B Sine wave noise at different frequencies

[Ephant]

I got the derivation of the formula. It's from this:

View attachment 343322

DR = 20 Log Vmax/Vmin
DR/20 = Log Vmax/Vmin
10^(DR/20) = Vmax/Vmin
Vmin = Vmax/10^(DR/20)

so where DR = 20

Vmin=Vmax/10

This was what I was referring to that Vmin is at least 10% of Vmax. I thought this applies to white noise and sine waves too. So they can't be applied? But both ADC/DAC and pure sine wave/white noise concept have noise floor. Why can't you apply them both? Why is Vmin=Vmax/10 only for DAC/ADC?

The above is the derivation of the mystery formula. The question "Why is Vmin=Vmax/10 only for DAC/ADC?" is very relevant because you use (I use) ADC to display the signal and white noise at the PC. So they become mixed up. And for many months. I actually thought Vmin=Vmax/10 applies to sine wave and white noise. I read dozens if not hundreds of articles for months. When Baloncore mentioned you can still detect sine wave below the noise floor. It jolted me.

I know Newton, Mozart, or the classical physicists, and classical specialists may be not even comprehend the meaning of ADCs and this may stretch the minds of Newtonians or Classicals. And I know this topic is getting off topic. So please answer the questions above for the last questions here. Thank you.

 

[Ephant]

This paragraph of word salad indicates to me that you still want your personal model to survive in spite of what you have been reading. If you only select the bits that 'sort of' fit with your ideas then you can conclude anything you choose from what you have read.

The Noise we are discussing is a totally random fluctuation of a signal. Forget the sine wave ideas - that's just Maths and comes later. There is nothing in a hot resistor (or a transistor etc.) that consists of a sine wave oscillator there's just random fluctuations of charge carriers in there. When you look at a signal on a wire with an oscilloscope you will see a fuzz around the wanted signal that fuzz / grass is at a level that depends on the bandwidth that's been admitted by the input filter. The noise level is defined in terms of the Power per unit frequency interval. (W/Hz, for instance). So a wide input filter will admit more noise power. If you use an input filter that will only just admit your wanted signal then the Signal to Noise Ratio will be the best you can achieve

The noise generated in a resistor has a flat power spectrum ('white noise'). It's called Johnson Noise and has the same power per Hz over the whole frequency range.. Other sources of noise (stars / transistors / diodes / thermionic valves) may not have a flat noise spectrum - but that's also for later.

You suddenly come up with the notion of an ADC. You are far too early with this; get the basics sorted first. Re-read your sources without bringing in your preconceptions. Don't try to bend what you read to fit your ideas and be prepared for a complete re-think about all this.

I missed this message yesterday. I need to understand both of them because my equipment is pure ADC that doesn't have amplifier. The signal is map directly into the ADC. I know because of the principle of superposition, the white noise rides on the sine waves. I understood about Johnson Noise and had even measured resistor noise. It's just the mystery formula that I can't get my head around. But I'm beginning to today after doing more reading. I read in PSE.

"The dynamic range of an ADC is the ratio of the biggest signal it can handle to the smallest signal it can resolve. For example, a 10 bit ADC resolves the input range into 1024 chunks. If the actual input voltage range is 0V to 1.023 volts then each chunk is 1 mV.
Maximum signal is 1.023Vp-p and minimum signal is 1mVp-p. The ratio is 1023 or in decibels this is about 60dB.
Formula: dynamic range is 20 log10(2^n) where n is the number of bits. "

Ok. If there is a signal of 10uV below the noise floor, can it be detected by the above with minimum signal of 1mVp-p? Remember Baluncore words that nearly made me fall down the floor or noise floor. "Take the FFT, power spectrum accumulate, and you will see the sine wave signal climb up out of the noise floor."

Or should an ADC have better resolution than the noise of the input signal?

What is the usual practice? Does the typical ADC resolution get below the noise floor?

