saturday, november 9, 2013 michael a. stein, md

The Illinois Society of The Illinois Society of Electroneurodiagnostic Electroneurodiagnostic

Technologists (ISET)Technologists (ISET)Fall Meeting:Fall Meeting:

Electronics Crash Course for Electronics Crash Course for TechnologistsTechnologists

Saturday, November 9, 2013Saturday, November 9, 2013

Michael A. Stein, MDMichael A. Stein, MD

Digital EEG System:Digital EEG System:TransformationTransformation

PART 2:PART 2: ‘‘BlackBox’ TransformationBlackBox’ Transformation


The next stage in The next stage in the EEG system the EEG system serves the serves the following functions:following functions: (1) Filtering of (1) Filtering of

unwanted activity unwanted activity outside of the outside of the desired bandwidth.desired bandwidth.

(2) Amplification of (2) Amplification of Desired Signal Desired Signal within the within the bandwidth.bandwidth.

(3) Noise reduction.(3) Noise reduction.


In this regards, 3 In this regards, 3 important important characteristics of EEG characteristics of EEG amplifiers are:amplifiers are: (a) A flat frequency (a) A flat frequency

response within the response within the passband (discussed in passband (discussed in Part 1 of this course).Part 1 of this course).

(b) A high common mode (b) A high common mode rejection ratio.rejection ratio.

(c) A high input (c) A high input impedance.impedance.

The latter 2 properties The latter 2 properties will be discussed later will be discussed later in this course.in this course.


First, a reminder from Part 1 aboutFirst, a reminder from Part 1 about : : In this regards, 3 important characteristics of In this regards, 3 important characteristics of

EEG amplifiers are:EEG amplifiers are:

(a) A flat frequency response (a) A flat frequency response within the passband (discussed within the passband (discussed in Part 1 of this course).in Part 1 of this course).

(b) A high common mode rejection ratio.(b) A high common mode rejection ratio. (c) A high input impedance.(c) A high input impedance.

In the case of a hi-fidelity sound system a bandwidth of In the case of a hi-fidelity sound system a bandwidth of approximately (20 – 20k Hz) with approximately equal gain approximately (20 – 20k Hz) with approximately equal gain is important since this is the range of audible frequencies.is important since this is the range of audible frequencies.

If the gain is not approximately equal in this range then If the gain is not approximately equal in this range then the reproduced sound heard by the listener will differ from the reproduced sound heard by the listener will differ from the sound which was recorded.the sound which was recorded.

Since the audio of cellular phones Since the audio of cellular phones typically only includes voice data, the typically only includes voice data, the frequency response needs to have frequency response needs to have relatively equal gain over a narrower relatively equal gain over a narrower bandwidth of about (300 – 3,000)Hz.bandwidth of about (300 – 3,000)Hz.

Since the EEG activity generated by the cortex which Since the EEG activity generated by the cortex which reaches the scalp has an even narrower bandwidth, and reaches the scalp has an even narrower bandwidth, and part of this is obscured by muscle artifact, the frequency part of this is obscured by muscle artifact, the frequency response only needs to be equal in gain from about (0.5 - response only needs to be equal in gain from about (0.5 - 70) Hz. 70) Hz.

Since lower and higher frequencies consist of artifacts, Since lower and higher frequencies consist of artifacts, they are deliberately filtered out.they are deliberately filtered out.


Although it is easier to understand these 3 Although it is easier to understand these 3 functions if thought of separately, they are functions if thought of separately, they are typically built into a single amplifier circuit.typically built into a single amplifier circuit. (1) Filtering of unwanted activity outside of the desired (1) Filtering of unwanted activity outside of the desired

bandwidth.bandwidth. (2) Amplification of Desired Signal within the bandwidth.(2) Amplification of Desired Signal within the bandwidth. (3) Noise reduction.(3) Noise reduction.

Operational Amplifier – aka: OpAmp

Differential Amplifier

Digital EEG System:Digital EEG System:Transformation:Transformation:

(1) Filtering of Unwanted Signal(1) Filtering of Unwanted Signal

Therefore, need to filter out frequencies that are both lower than and Therefore, need to filter out frequencies that are both lower than and higher than the desired bandwidth of the signal being measured (EEG).higher than the desired bandwidth of the signal being measured (EEG).

