noises and frequencies

[CaptDon]

I would say "Of course you measure audio frequencies over a given bandwidth, 20Hz to 20KHZ. Although in today's digital recording world you could measure from D.C. to 50KHZ in the higher sampling rate devices. But as to your question, you could measure the noise across the entire bandwidth which is often done or you can either 'bandpass' a portion of the audio or 'band-reject' an unwanted portion through filters and then measure remaining noise. So, you have never seen or used an oscilloscope in a lab environment? The modern digital sampling scopes can do any sort of math imaginable to a series of digital samples and you can even take those .CSV files and import them into MatLab and other math programs. You still are hung up on processes and terms you don't understand and ask the same sort of questions that do nothing but go round and round in circles. Tell us, what are you trying to do and how are you trying to do it. You have gotten endless answers including formulas to calculate noise vs. bandwidth and endless explainations of noise vs. impedance and you still haven't moved off of home plate towards first base. Give us some info, what the heck are you actually working on? You don't appear to be the correct choice for moving forward in the project. If your math skills are good there is endless information about noise and sources of noise and formulas that would make Einstein's head spin just by doing google searches. Good luck.

[Ogitek]

Although a medical student just starting. I'm interested in emotional feedback systems for integration to AI so I'm studying the emotional nervous and biopotential feedback control system in humans so can integrate to machines or prototypes similar to the Cyberdyne T-800.

Thanks for the many information. I'll study them at length and hopefully get a device for my own use and understanding. My school department doesn't use the machines yet because they are used only in other departments not accessible to me.

[David Hess]

So if the manufacturer uses an ordinary oscilloscope and measured 8mV noise at output using 1000 times gain deriving 8uV noise referred to input. So the 8uV is the spot noise?  what frequency is the 8uV given that his amplifier/unit has frequency adjustments of 20Hz, 50Hz, 100Hz, 1000Hz, 5000Hz, 10,000Hz?  Remember he said "The noise figure I gave was for broad-band, and we can't narrow it any more than that."

The amplifier's frequency adjustment sets the upper frequency limit in this case, so the spot noise measurement applies from DC, or whatever the low frequency cutoff is for the amplifier, and the selected high frequency limit.

The oscilloscope makes a "spot noise" measurement which is the total noise over a range of frequencies, or over a noise bandwidth, in peak-to-peak and in RMS.  In this case the noise bandwidth is determined by the device itself assuming that the measured spot noise is greater than the noise from the oscilloscope itself.

When you measure a signal in an oscilloscope like an audio source. Does it also do "spot noise" measurement of the entire audio? Is it not it just plots the amplitude and then frequency. How does the oscilloscope know how to distinguish if it is measuring signal or noise and need to decide whether to use "spot noise" like measurement process which is  the total noise over a range of frequencies, or over a noise bandwidth? You don't measure audio or signal over a range of frequencies, or over a bandwidth, do you?

A spot noise measurement is the total noise over a range of frequencies with a lower and upper frequency limit which depends on filtering.  Sometimes spot noise measurements are made with a bandpass filter centered at one particular frequency, like 1000 Hz, but there will still be a bandwidth.

The oscilloscope is actually measuring the total amount of noise over its own input bandwidth, like DC to 20 MHz or DC to 100 MHz or whatever the upper limit is.  However the total noise from the oscilloscope itself over 100 MHz might be 50 microvolts, so if it is connected to a source which is significantly larger, like something with 8 microvolts of input noise but with a gain of 1000 producing 8 millivolts at the oscilloscope input, then the noise from the oscilloscope itself can be ignored because it makes no significant contribution to the total noise.  Then the spot noise bandwidth is that of the source instead of the bandwidth of the oscilloscope.

Note that the shape of the filtering has an effect also.  The spot noise measurement includes the skirts of the filter outside of the -3dB points, and this is why the "noise bandwidth" is greater then the filter bandwidth.  For example a spot noise measurement from DC to 1000 Hz which relies on a single pole RC filter for the 1000 Hz -3dB bandwidth has a noise bandwidth 1.6 times greater, so 1600 Hz.

The same applies to the resolution bandwidth of an oscilloscope FFT or spectrum analyzer measurement which is why a correction factor has to be applied to get consistent units as explained in the article that I linked.  Spectrum analyzers which have the noise marker function are suppose to compute this for you.  For an oscilloscope FFT this correction depends on the FFT bin width and window function.