For Newtonians who can't comprehend ADCs. Just imagine noise floor as like ocean floor. And the signal as like detecting Dolphins or sharks deep into the ocean. To make this not so off-topic.

 

[sophiecentaur]

my equipment is pure ADC that doesn't have amplifier.

How do you know? What is the internal reference voltage? If it's not exactly the same as your maximum input signal then there will be some amplification somewhere. You are clearly so far out of your depth that you don;t even know which of your ideas are righand which ones are wrong.

the white noise rides on the sine waves.

There you go again; another meaningless statement.

For Newtonians who can't comprehend ADCs. Just imagine noise floor as like ocean floor

It just gets worseand worse. Please stop.

 

[sophiecentaur]

Before you make many gaffs, perhaps you could say how Noise Level is defined and measured. Merely looking at a fuzzy scope trace tells you nothing because it’s random!

 

[Ephant]

Before you make many gaffs, perhaps you could say how Noise Level is defined and measured. Merely looking at a fuzzy scope trace tells you nothing because it’s random!

I've spent several months measuring noises of amplifiers. I used the world's 2nd quietest ADC, the E1DA Cosmos ADC with the following noise floor.

I used it for example to measure the noise floor of an amplifier with bandwidth set to 1000Hz.

I know that as bandwidth increases, the noise increases. In the following it is originally set at 30000Hz, then I switched it to 1000Hz. Huge noises disappear. I know that noises spectrum are flat for each frequency, meaning there is equal distribution from each frequency. When I cut off above 1000Hz. Huge noises vanish.

In the following the amplifier has 10k Ohm resistor shorted.

Look. I'm really familiar with white noises. For months I just thought you couldn't measure below the noise floor so I was looking for the quietest amplifier to measure very very tiny signal. But has difficulty getting 1nV/Sqrt (Hz) amplifier with no noisy input stage. I'm connecting it to sensitive antennas and sensors in my backward to measure the cosmic background radiation and detect dark matter. When Baluncore said you can detect signal below the noise floor using FFT and power spectrum accumulate. It gave me new perspective and hope. I just want to verify what CERN has discovered (or not discovered). So I'll focus on Matlab and FFT in months ahead to learn to dive deep under the noise floor.

 

[DaveE]

LT1115
SSM2019
AD8429
JFE150
EL2125

 

[Ephant]

LT1115
SSM2019
AD8429
JFE150
EL2125

Been there. Done that. I mean. I was trying to create a 1nV/Sqrt(Hz) circuit before. My target was the INA849 with 1nV/Sqrt(Hz) noise spec but the problem is you need an input stage that is JFET with very low bias current, very low current noise, very high impedance. Without using such input stage. The higher bias current and higher current noise of the INA849 and the above would introduce errors and noise. So when you compute the other components. You get noises that are more than 10nV/Sqrt(Hz). For example at only 1000Hz bandwidth and using the OPA2132P JFET input stage with best case 8nV/Sqrt (Hz). . The noise is already

Source resistance (e.g. 10 kOhm for my Netech Signal Generator for example)
2x 5k input stage impedance gain setting resistors
2x op amps (8 nV/sqrt Hz for the OPA2132P)
Instrumentation amp (1 nV/sqrt Hz for the AMP01).

For bandwidth of 1 kHz:
So the calculation becomes:
10k Source resistance: 0.13 * Sqrt (10000 Hz) * Sqrt (1000Hz) = 411 nV rms
2x 5k Protection resistors: Sqrt(2) * 0.13 * Sqrt (5000) * Sqrt (1000Hz) = 411 nV rms
2x OP amps: Sqrt(2) * 8 * Sqrt (1000Hz) = 358 nV rms
I amp: 5 * Sqrt (1000) = 31.6 nV rms

The noise powers sum:
Total = Sqrt (411 ^2 + 411 ^2 + 358 ^2 + 31.6 ^2) =
= Sqrt ( 168,921 + 168, 921 + 128,164 + 998.56) = Sqrt (468,000) = 684 nV rms or 0.684 uV rms. This is only for 1000Hz.