This can be done with either analog or digital electronics by use of This can be done with either analog or digital electronics by use of both:both:

(1) Low frequency/high pass filters, and(1) Low frequency/high pass filters, and (2) High frequency/low pass filters.(2) High frequency/low pass filters. These two together (low frequency filter + high frequency filter) form a These two together (low frequency filter + high frequency filter) form a

bandpass or passband filter. Ideally, the bandpass will be the same as the bandpass or passband filter. Ideally, the bandpass will be the same as the bandwidth of the desired signal (EEG).bandwidth of the desired signal (EEG).

In Part 1 the filtering which was discussed is due to the biophysical In Part 1 the filtering which was discussed is due to the biophysical properties of the electrode and is unintended and can lead to properties of the electrode and is unintended and can lead to degradation in EEG signal quality.degradation in EEG signal quality.

In contrast, at this stage of the EEG amplifier, the filtering is In contrast, at this stage of the EEG amplifier, the filtering is designeddesigned to filter out unwanted signals outside of the desired bandwidth, while to filter out unwanted signals outside of the desired bandwidth, while passing EEG activity within the desired passband without change.passing EEG activity within the desired passband without change.

Reminder from Part 1: Terminology


(1) Filtering of Unwanted Signal(1) Filtering of Unwanted Signal Since there are both low Since there are both low

frequency and high frequency frequency and high frequency sources of noise, both low sources of noise, both low frequency and high frequency frequency and high frequency filters are needed.filters are needed.

Examples of low frequency noise Examples of low frequency noise sources:sources:

Cardiac pulsationCardiac pulsation SweatSweat Roving eye movementsRoving eye movements

Examples of high frequency noise Examples of high frequency noise sources:sources:

Line/Mains/60 HzLine/Mains/60 Hz Medical devices (oscillating Medical devices (oscillating

ventilators, etc.)ventilators, etc.) Cellular telephones, radios, etc.Cellular telephones, radios, etc.

Together these 2 filter types Together these 2 filter types combine to form a bandpass filter.combine to form a bandpass filter.

The objectives of the bandpass The objectives of the bandpass filter are:filter are:

To filter out as much undesired To filter out as much undesired signal as possiblesignal as possible

To pass as much desired signal as To pass as much desired signal as possible without altering itpossible without altering it



Since scalp EEG contains Since scalp EEG contains very low frequency very low frequency information (slow wave information (slow wave sleep, slow spike and wave, sleep, slow spike and wave, etc.), the low frequency etc.), the low frequency filter will need to have a filter will need to have a low cutoff frequency.low cutoff frequency.

In almost all systems there In almost all systems there is overlap in frequency is overlap in frequency between desired signal and between desired signal and unwanted signal.unwanted signal. (e.g. Slow spike and wave (e.g. Slow spike and wave

and cardiac pulsation and cardiac pulsation artifact).artifact).

A tradeoff is therefore A tradeoff is therefore necessary in the degree of necessary in the degree of filtering and the chosen filtering and the chosen cutoff frequency.cutoff frequency.

(1) Low Frequency Filtering:

Reminder from Part 1:Reminder from Part 1: Digital EEG System:Digital EEG System:Low Frequency FiltersLow Frequency Filters

(A) Low frequency (aka (A) Low frequency (aka high pass) filters:high pass) filters: (f(fcc) ) = 1 / (2π x RC) == 1 / (2π x RC) =

1 / (2π x t1 / (2π x tcc))

Example:Example: R = 10,000ΩR = 10,000Ω C = 16μFC = 16μF (f(fcc) ) = 1 / (2π x RC) == 1 / (2π x RC) = 1 / (2π x 10,000 x 16x101 / (2π x 10,000 x 16x10-6-6) = ) = 1Hz.1Hz.

(Therefore, this circuit (Therefore, this circuit creates a single pole, low creates a single pole, low frequency filter with a frequency filter with a cutoff frequency of 1 Hz.)cutoff frequency of 1 Hz.)



