B Sine wave noise at different frequencies

[Ephant]

The addition of random noise increases only as the root of the bandwidth.
Much noise is 1/f noise, so without a filter, the noise is limited.

But what if the op amp or resistor would still produce white noise at 900 Gigaherz and so on. Or did you mean its like black body where when the frequency is so high the photons wont be emitted forever? what is the limit in the frequency when the noise would diminish so low?

Nyquist says that A-D sampling must be done at twice the rate of the highest frequency present in the signal. That usually requires a low-pass filter.
https://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem

What if no low pass filter setting is set and sampling is set to 38400? does it mean the the circuit can accept noise up to 38400 bandwidth?

 

[Baluncore]

I cannot teach you signal processing theory by a thousand questions.

What if, at this point, you learned to search for, and read, the easily and widely available literature.

 

[sophiecentaur]

@Ephant
Q and A is a hopeless way to learn any subject. You don't know which questions to ask, you don't know how to express them and you probably will not understand or appreciate the answers. You have to do your own finding out and learning.

 

[AlexisBlackwell]

Hello Ephant! The noise in sine waves will vary depending on the frequency at which the waves are generated. At higher frequencies, noise may be more noticeable due to the higher signal energy at those frequencies. Thus, the noise will vary depending on the frequency at which the sine waves are generated.

 

[Baluncore]

@AlexisBlackwell Welcome to PF.

The noise in sine waves will vary depending on the frequency at which the waves are generated.

The title of this thread is misleading. Fundamentally, sine waves do not have noise, by definition they are pure sine waves.

The noise is a separate broadband signal, present in the same channel as the sine wave signal. That noise will be amplified and attenuated with the sinewave, as it is processed. The sine wave is a narrowband signal, that can be detected or separated, from the broadband noise.

Distortion of sine waves, during generation or later signal processing, results in integer harmonics of the sine wave being present. If the distortion is symmetrical it will have odd harmonics only, if asymmetric, even harmonics will also be present. Each harmonic is another pure sine wave, at a higher frequency than the fundamental. The harmonic energy, resulting from distortion, may fall outside the band limited channel that carries the fundamental signal.

The noise, accompanying the sine wave, will depend on the bandwidth of the channel. The appearance of the noise, in the time domain, will depend on the position of the fundamental sine wave within the bandwidth of the channel. Noise at lower frequencies than the sinewave will appear as a wandering of the sine wave baseline, while noise at higher frequencies than the sine wave, will appear as jagged detail on the sine wave. That explains the problem with the title of this thread.

 

[sophiecentaur]

The title of this thread is misleading.

This is always the problem. Such questions should really be bounced and required to be re-stated in proper terms. It's typical of the way 'knowledge' is spread over a loose information network that is the WWW. It is a system of chinese whispers about topics which have, in fact been understood formally for more than decades. That knowledge just gets degraded.

But how can we deal with this, without suppressing the good will of newbies or the under-informed? Perhaps the first reply should always contain a link to a 'friendly' source like Wiki. You can't hope to put someone straight with a short reply.

 

[Ephant]

After a whole day reading last week. I already found the answer in the following why white noise has high frequency limit. Also whether ADC can act like low pass filter. It can't really because above the Nyquest limit, aliasing can occur if the ADC has no low pass filter.

https://dsp.stackexchange.com/questions/9842/white-noise-vs-delta-pulse-and-ultraviolet-catastrofe

My question is a personal one to you guys now. See waveform below:

In your experience. What is the highest percentage of the amplitude of background noises in a sine wave when you think a signal can still be resolved. For example in the above is a 10uV, 50Hz signal from a signal generator with the amplifier set to 1000Hz bandwidth. In your estimate. What is the microvolt of the noise accompanying the sine wave if the amplitude of the sine wave above is 10uV? Do you think the noise amplitude is 3uV or 5uV? Remember amplifier noises is spec'd like 0.4uV at 1 to 30 Hz Referred to Input. This is the context of what I mean noises has amplitude like 0.4V noise. And based on your experience. What should be the percentage of noise in the overall amplitude for it to still be resolvable? To show I have researched it. I read 10% is the limit so the noise for 10uV signal should be 1uV only for the sine wave to still be resolvable. But in the above. The noise is like 3uV, right? But yet the sine wave can still be resolved or seen. So isn't the limit like 30% instead of just 10%? based on your experience?

 

[Baluncore]

So isn't the limit like 30% instead of just 10%? based on your experience?

There is no limit. Given sufficient time and samples, it is possible to dig anything out of the noise. Take the FFT, power spectrum accumulate, and you will see the sine wave signal climb up out of the noise floor.