What if for example your bandwidth is in higher KiloHertz or Megahertz. Then the noise would become high in the mV.

Is there any 1nV/Sqrt (Hz) instrumentation amp that doesn't require JFET input stage of 8nV/Sqrt (Hz) noise? JFET instrumentation amplifier may need so many components and putting this on a breadboard can create other noises.

Someone told me months ago that Sigma 5 discoveries don't need the signal to be above noises. I didn't know exactly what it meant. But after Baluncore told me you can see signal below the noise floor. It suddenly dawn on me what those guys may be doing.

 

[DaveE]

Sorry, your probably not going to get a design from us, certainly not me.
I would suggest more study/research/reading and less repeatedly asking general questions about noise and amplifiers. Trust me you have more to learn about this before you can build the highest performance circuits. There is some really good stuff on the web about this. You could start buy going to Analog Devices and TI websites, reading, and understanding, the many technical resources available there. Maybe buy and read a text book.

Maybe buy one of these? It's unlikely you can do better; certainly not this way.

 

[Baluncore]

Been there. Done that.

Then try a lock-in-amplifier.
https://en.wikipedia.org/wiki/Lock-in_amplifier

Note that switching CMOS analog gates have very low noise when being used as a mixer, to down-convert a noisy signal to DC. Follow that with a 1 Hz LPF to remove most of the noise, then a chopper stabilised CMOS amplifier.

 

[Ephant]

Sorry, your probably not going to get a design from us, certainly not me.
I would suggest more study/research/reading and less repeatedly asking general questions about noise and amplifiers. Trust me you have more to learn about this before you can build the highest performance circuits. There is some really good stuff on the web about this. You could start buy going to Analog Devices and TI websites, reading, and understanding, the many technical resources available there. Maybe buy and read a text book.

Maybe buy one of these? It's unlikely you can do better; certainly not this way.

Do you have idea what Instrumentation Amplifer they are using to have such an impressive 4nV/Sqrt (Hz)? Actually I discussed with over a dozen electronic designers in the internet. The best design is 17nV/Sqrt (Hz) noise. That is for 1nV/Sqrt (Hz) plus input stage of 8nV/Sqrt x 2 (the reason it's multiply by 2 is because the differential input needs the noise multiply by 2 according to one designer). Could the 4nV/Sqrt (Hz) you mentioned be a JFET main amp without any input stage amp? They say JFET main amps is more difficult to design and the noise may not be far off. But 4nV/Sqrt (Hz) for total equipment noise is really impressive.

Btw.. I read the Manchester University built many of the components at Large Hadron Collider (link below) Does anyone have any idea what kinds of amps they are using? Is it listed at public or a secret (like components of a nuclear warhead)?

https://www.mub.eps.manchester.ac.u...ding-equipment-for-the-large-hadron-collider/

Also I want to know if detectors at CERN have signal below the noise floor where they looked scout the noise floor or the amplifiers are incredibly low-noise and the signals pop out above the noise floor.. perhaps specially designed to them by say Texas Instruments?

 

[Baluncore]

... (the reason it's multiply by 2 is because the differential input needs the noise multiply by 2 according to one designer).

When you add or subtract two equal independent noise sources, the RMS sum of the noise amplitudes, rises by only √2.
At the same time, the differential signals are dependent, so the signal doubles, and the S/N ratio improves by 2/√2 = √2.

 

[Ephant]

When you add or subtract two equal independent noise sources, the RMS sum of the noise amplitudes, rises by only √2.
At the same time, the differential signals are dependent, so the signal doubles, and the S/N ratio improves by 2/√2 = √2.

Yes. That was why I was taught the following formula in computing for the noises in my equipment.

10k Source resistance: 0.13 * Sqrt (10000 Hz) * Sqrt (1000Hz) = 411 nV rms
2x 5k input stage gain settings resistors: Sqrt(2) * 0.13 * Sqrt (5000) * Sqrt (1000Hz) = 411 nV rms

The second above is composed of two 5k resistors and has same noise as the 10k in first. Sqrt (2) was used.

