Name that opamp!

[dannyf]

And some people's apparently futile attempt at understanding density functions,

[macboy]

it is nV/SQRT-Hz, not nV/SQRT-100kHz or nV/SQRT-5kHz. That's "Hz" as in just one.

You are clearly not an engineer.  That's the thing about "units".... unit means one. It's always one. It's kind of the point.

[dannyf]

You are clearly not an engineer.

S/he may not be an engineer but s/he is definitely an "engineer",

Apparently s/he is having lots of troubles understanding what a "density function" is.

[G0HZU]

GK, you keep using units of "nV" for noise density, but nV does not specify noise density. You can't leave off the per part of the units

I think you can if everybody in the room is familiar with noise specifications and uses these terms on a regular basis.

For example:

Input Noise Voltage at 1KHZ - less than 4 nanovolts

The quote above is from the OP's first post in the thread. It could/should have been presented better than this but to me that means the Vrms of the noise measured at a spot frequency of 1kHz (in a 1Hz bandwidth) is <4nV. I would be extremely surprised if anyone would interpret it any other way unless they were being deliberately silly or awkward.

In my line of work (RF) it's common to measure noise power in a 1Hz bandwidth eg in dBm/Hz. This (1Hz bandwidth) spot measurement can be done at one frequency or as many spot frequencies as the user feels is necessary. It could be helping to characterise a noise source, or the noise floor of a receiver or the close to carrier noise on a synthesiser.

[CaptnYellowShirt]

I'm going to ask a dumb question after watching this guy's video.

Where does the sqrt() part of the sqrt(Hz) come from? I realize this has a simple answer to it, but for whatever reason its escaping me now.

[dannyf]

Where does the sqrt() part of the sqrt(Hz) come from?

The answer comes from "energy" - the energy distribution is inverse to that of frequency. So the "equivalent" voltage, is the rms voltage that would have generated the same energy, would be inversely proportional the the sqrt of f.

You actually will never see that 4nv figure on the scope.

[G0HZU]

I'm going to ask a dumb question after watching this guy's video.

Where does the sqrt() part of the sqrt(Hz) come from? I realize this has a simple answer to it, but for whatever reason its escaping me now.

I don't really work with nV/rootHz much. Because I work mostly in the RF domain I measure the power of noise (in a 1Hz BW) in dB relative to 1mW = dBm/Hz. Usually this is done with 50R test gear like a spectrum analyser.

So someone who specialises in audio stuff can probably explain it better than me but see below:

Try and (temporarily) think in terms of power. If you were able to measure the power of a (flat/white) noise source at 10kHz inside a 1Hz measurement bandwidth (centred on 10kHz) and you got something like 1nW in this little 1Hz slice then it's really easy to go on to calculate/predict the power you would measure if you looked in a 10kHz bandwidth because you simply multiply the power by 10,000 (because in a 10kHz bandwidth you have ten thousand 1Hz slices each containing 1nW of noise power) So the power in a 10kHz BW would be 1nW x 10,000 = 10uW. Easy.

But it isn't that easy for voltage. Power is a function of V^2. So instead of multiplying the initial voltage figure of the noise source by 10,000 you would have to multiply by the square root of 10,000 to get the voltage for the 10kHz or 10,000 time higher bandwidth.

If you watch the video again you can see he does this. He multiplies 40nV by the square root of 10,000Hz (= 40nV*100) = 4uV. He then factors in the less than perfect LPF and therefore multiplies by 1.57 to get about 6.28uV.

[CaptnYellowShirt]

I remember reading about all this some years ago, but I never work/think in these terms so it fades pretty quickly.

In this case, is there a nominal 'load' the voltage spec is 'fed into' to think about it in terms of power or is it just the unity (1 ohm)?

And I'm also assuming that these values are assume an incoherent noise source?

