Measuring amplifier noise with scope?

[aneevuser]

I've built a differential preamp for a mic. with XLR output, circuit shown below:



The mic. has about 220R impedance, and the op amp is 1/2 of an NE5532. The amp. is supposed to have a low freq. voltage gain of 100 (40 dB) and and an upper 3 dB point of about 15 kHz.

I'm trying to measure the self-noise at the output with a DS1054Z and I've done the following:

1) I've shorted the inputs with a 220R resistor.
2) I've set the 20MHz b/w limit on the channel, and the channel and probe are on x1 setting
3) I'm measuring the RMS voltage on the channel
4) I've set the timebase to 10 ms so that the measured value include frequency components down to 100 Hz.

So the question is: given the above, is the RMS figure that I'm seeing on the scope going to be a valid representation of the amp's noise, or have I made some newbie error in my setup somewhere?

[tggzzz]

There's an old trick with non-digitising scopes.

Connect the signal to both channels; you will see two "fuzzy" traces. Move the traces so the fuzz partly overlaps,


then move one until the fuzz intensity of one trace is contiguous to the fuzz intensity of the other, e.g.


Switch the input coupling to GND, and the difference between the two traces is the RMS noise.



Source:  https://www.edn.com/calculate-and-measure-noise-values/

[exe]

I'd say measuring noise is a tricky topic. Anyway, here are a few questions that should help. I'd say, one need a low-noise preamp (LNA) because scopes are noisy and not very sensitive devices. So, in order to do any sensual measurements, be sure the signal is above noise noise floor of the scope. So, questions:

1. What's the noise floor of your oscilloscope? Is it measurably lower than noise from the opamp?
2. When measuring opamp noise, did you short its input?
3. Did you use a grounded shield and shielded connectors?
4. Is opamp supplied from a clean supply (e.g., batteries)?

[Vovk_Z]

Much easier to measure amp noise by soundcard (with specialized program, one ore another).

As for me, I use both soundcard and microvoltmeter (with real termo TrueRMS converter).

[magic]

The thing about soundcard measurements is that it requires knowing or measuring its sensitivity (how many volts for full scale output from the ADC). Once this is known, a soundcard is superior.

20MHz bandwidth is way too much, you probably only care about noise in the first 15kHz.
The scope may not have exactly 20MHz bandwidth if sampling rate is reduced due to long acquisition time and limited sample memory depth.
Scopes are noisier than audio gear, in general.

Noise of your circuit can be calculated.

Johnson noise of the 4k7 resistors: 8.7nV/rtHz per resistor
voltage noise of the NE5532: 5nV/rtHz total
current noise of the NE5532 times input resistance: 0.7pA/rtHz · 4700Ω = 3.3nV/rtHz per input pin

All sources add as RMS sums so the total input referred noise density is: sqrt(2·8.7² + 5² + 2·3.3²) nV/rtHz = some 10~20nV/rtHz

It will be somewhat more at low frequencies.

[David Hess]

There's an old trick with non-digitising scopes.

Almost all DSOs fail when making tangential noise measurements at this step:

or a DSO that emulates an analog scope

The ones which could work produce a density modulated display like a sampling oscilloscope.  But that is acceptable because there are two alternative ways to make the measurement on a DSO:

1. The standard deviation is equal to the RMS noise.  Just beware that some DSOs calculate this incorrectly on noise.  (1) See Dave's video about RMS measurements on DSOs.

2. It may be possible to use the FFT function directly however without a noise marker function, interpreting the results may be difficult.  https://www.edn.com/dsos-and-noise/

(1) I think the problem here is calculating the standard deviation on the processed and interpolated display record instead of the acquisition or processing record.

1. What's the noise floor of your oscilloscope? Is it measurably lower than noise from the opamp?

That part can be a real problem even with amplification because oscilloscopes, especially modern ones, tend to have very high input noise simply because of device physics and optimizing for highest unlocked bandwidth.  Old oscilloscopes used lower noise JFET input stages which were just fast enough to meet the input bandwidth requirements and this resulted in devices which were close to optimal for noise.