I own 2 amplifiers. One is the above with 5nV/Sqrt (Hz) AMP01 main amp with OPA2132P input stage (with 8nV/Sqrt (Hz) noise). The second is the $16750 gUSBamp used by major R&D research centers worldwide. I read of a Sigma 5 discovery where it was used. That was why I bought it second hand for $1000 plus.
It has this spec.

https://www.gtec.at/product/gusbamp-research/

Sensitivity 85,7 nV / +/- 250 mV
Noise level < 0.4 µV rms 1-30 Hz

A physicist told me it has no amplifier but only ADC where the signal is directly mapped into it.

At 1000Hz. Let's say the noise is 0.8µV rms. If there is a 0.1µV (100nV) signal. Can you see the 0.1µV (100nV) signal with the 0.8µV rms noise at 1000Hz using FFT or Power Spectrum Accumulate?

It doesn't use the technology or use the concept of lock-in amplifier or has no stand alone gain amplifier. Without using lock-in amplifier. How deep can you go beneath the noise floor and still see the signal? With its sensitivity or resolution of 85.7nV. Can you see a 95nV signal using FFT? Or not?

 

[Baluncore]

At 1000Hz. Let's say the noise is 0.8µV rms. If there is a 0.1µV (100nV) signal. Can you see the 0.1µV (100nV) signal with the 0.8µV rms noise at 1000Hz using FFT or Power Spectrum Accumulate?

Yes, but you must have sufficient samples. You will also benefit from amplification of the signal before the A-D converter.

 

[Ephant]

Then try a lock-in-amplifier.
https://en.wikipedia.org/wiki/Lock-in_amplifier

Note that switching CMOS analog gates have very low noise when being used as a mixer, to down-convert a noisy signal to DC. Follow that with a 1 Hz LPF to remove most of the noise, then a chopper stabilised CMOS amplifier.

I read about Lock-in-amplifier but I don't know why my dozens of electronic experts/advisors at PSE didn't suggest it. Maybe I didn't tell them what I was searching for.

Can lock-in-amplifier be used when you don't know the specific frequency you are looking for? Can it be used broadband? Specifically I'm scanning the dark matter sector in the 0 to 2400 Hz. Can a lock-in-amplifier help? Can it sweep through the 0 to 2400 Hz frequency with reference frequency that can move from 0 to 2400 Hz?
Or lock-in-amplifier not applicable in my application?

 

[Baluncore]

Can it be used broadband?

No. You would need to know what you are looking for.

FFT ± PSA does not need to know the signal.

If the signal pattern repeats, then use an FFT to do autocorrelation, which will detect the repeat period.

 

[Ephant]

No. You would need to know what you are looking for.

FFT ± PSA does not need to know the signal.

If the signal pattern repeats, then use an FFT to do autocorrelation, which will detect the repeat period.

Power Spectrum or Power Spectral Density software can also be used to navigate below the noise floor. Is it not? (which one is appropriate for my case)? I need to know the power of each frequency that FFT alone can't. There is a distinction between FFT and PSD and PS.

What is best Power Spectrum or Power Spectral Density software available? I just read that REW RTA is not accurate. It is only good for pink noise. I used it the past months and was wrong using it thinking its FFT was so accurate.

https://www.hometheatershack.com/threads/spectrum-rta-feature.9872/

 

[AlexisBlackwell]

When talking about noise in a signal, as in your example, it represents some random component that can be caused by various factors, such as electromagnetic interference or thermal movement of electrons in the device. This noise can be represented as a random signal with a certain spectral characteristic. When you change the frequency of a signal, its spectral content, including noise, also changes.

In your example, if the function generator produces a signal with different frequencies from 20 Hz to 20000 Hz, then the noise in each of these frequency regions may be different. For example, at higher frequencies the signal may be more susceptible to electromagnetic interference and other sources of noise, which may result in increased noise levels compared to lower frequencies.

