GaAs5 Body Sway6 The Earthrsquos wobble on its axis7 Magnitude of Ocean waves8 Magnitude of Earthquakes9 Magnitude of Thunder Storms10 Magnitude of Tornados11 Magnitude of Hurricanes12 Classical and Jazz Music13 Economic data

Environmental Noise

bull Every wire in your instrument can act like an antenna to pick up electromagnetic energy and convert it into an electrical signal inside your instrument

bull There are lots of things in the environment that are putting out Electromagnetic signals

bull There are two region that are relatively noise free 3Hz to 60Hz and 1 kHz to 500 kHz

bull Will often design instruments around these frequencies to take advantage to this low environmental noise

Hardware Solutions

bull Grounding and Shielding

bull Difference and Instrumentation Amplifiers

bull Analog Filtering

bull Modulation

bull Signal Chopping Chopping amplifiers

bull Noise from environment can often be dramatically reduced by shielding grounding and minimizing wire lengths Shielding - surrounding a circuit or the wires in the circuit with a conducting material then attaching that to ground

bull Environmental EM radiation canrsquot penetrate the conductor where it gets absorbed

bull Arranging optimum shielding is something of an art something of hit and miss

bull Very important in high resistance transducers (like glass electrodes or pH electrodes Here even tiny noise get dramatically amplified

bull Wiring ndashavoid loops to reduce parasitic inductance

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

Where1 Current in Carbon Composition resistors2 Current in Thin Metal Films (in the past not today)3 Current in Ionic Solutions4 All Solid-State components but especially Si MOSFET

GaAs5 Body Sway6 The Earthrsquos wobble on its axis7 Magnitude of Ocean waves8 Magnitude of Earthquakes9 Magnitude of Thunder Storms10 Magnitude of Tornados11 Magnitude of Hurricanes12 Classical and Jazz Music13 Economic data

Environmental Noise

bull Every wire in your instrument can act like an antenna to pick up electromagnetic energy and convert it into an electrical signal inside your instrument

bull There are lots of things in the environment that are putting out Electromagnetic signals

bull There are two region that are relatively noise free 3Hz to 60Hz and 1 kHz to 500 kHz

bull Will often design instruments around these frequencies to take advantage to this low environmental noise

Hardware Solutions

bull Grounding and Shielding

bull Difference and Instrumentation Amplifiers

bull Analog Filtering

bull Modulation

bull Signal Chopping Chopping amplifiers

bull Noise from environment can often be dramatically reduced by shielding grounding and minimizing wire lengths Shielding - surrounding a circuit or the wires in the circuit with a conducting material then attaching that to ground

bull Environmental EM radiation canrsquot penetrate the conductor where it gets absorbed

bull Arranging optimum shielding is something of an art something of hit and miss

bull Very important in high resistance transducers (like glass electrodes or pH electrodes Here even tiny noise get dramatically amplified

bull Wiring ndashavoid loops to reduce parasitic inductance

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

Environmental Noise

bull Every wire in your instrument can act like an antenna to pick up electromagnetic energy and convert it into an electrical signal inside your instrument

bull There are lots of things in the environment that are putting out Electromagnetic signals

bull There are two region that are relatively noise free 3Hz to 60Hz and 1 kHz to 500 kHz

bull Will often design instruments around these frequencies to take advantage to this low environmental noise

Hardware Solutions

bull Grounding and Shielding

bull Difference and Instrumentation Amplifiers

bull Analog Filtering

bull Modulation

bull Signal Chopping Chopping amplifiers

bull Noise from environment can often be dramatically reduced by shielding grounding and minimizing wire lengths Shielding - surrounding a circuit or the wires in the circuit with a conducting material then attaching that to ground

bull Environmental EM radiation canrsquot penetrate the conductor where it gets absorbed

bull Arranging optimum shielding is something of an art something of hit and miss

bull Very important in high resistance transducers (like glass electrodes or pH electrodes Here even tiny noise get dramatically amplified

bull Wiring ndashavoid loops to reduce parasitic inductance

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

Hardware Solutions

bull Grounding and Shielding

bull Difference and Instrumentation Amplifiers

bull Analog Filtering

bull Modulation

bull Signal Chopping Chopping amplifiers

bull Noise from environment can often be dramatically reduced by shielding grounding and minimizing wire lengths Shielding - surrounding a circuit or the wires in the circuit with a conducting material then attaching that to ground

bull Environmental EM radiation canrsquot penetrate the conductor where it gets absorbed

bull Arranging optimum shielding is something of an art something of hit and miss

bull Very important in high resistance transducers (like glass electrodes or pH electrodes Here even tiny noise get dramatically amplified

bull Wiring ndashavoid loops to reduce parasitic inductance

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

bull Noise from environment can often be dramatically reduced by shielding grounding and minimizing wire lengths Shielding - surrounding a circuit or the wires in the circuit with a conducting material then attaching that to ground

bull Environmental EM radiation canrsquot penetrate the conductor where it gets absorbed

bull Arranging optimum shielding is something of an art something of hit and miss

bull Very important in high resistance transducers (like glass electrodes or pH electrodes Here even tiny noise get dramatically amplified

bull Wiring ndashavoid loops to reduce parasitic inductance

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

bull To amplify signal but not noise instruments typically use a difference amplifier for first stage of amplification If this isnrsquot enough a circuit called an instrumentation amplifier is used

bull With these kinds of electronics can amplify signal 1000x and eject of noise

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

Analog Filtering

bull Most common way of improving SN is with a low-pass filter Lowbull pass means that it passes slow moving signals (low frequency) but

itbull stops signals with high frequencies the jiggling noisebull Can be done with just a resistor and a capacitor This method isbull most common used in older analog instrumentsbull 1048707 You have a switch on the consol where you change either thebull capacitor or the resistor that changes the time response of thebull instrument Does reduce high frequency noise but can also damagebull signal so you have to be careful how this is used At other times

canbull use a high pass filter to pass a high frequency signal but block a lowbull frequency driftbull 1048707 Also can use narrow band or band pass filters to let just certainbull frequencies through

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26

bull 1 J Johnson Thermal Agitation of

Electricity in Conductors Phys Rev 32

97 (1928) (the experiment)

2 H Nyquist Thermal Agitation of Electric

Charge in Conductors Phys Rev 32

110 (1928) (the theory)

• Johnson-Nyquist Thermal Noise
• Some Interesting Measurements
• Noise
• History
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• POWER SPECTRAL DENSITY OF THE RANDOM FLUCTUATIONS bull The frequency content of the random fluctuations are characterized by the power spectral density (PSD) bull PSD = power per unit frequency bull The noise spectrum of the random fluctuations is wide band or ldquowhiterdquonoise bull Therefore the PSD of the random fluctuations is constant and the power is calculated by PSD (f) (f1 - f2 ) where (f1 - f2) is the bandwidth of the measurement system bullThe mean-square of the random fluctuations can be reduced by reducing the bandwidth
• Slide 13
• In communications power is often measured in decibels relative to 1 milliwatt (dBm) assuming a 50 ohm resistance With these conventions thermal noise at room temperature can be estimated as
• Thermal Noise for Capacitances
• Slide 16
• Shot Noise
• Why
• Flicker or 1f Noise
• Where
• Environmental Noise
• Hardware Solutions
• Slide 23
• Slide 24
• Analog Filtering
• Slide 26