Since scalp EEG begins to Since scalp EEG begins to be obscured by muscle be obscured by muscle artifact above 30 Hz but artifact above 30 Hz but EEG signal includes EEG signal includes activity in this range as activity in this range as well, the high frequency well, the high frequency filter cutoff frequency is filter cutoff frequency is chosen as a tradeoff chosen as a tradeoff between these factors.between these factors.

In almost all systems there In almost all systems there is overlap in frequency is overlap in frequency between desired signal between desired signal and unwanted signal.and unwanted signal. (e.g. Paroxysmal fast EEG (e.g. Paroxysmal fast EEG

activity and cellular activity and cellular telephone artifact).telephone artifact).

(2) High Frequency Filtering:

Reminder from Part 1:Reminder from Part 1: Digital EEG System:Digital EEG System:High Frequency FiltersHigh Frequency Filters

(A) High frequency (aka (A) High frequency (aka low pass) filters:low pass) filters: (f(fcc) ) = 1 / (2π x RC) == 1 / (2π x RC) =

1 / (2π x t1 / (2π x tcc))

Example:Example: R = 100ΩR = 100Ω C = 16μFC = 16μF (f(fcc) ) = 1 / (2π x RC) == 1 / (2π x RC) = 1 / (2π x 100 x 16x101 / (2π x 100 x 16x10-6-6) = ) = 100 Hz.100 Hz.

(Therefore, this circuit (Therefore, this circuit creates a single pole, high creates a single pole, high frequency filter with a frequency filter with a cutoff frequency of 100 cutoff frequency of 100 Hz.)Hz.)



Together these two filters (low frequency filter and high Together these two filters (low frequency filter and high frequency filter) create a bandpass filter.frequency filter) create a bandpass filter.

Although this passband has some overlap with both low Although this passband has some overlap with both low and high frequency sources of noise/artifact, these occur and high frequency sources of noise/artifact, these occur mostly beyond the 3 dB cutoff frequencies and will mostly beyond the 3 dB cutoff frequencies and will therefore be reduced in amplitude at the output of the EEG therefore be reduced in amplitude at the output of the EEG amplifier.amplifier.

+ =

EEG Filter Examples:EEG Filter Examples:(1) Background Activity(1) Background Activity

No filters

Filters: (LFF = 1 Hz, HFF = 50 Hz)

EEG Filter Examples:EEG Filter Examples:(2) Interical Epileptiform Activity(2) Interical Epileptiform Activity

No filters


EEG Filter Examples:EEG Filter Examples:(3a) Ictal/Seizure Activity(3a) Ictal/Seizure Activity

No filters


EEG Filter Examples:EEG Filter Examples:(3b) Ictal/Seizure Activity(3b) Ictal/Seizure Activity

No filters

Filters: (LFF = 1 Hz, HFF = 50 Hz, Notch Filter = 60 Hz)


(2) Amplification of Desired Signal(2) Amplification of Desired Signal

Terminology:Terminology: Operational Amplifiers (aka: OpAmps).Operational Amplifiers (aka: OpAmps).

Simple electronic circuits which amplify the signal so that the Simple electronic circuits which amplify the signal so that the output is larger than the input.output is larger than the input.

Examples:Examples: (1) Cellular telephone transmission: (1) Cellular telephone transmission:

Signal needs to be amplified so there is enough power to carry Signal needs to be amplified so there is enough power to carry over great distances.over great distances.

(2) Hi-fidelity sound system:(2) Hi-fidelity sound system: Signal needs to be amplified so there is sufficient power to Signal needs to be amplified so there is sufficient power to

mechanically move the loudspeakers enough to create audible mechanically move the loudspeakers enough to create audible sound.sound.

(3) EEG system:(3) EEG system: Signal needs to be amplified so that it is large enough to be Signal needs to be amplified so that it is large enough to be

viewed on a computer monitor.viewed on a computer monitor.



There are different types of OpAmps There are different types of OpAmps and OpAmp circuits.and OpAmp circuits.