The easy place to start is watch to see if the displayed noise level increases when the amplifier is connected.  If it does not increase by several times, then the oscilloscope's input noise is too high.

Magic did the calculation up to 14 nV/SqrtHz.  Continuing, 14 nV/SqrtHz * Sqrt(17 kHz) = 1.82uV RMS * 1.6 Shape Factor = 3uV RMS * gain of 100 = 3mV RMS output noise.

The oscilloscope input noise is very unlikely to be better than 14nV/SqrtHz (2) so with an input bandwidth of 20 MHz and shape factor of 1.6, 100uV RMS.  So the measurement should be possible even if the oscilloscope input noise is several times higher but double check as I discussed above because I have seen some modern DSOs which were much worse than this.

(2) Some of my old 100 MHz analog oscilloscopes are a little bit better than this.

The scope may not have exactly 20MHz bandwidth if sampling rate is reduced due to long acquisition time and limited sample memory depth.

Sample rate should have no effect unless processing is done during decimation to improve resolution.  The DSO will happily return full input bandwidth, or the 20 MHz bandwidth from the analog input filter in this case, even if it violates Nyquist which means that the noise above Nyquist is aliased into the displayed lower frequencies.  The sample rate could be 100 kSamples/second and the input noise would still be calculated using the 20 MHz input bandwidth.  RF sampling voltmeters take advantage of this to make measurements into the GHz range with sample rates of 10s of kHz.

[aneevuser]

Thanks for the replies - some interesting info. for me to take in. I shall return to it when I've thought about it all a bit. However, for the moment:

1) With the settings as given in the OP, I measure about 490 uV(rms) noise floor for the scope i.e. with probe attached but leads shorted, and I measure about 3.5 mV(rms) of self-noise for the amp. I guess with those figures, the scope should have no problem measuring the noise of the amp?

2) At the moment, the amp is made up on breadboard. I've deliberately made no effort at shortening or twisting leads to minimise noise pickup, and I'm indeed seeing a fair bit of what looks like switching noise. Given David Hess's calculation above, I guess that I'm not going to see a vast improvement if I make the circuit up more carefully, or even made a PCB with nice short traces etc? At most it's only going to be about 0.5 mV(rms), no?

3) Can someone point me at a noise analysis for a differential amp? I've read section 8.8 in AoE, pages 520ff, but they don't treat the differential case there and I'm not entirely sure how to modify their approach correctly.

[aneevuser]

Magic did the calculation up to 14 nV/SqrtHz.  Continuing, 14 nV/SqrtHz * Sqrt(17 kHz) = 1.82uV RMS * 1.6 Shape Factor = 3uV RMS * gain of 100 = 3mV RMS output noise.

The oscilloscope input noise is very unlikely to be better than 14nV/SqrtHz (2) so with an input bandwidth of 20 MHz and shape factor of 1.6, 100uV RMS.  So the measurement should be possible even if the oscilloscope input noise is several times higher but double check as I discussed above because I have seen some modern DSOs which were much worse than this.

I can't really follow your calculation here - for example, I don't know what you mean by a "shape factor". Also, I have 220R across the inputs, so shouldn't there be a shot noise contribution from that? I don't think Magic included that, AFAICS.

Also, I was aiming for an input impedance of 4K7/2 =~ 2K3 - shouldn't that be the appropriate resistance to use when doing the Johnson noise calculations?

signed

A Slightly Baffled Noise Newbie

[aneevuser]

There's an old trick with non-digitising scopes...

Looks interesting but I didn't have much joy with this - my DSO has different colours for the different traces, and I found it very difficult to align them in any sensible way - I could see where one lot of fuzz began and the other ended too well - it may work better on a grey-scale analogue scope.