[G0HZU]

I think I might be confusing you... I only gave the power example/reference to show how easy it is to calculate the power in a wider bandwidth.
For another example of this, if you double the noise (measurement) bandwidth you will double the noise power you measure. This is quite intuitive.

However, if you double the noise (measurement) bandwidth you don't get double the voltage when you measure the voltage at the higher bandwidth. The voltage will only go up by the square root of 2 or 1.4142. Hope this helps...

[GK]

it is nV/SQRT-Hz, not nV/SQRT-100kHz or nV/SQRT-5kHz. That's "Hz" as in just one.

You are clearly not an engineer.  That's the thing about "units".... unit means one. It's always one. It's kind of the point.

You really can't admit that you were wrong, and never had a coherent point all along, can't you?

[GK]

You are clearly not an engineer.

S/he may not be an engineer but s/he is definitely an "engineer",

Apparently s/he is having lots of troubles understanding what a "density function" is.

I think that you are suffering from a "density function".

Input Noise Voltage at 1KHZ - less than 4 nanovolts per stage

Those are impossibly nice specs,

For us non engineers, please explain exactly what is either so remarkable or "impossibly nice" about the above quoted op-amp specification.
 

[CaptnYellowShirt]

I think I might be confusing you...

You wouldn't be the first... today... or even in the last hour. 

However, if you double the noise (measurement) bandwidth you don't get double the voltage when you measure the voltage at the higher bandwidth. The voltage will only go up by the square root of 2 or 1.4142. Hope this helps...

So I'm thinking this comes from the mathematics of adding (...summing, integrating, etc) incoherent phasors.

[G0HZU]

For us non engineers, please explain exactly what is either so remarkable or "impossibly nice" about the above quoted op-amp specification.

I doubt you will get an answer from dannyf... I haven't bothered to reply/comment to his posts on this thread.

dannyf is like a little boy who likes to run up and shout "stupid person!". But he just runs away if you challenge him.

[G0HZU]

So I'm thinking this comes from the mathematics of adding (...summing, integrating, etc) incoherent phasors.

Dunno if this helps but I often use white noise to cross check my test gear here. I have a homemade high(ish) level noise source that puts out a pretty flat noise spectrum out to 180MHz.

If I put it through a 2.8MHz high order LPF and into a decent (Anritsu) thermocouple power meter I can measure the total heating power of the noise energy inside that 2.8MHz bw.

I can adjust the noise power to show -21dBm on the power meter via the 2.8MHz LPF. The power head works right down to a few kHz. This power level is 7.94e-6W and the Vrms should be 20mV in a 50R system.

If I then feed the output to an old analogue true rms voltmeter terminated in 50R it indicates very close to 20mV (as expected) on the dial

If I then click down in 10dB steps via a precision attenuator I see (about) 6.3mV, 2mV, 630uV, 200uV and about 65uV on the bottom range of the voltmeter. The meter has a 20MHz BW and can see down to 10uV but it begins to read a bit high once you get down to a few tens of uV due to its own internal noise.

So the power is falling by a factor of 10 (10dB) in each case but the voltage is only falling by the square root of 10 (= 3.16) in each case.

If I return the attenuator to 0dB attenuation and measure the noise in a 1Hz bw using the noise marker on a decent spectrum analyser the analyser shows -86.0dBm/Hz at 1MHz.

This is about 11.21uV in a 1Hz BW. To predict the voltage in the full 2.8MHz bandwidth we simply use our known method of multiplying 11.21uV by sqrt of 2800,000 to get 18.8mV.

This 18.8mV is in pretty close agreement with the 20mV seen on the voltmeter. If I measured the true noise bandwidth of the high order 2.8MHz LPF the result might have worked out even closer but to get within about 0.5dB isn't a bad result especially when the various measurement uncertainties of my test gear are taken into account Note: The attenuator is very expensive and extremely accurate (with a very low VSWR) over all of the 50dB range.

[GK]

I would be extremely surprised if anyone would interpret it any other way unless they were being deliberately silly or awkward.