 

[Vanadium 50]

Given sufficient time and samples, it is possible to dig anything out of the noise.

Whether it is there or not!

 

[berkeman]

When talking about noise in a signal, as in your example, it represents some random component that can be caused by various factors, such as electromagnetic interference

If the noise in a system is from external EMI coupling in, it is almost by definition not random.

This noise can be represented as a random signal with a certain spectral characteristic. When you change the frequency of a signal, its spectral content, including noise, also changes.

Changing the frequency of a desired signal does nothing to the spectral content of the noise in a channel. Please take care not to post misinformation.

 

[Ephant]

Power Spectrum or Power Spectral Density software can also be used to navigate below the noise floor. Is it not? (which one is appropriate for my case)? I need to know the power of each frequency that FFT alone can't. There is a distinction between FFT and PSD and PS.

What is best Power Spectrum or Power Spectral Density software available? I just read that REW RTA is not accurate. It is only good for pink noise. I used it the past months and was wrong using it thinking its FFT was so accurate.

https://www.hometheatershack.com/threads/spectrum-rta-feature.9872/

I can't find any information in google what is the difference between using Power Spectral Density or Power Spectrum in looking for signal under the noise floor. What is the difference between Power Spectral Density and Power Spectrum? What would be more effective in navigating the noise floor?

I can't ask in the digital signal processing forums directly because I can't tell them I'm scanning the dark sector. If one just wants to seek some broadband peaks. Is Power Spectral Density more useful? For example. If I want to search for the peaks in the Dark Spectrum like the following. IS PSD more useful? This was the result of using Matcad N-ways Parallel Factor Analysis using Power Spectral Density in toy model or simulations.

 

[sophiecentaur]

looking for signal under the noise floor.

So far, despite having posted a number of screen shots, you haven't yet said what you mean by noise floor.

I can't tell them I'm scanning the dark sector.

What does that mean in grown up language?

 

[berkeman]

Yeah, what's a dark sector?

I can't ask in the digital signal processing forums directly because I can't tell them I'm scanning the dark sector.

 

[sophiecentaur]

I was beginning to wonder about Ephant. I was thinking tinfoil hats etc..

 

[Ephant]

So far, despite having posted a number of screen shots, you haven't yet said what you mean by noise floor.

In Audacity, I was taught days after this thread was started that I could add noises in Audacity and see how they mixed up. So I was able to visualize the earlier question why 50Hz has more jagged edge vs 900Hz. .

This is 50Hz signal with 1000Hz noise.

This is 900Hz signal with 1000Hz noise.

Before I used the 1000 Hz software low pass filter in Audacity on the following 30,000 Hz signal. I didn't know what would happen. I thought if you didn't put any low pass filter on the hardware itself (like a 2nd order Butterworth filter). The noises would overwhelm the lower frequency increasing its noise. After I ran it. It became clear to me what it means the frequency spectrum of white noise is flat. And how white noise is characterized by a flat spectrum, i.e. the variance is approximately the same at all frequencies. And it is retained even after passing via an ADC. That's why you can do digital filtering like brick wall

And with your descriptions in the following. How can I not understand Noise Floor already. Of course Noise Floor doesn't mean there is a floor at the circuit where noise collects. It's like Sky is the Ceiling. There is no actual ceiling.

"The Noise we are discussing is a totally random fluctuation of a signal. Forget the sine wave ideas - that's just Maths and comes later. There is nothing in a hot resistor (or a transistor etc.) that consists of a sine wave oscillator there's just random fluctuations of charge carriers in there. When you look at a signal on a wire with an oscilloscope you will see a fuzz around the wanted signal that fuzz / grass is at a level that depends on the bandwidth that's been admitted by the input filter. "

What does that mean in grown up language?