[Ogitek]

So if the manufacturer uses an ordinary oscilloscope and measured 8mV noise at output using 1000 times gain deriving 8uV noise referred to input. So the 8uV is the spot noise?  what frequency is the 8uV given that his amplifier/unit has frequency adjustments of 20Hz, 50Hz, 100Hz, 1000Hz, 5000Hz, 10,000Hz?  Remember he said "The noise figure I gave was for broad-band, and we can't narrow it any more than that."

The amplifier's frequency adjustment sets the upper frequency limit in this case, so the spot noise measurement applies from DC, or whatever the low frequency cutoff is for the amplifier, and the selected high frequency limit.

The oscilloscope makes a "spot noise" measurement which is the total noise over a range of frequencies, or over a noise bandwidth, in peak-to-peak and in RMS.  In this case the noise bandwidth is determined by the device itself assuming that the measured spot noise is greater than the noise from the oscilloscope itself.

When you measure a signal in an oscilloscope like an audio source. Does it also do "spot noise" measurement of the entire audio? Is it not it just plots the amplitude and then frequency. How does the oscilloscope know how to distinguish if it is measuring signal or noise and need to decide whether to use "spot noise" like measurement process which is  the total noise over a range of frequencies, or over a noise bandwidth? You don't measure audio or signal over a range of frequencies, or over a bandwidth, do you?

A spot noise measurement is the total noise over a range of frequencies with a lower and upper frequency limit which depends on filtering.  Sometimes spot noise measurements are made with a bandpass filter centered at one particular frequency, like 1000 Hz, but there will still be a bandwidth.

Thanks. pls give actual values of the total noise. For example..If noise at 100Hz is 2uV. And noise at 10,000Hz is 10uV. Is the total noise 2uV + 10uV = 12 uV  or is the total noise average of 2uV and 10uV or 6uV?

The oscilloscope is actually measuring the total amount of noise over its own input bandwidth, like DC to 20 MHz or DC to 100 MHz or whatever the upper limit is.  However the total noise from the oscilloscope itself over 100 MHz might be 50 microvolts, so if it is connected to a source which is significantly larger, like something with 8 microvolts of input noise but with a gain of 1000 producing 8 millivolts at the oscilloscope input, then the noise from the oscilloscope itself can be ignored because it makes no significant contribution to the total noise.  Then the spot noise bandwidth is that of the source instead of the bandwidth of the oscilloscope.

Note that the shape of the filtering has an effect also.  The spot noise measurement includes the skirts of the filter outside of the -3dB points, and this is why the "noise bandwidth" is greater then the filter bandwidth.  For example a spot noise measurement from DC to 1000 Hz which relies on a single pole RC filter for the 1000 Hz -3dB bandwidth has a noise bandwidth 1.6 times greater, so 1600 Hz.

The same applies to the resolution bandwidth of an oscilloscope FFT or spectrum analyzer measurement which is why a correction factor has to be applied to get consistent units as explained in the article that I linked.  Spectrum analyzers which have the noise marker function are suppose to compute this for you.  For an oscilloscope FFT this correction depends on the FFT bin width and window function.

[magic]

I think you don't understand some basicmost basics.

The whole "measurment" performed by your amplifier vendor works like this:
1. connect an oscilloscope to the output of the amplifier
2. connect a resistor of particular value to the input of the amplifier
3. switch the amplifier to one bandwidth option or another
4. look at the oscilloscope screen and measure peak to peak amplitude of whatever's there

There is nothing more to it and nothing to add or subtract or average.

[Ogitek]

I think you don't understand some basicmost basics.

The whole "measurment" performed by your amplifier vendor works like this:
1. connect an oscilloscope to the output of the amplifier
2. connect a resistor of particular value to the input of the amplifier
3. switch the amplifier to one bandwidth option or another
4. look at the oscilloscope screen and measure peak to peak amplitude of whatever's there

There is nothing more to it and nothing to add or subtract or average.

I know. What I was asking was how the oscilloscope compute the noises, does it add them like 2 + 10 = 12uV or average them like (2+10)/2 = 6uV?

I own a small oscilloscope but was only looking at signal before. I'll set it up to look at noises next week.