[tggzzz]

There's an old trick with non-digitising scopes...

Looks interesting but I didn't have much joy with this - my DSO has different colours for the different traces, and I found it very difficult to align them in any sensible way - I could see where one lot of fuzz began and the other ended too well - it may work better on a grey-scale analogue scope.

That's because you have a digitising scope!

You need more than a simple "grey scale" for the technique to work. FFI see David Hess' response.

[magic]

I have 220R across the inputs, so shouldn't there be a shot noise contribution from that?

Johnson noise, yes. Even more precisely, without the mic, the input still has 9.4kΩ differential impedance due to the two grounding resistors. So you should count that in parallel with the 220Ω. But none of that makes much difference, see below.

Also, I was aiming for an input impedance of 4K7/2 =~ 2K3 - shouldn't that be the appropriate resistance to use when doing the Johnson noise calculations?

Nope, because each of the input series resistors generates its own noise and this noise appears across the resistor and adds to the signal, from the opamp's perspective. This happens independently to each half of the differential signal so noise contributions from the two 4k7 resistors add up.

If you really want to push noise further you would need to reduce those resistors. And if that results in unacceptable input impedance, add more opamps and use the "instrumentation amplifier" topology.

Or just ask yourself how much noise you need
What are the mic's specs?

edit
And by the way, if your NE5532 look like those on the first pic below, they are not NE5532
https://www.eevblog.com/forum/projects/whats-inside-the-cheapest-and-fakest-jellybean-opamps/

[aneevuser]

[

Also, I was aiming for an input impedance of 4K7/2 =~ 2K3 - shouldn't that be the appropriate resistance to use when doing the Johnson noise calculations?

Nope, because each of the input series resistors generates its own noise and this noise appears across the resistor and adds to the signal, from the opamp's perspective. This happens independently to each half of the differential signal so noise contributions from the two 4k7 resistors add up.

What I'm finding difficult to see here is the appropriate equivalent circuit for the resistor network that allows to calculate the noise correctly. If I had each input connected independently to ground via a distinct R network, I believe that the appropriate noise resistance is simply the Thevenin resistance of that network, no?

However, here the inputs are not independent - they're connected via the 220R, and it's not at all clear to me how to analyse this from a theoretical point of view.

If you really want to push noise further you would need to reduce those resistors. And if that results in unacceptable input impedance, add more opamps and use the "instrumentation amplifier" topology.

By "instrumentation amplifier" topology, do you mean the paralleled-up identical amp approach?

Or just ask yourself how much noise you need
What are the mic's specs?

The noise I'm getting when recording is to my mind unacceptable so I want less. I think that part of the problem is that the mic. (Behringer XM8500) has a low sensitivity and so I need excessive gain (=> more noise) to get the o/p up to consumer line-in levels.

Anyway, as you can see, I know sweet FA about noise issues, so I'm using this as opportunity to learn about it.

edit
And by the way, if your NE5532 look like those on the first pic below, they are not NE5532
https://www.eevblog.com/forum/projects/whats-inside-the-cheapest-and-fakest-jellybean-opamps/

Thanks, but I got this years ago from RS or somewhere vaguely reputable, so I think it's probably OK. I now avoid ebay for components after I bought some fake varicaps there.

[Mechatrommer]

make your own 10X gain post-amplifier opamp module you'll see noise in DSO 10x bigger. maybe TL071 will do? or there are more plenty higher end low noise opamp out there. if you still cant see anything other than DSO noise floor, you can bet your circuit is as good as calm water.

[David Hess]

I can't really follow your calculation here - for example, I don't know what you mean by a "shape factor".

Shape factor is a correction for the finite high frequency roll-off of the amplifier or filter.  When the noise is calculated up to the bandwidth converting nV/SqrtHz to nV RMS, some of the noise above the bandwidth leaks through from above the -3 dB cutoff frequency.  If the filter was perfect, then the shape factor would simply be 1.  But for a single pole rolloff of -6 dB per octave, the correction for shape factor is 1.6.  Better filters have shape factors closer to 1.

