noises and frequencies

[Ogitek]

If a circuit has say less than 2 microVolt peak-to-peak noise at DC to 100 Hz with 10,000 Ohm source.

How would the noise increase at 1000 Hz? Would the noise become 8 microVolt or 30 microVolt? For a 1-10 mV signal. What must be the minimum noises in microVolt to make it produce good signal?

Please give actual example of other amplifiers to see how the noise behavior changes with frequency.

Thank you.

[IanB]

Homework question?

It would be good if you provide some of your own input, what information sources you have looked at, what analysis you have done yourself, where you are stuck with how to proceed?

I think people will be willing to help you solve problems where you are stuck, but just giving you an answer will help nobody, especially yourself.

[RoGeorge]

There are many types of noise.  Most of the noise is thermal noise.  At low frequencies, the 1/f noise is dominant.
See if this answer your questions:  https://en.wikipedia.org/wiki/Johnson%E2%80%93Nyquist_noise

[Ogitek]

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?

But the signal I'm after is  only1 to 5 millivolt. So won't the 8 milliVolt noise swamp the signal?

Is it very hard to create amplifier with 1 milliVolt resolution yet with noise of less than 2 microVolt at 1000 Hz instead of 100 Hz?

[magic]

What's the source impedance that the amplifier sees, i.e. the output impedance of the sensor (or whatever it is that you are amplifying)? Is it really 10kΩ?

How exactly are you measuring the noise? Did you also verify that it goes down to 2μVpp at 100Hz as expected?

What do you mean by "at 100Hz" or "at 1000Hz"? Does the amp have a bandwidth switch with options like 100Hz, 1kHz, 10kHz which means "from DC to 100Hz" etc and changing this setting changes the total amount of output noise? If so then your observation is not far off from expectations, the typical increase being proportional to square root of the increase in bandwidth (3.16x more noise for 10x more bandwidth).

[David Hess]

What do you mean by "at 100Hz" or "at 1000Hz"? Does the amp have a bandwidth switch with options like 100Hz, 1kHz, 10kHz which means "from DC to 100Hz" etc and changing this setting changes the total amount of output noise? If so then your observation is not far off from expectations, the typical increase being proportional to square root of the increase in bandwidth (3.16x more noise for 10x more bandwidth).

Exactly, for a flat noise spectrum which is typical at higher frequencies, noise is proportional to the square root of the bandwidth.

Sqrt(100)=10
Sqrt(1000)=31.6
The ratio of noise is 31.6/10 so a difference of 3.16 times.

At low frequencies flicker noise increases except in chopper stabilized amplifiers, but corner frequencies below 100 Hz are likely so flicker noise should be insignificant in this case depending on the design.

[Ogitek]

What's the source impedance that the amplifier sees, i.e. the output impedance of the sensor (or whatever it is that you are amplifying)? Is it really 10kΩ?

How exactly are you measuring the noise? Did you also verify that it goes down to 2μVpp at 100Hz as expected?

What do you mean by "at 100Hz" or "at 1000Hz"? Does the amp have a bandwidth switch with options like 100Hz, 1kHz, 10kHz which means "from DC to 100Hz" etc and changing this setting changes the total amount of output noise? If so then your observation is not far off from expectations, the typical increase being proportional to square root of the increase in bandwidth (3.16x more noise for 10x more bandwidth).

Yes, they have adjustment switches.

For 100 Hz, the noise is 2 microVolt peak-to-peak with 10 kOhm source impedance.

For 1000 Hz, the noise at 1000 gain measured at output is 8 milliVolt peak-to-peak with 100 Ohm source impednance, which they said should correspond to an approx. 8 microVolt noise figured referred to the the input.

I'd like to know something. If my input is 10mV, or 50mV or 100mV, is the noise input noise always constant at 8 microVolt? or is it related to the input voltage, given a fixed frequency?

[magic]

If the source is resistive then it has Johnson noise which is amplified by the amplifier like any other signal. This should be about 1μVpp for 10kΩ and 100Hz, or 0.3μVpp for 100Ω and 1kHz. This is a limit which cannot be reasonably improved upon with resistive sources. (An effective but usually unreasonable measure is cooling the resistor significantly).

This amplifier is probably not optimized for 100Ω source impedance. It is also possible that your source has noise other than Johnson noise. You could find out by connecting a 100Ω resistor to the amplifier (between signal input and ground).

[CaptDon]

To answer one of the questions, the noise (floor) would remain constant regardless of input signal amplitude. What you get is 'Signal to Noise Ratio' or how much bigger the desired signal output is in relation to the noise floor. Sounds like you are monkeying around with ECG / EKG type amplifiers. For medical use an 8uv input side noise floor is pretty good when referenced to a 1mv input 'chest' signal. There will be lots of filtering involved for certain signals like parsing out the breath rate very low frequency of 40Hz or less. The ECG / EKG signal requires greater bandwidth for the sharp QRS transitions and often you have 50Hz / 60Hz sharp notch filters to get rid of power line influences. If you have these questions and don't understand the math or specs involved why have you been chosen as 'the guy' to select a proper amplifier chain?