Ok. What happens if you disable the high pass filters in the circuit so all frequencies to RF or higher gets into the amplifier and oscilloscope. I actually did it before. Have you done this  before? Would the noises get into milliVolt and swamp all the signals? I will measure them at details now.

I also got one of the most noise free ADC in the world that beats even Audio Precision. The ADC manufacturer EIDA told me it can measure below 1 microVolt using REW.

https://www.linsoul.com/products/e1da-cosmos-adc

[magic]

An oscilloscope doesn't compute anything. It samples the input voltage N times per second and plots the resulting waveform on the screen. Noise is random variations in the output of the amplifier and that's what you'll see on the display.

[Ogitek]

Ok. Anyone, please give me an actual circuit that can do 1mV at 1000 Hz with less than 10 microVolt noise. Because the current manufacturer is selling me one for $1200. I can get a $20 unit but it has only 100 Hz limit. Can you get any less than $100 unit that can do 1000 Hz at microvolt noises? 

is this easy to build?  What IC has this spec?

[David Hess]

Thanks. pls give actual values of the total noise. For example..If noise at 100Hz is 2uV. And noise at 10,000Hz is 10uV. Is the total noise 2uV + 10uV = 12 uV  or is the total noise average of 2uV and 10uV or 6uV?

Uncorrelated RMS values are added using the square root sum of the squares.  So if you have two noise sources added together, you square each one, add, and then take the square root.

(2^2+10^2)^(1/2)=10.2

If your oscilloscope has a noise of 50 microvolts over 100 MHz, and your x1000 amplifier has an output noise of 10 millivolts over its bandwidth, then the measured noise would be:

((50x10^-6)^2+(10x10^-3)^2)^(1/2)=10 millivolts

Which is why I said that the oscilloscope noise can be ignored in your case.  The input referred noise of the amplifier is then 10 millivolts / 1000 or 10 microvolts.

[MathWizard]

Hey Mr. Hess, what's a good book for transistors with advanced topics like noise and temperature effects ? I don't want to get into Poisson equations and all that stuff yet, but I do want the text book with all that in it. I'm not deep enough into the semiconductor physics, I guess that's the kind of book it will have to be. But that's ok.

None of my books really get into noise and any amount of changing frequency and non-linear frequency effects.

[David Hess]

Hey Mr. Hess, what's a good book for transistors with advanced topics like noise and temperature effects ? I don't want to get into Poisson equations and all that stuff yet, but I do want the text book with all that in it. I'm not deep enough into the semiconductor physics, I guess that's the kind of book it will have to be. But that's ok.

None of my books really get into noise and any amount of changing frequency and non-linear frequency effects.

For noise and noise in connection with operational amplifiers, I suggest the various application notes published by Analog Devices.

For transistors and noise, the most approachable book I know of is Small Signal Audio Design by Douglas Self which covers voltage and current noise in bipolar transistors and JFETs in just a couple pages.

[Ogitek]

My pocket oscilloscope has vertical resolution of 10mV/div to 10V/div. The moderately price Rigor DS1054Z has vertical resolution or scale range of 500uV/div to 10V/div. Where will I get an oscilloscope with 1uV/div and cheap? What models are you guys using that can do this?

Also is it so hard to build a 1mV with 1000Hz with 1uV noise unit? Can't anyone do it? Is this harder than the Manhattan Project? (see the movie Oppenheimer to get an idea what this is)

[Someone]

My pocket oscilloscope has vertical resolution of 10mV/div to 10V/div. The moderately price Rigor DS1054Z has vertical resolution or scale range of 500uV/div to 10V/div. Where will I get an oscilloscope with 1uV/div and cheap? What models are you guys using that can do this?

Also is it so hard to build a 1mV with 1000Hz with 1uV noise unit? Can't anyone do it? Is this harder than the Manhattan Project? (see the movie Oppenheimer to get an idea what this is)

It is very easy, but you are yet to understand the electronics/physics behind it. Once you understand the principles it is obvious how to undertake the task.

Suggested starting points:
https://www.ti.com/lit/SBOA345
https://download.tek.com/document/LowLevelHandbook_7Ed.pdf

Yes, you can buy an already built/assembled circuit/IC that will magically work. But you pay for the expertise or excess performance beyond what you actually need. There are very cheap solutions but they require skill to understand where shortcuts can be taken. Your supervisor should be directing your study on the topic, rather than asking the internet for the end solution.