In this case there are two corrections for shape factor; your amplifier has a single pole cutoff of about 17 kHz from 470K in parallel with 20 picofarads, which I assumed the NE5532 is fast enough to support at a gain of 100, and the oscilloscope has a single pole cutoff at about 20 MHz.

Also, I have 220R across the inputs, so shouldn't there be a shot noise contribution from that? I don't think Magic included that, AFAICS.

Also, I was aiming for an input impedance of 4K7/2 =~ 2K3 - shouldn't that be the appropriate resistance to use when doing the Johnson noise calculations?

We both kept things simple by only including the highest noise sources which make the most contribution.  I didn't bother with flicker noise which increases at low frequencies either because it is usually insignificant over audio bandwidths and unspecified for almost all oscilloscopes.

There's an old trick with non-digitising scopes...

Looks interesting but I didn't have much joy with this - my DSO has different colours for the different traces, and I found it very difficult to align them in any sensible way - I could see where one lot of fuzz began and the other ended too well - it may work better on a grey-scale analogue scope.

It works great on an analog oscilloscope; better than 5% accuracy is readily achievable.  The only thing better is computing noise on a DSO using standard deviation assuming that it does it correctly but how do you know unless you have some way to test it?

[David Hess]

If you really want to push noise further you would need to reduce those resistors. And if that results in unacceptable input impedance, add more opamps and use the "instrumentation amplifier" topology.

By "instrumentation amplifier" topology, do you mean the paralleled-up identical amp approach?

He means use a true differential input circuit which lacks those relatively high impedance resistor networks on the inputs and their contribution to noise; the disadvantage is an increase of input voltage noise by 3 dB but the decrease in current noise and Johnson noise from resistors more than makes up for it.  The first example here shows it:

https://en.wikipedia.org/wiki/Instrumentation_amplifier

Now all of the resistors can be lower in value, consistent with the drive capability of the operational amplifiers, without loading the source so their contributions from Johnson and current noise are minimized.  Note that only the differential preamplifier stage contributes significant noise because its gain divides the noise contribution of the following instrumentation amplifier stage.

Douglas Self's book "Small Signal Analog Design" shows this circuit configuration but with two transistors replacing the two operational amplifiers which allows tailoring the ratio between input voltage and input current noise by adjusting their operating current.

And that answers:

3) Can someone point me at a noise analysis for a differential amp? I've read section 8.8 in AoE, pages 520ff, but they don't treat the differential case there and I'm not entirely sure how to modify their approach correctly.

Essentially the differential configuration increases input voltage noise by 3dB (1.414) because two separate amplifiers are contributing it.  A single ended configuration using a transformer followed by non-inverting amplifier would inherently have a 3dB advantage in noise and used to be common for microphone input amplifiers.

[magic]

What I'm finding difficult to see here is the appropriate equivalent circuit for the resistor network that allows to calculate the noise correctly.

Frankly, I identified the offending resistors heuristically: they are in series with the signal source from the opamp's perspective. The lower resistor has its left end connected to ground through (4700||(4700+220)) and the right end through 470k, so essentially all its noise voltage appears on the right side and is indistinguishable from "cold" signal. The upper resistor has its right end maintained at constant voltage by the opamp, so its noise voltage appears as random variation on the left side, which cause random variations in the resistor's current, indistinguishable from "hot" signal.

If you want a single number, off the top of my head I would say you should calculate the equivalent resistance of the whole input network between the input pins of the opamp.

The noise I'm getting when recording is to my mind unacceptable so I want less. I think that part of the problem is that the mic.