(a)(a) For a basic inverting OpAmp: For a basic inverting OpAmp: RRinin = input resistance = input resistance RRff = feedback resistance = feedback resistance Gain = amplification factor -(VGain = amplification factor -(Voutout / V / Vinin) = -(R) = -(Rf f / R/ Rinin) )

(b)(b) For a non-inverting OpAmp: For a non-inverting OpAmp: Gain = +(VGain = +(Voutout / V / Vinin) = +(1 + (R) = +(1 + (R2 2 / R/ R11))))



(c)(c) For a Differential For a Differential OpAmp:OpAmp: There are 2 inputsThere are 2 inputs

(The difference between (The difference between the 2 inputs is the 2 inputs is amplified.)amplified.)

RRinin = input resistance = input resistance RRff = feedback resistance = feedback resistance RRgg = ground resistance = ground resistance

VVoutout = = (R(Rff + R + R11)xR)xRgg x x VV2 2 _ _ (R(Rff)) x x VV11

(R(Rgg + R + R22)xR)xR1 1 (R(R11))



Differential Differential Amplifiers:Amplifiers: Used for nearly all Used for nearly all

neurodiagnostic neurodiagnostic applications.applications.

More meaningful More meaningful since difference since difference between two inputs between two inputs is amplified.is amplified.

Better noise Better noise reduction.reduction.



Differential Amplifier Function:Differential Amplifier Function: (The difference between the 2 inputs is amplified.)(The difference between the 2 inputs is amplified.)



Use of Differential Inputs for typical Use of Differential Inputs for typical EEG montagesEEG montages::

(a) (a) Bipolar Montage:Bipolar Montage:



Use of Differential Inputs for typical Use of Differential Inputs for typical EEG montagesEEG montages::

(b) (b) Referential Montages:Referential Montages:

Common Reference Common Average Reference


(3) Noise Reduction(3) Noise Reduction

Why is noise reduction improved with a Why is noise reduction improved with a differential amplifier compared to a unipolar differential amplifier compared to a unipolar OpAmp?OpAmp?

The unipolar OpAmp amplifies the difference between a The unipolar OpAmp amplifies the difference between a single input channel and ground.single input channel and ground.

In biomedical applications, ground is typically In biomedical applications, ground is typically physically far removed from the signal being measured physically far removed from the signal being measured (e.g. EEG electrodes).(e.g. EEG electrodes).

Unipolar Operational Amplifier – aka: OpAmp

Differential Amplifier

Digital EEG System:Digital EEG System:Transformation:Transformation: (3) Noise Reduction(3) Noise Reduction

Why is noise reduction improved with a differential Why is noise reduction improved with a differential amplifier compared to a unipolar OpAmp?amplifier compared to a unipolar OpAmp? Since the two input channels (signal and ground) are separated in Since the two input channels (signal and ground) are separated in

space, they will be subject to different noise sources space, they will be subject to different noise sources (environmental noise (radio, cell phone, medical instrumentation, (environmental noise (radio, cell phone, medical instrumentation, etc), 60 Hz line noise, etc.).etc), 60 Hz line noise, etc.).

This difference in noise sources creates a difference at the input of This difference in noise sources creates a difference at the input of the amplifier which then gets amplified by the gain factor of the the amplifier which then gets amplified by the gain factor of the unipolar amplifier along with the desired signal. This leads to a unipolar amplifier along with the desired signal. This leads to a noisy output.noisy output.


Why is noise reduction improved with a differential Why is noise reduction improved with a differential amplifier compared to a unipolar OpAmp?amplifier compared to a unipolar OpAmp? Amplifiers also generate their own internal electronic noise.Amplifiers also generate their own internal electronic noise. Since the 2 inputs in a unipolar amplifier have unbalanced Since the 2 inputs in a unipolar amplifier have unbalanced

resistance/impedance, there will be a difference in the level of resistance/impedance, there will be a difference in the level of noise at each of the 2 amplifier inputs which will be amplified noise at each of the 2 amplifier inputs which will be amplified along with the desired signal also leading to a relatively noisy along with the desired signal also leading to a relatively noisy output signal.output signal.