[David Hess]

My pocket oscilloscope has vertical resolution of 10mV/div to 10V/div. The moderately price Rigor DS1054Z has vertical resolution or scale range of 500uV/div to 10V/div. Where will I get an oscilloscope with 1uV/div and cheap? What models are you guys using that can do this?

Oscilloscopes run out of noise performance before they run out of vertical sensitivity.  500 uV/div and better is only useful when combined with suitably low noise.

Old Tektronix oscilloscopes which supported the 7A22/5A22 differential amplifier had a sensitivity of 10 uV/div and bandwidth of 1 MHz, but not at the same time which is why this amplifier has variable user selected bandwidth.  Tektronix also made this amplifier as a standalone unit  with the part number AM502 which could be used with any oscilloscope.

Also is it so hard to build a 1mV with 1000Hz with 1uV noise unit? Can't anyone do it? Is this harder than the Manhattan Project? (see the movie Oppenheimer to get an idea what this is)

If a singled ended input is acceptable, then most precision operational amplifiers can meet those requirements easily.  Use the simple non-inverting configuration and add a feedback capacitor to control bandwidth, so all of 4 parts total, plus decoupling capacitors and a power source.  An LT1007 with a 1000 Hz bandwidth limit will yield a noise of about 0.25 uV rms noise and will be suitable for source impedances around 1 kilohm.  A more modern OPA140 which has JFET inputs will do a little better with higher source resistances because of lower input current noise, but noise from the source will dominate as the source resistance increases.

The AM502 mentioned above also delivers about this level of performance but has a differential input.  Duplicating this with parts and a circuit is more involved.  I might use a pair of OPA140s to make a low noise differential preamplifier (5 parts), followed by a difference or instrumentation amplifier to produce a single ended output which can drive an oscilloscope or other test instrument, but this will be slightly higher noise than an AM502, although still well below 1 microvolt up to 1000 Hz.

[Ogitek]

My pocket oscilloscope has vertical resolution of 10mV/div to 10V/div. The moderately price Rigor DS1054Z has vertical resolution or scale range of 500uV/div to 10V/div. Where will I get an oscilloscope with 1uV/div and cheap? What models are you guys using that can do this?

Oscilloscopes run out of noise performance before they run out of vertical sensitivity.  500 uV/div and better is only useful when combined with suitably low noise.

Old Tektronix oscilloscopes which supported the 7A22/5A22 differential amplifier had a sensitivity of 10 uV/div and bandwidth of 1 MHz, but not at the same time which is why this amplifier has variable user selected bandwidth.  Tektronix also made this amplifier as a standalone unit  with the part number AM502 which could be used with any oscilloscope.

Also is it so hard to build a 1mV with 1000Hz with 1uV noise unit? Can't anyone do it? Is this harder than the Manhattan Project? (see the movie Oppenheimer to get an idea what this is)

If a singled ended input is acceptable, then most precision operational amplifiers can meet those requirements easily.  Use the simple non-inverting configuration and add a feedback capacitor to control bandwidth, so all of 4 parts total, plus decoupling capacitors and a power source.  An LT1007 with a 1000 Hz bandwidth limit will yield a noise of about 0.25 uV rms noise and will be suitable for source impedances around 1 kilohm.  A more modern OPA140 which has JFET inputs will do a little better with higher source resistances because of lower input current noise, but noise from the source will dominate as the source resistance increases.

The AM502 mentioned above also delivers about this level of performance but has a differential input.  Duplicating this with parts and a circuit is more involved.  I might use a pair of OPA140s to make a low noise differential preamplifier (5 parts), followed by a difference or instrumentation amplifier to produce a single ended output which can drive an oscilloscope or other test instrument, but this will be slightly higher noise than an AM502, although still well below 1 microvolt up to 1000 Hz.

Single ended means 1 channel only?

If they would be built using breadboard only, what noises are introduced?

Should they be built using 0603 SMD to lessen noises?  The smaller the components the lesser the noises?

If you would build them, what PCB and components would you use?

Can you build me one? Would $300 or $500 be ok for the service? Anyone?

[David Hess]

Single ended means 1 channel only?