Well, simple question, what happens to the recorded noise when you replace the mic with an quivalent resistor?

edit
As for the noise of the in-amp topology, there are of course better chips than NE5532 out there. Right off the bat, NE5534 has about 1.5x less noise to perfectly compensate for the noisier topology. NJM2068 is a cheap dual about on par with NE5534, though I'm not sure about its distortion performance. NJM2122 is not much pricier and very low noise. Or pull out the big guns like LM4562, OPA1612, LT1028. Finally, there are dedicated integrated in-amps like the various INA-whatevers from Burr-Brown/TI and people sometimes build mic preamps with them too.

[aneevuser]

If you really want to push noise further you would need to reduce those resistors. And if that results in unacceptable input impedance, add more opamps and use the "instrumentation amplifier" topology.

By "instrumentation amplifier" topology, do you mean the paralleled-up identical amp approach?

He means use a true differential input circuit which lacks those relatively high impedance resistor networks on the inputs and their contribution to noise; the disadvantage is an increase of input voltage noise by 3 dB but the decrease in current noise and Johnson noise from resistors more than makes up for it.  The first example here shows it:

https://en.wikipedia.org/wiki/Instrumentation_amplifier

Now all of the resistors can be lower in value, consistent with the drive capability of the operational amplifiers, without loading the source so their contributions from Johnson and current noise are minimized.  Note that only the differential preamplifier stage contributes significant noise because its gain divides the noise contribution of the following instrumentation amplifier stage.

OK, that looks promising - I guess it's based on the idea that to minimise noise figure in a composite system, you want high gain/low noise in the first amp.

However, it looks a little too good to be true - in my setup, won't I still need a resistance to ground at the inputs of the instrumentation amp, to satisfy input bias current requirements? If so, doesn't that undermine the whole argument that you've made?

[magic]

The 220Ω resistance of the mic will largely mix and equalize the two bias currents before they enter the grounding resistors. The sum of the two bias currents will flow through the parallel combination of grounding resistors producing relatively high common mode noise due to their high resistance, the difference between them will flow through the mic, resulting in much lower differential mode noise which is the noise that matters.

[aneevuser]

If you want a single number, off the top of my head I would say you should calculate the equivalent resistance of the whole input network between the input pins of the opamp.

Having thought about this a bit, each input sees the Thevenin resistance to ground of the network as calculated at the appropriate point, and will thus see potentially different resistances from the POV of noise - but these won't be entirely uncorrelated noise sources, so we can't simply add them in the usual way. Hmm, this is all too damn tricky for a clueless noob such as myself.

The noise I'm getting when recording is to my mind unacceptable so I want less. I think that part of the problem is that the mic.

Well, simple question, what happens to the recorded noise when you replace the mic with an quivalent resistor?

Well, that's exactly the setup I've got - a 220R directly across the inputs. Or am I misunderstanding what you're saying here? I don't have the XLR cable connected, but I have done that in the past when I was trying to listen for mains hum rejection - I had the XLR cable with the 220R between hot and cold at the mic end.

As for the noise of the in-amp topology, there are of course better chips than NE5532 out there.

Yeah, I could look at other opamps, but I'd like to push what I've got as far as possible before I do that. The instrumentation amp idea looks promising.

[aneevuser]

The 220Ω resistance of the mic will largely mix and equalize the two bias currents before they enter the grounding resistors. The sum of the two bias currents will flow through the parallel combination of grounding resistors producing relatively high common mode noise due to their high resistance, the difference between them will flow through the mic, resulting in much lower differential mode noise which is the noise that matters.

Thanks, but I can't follow this at all - can you put up a circuit diagram so I can see what you're describing?

[magic]

Look at the schematic here
https://www.audiomasterclass.com/newsletter/the-famous-5-preamp-everything-you-need-to-know

Each INA input injects noise current into one of the 2k2 resistors R4/R5. However, at audio frequencies, impedance of the coupling capacitor C1/C2 is very low and impedance of the mic is low too so each noise current splits in half and flows through both 2k2 resistors, producing common mode noise which is ignored by the INA.