Why is noise reduction improved with a differential Why is noise reduction improved with a differential amplifier compared to a unipolar OpAmp?amplifier compared to a unipolar OpAmp? In comparison, with EEG systems, In comparison, with EEG systems, a differential amplifiera differential amplifier

typically amplifies the differences between 2 nearby biological typically amplifies the differences between 2 nearby biological inputs (e.g. 2 adjacent EEG electrodes).inputs (e.g. 2 adjacent EEG electrodes).

Since these input signals are close, they are subject to Since these input signals are close, they are subject to essentially the same noise sources. essentially the same noise sources.

Since the same noise sources are present at both inputs, and the Since the same noise sources are present at both inputs, and the differencedifference between the two inputs is amplified, the noise should between the two inputs is amplified, the noise should cancel when the 2 input signals are “subtracted”.cancel when the 2 input signals are “subtracted”.


Why is noise reduction improved with a differential Why is noise reduction improved with a differential amplifier compared to a unipolar OpAmp?amplifier compared to a unipolar OpAmp? Also, both inputs of the differential amplifier have similar input Also, both inputs of the differential amplifier have similar input

resistance/impedance. resistance/impedance. Therefore the internal noise from the amplifier is nearly the Therefore the internal noise from the amplifier is nearly the

same at both input channels and nearly cancels as well.same at both input channels and nearly cancels as well.


Terminology:Terminology: One important property of amplifiers One important property of amplifiers

relating to noise reduction is their relating to noise reduction is their Common Mode Reduction Ratio Common Mode Reduction Ratio (CMRR).(CMRR).


Terminology: CMRRTerminology: CMRR Since a differential amplifier Since a differential amplifier

amplifies the differenceamplifies the difference between between the signals present at its 2 inputs, the signals present at its 2 inputs, the components of the signals which the components of the signals which are the same (or in are the same (or in commoncommon) at the ) at the 2 inputs will be cancelled. 2 inputs will be cancelled.


Terminology: CMRRTerminology: CMRR Because CMRR can vary over a very wide Because CMRR can vary over a very wide

range (roughly 1:1,000,000) this value is range (roughly 1:1,000,000) this value is typically expressed on a logarithmic scale typically expressed on a logarithmic scale in decibels (dB).in decibels (dB). CMRR in dB = 20 x log (reduction ratio).CMRR in dB = 20 x log (reduction ratio). Example:Example:

If a differential amplifier reduces the common mode If a differential amplifier reduces the common mode signal at its 2 inputs by a factor of 10,000 compared signal at its 2 inputs by a factor of 10,000 compared to the desired/differential (e.g. EEG signal), then:to the desired/differential (e.g. EEG signal), then:

CMRR = 20 x log 10,000 = 20 x log 10CMRR = 20 x log 10,000 = 20 x log 1044 = 20 x 4 = 80 = 20 x 4 = 80 dB.dB.

The CMRR in this case then is 10,000 = 80 dB.The CMRR in this case then is 10,000 = 80 dB.


In this regards, 3 In this regards, 3 important characteristics important characteristics of EEG amplifiers are:of EEG amplifiers are: (a) A flat frequency (a) A flat frequency

response within the response within the passband (discussed in passband (discussed in Part 1 of this course).Part 1 of this course).

(b) A high common mode (b) A high common mode rejection ratio.rejection ratio.


The latter 2 properties will The latter 2 properties will be discussed later in this be discussed later in this course.course.

Reminder from Part 1:Reminder from Part 1:Digital EEG System:Digital EEG System:

Input: ElectrodesInput: Electrodes The scalp/conductive gel/electrode The scalp/conductive gel/electrode

interface acts as a load on the EEG interface acts as a load on the EEG amplifier input.amplifier input.

The primary property which differs at the scalp/conductive The primary property which differs at the scalp/conductive gel/electrode interface level is the impedance. gel/electrode interface level is the impedance.

Keratin and oils in the skin increase impedance. These can Keratin and oils in the skin increase impedance. These can be reduced during skin preparation by use of abrasives be reduced during skin preparation by use of abrasives and alcohol prep respectively.and alcohol prep respectively.