Signal ended means a signal and ground wire, like with a coaxial cable.

A differential input would mean two signal wires, positive and negative, and a third ground connection which may or may not be present.

If they would be built using breadboard only, what noises are introduced?

None, but it may benefit from a metal enclosure for shielding.

Should they be built using 0603 SMD to lessen noises?  The smaller the components the lesser the noises?

In theory the smaller layout which surface mount parts allow will pick up less noise, but at this bandwidth and sensitivity it will not make much difference.  It will likely pick up your hand waving around it from electrostatic coupling, but it isn't something I would worry about.

If you would build them, what PCB and components would you use?

Newer parts like the OPA140 are only available in surface mount, so SO-8 style packages might be considered the expected standard for construction now.

Can you build me one? Would $300 or $500 be ok for the service? Anyone?

For that much you could buy a used Tektronix AM502 and TM501 or TM503 power supply mainframe to power it.

A quick search turned up these:

http://www.aricorp.com/OSP-1.html
https://www.amazon.com/Amplifier-Portable-Oscilloscope-Electronic-Engineers/dp/B0B7XML13N
https://www.ebay.com/itm/165597846810

The OSP-1 linked above, which should do exactly what you need, is basically a remake of the Tektronix AM502.  What I proposed with a couple of operational amplifiers has similar performance but is not as fast.

Approximately where are you in the US?  I am in New Hampshire.

[Ogitek]

Single ended means 1 channel only?

Signal ended means a signal and ground wire, like with a coaxial cable.

A differential input would mean two signal wires, positive and negative, and a third ground connection which may or may not be present.

All Biopotential amplifiers use differential input. Why, which of them is single ended?

You can ship it to Delaware. So what ICs and components  you'd use with differential input besides AM502 and 1mV, 1000 Hz, with 1 uV noise?

Thanks.

If they would be built using breadboard only, what noises are introduced?

None, but it may benefit from a metal enclosure for shielding.

Should they be built using 0603 SMD to lessen noises?  The smaller the components the lesser the noises?

In theory the smaller layout which surface mount parts allow will pick up less noise, but at this bandwidth and sensitivity it will not make much difference.  It will likely pick up your hand waving around it from electrostatic coupling, but it isn't something I would worry about.

If you would build them, what PCB and components would you use?

Newer parts like the OPA140 are only available in surface mount, so SO-8 style packages might be considered the expected standard for construction now.

Can you build me one? Would $300 or $500 be ok for the service? Anyone?

For that much you could buy a used Tektronix AM502 and TM501 or TM503 power supply mainframe to power it.

A quick search turned up these:

http://www.aricorp.com/OSP-1.html
https://www.amazon.com/Amplifier-Portable-Oscilloscope-Electronic-Engineers/dp/B0B7XML13N
https://www.ebay.com/itm/165597846810

The OSP-1 linked above, which should do exactly what you need, is basically a remake of the Tektronix AM502.  What I proposed with a couple of operational amplifiers has similar performance but is not as fast.

Approximately where are you in the US?  I am in New Hampshire.

[CaptDon]

Dave, I like the fact that you mentioned the AM-502 since it is able to do single end or differential with bandwidth selection. It truly is a useful piece of the Tek 500/5000 modular series! I wish it would have had more available bandwidth, greater than 1 MHz. I use mine rarely but 'When you need it there is nothing else like it'. I probably use mine at most once per year but I would never sell it!! I have the RM-506, TM-503 and TM-502. I also have a stripped down TM-502 mounted to a wood base with bottom guide rails which I use when calibrating the 500 series modules. Wish I had the RM-5006 so I could take advantage of the 5000 series modules!! Cheers!! (B.T.W., I often see TM-506 and RM-506 units surplused out of medical institutions with all 6 slots filled with AM-502's. Sad that often these institutions just put their old equipment in the crusher, I think it is a requirement!)

[David Hess]

All Biopotential amplifiers use differential input. Why, which of them is single ended?

You can ship it to Delaware. So what ICs and components  you'd use with differential input besides AM502 and 1mV, 1000 Hz, with 1 uV noise?

Based on your earlier post:

I'm scouting for a Bioamplifier for my medical school studies. Manufacturer spec is it has noise of less than 2 microVolt at 100 Hz. But noise becomes 8 microVolt or 8 millivolts at 1000X gain at 1000 Hz. Why does noise increase (much higher) at higher frequencies?