Well, that's exactly the setup I've got - a 220R directly across the inputs.

Fine, I thought that "recording" meant "with a mic". If you get noise with a resistor, it has to be coming from the preamp, particularly if we calculated that the preamp makes a lot more more noise than a 220Ω resistor.

I agree, swapping opamps at this point is futile. The largest source of noise are resistors.

[aneevuser]

Look at the schematic here
https://www.audiomasterclass.com/newsletter/the-famous-5-preamp-everything-you-need-to-know

Each INA input injects noise current into one of the 2k2 resistors R4/R5. However, at audio frequencies, impedance of the coupling capacitor C1/C2 is very low and impedance of the mic is low too so each noise current splits in half and flows through both 2k2 resistors, producing common mode noise which is ignored by the INA.

OK, so if I understand you right here, you're saying that we have a single source of current noise that then appears, due to your splitting argument, as common mode noise to the amp, which has good CMR, so we can neglect it?

However - and I don't want to seem too dimwitted here - but... don't we have essentially the same front end resistor setup that I currently have - 2K2 at the inputs, so we have precisely the same *Johnson noise* problem as I do currently? Sticking two resistors at the the front end of the instrumentation amp seems to negate the argument given by David Hess, where he said "use a true differential input circuit which lacks those relatively high impedance resistor networks on the inputs and their contribution to noise".

Am I confused?

[aneevuser]

I can't really follow your calculation here - for example, I don't know what you mean by a "shape factor".

Shape factor is a correction for the finite high frequency roll-off of the amplifier or filter.  When the noise is calculated up to the bandwidth converting nV/SqrtHz to nV RMS, some of the noise above the bandwidth leaks through from above the -3 dB cutoff frequency.  If the filter was perfect, then the shape factor would simply be 1.  But for a single pole rolloff of -6 dB per octave, the correction for shape factor is 1.6.  Better filters have shape factors closer to 1.

OK, that makes sense. BTW, is there some classic "Noise Theory for Electronics" text that I should be aware of? I'm quite like to see some derivations of all this stuff from first principles (I'm Mr Theoretical - making real stuff scares me) but I don't know what the literature is like here.

In this case there are two corrections for shape factor; your amplifier has a single pole cutoff of about 17 kHz from 470K in parallel with 20 picofarads, which I assumed the NE5532 is fast enough to support at a gain of 100, and the oscilloscope has a single pole cutoff at about 20 MHz.

The quoted GBW is 10 MHz, so with a gain of 100 the upper 3dB point is at 100 kHz - that should be fine, I think?

Anyway this is the most incredibly useful thread - I'm amazed by the technical quality of some of the people on this site. Thanks.

[magic]

For the record, NE5532 has over 30MHz GBW at frequencies that matter and for NE5534 it's over 60MHz and perhaps up to 80MHz from some manufacturers, IIRC.

The trick? Gain falls faster that 6dB/octave starting at a few hundred kHz.

[David Hess]

OK, that looks promising - I guess it's based on the idea that to minimise noise figure in a composite system, you want high gain/low noise in the first amp.

Serious audio equipment uses a pair of transistors for the differential preamplifier instead of two operational amplifiers but the result is the same and using operational amplifiers is easier.

However, it looks a little too good to be true - in my setup, won't I still need a resistance to ground at the inputs of the instrumentation amp, to satisfy input bias current requirements? If so, doesn't that undermine the whole argument that you've made?

That is right; a DC connection to common is still required at the input to supply the input bias currents however it is the source impedance which determines input noise.

The quoted GBW is 10 MHz, so with a gain of 100 the upper 3dB point is at 100 kHz - that should be fine, I think?

Yes, that will be fine.  However one advantage of the three operational amplifier instrumentation amplifier is that the total gain is divided up between stages so frequency response and distortion can be better.  Effectively you have 3 * 10 MHz GBW = 30 MHz GBW to work with instead of just 10 MHz GBW.