[Ogitek]

The school didn't plan to buy a new one, but they have budget and I'm just suggesting them to buy one, and hence choosing what to write in the proposal.

The manufacturer told me "You are asking us to copy your A-D system for this request. The noise figure I gave was for broad-band, and we can't narrow it any more than that. In addition, your A-D system will have some impact on noise, and we have no way of knowing that."

What does "A-D" mean?  My request for them was to test at 1000 Hz, because their only data is 100 Hz. So it seems they tested the broad-band which is 10kHz (because the adjustments can reach 10kHz). But from 100 Hz to 10,000 Hz, the noise only increases many times instead of just 4.

sqrt (100) = 10
sqrt (10000) = 100

100/10 = 10X, but the noise increase from 2 uV (at 100Hz) to 8 uV (at 10,000Hz) is only 4X (8uV/2uV) not 10X. Could it be because the source impedance used for the 10kHz test was 100 Ohm only)?

Also the source is just skin, so how could the A-D (whatever this is) system will have some impact on noise?

[CaptDon]

Because they are referring to an Analog-to-Digital conversion which they are assuming you are doing to the analog chest signal. The 'noise' in your A to D converter would to a large degree depend upon how many bits of resolution your converter has. For example an 8 bit converter vs. a 12 bit converter. The 12 bit would have smaller step increments and would appear to have less noise as the least significant bits of resolution tend to dither back and forth even though the sample remains constant. Also a faster sample / conversion rate would tend to appear as a less noisy signal. They have no way of knowing what you are doing with the post amplification signal and perhaps you are not even running it into a digitizing circuit? Open skin contact measured as a human with normal skin moisture holding DVM probes (one in each hand) and squeezing the probe tips with the fingers shows typically 10K ohms to 50K ohms. With ECG /EKG 'sticky pads' attached to a shaven chest the 'source impedance' could run 1K ohms to 10K ohms but usually on the lower side once skin acids and sweat enter the picture! Cheers mate, hope this info helps.

[Ogitek]

The manufacturer told me he used oscilloscope to check for the 8mV output at 1000X gain so he figured the noise is 8uV referred to the input (this is using a 100 Ohm source impedance). The unit has frequency adjustments of 20Hz, 50Hz, 100Hz, 1000Hz, 5000Hz, 10,000Hz.

But is it not a spectrum analyzer is the right tool to check for noises? How accurate is an ordinary oscilloscope compared to spectrum analyzer?

We know most spectrum analyzers (except the very expensive ones)  have minimum 9kHz. But then the unit has a 10kHz setting. If he used spectrum analyzer, does the following relationship still hold?

Sqrt (10000Hz) = 100
Sqrt (100) = 10

So if the noise at 10,000 Hz is 8uV. Then the noise at 100Hz is 0.8uV (10 times less)? 

I think he just used an ordinary oscilloscope which may be less accurate?

[CaptDon]

A spectrum analyzer could show the frequencies at which the noise occurs which may be of some concern. The oscilloscope will simply show a Peak to Peak signal and sophisticated scopes can make the measurement automatically. You may gain some frequency information from a scope. Singer Metrics made an 'ultrasonic' Spectrum analyzer that went from D.C. to 600KHz. Low frequency tailored analyzers are common and used to examine bearings in machines and often in very high speed devices like turbine engines and turbochargers. Certain peaks in frequencies can often indicate a bearing approaching failure. Low frequency (audio range) analyzers are also used during engine testing looking for pre-detonation, piston slap, piston wrist pin slap, and characterizing engine sounds which are normal and should be ignored by the E.C.U.'s F.F.T. analytics as well as abnormal sounds that indicate an abnormal running condition or destructive failure. Sounds like your medical lab needs to hire a good electronics technician.

[David Hess]

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.

Over 100 MHz, the best typical oscilloscope input noise is about 30 microvolts RMS, but 100 microvolts or higher is more common.  In your case the input noise measurement can be made because it is being amplified first, and limiting the oscilloscope bandwidth to 20 MHz or lower further helps.

An oscilloscope with the FFT function (and averaging of the FFT results, which is not a given) can then make a noise density measurement, which is what a spectrum analyzer can do.  In both cases the noise density measured depends on the resolution bandwidth (RBW) of the oscilloscope FFT or spectrum analyzer.  A spectrum analyzer should have a "noise marker" function which takes this into account to return the noise density within a 1 Hz bandwidth, but almost all oscilloscopes lack this function (1) so you have to do the math yourself after determining the correction factor which depends on the FFT bin width and window function.  This article discusses the problem:

https://www.edn.com/dsos-and-noise/

Basically it is going to come down to using a DSO to make spot noise measurements instead of noise density measurements because they lack the functionality to do the later properly, but a spot noise measurement is probably more useful anyway in your application and oscilloscopes work fine for this.