In grown up language. It means ordinarily, dark matter (we who tried to detect it call it the dark sector) shouldn't interact with ordinary matter, even down to the photons. But the Big Bang should logically produce some kind of relics that can bind them together, sort of a coupler (restoring higher symmetry state lower than the electroweak plasma). In the past. They tried to find equations that could produce all the constants of nature, but couldn't. So the universe is more complicated than simple minded idea of it. And the idea is just slowing coming around the corner, and CERN is still transitioning to the idea the universe is more complicated than their rigid ideas as Sabine Hossenfelder kept saying.

Some of us believe ordinary and dark matter can be glued together. And we tried to detect it. No harm trying to detect it too for us civilians. But remember CERN are also composed of Civilians too, and very human.

 

[Ephant]

Oh. I couldn't edit the above message anymore. In the attachments I forgot to delete. The 3rd image is the white noise not yet filtered to 1000Hz, so it is still causing jagged edge even to 900Hz signal. Also the noise amplitude is just 0.3 while the sine wave is 0.8.

The noise and sine amplitude should be the same in the simulation, isn't it? The maximum is 1.0 but I used 0.8 to show the baseline better. I should have used 1.0 maximum amplitude white noise in the noise generator?

In the following I used 0.8 Noise with half right filtered to 1000Hz noise and a 50Hz signal

In the following I used 0.8 amplitude Noise with half right filtered to 1000Hz noise and a 900Hz signal.

Why do I share them? because it was when I saw them that I totally understand and visualize the reasons for jagged edges. You can let newbies try the Audacity noise generators who may not understand too.

About probing the noise floor using FFT. It is possible that many who didn't intend to probe the noise floor and using FFT just to view the signal above noise floor can unintentionally get signal from below the noise floor, is this right?

I need to know because if you show signals you acquired and didn't say some signal was below the noise floor. People who want to duplicate your result may only focus above the noise floor.

Also what would happen if you don't use FFT but just use Power Spectral Density analysis on the noises. Would you also be able to probe below the noise floor using PSD? This is my last question.

About my experiments to duplicate one done by a university. If I can't replicate it and it is faulty. Then the prospect of Particle Dessert for the next centuries is a possibility. But if I can replicate it. I'll share far and wide the findings of the University and all resources of CERN must be re-orient to the discovery instead of no major discoveries besides the Higgs. I'll update on the result months from now if I'm still here. I can't share the source now because it is not peer reviewed and may attract the wrath of the moderators. If I found sigma 5 results. I'll try to write or make other write a paper that can be peer reviewed and share here.

 

[sophiecentaur]

People who want to duplicate your result may only focus above the noise floor.

What exactly do you mean by this?

About my experiments to duplicate one done by a university.

What form do your experiments take? Is there any hardware or is it all on a simulator (which someone else wrote)?

CERN must be re-orient to the discovery instead of no major discoveries besides the Higgs.

So that's all they've achieved? They must be glad that you are around to put them on the right lines.

 

[Ephant]

What exactly do you mean by this?

I mean supposed a team used one hour sampling, and you use only 1 minute sampling and didn't know they used one hour to probe below the noise floor. Then you can't get the same data they have. I think this answers to my own question.

What form do your experiments take? Is there any hardware or is it all on a simulator (which someone else wrote)?

I'm just duplicating the experiment using room size Faraday cage (not yet built), very sensitive sensors and amplifiers, Matcad FFT/PSD/Paralac analysis etc.

So that's all they've achieved? They must be glad that you are around to put them on the right lines.

I mean the Large Hadron Collider major discovery was only the HIggs. Of course other accelerators/equipments before that confirmed the Standard Model like quarks, electroweak and others.

Since I'm getting some idea of the difference between FFT and Power Spectral Density. I googled a lot with some sites saying the spectrum looks the same, only the label varies, with the latter in W/Hz or other units. And will ask more in PSE, then I'll end up this thead with the following.

I think it may be more pessismistic to show them. 'll tell you why.
[Mentor Note: Several paragraphs of mystic nonsense deleted from this post]


Thank you guys for all the help. I have no futher questions about the subjects of this thread.

 

[berkeman]

I have no futher questions about the subjects of this thread.

Thread is closed then.