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current noise calculation

jian wang87
Intellectual 370 points

Hi 

I downloaded the Analog Engineering's calculator, when I using the Noise calculation, what's the formula for the Current Noise RTO.  

my calculation is as below:

Noise Gain=1+Rf/R1

FH=GBW/Noise Gain = 8M/11

BW=1.57*FH

1st: calculate the broadband for R1//RF; EnBB1 = (BW)^0.5 * 400fA * R1//RF

2st: calculate the 1/f for R1//RF; Enf1 = 20pA*0.1^0.5*(ln(BW/0.1))^0.5* R1//RF

same for RS

EnBB2 = (BW)^0.5 * 400fA * Rs

Enf2 = 20pA*0.1^0.5*(ln(BW/0.1))^0.5* Rs

so RTI_CurrentNoise = (EnBB1^2+Enf1^2+EnBB2^2+Enf2^2)^0.5

RTO=RTI_CurrentNoise * NoiseGain = 4.307 uVrms which is not same to 4.78uV.

So please help to check? thanks

  • 0
    TI__Guru 51691 points

    Hi Wang Jian,

    I was unable to get current noise RTO of  4.78uVrms displayed in the calculator. I have asked an engineer to take a look at this. Here is my calculation. 

    If you have any additional questions, please let me know. 

    Best,

    Raymond

  • 0
    TI__Guru 61920 points

    You have calculated RTO noise based on 1/f  and broadband current noise but you neglected to include resistor thermal noise - see below.

    Thermal noise of 1kohm resistor is about ~4nV/rt-Hz.

  • 0 in reply to Raymond Zhang1
    Intellectual 370 points

    Raymond, thanks very much. it's very clear.

    I still have some questions.

    1: Req: in your calculation, Req=Rs + R1//RF, right? in some application note, Req = ( Rs^2 + (R1//RF)^2 )^0.5,  this method takes Rs and R1//RF as independent noise term.

    2: fo: why fo using 1Hz, how to choose the fo? I my calculation, I choose 0.1Hz

    3: For EnRTO , why Enflicker don't need to be multiplied by 11? 

    thanks again!

    regards

    wangjian

  • 0 in reply to Marek Lis
    Intellectual 370 points

    thanks Marek Lis!
    here we just focus on the current noise calculation.  for resistor noise there is another space named "Resistor Noise RTO" in above picture.

  • 0 in reply to jian wang87
    TI__Guru 51691 points

    Hi Wang Jian,

    1: Req: in your calculation, Req=Rs + R1//RF, right? in some application note, Req = ( Rs^2 + (R1//RF)^2 )^0.5,  this method takes Rs and R1//RF as independent noise term.

    I was using Req=Rs + R1||RF (assumed correlated variables). If both resistor values are uncorrelated (independent), then your Req equation is correct.

    If Rs and R1||RF values are uncorrelated, then your current noise calculation of 4.307 uVrms is closer (I calculated around 4.3003 uVrms, basically rounding errors). And I think that Rs and R1||RF values should be uncorrelated, and total current noise RTO is 4.30  uVrms. I will ask an engineer to check the calculation in the tool again. Thanks for pointing out the discrepancy. 

    2: fo: why fo using 1Hz, how to choose the fo? I my calculation, I choose 0.1Hz

    1/f voltage noise spectra density is normalized to 1Hz by definition. 0.1Hz (10 sec time constant) is the lowest given frequency on the 1/f curve typically.  If you look at the following voltage noise density plot vs. frequency, the area of under the normalized 1/f noise at 1 Hz is approx. equal to the integrated area under the 1/f curve, and I think that this is the reason. If one is integrating the 1/f noise down to 10mHz in the plot, the percentage error contributed from the calculation will be insignificant from the equation below (EnBB^2 is the dominated noise error contributor in the equation). 

     

    3: For EnRTO , why Enflicker don't need to be multiplied by 11? 

    The a, b, c terms above (Marek's slide) are uncorrelated noise variables, and that is why the total noise voltages are a "root sum of squares" terms. Gains of the circuit only applicable to the output of op amp (RTO), and flicker noise is independent of circuit's gain noises.

    Best,

    Raymond