RF spectrum analyzers have a lower limit of about 9 kHz because of input coupling limitations (2) and because the mixing process moves the high phase noise part of the local oscillator to low frequencies, so they are typically very limited at low frequencies anyway.  A low frequency dynamic signal analyzer can produce a low noise measurement down to DC, but is essentially doing the same thing that an oscilloscope FFT is doing, but properly.

(1) The lack of oscilloscopes which support this properly is a real shame since they should be good at it.  The DSO should also allow averaging of the FFT result *without* averaging the input signal, but many modern DSOs cannot get this right either.

(2) Some old spectrum analyzers had an option which swapped the leads of the first mixer and removed the input coupling so they could operate down to DC, but they still had high noise at low input frequencies.

[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."

[magic]

Sounds like it's the total noise at all frequencies from DC (or some lowest frequency the amp can pass, maybe a few Hz, if it isn't DC coupled) up to 20/50/100/1000/10000 Hz.

Also, 8μVpp from 100Ω source at 1kHz bandwidth is not a good result, it could be less than 1μV. Look for a different amplifier if it makes a difference for you.

[Ogitek]

How is input impedance related to it. I mean. For example at spec of 100 Hz and the noise is 2 microVolt peak-to-peak with 10 kOhm source impedance. What happens if it is 100 Ohm source?

[G0HZU]

Please give actual example of other amplifiers to see how the noise behavior changes with frequency.

If it helps, I have an old Tektronix 8GHz spectrum analyser that works really well down to AF frequencies. It's a 50 ohm system and I usually fit a low noise preamp ahead of it if I want to look at very small signals. The advantage that the spectrum analyser offers is that it can show how the noise level changes with frequency right down to AF frequencies.

The LF preamp has about 28.6dB gain and the noise figure is about 4dB. If I place a very sharp 2.5MHz LPF after the preamp I can define the noise bandwidth as 2.5MHz. If the gain is 28.6dB and the noise figure is 4dB it should be possible to calculate the Vrms of the noise at the output of the amplifier.

The noise bandwidth is 2.5MHz or 2.5e6 Hz. 10*log(2500000) = 64dBHz

So the output noise power should be -174 + gain + noise figure + 64dBHz = -174 + 28.6 + 4 + 64 = -77.4dBm. This is 1.811e-11W. In a 50 ohm system this will be 30uV because power = (V*V)/R

So a 50R terminated Vrms meter connected to the output of the preamp + LPF should read 30uV rms for the noise at the amplifier+LPF output.

This all assumes that the noise figure of the LF preamp is flat from 2.5MHz down to audio frequencies. The old Tek spectrum analyser shows that the noise level is flat although it struggles a bit below about 1kHz due to its own internal spurious terms. There will be better analysers available than my old Tek, especially if they have been designed for low noise audio work. However, my analyser is OK to use as a quick demo here. I've used it to measure the noise figure of various low frequency amplifiers in the past, but usually down to about 1kHz rather than 100Hz.

[G0HZU]

One thing to watch out for is ground loop noise/spurious especially if you connect various bits of test equipment together. I usually power the LF preamp and any DUT with a battery to minimise this issue. Also be wary of out of band noise and spurious up at higher frequencies. These can dominate any measurements if you are not careful and this can cause confusion.

My background is in RF, not AF but I do have some experience measuring low noise stuff down at audio frequencies.

[Ogitek]

Sounds like it's the total noise at all frequencies from DC (or some lowest frequency the amp can pass, maybe a few Hz, if it isn't DC coupled) up to 20/50/100/1000/10000 Hz.

Also, 8μVpp from 100Ω source at 1kHz bandwidth is not a good result, it could be less than 1μV. Look for a different amplifier if it makes a difference for you.

Please tell me. Why is a 8μVpp from 100Ω source at 1kHz bandwidth not a good result when the input signal I'm after is 1mV and not 1 uV?
The amplifier unit has this spec:

Input impedance: 10 megaOhms
Freq response  DC to 10kHz +/- 3 dB
Frequency rolloff     -12 dB/octave
Common mode rejection  90 dB minimum
Noise      Less than 2 uV peak-to-peak, DC to 100 Hz, with 10kOhm source
Output configuration    Single-end
Output impedance  1000 ohms.

I know that with 100 Ohm source impedance instead of 10 kOhm, it would have better voltage divider performance with respect to the 10 megaOhm input impedance. But with 10 megaOhm, is it not 100 Ohm vs 10,000 Ohm is not much difference?

What other amplifier do you or anyone heard with better performance?