Even with these preparation measures, the skin leads to Even with these preparation measures, the skin leads to the highest degree of signal quality loss in the input stage the highest degree of signal quality loss in the input stage of the EEG system.of the EEG system.

The impedance of the electrode/electrolyte interface The impedance of the electrode/electrolyte interface ranges from 100’s of Ohms (Ωs) to MegaΩs depending on ranges from 100’s of Ohms (Ωs) to MegaΩs depending on the frequency of the signal and the quality of skin the frequency of the signal and the quality of skin preparation.preparation.


AmplifierAmplifier Input ImpedanceInput Impedance

High EEG amplifier input impedance is also High EEG amplifier input impedance is also important in order to maintain a flat frequency important in order to maintain a flat frequency response within the desired bandwidth.response within the desired bandwidth.

The impedance of the EEG electrodes act as a The impedance of the EEG electrodes act as a load on the input of the differential amplifier.load on the input of the differential amplifier.

InputAmplifier

Since the skin/electrolyte/electrode interface is the input to Since the skin/electrolyte/electrode interface is the input to the amplifier and has both resistive and capacitive the amplifier and has both resistive and capacitive components, once connected to the amplifier, the resulting components, once connected to the amplifier, the resulting circuit has:circuit has: (a) voltage divider properties.(a) voltage divider properties. (b) filter properties(b) filter properties

Both of these are undesired properties in this application Both of these are undesired properties in this application which we try to minimize with proper skin preparation which we try to minimize with proper skin preparation techniques and choice of electrode materials.techniques and choice of electrode materials.

InputAmplifier

Reminder from Part 1:Reminder from Part 1: Digital EEG System:Digital EEG System:

Low Frequency FiltersLow Frequency Filters

(A) Low frequency (A) Low frequency (aka high pass) (aka high pass) filters:filters: (f(fcc) ) = 1 / (2π x RC) = 1 / (2π x RC)

==

1 / (2π x t1 / (2π x tcc))

Input Interface Stage:Input Interface Stage:Undesired Filter PropertiesUndesired Filter Properties

The circuit to the right is a The circuit to the right is a simplified model of the reactance simplified model of the reactance component of the combined EEG component of the combined EEG electrode-Amplifier input interface.electrode-Amplifier input interface.

This functions as a low frequency This functions as a low frequency filter and filters out low filter and filters out low frequencies. frequencies.

Unlike the electronic filters built Unlike the electronic filters built into the EEG amplifier circuit to into the EEG amplifier circuit to filter out unwanted signals outside filter out unwanted signals outside of the desired passband, this of the desired passband, this filtering is undesired and if not filtering is undesired and if not properly controlled can lead to properly controlled can lead to unintentional and undesired unintentional and undesired filtering of frequencies within the filtering of frequencies within the desired passband and distort the desired passband and distort the recorded EEG signal.recorded EEG signal.

This undesired filtering is due to This undesired filtering is due to the the capacitivecapacitive properties of the properties of the skin/electrolyte/electrode interface.skin/electrolyte/electrode interface.


Input: ElectrodesInput: Electrodes

For a voltage divider:For a voltage divider: Vout = Vin x (R2/R1+R2)Vout = Vin x (R2/R1+R2) In other words, the voltage divider divides the In other words, the voltage divider divides the

input voltage by the ratio of resistances in the input voltage by the ratio of resistances in the circuit.circuit.

Input Interface Stage:Input Interface Stage:Undesired Voltage Divider PropertiesUndesired Voltage Divider Properties

The circuit to the right is a The circuit to the right is a simplified model of the resistive simplified model of the resistive component of the combined EEG component of the combined EEG electrode-Amplifier input electrode-Amplifier input interface.interface.

This functions as a voltage This functions as a voltage divider. divider.

This leads to This leads to unintended/undesired unintended/undesired attenuation of the signal being attenuation of the signal being measured which decreases the measured which decreases the signal-to-noise ratio of the EEG signal-to-noise ratio of the EEG system which leads to a poorer system which leads to a poorer quality signal.quality signal.

This undesired attenuation is due This undesired attenuation is due to the to the resistiveresistive properties of the properties of the skin/electrolyte/electrode skin/electrolyte/electrode interface.interface.


