# OPA301: Noise Caculation

Part Number: OPA301

Hello.
In the data sheet, there is 40uVpp, 0.1-1MHz.
I tried to get this number from the Noise density graph, but failed. Attached my calculations, based on you “Lecture Manual”.
Data from the data sheet:
Input Voltage Noise, f = 0.1Hz to 1MHz 40µVPP

From the Noise density graph:

enf=0.3µV/√Hz at 10Hz
f0=10 Hz
ennormal= enf√ f0=0.3*√10=0.95µV/√Hz at 1Hz
fL=0.1 Hz , fH=1 MHz
enflicker= ennormal√(ln(fH/ fL))=0.95*√(ln(1M/ 0.1))= 0.95*√(ln(107))=0.95*√(ln(107))= 0.95*√(4)=3.8 µVrms
enflicker(pp)=6* enflicker=6*3.8=22.8 µVPP

### 4 Replies

• HI Shlomo,

It seems that the 40 uVpp in 0.1-1MHz range comes from this Application Report:

Enflicker = En_white*√Fcn*(ln(fH/fL)) - (1)

where, En_white (white noise) = 3 nV/√Hz from the datasheet

and Fcn is the frequency at which noise is √2 x white noise specification. For 3nV/rtHz white noise, the Fcn then will be 250kHz at √2x3nV/rtHz from the below noise spectral density figure.

If you plug-in the numbers into the Enflicker noise equation, you should get ~6.02 uVrms.

So, Enflicker (pp) = 6*Enflicker(rms) = 6*6.02 = 36.12 uVpp

I think there is some fudge factor or round off associated with making the Enflicker(pp) close to 40 uVpp (0.1-1MHz range) in the OPA301 datasheet.

Best Regards,

Rohit

• In reply to Rohit Bhat:

Hi Rohit,

What it is still not clear:

1. What is the explanation to use the method which I used?( get the Ennormal- the 1/f voltage noise spectral density normalized to 1Hz).

2. Why using this method gives a different result?

Thanks again

Shlomo

• In reply to Shlomo Perlshtein:

Hi Shlomo,

The difference between the two approaches mainly lies with the calculation for En-normal noise, whereas the 1/f frequency integration from fL to fH stays the same. I think ultimately the correct result should be total integration of the noise area from fL to fH, and either method should give the correct result.

But, I think I agree with your calculation for the input voltage noise from 0.1Hz to 1MHz to be 22.8 uVpp, and not 40 uVpp.

Another way to calculate the 1/f corner frequency (fcn) in the App note I provided is by first determining the K^2-device constant and then the fcn which is required for calculating the En-normal noise. The K^2 term is determined by subtracting white noise from the equivalent input noise at the lowest possible frequency (10Hz in this case) in the voltage noise density curve of OPA301 and multiplying by its frequency (10Hz). The fcn is then the ratio of K^2 and en_white^2.

So, K^2 = [en^2 - en_white^2]x lowest freq = [(300nV/rtHz)^2 - (3nV/rtHz)^2]x10 = 899910 (nV/rtHz)^2
The 1/f corner frequency then becomes, fcn = (K^2)/(en_white^2) = 899910/9 ~ 100kHz

As a result, the Enflicker = En_white*√Fcn*(ln(fH/fL)) = (3 nV/√Hz)*√100kHz*(ln(10^7)) = 3.8 uVrms

So ultimately, enflicker(pp)=6* enflicker=6*3.8=22.8 µVPP

The first method I provided seems to not work in this case because the 1/f corner frequency may not have been drawn properly for the voltage noise density curve in the OPA301 datasheet. I think that's why the number reported in the datasheet is 40 uVpp and not 22.8 uVpp in the 0.1Hz to 1MHz frequency range.

Best Regards,
Rohit
• In reply to Rohit Bhat:

Hi Rohit,

Thanks again for completing the answer. I suppose that issue is resolved.

Shlomo