[magic]

Why is a 8μVpp from 100Ω source at 1kHz bandwidth not a good result

Simply because it could be a few times lower, under these particular circumstances.

when the input signal I'm after is 1mV and not 1 uV?

If you care about 1mV signals which will become 1V after 1000x gain then this level of noise is probably harmless.

[Ogitek]

Sounds like it's the total noise at all frequencies from DC (or some lowest frequency the amp can pass, maybe a few Hz, if it isn't DC coupled) up to 20/50/100/1000/10000 Hz.

Also, 8μVpp from 100Ω source at 1kHz bandwidth is not a good result, it could be less than 1μV. Look for a different amplifier if it makes a difference for you.

If 8uV is the total noise. How is it derive with respect to each of this frequency? 20/50/100/1000/10000 Hz?   I mean you average them like the 100 Hz has 1 uV noise, the 10000 has 20uV noise. So 8uV is the average of them?

How does the oscilloscope algorithm compute for it?

[donlisms]

I will make one observation. You ask many questions using the terms like "at this frequency."  The answers refer to "bandwidth."  I have a feeling you don't really understand this yet.

I'm quite sure there are some pedants here who will object to my description. My assumption is that you know medicine, not these things.  I suspect your intuition has lead you off track, and it might help to go through it step by step.

Noise measurements are really only useful across a range of frequencies. When the specs say 2uV "from DC to 100Hz", they're not saying "choose any specific frequency between 0 and 100 Hz, say 37Hz, and the noise will be 2uV."  No. It's not at some single frequency.

Conceptually, the input noise signal is filtered so that fluctuations in the signal that happen faster than 1/100 second are removed.  Only the slower fluctuations remain. This is the significance of the various frequencies mentioned in the specs, and in most of the discussion here.  It is the dividing line between the slower fluctuations, which will be measured, and the faster fluctuations, which are ignored. It is the upper speed limit. With this amplifier, the lower limit is always 0.

Once the fast parts are removed, we're left with one signal, which is to say, one voltage at any instant in time. The voltage wiggles up and down.

If we keep only motions slower than 1/100 second, the voltage wiggle is less than 2uV.  If we raise the limit to keep only fluctuations slower than 1/1000 second, the wiggle is always less than 8uV.

There is only one voltage.  It changes.  We are not measuring those changes AT a specific frequency. We're just measuring the voltage fluctuations from instant to instant.  The frequency choice was used earlier, to decide the upper speed limit for the noise of interest.

When we choose the filter frequency, we're saying "I don't care about any fluctuations faster than ...such...  Just ignore them.  The only meaningful variations are below that speed."  I don't know medicine, but I guess that frequency selection for the amplifier is much more about the meaning of the voltage changes, rather than specifically about electronics-induced noise.  In other words, it's more interesting to filter out the high frequencies of the actual input voltage coming in from the sensor, than to get all tied up in the impact of noise generated in the circuit, which, if I understand it, is much smaller than the signal coming in, and therefore can be ignored.  Probably.  Maybe. 

[CaptDon]

Ogitek, I think you have us puzzled here. If you are in a BioMedical Electronic Technician course then your curriculum should be explaining all of this to you. If you are in a medical course then why have you been selected to specify and purchase an amplifier when you obviously know very little about electronics and amplifiers? If you are in a medical course of study why doesn't the university have everything needed on hand? When the supplier of the amplifier gave you a test spec of 8uv peak to peak and for medical studies your total bandwidth after amplification will probably be 10KHz or less the noise isn't likely to rise much above that at any input impedance. Wrap your mind around 'Signal to Noise Ratio' (SNR). Your signal of interest is around 1mv and your apparent noise is 8uv or let's say 10uv to make the math easy. So the SNR is mathematically is 100:1 or in decibels I think that equates to 40Db in voltage ratio (not power ratio). In the medical field that 8uv is tiny compared to the ambient noise from power lines, electrosurgical units nearby, and possible E.M.I. from other machines and even the lighting in the room. If someone has tasked a surgical medical student to specify the purchase of an amplifier then they missed the boat on assigning tasks. If you are a BioMedical student then you should be able to give us the answers as opposed to asking questions. Tell us what you are doing or how you intend to do it and maybe we can offer more targeted advice. You seem to ask the same questions in different ways that prove you have no understanding of electronics and as such probably should not be tasked with purchasing a particular piece of electronic amplification equipment. I hope we can help you but so much of this makes no sense? I have 5 years as a B.M.E.T. in a hospital with 18 O.R.'s + 3 trauma surge tables and 3 more N.I.C.U. tables + Cath Labs and OB/GYN. The majority of 'amplifiers' I dealt with as a repairman / technician / calibrator were from a company called SpaceLabs. There were also some G.E. / Marquette stuff and a few oddballs.

[Ogitek]

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?