I think you need an amplifier with a differential input like an AM502 or the OSP-1 that I linked.

[David Hess]

Dave, I like the fact that you mentioned the AM-502 since it is able to do single end or differential with bandwidth selection. It truly is a useful piece of the Tek 500/5000 modular series! I wish it would have had more available bandwidth, greater than 1 MHz. I use mine rarely but 'When you need it there is nothing else like it'. I probably use mine at most once per year but I would never sell it!! I have the RM-506, TM-503 and TM-502. I also have a stripped down TM-502 mounted to a wood base with bottom guide rails which I use when calibrating the 500 series modules. Wish I had the RM-5006 so I could take advantage of the 5000 series modules!! Cheers!! (B.T.W., I often see TM-506 and RM-506 units surplused out of medical institutions with all 6 slots filled with AM-502's. Sad that often these institutions just put their old equipment in the crusher, I think it is a requirement!)

The AM502 was based on earlier designs so Tektronix had a long history with that type of amplifier.  They also made some oscilloscopes that had the AM502 functionality built in, which indeed were intended for the biomedical community.  I acquired several 7A22s, which are the same thing as an AM502 but for the 7000 series oscilloscopes, before I managed to purchase a AM502, and they are indispensable in some applications where before I would have had to design and build my own custom amplifier.

Bandwidth is limited to 1 MHz because despite its low input noise, noise still limits its sensitivity at the highest sensitivity ranges.  Of course this is not a problem because it has user adjustable bandwidth to reduce noise.  You can find the same thing with the Tektronix 7A13 100 MHz amplifier which has too much noise to make good use of its 1 mV/div sensitivity, so it includes a switchable 5 MHz bandwidth limit; a 20 MHz bandwidth limit would have left it too noisy.

I think a modern design could have about 5 times lower noise than the AM502 using a pair of low noise audio JFETs from Linear Systems.  It should be possible to retrofit an AM502, but I am not aware of anybody trying it.

[Ogitek]

All Biopotential amplifiers use differential input. Why, which of them is single ended?

You can ship it to Delaware. So what ICs and components  you'd use with differential input besides AM502 and 1mV, 1000 Hz, with 1 uV noise?

Based on your earlier post:

I'm scouting for a Bioamplifier for my medical school studies. Manufacturer spec is it has noise of less than 2 microVolt at 100 Hz. But noise becomes 8 microVolt or 8 millivolts at 1000X gain at 1000 Hz. Why does noise increase (much higher) at higher frequencies?

I think you need an amplifier with a differential input like an AM502 or the OSP-1 that I linked.

Can one also create 1mV differential circuit at 10,000 Hz (instead of just 1000Hz) with only 1uV spot noise instead of 8uV spot noise. What components will you use at 1mV, 10000Hz with below 1 uV spot noise?

[MathWizard]

https://pearl-hifi.com/06_Lit_Archive/14_Books_Tech_Papers/Motchenbacher_Connelly/Low-noise_Electronic_Design.pdf

I bought some legit "low noise" parts, like BC550, and COS77/277 opamps ages ago, but so far didn't try any til I made a 100MHz JFET buffer probe. IDK if it's any better IRL, but in the sim, for it barely makes a difference what BJT's I used. But I'm not up to adding in noise sources yet.

But I want to build something to see what those parts can do.

[David Hess]

Can one also create 1mV differential circuit at 10,000 Hz (instead of just 1000Hz) with only 1uV spot noise instead of 8uV spot noise. What components will you use at 1mV, 10000Hz with below 1 uV spot noise?

Well, let's do an not unduly complicated paper design using the best operational amplifiers available for this application.  We want low noise from DC to 10 kHz, which also means low offset voltage drift, and low input bias current and low input current noise to support higher source resistance.

A two operational amplifier differential input stage will provide the highest possible input impedance and common mode noise rejection, but double the noise.  Current noise can be ignored for JFET inputs with the resistances we will calculate.  Actual noise is a little bit higher because it rises below 10kHz, but not by a lot.