Or just clueless.

If a spot (center) frequency is specified it is obvious that any attendant voltage stated is rms noise in a 1-Hz bandwidth (as per convention), even if it is not followed with "sqrt-Hz". I mean, what else could it be? If a pedant wants to take me to task for not using strict notation, then fine, I am content to just roll my eyes,  but giving a condescending lecture designed to infer that I don't know what I am talking about because I neglected to repeatedly restate the obvious is just playing like a dickhead.   

On Semi neglect the "sqrt-Hz" in some of their transistor datasheets, for example:



The vertical scales are just nV/pA. However, even so the note is pretty much superfluous, they do specify the1-Hz measurement bandwidth in words. In a way though, that is probably a more logical approach to specifying the 1-Hz measurement bandwidth than by effectively saying that it is the square root of one, but someone unknowing couldn't infer from either of those graphs that the noise voltage/current increases in a wider measurement bandwidth by the square root of the bandwidth increase in Hz. 

Incidentally, 4nV at 1kHz is pretty run-of-the-mill for bipolar op-amp voltage noise performance; a far cry from "impossibly nice". The best op-amps do 0.9nV typ. (e.g. LT1115, ADA4898-X). The ADA4898-2 is a dual op-amp in a standard package. I'm not a IC designer, but if they can fit two 0.9nV op-amps on a single die I don't know why they couldn't put two 0.9nV input stages in parallel to make a single 0.64nV (0.9/(sqrt-2)) op-amp. It would have double the current noise and input bias current, but could still be a useful part for low source impedance applications.

[dannyf]

Wow, a week or so has passed and some people still struggle with density functions,

[GK]

Wow, a week or so has passed and some people still struggle with density functions,

I don't know if this is your own special way of seeking help, but I should point out that persistently referring to oneself in the third person is typically a sign of some kind of psychological disturbance. Also, you have yet to answer my request, repeated again:

Input Noise Voltage at 1KHZ - less than 4 nanovolts per stage

Those are impossibly nice specs,

For us non engineers, please explain exactly what is either so remarkable or "impossibly nice" about the above quoted op-amp specification.

Though I do know that I ask in vain. A probability density function cannot be applied for any possibility of dannyf posting something intelligent or insightful in this thread topic.
 

[CaptnYellowShirt]

I don't know if this is your own special way of seeking help, but I should point out that persistently referring to oneself in the third person is typically a sign of some kind of psychological disturbance.

[CaptnYellowShirt]

So I'm reading an academic paper today where the author claims a shielded DUT enclosure and preamp yield a "spectral voltage density S_u(f) of the background noise is 2x10^-16 V^2 s at 10 Hz."

To confirm... that's a -16 as in 0.1 femtovolts.

There's nothing special about his setup. Its a paper form the 1980's. He's using a 12bit / 20kHz A/D (controlled by turbo pascal ... ftw). Is there any way this is real? And if not, what mistake is he likely making?

[dannyf]

Is there any way this is real?

That's just a tad better than my NE5532 - which can be made to produce better noise figures than his.

All it takes is rudimentary understanding of how "density function" works.

[G0HZU]

So I'm reading an academic paper today where the author claims a shielded DUT enclosure and preamp yield a "spectral voltage density S_u(f) of the background noise is 2x10^-16 V^2 s at 10 Hz."

To confirm... that's a -16 as in 0.1 femtovolts.

There's nothing special about his setup. Its a paper form the 1980's. He's using a 12bit / 20kHz A/D (controlled by turbo pascal ... ftw). Is there any way this is real? And if not, what mistake is he likely making?

Messing around with low frequency VF opamps isn't really my thing but I can have a go at answering your question...

If you look at the units you have quoted then the number does make sense.

In my (RF) world I work in dBm/Hz for measuring the power spectral density of white noise. i.e. I measure the power of noise in a 1Hz bandwidth.