In this regards, 3 important In this regards, 3 important characteristics of EEG amplifiers are:characteristics of EEG amplifiers are:

(a) A flat frequency response within (a) A flat frequency response within the passband (discussed in Part 1 of the passband (discussed in Part 1 of this course).this course).

(b) A high common mode rejection (b) A high common mode rejection ratio.ratio.


The latter 2 properties will be The latter 2 properties will be discussed later in this course.discussed later in this course.

This voltage divider effect at the input stage of the loaded EEG amplifier also explains why a high input impedance amplifier is needed.


Therefore, to avoid Therefore, to avoid undesirable signal loss at undesirable signal loss at the input stage of the EEG the input stage of the EEG amplifier, the following amplifier, the following are necessary:are necessary: Low electrode impedance.Low electrode impedance. High amplifier input High amplifier input

impedance.impedance.

This voltage divider effect at the input stage of the loaded EEG amplifier also explains why a high input impedance amplifier is needed.


Input: ElectrodesInput: Electrodes For a voltage divider:For a voltage divider: Vout = Vin x (R2/R1+R2)Vout = Vin x (R2/R1+R2) In other words, the voltage divider divides the In other words, the voltage divider divides the

input voltage by the ratio of resistances in the input voltage by the ratio of resistances in the circuit.circuit.

Digital EEG System:Digital EEG System:Input: ElectrodesInput: Electrodes

For a voltage divider:For a voltage divider: Vout = Vin x (R2/R1+R2)Vout = Vin x (R2/R1+R2)

R2 = the amplifier input resistanceR2 = the amplifier input resistance R1 = the resistance of the electrode complexR1 = the resistance of the electrode complex

Example1:Example1: R2 = the input impedance of the EEG amplifier =1 MΩR2 = the input impedance of the EEG amplifier =1 MΩ R1 = the resistance of the EEG electrode complex = 100ΩR1 = the resistance of the EEG electrode complex = 100Ω The voltage is divided/attenuated by a factor of (R2/R1+R2) = The voltage is divided/attenuated by a factor of (R2/R1+R2) =

1,000,000/(1,000,000 + 100) = 0.999. 1,000,000/(1,000,000 + 100) = 0.999. Therefore, there is very little loss or attenuation in this circuit.Therefore, there is very little loss or attenuation in this circuit.




Example2:Example2: R2 = 1 MΩR2 = 1 MΩ R1 = 100,000Ω (due to poor scalp preparation and/or a defective R1 = 100,000Ω (due to poor scalp preparation and/or a defective

electrode).electrode). The voltage is divided/attenuated by a factor of (R2/R1+R2) = The voltage is divided/attenuated by a factor of (R2/R1+R2) =

1,000,000/(1,000,000 + 100,000) = 0.910. 1,000,000/(1,000,000 + 100,000) = 0.910. This leads to 9% loss or attenuation in this circuit which will lead to significant This leads to 9% loss or attenuation in this circuit which will lead to significant

decrease in the signal-to-noise ratio, and imbalance of this channel compared to decrease in the signal-to-noise ratio, and imbalance of this channel compared to the other EEG channels.the other EEG channels.




Example3:Example3: R2 = 10,000 Ω (due to a poor or inexpensive amplifier design with low R2 = 10,000 Ω (due to a poor or inexpensive amplifier design with low

input impedance).input impedance). R1 = 1,000Ω.R1 = 1,000Ω. The voltage is divided/attenuated by a factor of (R2/R1+R2) = 10,000/(10,000 + The voltage is divided/attenuated by a factor of (R2/R1+R2) = 10,000/(10,000 +

1,000) = 0.910. 1,000) = 0.910. This also leads to 9% loss or attenuation in this circuit which again will lead to This also leads to 9% loss or attenuation in this circuit which again will lead to

significant decrease in the signal-to-noise ratio, and imbalance of this channel significant decrease in the signal-to-noise ratio, and imbalance of this channel compared to the other EEG channels.compared to the other EEG channels.

saturday, november 9, 2013 michael a. stein, md

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