OPA828   0.57uVrms to 10kHz   0.82uVrms   8.2nV/SqrtHz   4 kilohms
OPA140   0.72uVrms to 10kHz   0.69uVrms   6.9nV/SqrtHz   2.8 kilohms
ADA4625   0.47uVrms to 10kHz   0.88uVrms   8.8nV/SqrtHz   4.6 kilohms

The first number is the voltage noise from the amplifier, the second number is the maximum noise from the source to stay below 1uVrms noise, the third number is the associated noise density to stay below 1uVrms noise, and the last number is the source resistance which would produce that noise.

So for each amplifier type, the last number shows the maximum source resistance which will keep the total input noise below 1uVrms, from DC to 10kHz.  As the amplifier noise decreases, then maximum source resistance that can be tolerated increases.

So noise below 1uVrms to 10kHz is very feasible, at least with low source resistances.  If the bandwidth only extends to 1kHz, then higher source resistances are tolerable.

Note that the source resistance applies to both inputs of each operational amplifier and the feedback networks add their own noise, so I am assuming that the feedback network has an arbitrarily low parallel resistance for arbitrarily low noise.  In this case that may require that buffers be added to the output of each operational amplifier to drive the their own feedback networks, but hey, we spared no expense.  For buffers I might use AD812 current feedback amplifiers, but 4 transistor diamond buffers or something more complicated could also be used.  Adding the buffers may require some frequency compensation tweaks around the operational amplifiers to maintain stability.

If the source resistances are significantly lower, then the JFET operational amplifiers can be replaced with bipolar input parts for lower noise.  Or a low noise discrete JFET pair from Linear Systems could be used for lower noise at higher source resistances, but examine the AM502 schematics to see how complex this could be.

[Ogitek]

Can one also create 1mV differential circuit at 10,000 Hz (instead of just 1000Hz) with only 1uV spot noise instead of 8uV spot noise. What components will you use at 1mV, 10000Hz with below 1 uV spot noise?

Well, let's do an not unduly complicated paper design using the best operational amplifiers available for this application.  We want low noise from DC to 10 kHz, which also means low offset voltage drift, and low input bias current and low input current noise to support higher source resistance.

A two operational amplifier differential input stage will provide the highest possible input impedance and common mode noise rejection, but double the noise.  Current noise can be ignored for JFET inputs with the resistances we will calculate.  Actual noise is a little bit higher because it rises below 10kHz, but not by a lot.

OPA828   0.57uVrms to 10kHz   0.82uVrms   8.2nV/SqrtHz   4 kilohms
OPA140   0.72uVrms to 10kHz   0.69uVrms   6.9nV/SqrtHz   2.8 kilohms
ADA4625   0.47uVrms to 10kHz   0.88uVrms   8.8nV/SqrtHz   4.6 kilohms

The first number is the voltage noise from the amplifier, the second number is the maximum noise from the source to stay below 1uVrms noise, the third number is the associated noise density to stay below 1uVrms noise, and the last number is the source resistance which would produce that noise.

So for each amplifier type, the last number shows the maximum source resistance which will keep the total input noise below 1uVrms, from DC to 10kHz.  As the amplifier noise decreases, then maximum source resistance that can be tolerated increases.

So noise below 1uVrms to 10kHz is very feasible, at least with low source resistances.  If the bandwidth only extends to 1kHz, then higher source resistances are tolerable.
<snipped>

I used an impedance checker. My electrode and wire to skin impedance is about 10k to 20k. The test at 8uV noise was at 100 Ohm. If the source resistance increased from 100 ohm to say 15,000 ohm. How do you compute what the noise of 8uV would become? And how is noise related to the input resistance/impedance. The unit has input impedance of 10 megaohms (see last message for the full spec sheet). If you'd use the voltage divider concept. The 100 ohm vs 15,000 ohm would not have much significant against the 10 megaohm input impedance. But how about noise? Why is noise more affected by increase in the input impedance.

Also stand alone EEG, ECG, EMG units have fixed frequency. In the UFI unit, it is adjustable from 20, 50, 100, 1000, 5000, 10000 Hz. What parts of the circuits need adjustments for these switches? And would they introduce more noises? Why. Thanks!

[Someone]

If the source resistance increased from 100 ohm to say 15,000 ohm. How do you compute what the noise of 8uV would become? And how is noise related to the input resistance/impedance.

Its not going to get simpler than this:

Suggested starting points:
https://www.ti.com/lit/SBOA345