Noise Analysis

[Carl-NC]

In Eric's thread I promised to write up some noise basics. Attached are 2 pages that cover resistor thermal noise. This doesn't quite answer JC's riddle about infinite resistors, so I s'poze I will have to write some more. I'll try to get a couple more pages uploaded in a day or two. And, maybe put it all in FrameMaker and make a nice PDF out of it.

- Carl

[Carl-NC]

Sorry about the image sizes, they are 150dpi, US 8.5x11 page size.

[JC1]

EE

Hi Carl,

I'm easy confused, you are saying the noise is dependent on R2 (what you said) or did you mean the input resistor R1?

Anyway, nother link, has similar equations, burr brown stuff.

http://focus.ti.com/docs/apps/catalo...tName=sboa066a

download this, let me know what you think.

[JC1]

EE

Hi Carl,

The burr brown app notes all have TI titles now. Some they charge for now @#$%^&&.

Ti bought burr brown long time ago. You know this. others may not.

can't beat em? buy em!

you better. before they beat you.

anyway. thought would clear that up. my old one still says burr brown, don't know if TI changed the equations or not.

[JC1]

EE

Hi Guys,

Take a look at the above link.

In equation 2 he has the terms. Each one can contribute to noise in its own special way.

forget the sum of the squares for a moment and looking at each item seperately we have.

opamp voltage noise * gain +

input current noise * gain +

input resistor thermal noise * gain +

input current noise * feedback resistor +

feedback resistor thermal noise * sqrt of gain


thems the bad guys?

i guess according to this it is. still might be other sources.

[JC1]

EE

Whoops, bad math. After I left I got thinking, got the last term wrong.

Should be.

sqrt of (thermal noise of Rf * gain)

hate it when i do that.

[Carl-NC]

Hi Carl,

I'm easy confused, you are saying the noise is dependent on R2 (what you said) or did you mean the input resistor R1?

Anyway, nother link, has similar equations, burr brown stuff.

http://focus.ti.com/docs/apps/catalo...tName=sboa066a

download this, let me know what you think.

Yes, R2, not R1...

I will not go into as much detail as the TI app note, which hopefully will keep things a little clearer.

- Carl

[JC1]

EE

Hi Carl,

Running the numbers. for 5534, 1k in, 1Meg feedback, gain =1000, using 3.5 nV and 1.5 pA.

Vn=3.5uV

sqrt---Inputcurrentnoise*Rs*G*G=1.5uV

sqrt---Rs thermal*G*G=4.1uv

Inputcurrentnoise*Rf=1.5uV

sqrt---Rf thermal*G=4.1uV

So looks like in this case, since G=1000 and Rs and Rf differ by a factor of 1000 then

Rs and Rf tie as the bad guys, with op amp voltage noise coming in a close second. (diplomatic of em)

Change the numbers a bit and a different horse wins.

Anyway run the numbers on your calculator.

Back to work.

Them buttons don't push themselves you know.

[JC1]

EE

Hi Guys,

For the above example the total noise (sqrt sum of sqs) is
7.1uV.

Dropping the input resistor to 100 ohms and feedback to 100,000 ohms, the total noise is 3.9 uV.

This is getting close to the 3.5 uV of the opamp input voltage noise. Therefore dropping them further won't help as much, and make other problems.

The contribution of noise by the input and feedback resistor is still equal but less.

I put this one in MathCad now and so playing around.

[JC1]

EE

Hi Carl,

So seems the feedback resistor does matter (especially 1Meg), as you mentioned there.

Think I said that once, along time ago, in another forum.

Got alot of Johnson noise for it, if I remember right.

Got corrected.

heh heh

[JC1]

EE

Hi Eric,

Hope you're getting this.

Part of Classwork.

There will be a test.

Performance.

So build it yourself, lots of time, hmmmm, Receipe.

Take a 1.0 nV/rtHz or less JFet, add a drain resistor, add opamp, close loop on whole thing.

No not that easy, but not that bad either.

Good start?

[Carl-NC]

Page 3... explains "noise bandwidth".

[Ferric Toes]

Hi Carl,

Going back to 4) in your first write up (inverting opamp), I still can't get my head around the statement "Total noise depends on the value of R2 and gain, not R1"

In the case of R1 = 1k and R2 = 10k, voltage noise for the resistors = 4nV and 13nV respectively (figures rounded and rt/Hz implied). Using your formula, I get a total noise output of 42.05nV, of which 40nV is contributed by R1 and the opamp gain.

Eric.

[Carl-NC]

I've decided I don't like the way I worded that statement... clearly, R1 contributes noise and, in fact, for any gain > 1, it contributes more noise than R2. What I was trying to show is that, often, you can get a noise equation in a form where it's very easy to see certain trade-offs, and to quickly "back out" the component values you need to achieve a certain noise.

For the inverting opamp, vn^2 = 4KT*R2*(1+G) shows that, for a given required gain, I can express noise solely as a function of R2. I could also express noise solely as a function of R1: vn^2 = 4KT*R1*G*(1+G). Perhaps this second expression is more useful in a PI front-end, as we are more concerned about the value of R1 (in limiting the current through the clamping diodes) than the value of R2.

The 3rd page shows a similar end result, where the noise of a simple RC low-pass filter is KT/C. Obviously, the resistor is the source of the noise, but in designing the circuit you would select the capacitor value for the desired maximum noise, then back into the resistor value needed for the cutoff frequency. This is, in fact, how ADC sample-and-holds are designed.

So I hereby reword my statement: "Note that the total noise can be reduced to just R2 and the gain, which simplifies calculations. It can also be reduced to just R1 and the gain."

- Carl

[JC1]

EE

Hi Gentlemen,

Carl, good forum, had to think about that last statement for a bit.

Then realized that R1 and gain works because R2 is defined by gain and R1.

R2 and gain works because R1 is defined by gain and R2.

since gain magnitude is R2/R1, of course.

Yes my shorthand numbers up there are /rtHz.

So 7.1 uV/rtHz times sqrt of bandwidth (100,000) times 6 to convert to peak to peak = 13.5 mV

Ran bunch of numbers interesting results.

1k in and 10k feedback and 5534 makes 0.071 uV/rtHz.
but when you gain it up a 100 then equals 7.1uV.

Voltage noise 3.5 uV. so that is min. till change amp.

So Eric you should see about 15 to 20 mV peak to peak noise on the scope on your circuit. If alot higher then you got some noise that is not part of these parts.