 

[Ephant]

There is no limit. Given sufficient time and samples, it is possible to dig anything out of the noise. Take the FFT, power spectrum accumulate, and you will see the sine wave signal climb up out of the noise floor.

Even if the sine wave signal is below the noise floor? Or must it be at least the same level as the noise floor? Or must be above the noise floor? If so, how many percentage above the noise floor can FFT resolve it?

 

[Baluncore]

Even if the sine wave signal is below the noise floor?

Yes, even if it is one thousandth, or one millionth, of the noise, the sine wave can still be detected and extracted, if you know about Fourier transforms and power spectrum accumulation.

 

[Ephant]

Really? but for real time processing like listening to radio where Fourier transforms and power spectrum accumulation is not possible because the signal is not repetitive. Then what must be the percentage of noise for the signal to resolved? For example. With 5uV noise. Can a radio signal with 10uV amplitude still be resolved? Without FFT or digital analysis.

 

[Baluncore]

With 5uV noise. Can a radio signal with 10uV amplitude still be resolved?

Define resolved.
Without processing, I can hear a sine wave that is 20 dB below the noise.
It all depends on the bandwidth of the signal, and the bandwidth of the noise.

 

[sophiecentaur]

After a whole day reading last week. I already found the answer in the following why white noise has high frequency limit. Also whether ADC can act like low pass filter. It can't really because above the Nyquest limit, aliasing can occur if the ADC has no low pass filter.

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.

 

[Ephant]

Define resolved.
Without processing, I can hear a sine wave that is 20 dB below the noise.
It all depends on the bandwidth of the signal, and the bandwidth of the noise.

I'll review what I read. I think what I read is only true for ADC, where for example if you have a 10mV signal, the resolution should at least be 10% minimum to have good dynamic range to resolve the signal. Because if you have 10mV signal and your ADC resolution is only 5mV smallest. It may not resolve the signal. I thought this was also related to white noise and signal in general, but I guess it's only related to ADC. But thanks for letting me know that in white noise in amplifier. Signal can still be seen even below the noise floor. I thought the rule is always the signal has to be certain level above the noise floor. I guess i'm mixing the concept of noise floor in amplifier versus noise floor in ADC. I'll reflect on it.

 

[sophiecentaur]

where for example if you have a 10mV signal, the resolution should at least be 10% minimum to have good dynamic range to resolve the signal.

'fraid this doesn't make much sense either.

I'll reflect on it.

More than just 'reflection' required here. You need more input too. The term "noise floor" is not an exact one - it's an arm waving description and contains no Maths. Like i already said, sort out the basics before going down the digitising route.

 

[Baluncore]

"The most difficult subjects can be explained to the most slow-witted man if he has not formed any idea of them already; but the simplest thing cannot be made clear to the most intelligent man if he is firmly persuaded that he knows already, without a shadow of doubt, what is laid before him." – Leo Tolstoy

 

[Ephant]

'fraid this doesn't make much sense either.


More than just 'reflection' required here. You need more input too. The term "noise floor" is not an exact one - it's an arm waving description and contains no Maths. Like i already said, sort out the basics before going down the digitising route.

Last week I was reading a bunch of articles which I saved in my samsung phone. I saved hundreds of articles over the years. I didn't know why my samsung browser couldn't capture screen. Then I read about Secret Mode being on last weekend at google. So I searched about it in my settings and saw a Secret Mode reset. I reset it. Unfortunately, when I reset it, I couldn't access the hundreds of important technical articles I read anymore. And couldn't recover them. Lesson. Don't save important non-personal information in Secret Mode.

The past hours I was googling for this formula trying to recall the context. But couldn't find it. It involves something like this, Vmin= Vmax/10 (dB/20) where dB is the dynamic range. So if the dynamic range is 20, then Vmin=Vmax/10. Do you know what the formula apply to? I couldn't find the formula anywhere in google the past hours. So please give me a new reference about it or something related to it if the wordings are not correct. All I remember last week was when I was thinking of 10uV as the Vmax, then I thought 1uV is the Vmin so thinking 10% is the required value. I've been searching for the article to clarify what it means, but it is forever lost in my samsung. Unless you can still recover the saved pages after Secret Mode reset?

 

[Baluncore]

I couldn't find the formula anywhere in google the past hours. So please give me a new reference about it or something related to it if the wordings are not correct.

Why waste your time. You are probably better off without that preconception.

 

[Ephant]

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

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?

 

[sophiecentaur]

. I didn't know why my samsung browser couldn't capture screen.

How is this relevant? You could store the whole of Wikipedia but, if you don't actually read stuff, it's wasted effort.
In your mystery formula, you should realise that "dB" conventionally is the unit Decibel and not a symbol for a variable. It is the ratio of two powers.

 

[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?