NOTE:
Power is a function of V^2
The period of a waveform is measured in seconds  = 1/F(Hz)

So (in a 50 ohm environment) I could choose to convert the power spectral density units from dBm/Hz  to (V^2)/Hz because I know I'm in a 50 ohm environment

or I could convert them to (V^2).s  where s = 1 second = 1/(1Hz)

or I could convert this again from (V^2)/Hz to V/rtHz  by taking the square root of both the top and bottom terms which delivers familiar units for opamp users.

Have a go at converting  2x10^-16 V^2 s  across to V/rtHz to see if the number looks more familiar to you. 


Note: in your example above at 10Hz you are  close to the typical 1/f knee/cutoff in the noise response of a typical opamp aimed at audio use. So in this region the noise response won't be flat as it won't quite be in the white noise region.

[CaptnYellowShirt]

So I'm reading an academic paper today where the author claims a shielded DUT enclosure and preamp yield a "spectral voltage density S_u(f) of the background noise is 2x10^-16 V^2 s at 10 Hz."

To confirm... that's a -16 as in 0.1 femtovolts.

There's nothing special about his setup. Its a paper form the 1980's. He's using a 12bit / 20kHz A/D (controlled by turbo pascal ... ftw). Is there any way this is real? And if not, what mistake is he likely making?

Messing around with low frequency VF opamps isn't really my thing but I can have a go at answering your question...

If you look at the units you have quoted then the number does make sense.

In my (RF) world I work in dBm/Hz for measuring the power spectral density of white noise. i.e. I measure the power of noise in a 1Hz bandwidth.

NOTE:
Power is a function of V^2
The period of a waveform is measured in seconds  = 1/F(Hz)

So (in a 50 ohm environment) I could choose to convert the power spectral density units from dBm/Hz  to (V^2)/Hz because I know I'm in a 50 ohm environment

or I could convert them to (V^2).s  where s = 1 second = 1/(1Hz)

or I could convert this again from (V^2)/Hz to V/rtHz  by taking the square root of both the top and bottom terms which delivers familiar units for opamp users.

Have a go at converting  2x10^-16 V^2 s  across to V/rtHz to see if the number looks more familiar to you. 


Note: in your example above at 10Hz you are  close to the typical 1/f knee/cutoff in the noise response of a typical opamp aimed at audio use. So in this region the noise response won't be flat as it won't quite be in the white noise region.

So ... 4.5 nV at whatever his FFT bin-width was.

I'm familiar with power spectrums and the V^2 units. But not so much with the V^2-sec units. Is this a common way to express 1/f noise measurements?

[G0HZU]

It's late and I'm off to bed but I don't think you have worked that out correctly... Maybe if you posted a link to the paper in question someone could look at it for you.

I'm afraid I really don't do anything with hifi audio so I'm not the right person to elaborate on any of this low noise AF opamp stuff.

However, I did go through a phase of using low noise opamps for design work but this was with wide bandwidth £££ CFB type opamps for use in EW/ESM receiver design many, many years ago. eg as the final output stage for driving an ADC in a narrowband digital IF.

I think the only low noise wideband VFB opamp I used for this type of receiver design was a 1.8GHz? GBW opamp with about 1nV/rtHz noise performance at 1MHz and an output IP3 of over +45dBm at a couple of MHz. These high cost/performance devices have high 1/f noise across the audio band but this didn't bother me as frequencies this low were out of band for me. So I was only ever interested in the white noise part of the noise graphs. eg I was interested in noise and linearity across a few hundred kHz to perhaps a few MHz. In their day this type of opamp was almost the perfect choice for my application but these days our receiver designs have digital IF bandwidths of 40-100MHz or more centred up at VHF. So opamps can't be used anymore...

[CaptnYellowShirt]

It's late and I'm off to bed but I don't think you have worked that out correctly...

Well this is just a math mistake.  How's 14 nV / rtHz sound?